Analysis of the Long-Term Dynamics of Ungulates in Sikhote-Alin Zapovednik, Russian Far East
Analysis of the long-term dynamics of ungulates
in Sikhote-Alin Zapovednik, Russian Far East
P.A. Stephens, O.Yu. Zaumyslova, G.D. Hayward and D.G. Miquelle
Collaborators:
Sikhote-Alin State Biosphere Zapovednik
Wildlife Conservation Society
University of Wyoming
USDA Forest Service
Analysis of the long-term dynamics of ungulates in Sikhote-Alin Zapovednik,
Russian Far East
A report to the Sikhote-Alin Zapovednik and USDA Forest Service
Philip A. Stephens*
Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA
Olga Yu. Zaumyslova
Sikhote-Alin State Biosphere Zapovednik, Terney, Terneiski Raion, Primorski Krai, Russia
Gregory D. Hayward
Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA;
USDA Forest Service, Rocky Mountain Region, PO Box 25127, Lakewood, CO 80225, USA
Dale G. Miquelle
Wildlife Conservation Society, Russian Far East Program, Vladivostok, Primorye Krai, Russia
2006
* Present address: Department of Mathematics, University of Bristol, University Walk, Bristol,
BS8 1TW, UK; [email protected]
EXECUTIVE SUMMARY
Study and findings
1. The winter transect count involves monitoring game species by counting tracks of animals that intersect with a stable network of transects, surveyed during periods of snow cover. It is the main method of estimating the number of many game animals in the Russian Federation. For over four decades, this approach has been used consistently to monitor a variety of species in Sikhote-Alin Zapovednik (SAZ), Russian Far East. Hitherto, this extensive data set has not been rigorously analysed to assess trends and ecological relationships in a variety of species, or to assess its potential and limitations with regard to informing management of SAZ. We present such an analysis, focused on six of the larger game species occurring in SAZ: red deer (Cervus elaphus), wild boar (Sus scrofa), roe deer (Capreolus pygargus), musk deer (Mochus moschiferus), sika deer (Cervus nippon) and moose (Alces alces).
2. The principle objectives of this work were to examine spatial pattern in the occurrence of the species of interest; to investigate methods for estimating population densities from the track encounter data; to assess factors underlying temporal changes in populations of the more abundant species; to analyse the survey protocol and recommend practices whereby it might be improved; and to determine the likely impact of Amur tigers (Panthera tigris altaica) on potential prey species. Through these analyses, we aimed to inform understanding of the distribution and dynamics of the ungulates within SAZ, to aid ongoing efforts to manage the area for the benefit of the endangered Amur tiger, and to integrate the disparate Russian and English language literatures on estimating animal abundance from indirect sign, thereby contributing to this important yet contentious field.
3. Comparisons of track encounter rates among forest types and drainages suggested few consistent patterns of animal distribution beyond those already recognised by accepted divisions of SAZ into three broad habitat zones (the coastal, oak-birch zone; the central belt, dominated by mixed Korean pine and deciduous forests; and the north-western, higher altitude areas, dominated by spruce and fir forests). Within the oak-birch zone, however, sika deer show pronounced differences in their use of the coastal oak forests and mixed birch and aspen forests further inland. Though less marked, the data suggested that other species may also show differences in their use of these areas. Consequently, we recommend that, in future, the oak-birch zone should be divided into two separate survey units, recognising the existence of four (rather than three) broad habitat zones for survey purposes.
4. Three methods for estimating ungulate absolute population densities from track counts were compared, including a correction factor based on the relationship between track counts and total counts of deer in experimental plots; the established Formozov- Malyeshev-Perelshin (FMP) formula based on records of animal daily movement distances; and a computationally-intensive simulation approach based on two- dimensional records of animal daily movements. The simulation and FMP approaches gave very similar estimates, supporting the existing belief in Russia that the FMP formula is theoretically sound and generally robust to the different movement patterns of ungulate species. The correction factor tended to overestimate densities but this is unsurprising,
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given that data used to develop the correction factor came from other study areas, where animal movements may be very different.
5. We stress that no method for estimating density from indirect sign is robust to violations of underlying assumptions. In particular, no method can fully compensate for biases arising from a survey network that does not adequately represent the area of interest. All methods based on indirect sign also require independent validation, ideally using monitoring based on direct sightings. Specific recommendations for enhancing the validity of the track count surveys are given below.
6. Two of the methods for estimating ungulate abundance from track encounter rate depend on good data on animal 24-hour movements. These data are currently limited for SAZ but preliminary analyses indicated that movement distances may be affected by time of year and group size (for red deer and roe deer), and a combination of habitat type and time of year (for wild boar). Understanding how travel distances are affected by different conditions is essential for improving the accuracy of density estimation and we urge further collection of these data in a range of conditions.
7. Differences between ungulate densities in the three major habitat zones of SAZ are pronounced and we assumed that data would always be stratified at this level, at the very least. Finer levels of stratification, including stratification by drainage basin and by forest formation were compared. These different types of stratification seldom had strong effects on estimates. However, analyses indicated that stratification by forest formation could be vulnerable to outliers and, consequently, stratification by drainage basin is recommended. It remains to be seen whether this will be necessary, if a four zone approach to the surveys is adopted (see further below).
8. Non-parametric bootstrapping was used to derive confidence intervals around estimates of ungulate densities. This method is free from many of the assumptions required by other suggested methods for estimating confidence intervals about estimates derived using the FMP formula. Using non-parametric bootstrapping also avoids the requirement for estimates of parameters such as average group size and average crossing rate for the paths of individual animals, both of which can be very difficult to obtain.
9. Overall, densities of ungulates tend to be highest in coastal areas and lowest in the spruce-fir, montane forests. Red deer were the most abundant species (1.5 to 3.0 km-2 throughout SAZ), followed by roe deer (1 to 2.5 km-2). At present, sika deer occur only in the oak-dominated forests on the coast but their population appears to be growing rapidly (now exceeding 1 km-2 in that area). Less is known about musk deer daily movements but analyses indicated that this species shows the opposite trend to the other ungulates in SAZ, with the highest densities in montane, spruce-fir forests, and the lowest densities towards the coast. Overall, mean musk deer density throughout SAZ is approximately 1 km-2. Wild boar show substantial fluctuations throughout the coastal and central areas but are at generally low abundance in both, seldom exceeding 0.1 to 0.5 km-2. Finally, moose tracks are encountered too rarely to analyse. That moose track encounters have virtually ceased since 1980, suggests that this species (which is at the southern extent of its range in SAZ) may have shifted northward in response to increasing temperatures.
10. Analyses of changes in track encounter rates within years suggested that encounters of the tracks of several species (including red deer, roe deer and musk deer) show
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pronounced declines from early to late winter. Although this results partly from changes in travel distances as winter progresses, it is also possible that species distributions shift throughout winter. Survey routes that accurately represent the entire area of interest are essential if this phenomenon is to be understood (see further below).
11. In spite of the rigour with which SAZ is surveyed, the track data are prone to census error and resultant estimates of density are noisy. This leads to difficulties in determining the major factors dictating the dynamics of each species. Nevertheless, evidence for density dependent processes was found in several populations. Additionally, climate, competition, quality of mast crops and protection from poaching all influence the studied populations. Dynamics of the red deer and sika deer populations are currently best understood. There is evidence for competition between these species and, also, for climate effects acting in different directions. In particular, increasing temperatures appear to have a positive effect on the sika deer population but a negative effect on red deer populations in the coastal and central zones. By contrast, red deer in the spruce-fir zone are positively affected by increasing temperatures, suggesting that the species may be shifting its distribution northwards and to higher altitudes as mean temperatures increase.
12. Assessments of the survey protocol and of the relationship between survey effort (kilometres of transects conducted per year) and precision, emphasised two major points. First, that survey design depends critically on the goals of monitoring, in particular, whether relative indices of abundance are sufficient or absolute estimates of abundance are desired, and whether it is necessary to detect trends in animal abundance. If the detection of trends is a goal of the monitoring, then it is important to establish what magnitude of trend should be detectable and over what time period. Secondly, analyses also highlighted the fact that, for a given set of goals, required survey effort is affected by the density, movement behaviour and grouping behaviour of the species considered. Low densities, short daily travel distances and clumped distributions all increase the uncertainty in abundance indices. Thus, some species will be harder to monitor as accurately as others. Different monitoring goals will be relevant to different species (see further below).
13. Simple analyses of the likely effects of tigers on prey populations indicated that these are likely to be small relative to the estimated effects of other large carnivores on their prey. This accords with findings from the temporal analyses, which showed no evidence for a strong effect of tigers on prey populations. Although the social intolerance of tigers may play a role in limiting their local density and, hence, their effects on prey, this is unlikely to be important at the relatively low prey densities in SAZ. More likely, the generally low impact of tigers on prey results from their relatively low energetic requirements when compared to many other large carnivores.
Specific recommendations
This study highlighted a variety of improvements that could be made to the monitoring work conducted in SAZ. Ultimately, the goals of Zapovednik monitoring are for the managers of the Zapovednik system to designate. However, some suggested goals and recommendations include:
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1. Use a four-zone classification of SAZ for ungulate monitoring. This is discussed in more detail in the report but the zones would include the coastal zone (dominated by oak forests), the inner-coastal zone (dominated by birch-aspen forests), the central zone (dominated by Korean pine-deciduous forests) and the montane zone (dominated by spruce-fir forests).
2. Define an overall goal for monitoring ungulates. This should specify whether monitoring should produce only an index of relative abundance, or estimates of absolute abundance also. It should also specify the units of interest (both species and zones) and whether trend detection is important. If trend detection is important, the magnitude of trends and the time periods over which these should be detected must also be defined. We suggest that the goal be defined as follows: Ungulate monitoring in SAZ will provide estimates of the absolute abundance in winter of ungulates in the four major habitat zones. At least 1000 km of surveys will be conducted annually, distributed equally over the four zones. The aim of this will be to give the maximum power to detect trends in numbers of the more abundant species in the habitats most important to that species. A design capable of detecting a 15% annual decline after 5 years of monitoring will be achievable for most species.
3. Recognise limitations and adapt to priorities and changing conditions. It is vital that the limitations of the monitoring be recognised including, in particular, that density estimates are associated with considerable uncertainty, and that species at lower abundance, with shorter daily travel distances and with highly clumped behaviour will be subject to greater uncertainty, such that trends are harder to detect with confidence. The monitoring protocol should also be adaptable to changing priorities and to changes in conditions (such as increasing or decreasing densities of certain species).
4. Validate the relationships between track counts and density estimates. Independent estimates of density must be generated using alternative methods, in order to indicate how accurately density is estimated by current methodologies. In particular, we recommend the use of distance sampling and aerial surveys (combined with sightability models) as potential methods for validating the track count index.
5. Assess bias in transect network. Assess bias in the transect network using GIS analyses and by comparing results of randomly placed transects to the existing network within a number of basins of the reserve. If a significant bias is detected, there are two alternatives to address this bias: (i) if the bias is stable and predictable across all areas and all conditions, apply a simple correction factor; (ii) if the bias is not stable and is difficult or impossible to predict, relocate transects to approximate a random sampling effort.
6. Improve data base on daily travel distances. Daily travel distances must be collected during the time frame in which surveys are conducted, as there is evidence that travel distance drops in late winter. Data on travel distances must also be collected across the range of environmental parameters that are likely to affect movements. Our initial analyses suggest that group size, time of year and habitat type are the primary drivers of daily travel distance. Collecting data over the full range of possible values for each of these parameters will be important in deriving appropriate estimates of travel distance for ungulates within the Zapovednik.
7. Collect data on the numbers of animals that made each set of tracks encountered. To collect data not only on the number of sets of tracks of each species encountered on
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transects but, also, on the number of these that were made by single animals or groups of various sizes, is likely to be awkward, especially from the point of view of data storage. Nonetheless, our analyses showed that size of the travelling group may be important in dictating the travel distance of some species. Consequently, collecting such data will be helpful for improving the accuracy of density estimates. The data could also be useful for determining group size distributions, which will have important implications for error calculations and other aspects of understanding demography of the studied species.
8. Eliminate the recording of “nabrods”, or multiple, uncountable crossings. Eliminate records of “nabrod” in SABZ dataset by training all observers to circle nabrods and report actual numbers of tracks to the best of their ability.
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ACKNOWLEDGEMENTS
This monograph is the result of a long-term collaborative effort between Sikhote-Alin Zapovednik and the Wildlife Conservation Society. We thank A.A. Astafiev, Director of Sikhote-Alin, for continual support of these mutually beneficial, ongoing efforts. We also thank M. Hornocker and H. Quigley, who had the wisdom and courage to initiate the Siberian Tiger Project, and select Sikhote-Alin Zapovednik as its base. M.N. Gromyko, and L.V. Potikha have both acted as Assistant Directors of Science for Sikhote-Alin Zapovednik and facilitated our collaborative efforts. E.N. Smirnov, our scientific collaborator for the Amur Tiger Project, has been instrumental in all phases of the work. A.E. Myslenkov provided much data on daily travel distances of ungulates, a pivotal part of the database which is used here. T. Merrill provided the first GIS database training for Zapovednik personnel, and helped design and implement database development. We thank other members of the Zapovednik staff for their help and advice including, especially, Luba Khubotnova, whose assistance with translation during meetings was invaluable. This work was funded by the U.S. Forest Service, International Programs, part of the U.S. Department of Agriculture, to whom we are most grateful. In particular, we would like to thank Liz Mayhew, Lara Peterson and Jen Peterson for all of their support and logistical advice throughout the project. The bulk of the analytical work was conducted at the University of Wyoming, USA, and we thank the University for support. In particular, we are grateful to heads of the Zoology and Physiology Department, N. Stanton and G. Mitchell, as well as S.D. Hutton in International Student Services. Translations were completed by E. Nikolaeva, A. Murzin, and D. Karp. G. Contraras facilitated the translation of Russian scientific articles into English. Many others provided advice on research approaches, translation of materials and statistical techniques. In particular, we thank the following: C. Nations, C. Martínez del Rio, S. Buskirk, R. Freckleton, R. King, A. Cardinali, C. Anderson, J. Crait and K. Gerow. Finally, PAS and GDH would like to thank all those in Terney and Vladivostok who made their visits so enjoyable and useful. Many of those are already listed but, additionally, we thank John Goodrich, Marina Miquelle, Galia Safanov, Zheny Gishko, Kolya Reebin, Sasha Reebin, and Volodia Melnikov.
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PREFACE
The Russian Zapovednik system is renowned throughout the world for its dedication to preserve representative intact ecosystems. As impressive as the conservation goal is the secondary goal of
Zapovedniks to monitor and observe those ecosystems, and the changes that occur within them.
Long-term observations provide an opportunity to understand the impact of humans on natural processes by comparing protected and unprotected areas, but they also provide unique opportunities to better understand long-term dynamics of animal populations that reside in preserves relatively free of human influence. Most Zapovedniks have retained a trained scientific staff that has collated vast archives of data of great potential in understanding long-term dynamics of natural ecosystems.
Such is the case with Sikhote-Alin Zapovednik. Since 1962, annual winter transect routes (beli trappa), have been conducted to monitor populations of wildlife. The value of such data may not have been immediately apparent to those who initiated data collection, but who nonetheless went to painstaking lengths to insure that this data was archived and saved for future generations. Thus, a “treasure” of data resided in the archives of Sikhote-Alin, mainly to be found in the yearly “Chronicles of Nature” that are produced each year to document the biological and ecological “status” of the reserve.
The Amur Tiger Project began in 1992 as a collaborative program between the Wildlife
Conservation Society (initially the Hornocker Wildlife Institute, which has since merged with
WCS), and Sikhote-Alin Zapovednik to study the ecology of the Amur tiger within the boundaries of the Zapovednik. From the beginning, it was clear that understanding the relation of tigers to their prey would be a primary component of our efforts. In Sikhote-Alin Zapovednik, in particular, it was clear there were unique opportunities to study long-term dynamics of tigers and their prey. Not only were there winter transect routes that provided a standardized means of assessing prey abundance, but since 1966 E. N. Smirnov had collated all observations of tigers to
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derive yearly estimates of tiger abundance. Thus, the opportunity to assess and understand temporal changes in abundance of both predator and prey populations was enormous.
To make effective use of the archived information from Sikhote-Alin Zapovednik, it was clear that transformation into a digital geo-referenced dataset would be necessary. Therefore, the
Wildlife Conservation Society and Sikhote-Alin Zapovednik worked jointly to develop such a
GIS database, one of the first in the Russian Far East, which could be used to record all data from winter routes, and link them to other geographic and biological features of the reserve. Olga
Zaumyslova took primary responsibility for overseeing this transformation of data, with the assistance of many GIS and computer specialists, both Russian and American. This process took seven years to reach its present stage and is, in fact, ongoing. We now have a 40-year database that provides a record of ungulate and tiger abundance within Sikhote-Alin Zapovednik. Such long-term databases on carnivores and prey are exceedingly rare, and in fact, this particular dataset represents the only tiger-prey database of its kind in the world.
To maximize effectiveness of this database, we requested additional assistance for analyses from the University of Wyoming. Specific aims of the analyses were discussed by representatives of Sikhote-Alin, WCS, and University of Wyoming at the SAZ headquarters in
Terney, Primorski Krai, on the 17th of March, 2003, where it was agreed that the principal aim of this study was to use the extensive data from the winter transect counts to analyse the long-term population dynamics of ungulates within SAZ. We were interested first in determining the most appropriate means to convert track abundance indices of ungulates to estimates of absolute abundance - a theme that has concerned practical and theoretical Russian biologists for years.
While it was initially unclear how much we had to contribute to this extensive Russian literature, we felt there was an opportunity to compare existing approaches to controlled simulations, and to explore alternative statistical approaches to estimating abundance.. The Sikhote-Alin database represented a unique opportunity to compare various approaches to estimating ungulate abundance, and to assess variation in these approaches. With the most accurate information on
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ungulate densities possible, we would then be ready to assess the relationship between predators and prey, and specifically, what, if any, parameters could explain numerical changes in both predators and prey. In summary we were interested in addressing the following objectives: examining spatial pattern in the occurrence of the species of interest; investigating methods for estimating population densities from track encounter data; assessing factors underlying temporal changes in populations of the more abundant species; assessing the potential impact of tigers on ungulate populations; and analysing the existing survey protocol to assess its capacity to detect change in ungulate populations, and to make recommendations to improve the survey protocol.
This report represents our first attempt to address these issues. While there are still many questions, we believe that this work provides a useful contribution to our understanding of how to estimate ungulate abundance, of the factors affecting ungulate abundance, and about the relationship between tigers and their prey.
Dale G. Miquelle
Terney, 2006
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TABLE OF CONTENTS
Executive Summary i Study and findings i Specific recommendations iii Acknowledgements vi Preface vii Table of Contents x
1. General introduction 1 1.1 Background and aims 1 1.2 Study area 4 1.3 Data and data collection 4 1.4 Structure of the report 9
2. Spatial analyses of ungulate distributions 10 2.1 Background 10 2.2 Methods 10 2.2.1 Analysis of track encounter rates among drainage basins 10 2.2.2 Analysis of track encounter rates among forest types 11 2.3 Results 15 2.3.1 Comparison of track encounter rates among drainage basins 15 2.3.2 Encounter rates in different forest formations 17 2.4 Discussion 18
3. Track encounter rates and ungulate densities 20 3.1 Background 20 3.2 Methods 22 3.2.1 Movement data 22 3.2.2 Estimation of deer density using a correction factor 24 3.2.3 Confidence intervals for density estimation 25 3.2.4 Stratification and weighting of density estimates 28 3.2.5 Estimation of density using the FMP formula 29 3.2.6 Estimation of density using simulations 32 3.3 Results 33 3.3.1 Movement data 33 3.3.2 Estimating density: comparison of weighting approaches 38 3.3.3 Parameters for density estimation by the FMP formula and simulation methods 42 3.3.4 Comparison of estimators 46 3.3.5 Final estimates of density 47 3.4 Discussion 47
4. Temporal analyses of ungulate population dynamics 54 4.1 Background 54 4.2 Methods 62 4.2.1 Within-year variation in track encounters 62 4.2.2 Linear trend analysis 63 4.2.3 Detecting density dependence 64
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4.2.4 Time-series analysis 69 4.2.5 Putative factors influencing population growth 72 4.2.6 Selection of data sets for density dependent and time-series analyses 78 4.3 Results 80 4.3.1 Within-year variation in track encounters 80 4.3.2 Linear trend analysis 82 4.3.3 Density dependence 84 4.3.4 Time-series analysis 87 4.4 Discussion 94 4.4.1 Within-year variation in track encounters 94 4.4.2 Linear trend analyses 95 4.4.3 Density dependence 96 4.4.4 Time-series analysis 98 Appendix 4A 102 Appendix 4B 105
5. Survey protocol 112 5.1 Background 112 5.2 Methods 113 5.2.1 Zero counts and the length of transect segments 113 5.2.2 Survey effort and associated error 113 5.2.3 Power analyses and required survey effort 115 5.3 Results 116 5.3.1 Zero counts and the length of transect segments 116 5.3.2 Survey effort and associated error 116 5.3.3 Power analyses and required survey effort 118 5.4 Discussion 120
6. Tiger-prey relationships 123 6.1 Background 123 6.2 Methods 124 6.2.1 Estimating the requirements of tigers 124 6.2.2 Estimating the impacts of tigers 126 6.3 Results 128 6.3.1 Requirements of tigers 128 6.3.2 Estimated impacts of tigers 130 6.4 Discussion 132
7. General discussion 137 7.1 Ungulate densities and the utility of the survey protocol 137 7.1.1 Accuracy of data 138 7.1.2 Precision of estimates 141 7.2 Estimating animal density from sign 143 7.3 Ungulate dynamics and tiger conservation 144 7.4 Specific recommendations 146 7.5 Concluding remarks 148
References 150
xi Analysis of ungulate dynamics
1. GENERAL INTRODUCTION
1.1 Background and aims
The winter transect count involves monitoring game species by counting the number of sets of tracks of those species that intersect with a stable network of transects, surveyed during periods of snow cover. It is the main method of estimating the number of many game animals in large territories of the Russian Federation (Lomanov, 2000). In Sikhote-Alin Zapovednik (Reserve)
(SAZ), winter transect counts have been conducted each winter since 1962. In SAZ, tracks of approximately 20 species of mammals have been recorded during winter transect counts, including six species of ungulates: red deer (Cervus elaphus), wild boar (Sus scrofa), roe deer
(Capreolus pygargus) (Nowak, 1999), musk deer (Mochus moschiferus), sika deer (Cervus nippon) and moose (Alces alces).
These data have been analysed previously to investigate the population dynamics of one or more ungulate species (e.g. Zaumyslova, 2000; Zaumyslova et al., 2001) but, for three reasons, we have extended these investigations and subjected all of the long-term data on ungulate species to further, rigorous analyses. Our principal motivations included: (i) the importance of gaining accurate knowledge regarding the densities of ungulates in SAZ and the utility of the survey protocol; (ii) the broader contribution that our analyses can make to the field of estimating animal population density from indirect sign; and (iii) the importance of understanding ungulate dynamics in SAZ, in order to inform management of the Amur tiger (Panthera tigris altaica).
First, there is a need to determine the relationship between track encounter rates derived from winter transect counts and absolute abundance of wildlife, a topic that has received considerable attention in other parts of the Russian Federation (e.g. Chelintsev, 1995; Smirnov,
1973) but not in SAZ. Here, we present a rigorous analysis of the methods available to relate track encounter rates to indices of abundance. This process allows us to assess the constraints on
1 Analysis of ungulate dynamics further analyses of the long-term data and to make recommendations for improving the survey protocol.
Secondly, in areas where ungulates are abundant or occur in open terrain, they are often surveyed using direct count methods, such as aerial counts (e.g. Noyes et al., 2000; Rabe et al.,
2002; Walter & Hone, 2003). For populations at lower density or in heavily vegetated terrain, aerial surveys are still possible using thermal imaging (e.g. Dunn et al., 2002; Haroldson et al.,
2003; Havens & Sharp, 1998) but this technology is seldom available. Instead, researchers often rely on extrapolating from indirect sign, such as tracks or scat (e.g. De Young et al., 1988;
Mandujano & Gallina, 1995; Marques et al., 2001; Mooty et al., 1984). Issues arising from these techniques have broad applicability to surveying a large number of low density or low-visibility species by indirect sign, including many species of carnivore. The use of indirect sign to estimate abundance is an important but highly contentious field (e.g. Barnes, 2001; Buckland et al., 1993;
Carbone et al., 2001; Carbone et al., 2002; Collie & Sissenwine, 1983; Diefenbach et al., 1994;
Frantz et al., 2004; Jennelle et al., 2002; Ogutu & Dublin, 1998; Patterson et al., 2004; Sadlier et al., 2004; Schwarz & Seber, 1999; Thompson et al., 1998; Wasser et al., 2004; Wilson &
Delahay, 2001). The SAZ monitoring data set is unusual in its length and in the consistency with which surveys have been conducted (cf. Stephens et al., 2001, for example). As a result, using the SAZ data to analyse methods for estimating density from sign provides a rare opportunity to contribute to this debate by analysis of a very extensive data set and by combining recent developments from both the Russian and English literatures.
Finally, six ungulate species in SAZ are all potential prey of the Amur tiger. The tiger is listed as an endangered species (IUCN, 2002) and, among its subspecies, the Amur tiger appears to be one of the rarest. Long-term data from track surveys throughout the Amur tiger’s range indicate that the population declined to a bottleneck of 20-30 individuals in the 1930s and 1940s but has since shown a substantial recovery (Kucherenko, 2001; Smirnov & Miquelle, 1999).
However, traditional methods of monitoring were not standardised, preventing calculation of
2 Analysis of ungulate dynamics error associated with population estimates; hence, the exact magnitude of the Amur tiger’s recovery remains uncertain (Hayward et al., 2002). Increasingly, it is recognised that prey availability is a key factor dictating tiger distribution (Karanth & Nichols, 1998; Karanth et al.,
2004; Karanth & Sunquist, 1992), with tiger densities positively related to the densities of ungulate prey (Miquelle et al., 2005). For the Amur tiger, in particular, detailed analyses of distribution in relation to a suite of habitat variables indicated that the distribution of prey is the single most important factor determining the tiger’s geographic range (Miquelle et al., 1999).
Specifically, the Amur tiger shows an overlap of approximately 61% with the distribution of red deer which has previously been shown to make up the majority of its diet (Miquelle et al., 1996).
Furthermore, within their broader geographic range, tigers appear to select home ranges that contain a greater than average proportion of riverine forest, a habitat noted for its potentially high prey abundance (Miquelle et al., 1999). Simple models of population dynamics also indicate that the tiger may be more vulnerable to depletion of its prey than to commercial poaching, a factor usually cited as its greatest potential threat (Karanth & Stith, 1999). Clearly, knowledge of the distribution, dynamics and abundance of prey species is of crucial importance to the conservation of tigers. Indeed, it has been suggested that “enhancing and monitoring the tiger's prey base is perhaps the single most important task facing wildlife managers across Asia” (Karanth, 1999).
The principal aim of this study was to use the extensive data from the winter transect counts to analyse the long-term population dynamics of ungulates within SAZ. Within this main aim, five inter-related objectives were identified, as follows:
• Spatial analyses of ungulate distributions.
• Analyses of the relationship between track encounter rates and ungulate densities.
• Temporal analyses of ungulate population dynamics.
• Assessment of the current survey protocol, with suggestions for improvement.
• Theoretical assessment of the prey requirements of tigers and the potential impact of
tigers on prey.
3 Analysis of ungulate dynamics
1.2 Study area
Sikhote-Alin State Biosphere Zapovednik is located in north-eastern Primorski Krai (Province) in the southern Russian Far East, some 400 km northeast of Vladivostok. Portions of SAZ border the Sea of Japan (Fig. 1.1) but its major feature is the Sikhote-Alin Mountains, a low range (most peaks are below 1200m) running through Primorski and Khabarovski Krais and paralleling the
Sea of Japan. Created in 1935 as a one million hectare Zapovednik, and approved as a Biosphere
Zapovednik in 1978, SAZ has varied greatly in size over time (Gromyko, 2005), but the current size of the Reserve is 4,000 km2.
Vegetation within the reserve is classified into seven dominant forest formations (see further in Section 2), based on a Forest Inventory (Lesostroitsva) conducted on the Zapovednik in
1979. However, for the majority of our analyses we used a greatly simplified classification, dividing the area into three broad habitat zones (Fig. 1.1). The coastal forest zone below about
250m above sea level (a.s.l.) has withstood severe impacts from fire and human disturbance, and is dominated by Oak-birch forests. Further inland and at slightly higher altitudes, the central belt of SAZ is dominated by mixed Korean pine-deciduous forests. Finally, the most westerly and high altitude areas of SAZ (from 800 up to approximately 1300m a.s.l.) are dominated by mixed spruce and fir forests. The lower portion of the Kolumbe Basin, added to the Reserve in 1996, is also dominated by spruce-fir forests but, because long-term data have not been collected there by reserve staff, this portion of the reserve is not included in our analyses.
1.3 Data and data collection
The main database consists of survey data spanning the period from 22-Jan-1963 to 4-Mar-2003.
Biological years are usually taken to run from spring to spring and, hereafter, we refer to any winter period from October to April by the year at the start of that winter. It follows that the data span the period of the biological year 1962 to the biological year 2002. Data from the biological
4 Analysis of ungulate dynamics years 2001 and 2002 were added following the preliminary analyses. Most analyses incorporate these data but where they do not, that absence is indicated in the report.
Figure 1.1. Map of SAZ showing the major regions of different habitat types.
5 Analysis of ungulate dynamics
Winter transects were broken into transect “segments” each of which is intended to represent a continuous sample of a single habitat type and/or aspect. Collectively, the database consists of records from 9,612 transect segments. The total length of transects surveyed in any one year varied from just under 100 km in 1964 to nearly 1800 km in 1985. In general, the total length of transects increased throughout the 1960s to 1971, after which time it averaged 872 ±
294 (standard deviation; SD) km per year, with a low in 1982 and a high in 1985 (Fig. 1.2).
Route locations are shown in Section 2, Fig. 2.1).
For each winter transect count, tracks of each ungulate species were recorded if the fieldworker assessed that the tracks were created in the previous 24-hour period. Along each transect segment, in addition to the counts of tracks, habitat type, relief and snow depth, as well as date, route and location, were recorded. Encounter rates during the study period (averaged over all habitat types) are shown in Fig. 1.3 for the six principal ungulates.
In addition to the main database, several other data sources were developed to aid analyses. These include records of 24-hour movements for four ungulate species, assessment of mast crops in SAZ, data on human populations in Terney Raion (county), potential human impacts on the reserve (e.g. road abundance in proximity to the reserve, level of poaching), and climate from three weather stations in the region of SAZ.
2000
1800 1600
1400
1200
1000 800 600
400
Total length of transects (km) 200 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Year Figure 1.2. Total length of all transects surveyed in SAZ during the study period.
6 Analysis of ungulate dynamics 4.0 (a)
3.0
2.0
1.0
0.0 1962 1972 1982 1992 2002
2.0 (b)
) -1 1.5
1.0
0.5
Mean encounterrate (km
0.0 1962 1972 1982 1992 2002
0.8 (c)
0.6
0.4
0.2
0.0 1962 1972 1982 1992 2002
Year
Figure 1.3. Annual track encounter rates for: (a) red deer (solid line) and wild boar (dashed line); (b) roe deer (solid line) and musk deer (dashed line); (c) sika deer (solid line) and moose (dashed line).impacts on the reserve (e.g. road abundance in proximity to the reserve, level of poaching), and climate from three weather stations in the region of SAZ.
7 Analysis of ungulate dynamics
Daily movement data for red deer, roe deer, sika deer and wild boar were collected by two methods. The first of these was used primarily for wild boar and involved locating a set of fresh tracks and following it backwards to the previous night’s bed site. This location was recorded and the following day, the tracks were followed from that point until the next bed site
(from the intervening night) was reached. The second method was similar but involved visual observations of animals. The location and time of the observation were recorded and, the following day, tracks were followed from that point until the animal was seen again, ideally at approximately the same time as on the previous day. Use of radio-collared red deer increased the efficiency of data collection for that key species (Myslenkov & Voloshina, 2005). The data were stored as vectors, with each total path broken down into moves (e.g. see Turchin, 1998), defined by an angle and a distance. Both straight line and total lengths of each move were recorded. For each path, data were also collected on factors that could influence path characteristics. These included species, sex and age of the individual(s) tracked, time of year, habitat and snow conditions.
Data on mast abundance were also available for SAZ from throughout the study period.
Mast abundance was measured for both oak and Korean pine, using a system of regularly assessed plots, each 1m2. The numbers of acorns and pine cones within these plots were measured and, since 1934, have been equated to an ordinal scale for each mast type, with 1 indicating a very low density of nuts and 5 indicating an exceptionally good year.
Finally, data on climate were available from two weather stations in the region of SAZ:
Terney weather station (close to the town of Terney, Fig. 1.1) and Melnichnoye weather station in the main mountain range, approximately 18 km due west of the northwest boundary of SAZ.
Data available from these weather stations include mean snow depths for each 10 day period during winter, as well as temperature and precipitation data from throughout the year.
8 Analysis of ungulate dynamics
Correlations between weather records from the two stations are high and, as the data from
Melnichnoye are more reliable, these are the data that were used for our temporal analyses of ungulate dynamics (Section 4).
1.4 Structure of the report
The remaining sections of this report are divided between the five objectives listed in Section 1.1
(Sections 2 to 6) and a broad discussion of the findings (Section 7). The sections on individual objectives present the background, methods, results and conclusions relevant to that section, and are intended to be readable on their own. There is, however, considerable overlap between sections and, consequently, cross-references are included where relevant. The aim of Section 7 is to bring the individual objectives together in a more coherent manner. Where necessary, species and habitat codes are used in tables and figures. These are summarised in Tables 1.1 and 1.2, respectively.
Table 1.1 Species codes used in the report
Species Code
Moose MO Musk deer MD Red deer RE Roe deer RO Sika deer SD Wild boar WB
Table 1.2 Habitat codes used in the report
Habitat Code
Oak-birch OB Korean pine-deciduous KD Spruce-fir SF
9 Analysis of ungulate dynamics
2. SPATIAL ANALYSES OF UNGULATE DISTRIBUTIONS
2.1 Background
Understanding the spatial pattern of ungulate abundance is important for two reasons. First, knowledge of the relative abundance of different species within different parts of SAZ has implications for management and for developing the sampling protocol. Secondly, spatial analyses are required to determine a suitable approach for stratification of the winter transect count data for further analyses. Many spatial divisions based on geographical or habitat boundaries are recognised within SAZ. Perhaps the most striking differences in ungulate abundance are seen between the three habitat zones identified in Section 1.2. Even a cursory examination of track encounter rates throughout the study period suggests that track encounter rates vary greatly among the three zones annually, and supports division of the reserve into those three zones for data analyses. For that reason, further analyses employ the habitat zone as the most basic level of data stratification. Further stratification of the data is possible on the basis of both drainage basins and finer-scale habitat divisions (e.g. vegetation types). In this section, we assess data within these subdivisions in more detail and analyse the importance of further stratification of the data. In doing this, we also provide an indication of the heterogeneity of ungulate distributions, suggesting which drainage basins and habitats are most important for the various ungulate species.
2.2 Methods
2.2.1 Analysis of track encounter rates among drainage basins
To assess whether there are consistent differences in ungulate encounter rates between drainage basins, we compared annual track encounter rates in each drainage with those in the broader habitat category to which it belongs. In spite of the chance that certain drainages will deviate from the mean for the overall category in certain years, only deviations in consistent
10 Analysis of ungulate dynamics directions across multiple years will indicate that the drainage shows a clear tendency to have ungulate densities that differ from the annual mean.
SAZ was divided into 13 major drainage basins, each of which occurs entirely within one of the habitat zones (see Table 2.1 and Fig. 2.1). Where Eh,y is the average track encounter rate for a given habitat type (h) and year (y), and Eb,y is the average track encounter rate for a given drainage basin (b) and year, the overall encounter rate in a given basin relative to the mean for the habitat zone is given by:
Y Eb,y / Eh,y ∆b = ∑ (2.1) y=1 Y
where ∆b is the mean deviation for basin b and Y is the total number of years during which a given species occurred in the habitat and was surveyed in that basin. That the mean deviation is calculated from annual ratios will tend to normalize the data and, consequently, we used a standard approach for calculating confidence intervals, where the confidence intervals are symmetric, and of magnitude I, given by:
I = s / √n · τ (2.2)
Here, s is the standard deviation, n is the sample size and τ is the α = 0.025 t-statistic associated with n-1 degrees of freedom.
2.2.2 Analysis of track encounter rates among forest types
A number of classifications of vegetation type have been used in SAZ. In addition to the broad habitat zones discussed above (Fig. 1.1), vegetation can be characterised more specifically by dominant forest formations (referred to here as “forest types”) (Fig. 2.2 and Table 2.2). To a large extent, the relative prevalence of these forest types defines the major habitat zones in SAZ and, consequently, analyses of the relative preference of forest types can be conducted without
11 Analysis of ungulate dynamics
Figure 2.1. Fourteen drainage basins (including the new addition of lower Kolumbe, which was not used in analyses) and primary survey routes used to assess variation in track encounter rate across Sikhote-Alin Zapovednik, based on winter transect routes, 1962 to 2002.
12 Analysis of ungulate dynamics stratification by the major habitat zone in which each forest type is found. For this reason, mean deviation for any forest type f, was calculated as:
Y E f , y / E y ∆ f = ∑ (2.3) y=1 Y where Ef,y is the average track encounter rate for a given vegetation type and year, Ey is the overall average track encounter rate for that year, and Y is the total number of years during which that vegetation type was surveyed.
Table 2.1 Major drainage basins in SAZ
Habitat category Drainage Drainage name Drainage size number (km2)
Oak-birch 1 Abrek 42.7 2 Blagodatnoe 53.7 3 Khuntami 75.4 4 Inokov 55.2 7 Kunaleyka 104.0 8 Kuruma 302.9 9 Lianovaya 135.8
Korean pine-deciduous 5 Jigitovka 152.5 10 Serebrianka 922.0 11 Tayozhnaya 115.0 12 Yasnaya 106.2 13 Zabolochennaya 309.0
Spruce-fir 6 Kolumbe 1099.0
Table 2.2 Forest types in SAZ
Description Area of forest type within each zone (km2): Oak-birch Korean pine-deciduous Spruce-fir
Riverine 13.1 7.0 17.2 Oak 379.7 65.0 - Birch/aspen 239.3 128.1 52.2 Pine-deciduous 6.7 145.9 25.0 Northern pine 23.4 699.8 555.5 Larch 27.9 116.3 203.6 Fir 9.9 364.4 784.3
13 Analysis of ungulate dynamics
Figure 2.2. Map showing distribution of major vegetation groups within SAZ
14 Analysis of ungulate dynamics
2.3 Results
2.3.1 Comparison of track encounter rates among drainage basins
Average ratios between encounter rates in each basin and mean encounter rate for the whole major habitat category are shown in Fig. 2.3. Analyses were conducted for the entire study period
(biological years 1962 – 2002) and, also, for the most recent five years (1998 – 2002). Clearly, the ratio of encounter rates in the Kolumbe basin to the encounter rates in spruce-fir areas is always unity, as the Kolumbe drainage makes up the entire spruce-fir zone in SAZ.
Consequently, no results are shown for the spruce-fir area. For species in the other habitats, Fig.
2.3 suggests few consistent patterns of occurrence which must, in any case, be treated with caution and interpreted only in light of the limitations on sample sizes within each basin.
Nevertheless, a few general observations are possible on the basis of this analysis. These include first, that patterns have not always remained consistent throughout the study period. Perhaps a striking example of this is the relative decrease in red deer use of Abrek, to the point that they are relatively uncommon in that drainage now. By contrast, sika deer appear to have become relatively more common in that area in recent years, a fact that may account for the reduction in red deer numbers. Elsewhere, sika deer appear to have a selective advantage over red deer
(Abernathy, 1994) and a decline in red deer in south-western Primorye appears to be the result of an increase in sika deer (Pikunov et al., 2000). A second finding is that, at least for roe and sika deer, several of the oak-birch drainages along the southern border of SAZ appear to have relatively low abundances. This may be indicative of source-sink dynamics, with areas to the south of SAZ acting as a sink due to higher rates of off-take where human populations and access are relatively high. Thirdly, although they are seldom strikingly different from the average for any one species, both Blagodatnoe and Khuntami appear to be good areas for several of the ungulates that are common in oak-birch habitat (i.e. red deer, roe deer, sika deer and wild boar).
Finally, there appear to be few obvious patterns in the relative abundance of any species in
Korean pine-deciduous areas.
15
4.0 6.0 (a) (d) 5.0 3.0 4.0
2.0 3.0
2.0 1.0 1.0
0.0 0.0
4.0 10.0 Abrek Abrek Inokov Inokov Kuruma Kuruma Huntami Huntami Yasnaya Yasnaya (b) Jigitovka (e) Jigitovka Lianovaya Lianovaya Kunaleyka Kunaleyka Serebrianka Serebrianka Tayozhnaya 8.0 Tayozhnaya Blagodatnoe Blagodatnoe 3.0 Zabolochennaya Zabolochennaya 6.0 2.0 4.0
1.0 2.0
0.0 0.0
5.0 5.0 Abrek Abrek Inokov Inokov Kuruma Kuruma Huntami Yasnaya Huntami Yasnaya Jigitovka (c) Jigitovka Lianovaya Lianovaya
(f) Kunaleyka Kunaleyka Serebrianka Tayozhnaya Serebrianka Tayozhnaya Blagodatnoe 4.0 Blagodatnoe 4.0
Zabolochennaya Zabolochennaya 3.0 3.0
2.0 2.0
1.0 1.0
0.0 0.0
Mean ratio of encounter rate in basin to encounter rate in habitat zone Abrek Abrek Inokov Inokov Kuruma Kuruma Huntami Yasnaya Huntami Yasnaya Jigitovka Jigitovka Lianovaya Lianovaya Kunaleyka Kunaleyka Serebrianka Tayozhnaya Serebrianka Tayozhnaya Blagodatnoe Blagodatnoe Zabolochennaya Zabolochennaya Figure 2.3. Ratios of track encounter rate in basins to major habitat encounter rate, averaged over all years in which the species occurred in the habitat and surveys were conducted in each basin. Oak-birch habitat (green bars) and Korean pine-deciduous habitat (brown bars) are shown for full study period (dark bars) and last five years (light bars) Panels show: (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer, (e) moose, (f) wild boar. Broken lines show ratios of one and error bars show 95% confidence intervals. Some very large confidence intervals have been truncated for clarity.
Analysis of ungulate dynamics
2.3.2 Encounter rates in different forest formations
For several ungulate species, the analysis of track encounters within different forest types (Fig.
2.4) provided more striking patterns of preferences than those seen in the comparison of drainage basins. With a few exceptions, patterns are generally as expected from what is known about the ecology of the species and are summarised in Table 2.3. Red deer preferred riverine habitat types, and avoided larch and spruce-fir forest types. Roe deer preferred both riverine and oak forests, and avoided not only larch and spruce-fir, but also both pine forest types. Sika deer preferred only oak forest, and avoided all but riverine forests (which were used approximately in accordance with availability). In contrast, musk deer preferred northern pine, larch, and spruce- fir forests, used Korean pine-deciduous in proportion to availability, and avoided riverine, oak, and birch forests. Moose preferred only larch and spruce-fir forests, and avoided all others except
Korean pine-deciduous forests. Wild boar showed a preference only for Northern pine forests.
That these patterns were evident in spite of the potentially confounding effects of different encounter rates in different habitat zones and drainage basins suggests that forest type is an informative factor and that stratification of data by forest type (within habitat zones) may help to increase the accuracy of density estimates.
Table 2.3 Summary of relationships between encounter rate and forest type for ungulate species (+ indicates preferred habitats, - indicates avoided habitats)
Species Vegetation type Red deer Roe deer Sika deer Musk deer Moose Wild boar
Riverine + + - - Oak + + - - Birch/aspen - - Pine-deciduous - - - Northern pine - - + - + Larch - - - + + - Fir - - - + + -
17 Analysis of ungulate dynamics
2.4 Discussion
In this section, we have shown how the long term track survey data from SAZ can be used both to
assess the need for post-stratification of data, and to gain some insight into the heterogeneity of
ungulate distributions. Within habitat zones, different species of ungulate show some consistency
in the drainage basins in which they are encountered most frequently, although for the majority of
species and basins, variation between years (as indicated by the error bars in Fig. 2.2) is
sufficiently large to suggest that no strong preferences exist for any drainage. Rather, it is likely
2.0 (a) 3.0 (d) 1.5 2.0
1.0 1.0 0.5
0.0 0.0
2.5 10 (b) (e) 2.0 8
1.5 6 type to encounter rate in Zapovednik Zapovednik in rate encounter to type 1.0 4
0.5 2
0.0 0 4.0 (c) 3.0 (f)
3.0 2.0 2.0
1.0 1.0
0.0 0.0 Mean ratio of encounter rate in forest forest in rate of encounter ratio Mean Fir Fir Oak Oak Larch Larch Riverine Riverine
Birch/aspen Birch/aspen Northern pine Northern pine Pine/deciduous Pine/deciduous Figure 2.4. Relative encounter rates within vegetation groups for: (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer, (e) moose, (f) wild boar.
18 Analysis of ungulate dynamics that populations move among drainages in response to temporal heterogeneity in habitat quality.
Nevertheless, some patterns were seen in the use of different drainages, including a tendency for
Blagodatnoe and Khuntami to have relatively high populations of several species, whilst several of the drainages further inland but within the same habitat zone, had relatively low abundances, especially of deer. This finding may be explained by the distribution of forest types within the oak-birch zone (see Fig 2.1). In particular, although we have considered the oak-birch zone as a single habitat zone, it is clear that oak predominates in the coastal area, whilst birch and aspen dominate more inland parts of the zone. The distinct nature of this separation, visible in Fig. 2.2, might suggest that a four zone habitat classification would be more useful in SAZ. Alternatively, the variation in distribution within the oak-birch habitat zone may reflect preference with coastal areas, where snow density is generally less throughout the winter. Probably some combination of variation in snow density, mast distribution (in some years) and perhaps some other features of the forest types explain this pattern. Again, however, different climatic influences (particularly that of the coast) might support division of the oak-birch zone into two zones. We return to these ideas in Section 7.
The strong influence of habitat in explaining patterns seen among different drainages, together with the striking disparities in encounter rates among forest types (Fig. 2.4), suggest that forest type is a fundamentally important factor explaining variation in ungulate abundances within the different zones. The patterns of apparent preference and avoidance are largely what would be expected, although there are some unexpected results, such as the apparent preference of wild boar for northern pine areas, in contrast to its average abundances in mixed pine and deciduous areas. This type of anomaly is likely a result of much finer scale patterns in the mosaic of habitats and would require a higher resolution of analysis than is possible using the winter transect count data alone. Overall, however, it appears likely that stratification of survey data by either drainage basin or vegetation type will improve the accuracy of density estimates, and we build on this finding in the following section.
19 Analysis of ungulate dynamics
3. TRACK ENCOUNTER RATES AND UNGULATE DENSITIES
3.1 Background
Caughley (1977, p.12) observed that “The majority of ecological problems can be tackled with the help of indices of density, absolute estimates of density being unnecessary luxuries.” For three reasons, however, it is important to know the relationship between track encounter rates and absolute densities of ungulates within SAZ. First, the process of converting track encounter rates into estimates of density may help to identify sources of error in the estimates of density. As such, the process may help with constructing confidence boundaries for predicted population densities and identifying required differences in track encounter rates necessary to infer a difference in population density. Secondly, analysing the long-term dynamics of ungulates within
SAZ will, necessarily, require some form of standardisation of abundance indices between different areas within the reserve. Converting indices of relative abundance into estimates of density will provide this standardisation. Thirdly, if it is possible to estimate absolute densities from the winter transect count data, these would also be very useful in their own right for management in SAZ. In particular, emerging evidence suggests that tiger numbers may be closely related to prey biomass (Karanth et al., 2004; Miquelle et al., 1999) and it would be useful to determine with greater accuracy how tiger and prey densities fit this pattern in SAZ (see further in Section 6).
Although the question of how best to convert track data into density estimates has been considered by Russian biologists for decades (e.g. Formozov, 1932), in the English language scientific literature the topic is surprisingly rare, as is evidenced by the paucity of coverage the subject receives in recent reviews (Schwarz & Seber, 1999) and textbooks (Williams et al., 2002).
In North America, some of the most elaborate work on this subject has used probability sampling to estimate the size of a number of low density populations, using data on track encounters and daily movement (e.g. Anderson & Lindzey, 1998; Becker, 1991; Becker et al., 1998; Garant &
20 Analysis of ungulate dynamics
Crete, 1997; Van Sickle & Lindzey, 1991). Becker (1991) described two approaches to probability sampling but both are reliant on a systematic survey design, in which transects are laid out parallel to each other. Probability sampling is, thus, most practical when aerial surveys are possible and is less relevant to the surveys conducted in SAZ. Consequently, we used three approaches that are derived largely from the Russian literature on estimating ungulate population densities from survey data, all of which could be directly applied to the data from SAZ.
The first and simplest method for estimating density from track encounters is an empirical correction factor, used to translate combined encounter rates of deer tracks into estimates of deer density and associated confidence intervals. This correction factor was derived by regressing observed numbers of deer within a plot (determined by expert assessment of tracks entering and leaving the plot) on numbers of tracks encountered when the plot perimeter was walked (Gerow et al., 2005). The second method to estimate ungulate densities from survey data uses a formula known variously as the Formozov (Mirutenko, 1986) or Formozov–Malyashev–
Pereleshin formula (Kuzyakin, 1983). All of these authors were involved in prompting the derivation of the formula but it was perhaps most comprehensively set out by Chelintsev (1995).
The formula is based on probabilistic encounters between randomly placed and orientated animal paths and surveyed routes. Hereafter, we refer to it as the FMP formula. The third approach that can be used to assess the relationship between track encounters and population density is simulation modelling. Using empirical records of movement patterns, large numbers of simple simulations can be performed to provide a relationship between track encounter rates and densities of paths. Simulation modelling is a computerised version of graphical techniques which have a long history in Russia (e.g. Kuzyakin, 1983).
The second and third of these methods require estimates of daily travel distance and actual daily travel routes, respectively. In this section, we begin by detailing the analysis of the movement data, before going on to describe the estimation of population density by each of the three methods described above.
21 Analysis of ungulate dynamics
3.2 Methods
3.2.1 Movement data
Movement data were collected as described in Section 1.3 and stored as vectors, with each total path broken down into moves (e.g. see Turchin, 1998), defined by an angle and a distance. Both straight line and total lengths of each move were recorded. Total lengths were used when assessing the total distance travelled on any path but for assessing the probability of track encounters, straight line distances were sufficient. This is because local re-crossings were ignored when transect data were collected.
To assess which factors influenced path characteristics, we first assessed general effects on both travel distance and tortuosity (or curvilinearity) of the paths. Tortuosity was expressed in terms of the turning rate (klinokinesis), measured as the mean degrees turned per metre travelled
(Murdie & Hassell, 1973). Initial analyses indicated that travel distance was the most important characteristic likely to affect the probability of encountering paths during transects (see Section
3.3.1). Consequently, further analyses were conducted to compare the performance of a variety of simple, one- or two-factor models, in explaining travel distances.
Two of the factors measured were mast abundance and snow depth. The data on mast abundance have been described above (Section 1.3). Unfortunately, daily movements have not been recorded in a wide range of mast conditions. Consequently, the five-point indices for oak and Korean pine mast were collapsed into just two categories each: good or poor. Specifically, the indices were taken to indicate a poor mast crop in years when the recorded mast index was between zero and two, inclusive. All other years, with mast scores of from three to five, were categorised as good mast years.
Daily movements were also recorded in relatively few snow depths, preventing the use of snow depth as a continuous variable. Analyses of energy expenditure suggest that costs of locomotion increase abruptly in snow depths above a certain proportion (40 – 60%) of ungulate breast height (Parker et al., 1984). We decided to classify snow depth into shallow or deep on the
22 Analysis of ungulate dynamics basis of whether it fell above or below an approximate threshold related to size. For red deer, we used a value of 45cm as the threshold (Parker et al., 1984) whilst for roe deer, we used 25cm. For wild boar, the threshold used was 20cm.
Models were compared using Akaike’s Information Criterion (AIC), modified for small sample sizes (AICc). AIC and AICc converge as sample size increases, so it is generally better to use AICc (Burnham & Anderson, 2002). All the models proposed were simple linear models, for which AICc can be calculated as follows (Burnham & Anderson, 2002):
2K(K +1) AIC = AIC + (3.1) c n − K −1 where K is the number of parameters (including the constant and an error term), n is the sample size (or number of data points) and AIC is given by the formula:
AIC = −2 ⋅ log(l) + 2K (3.2) where log(ℓ) is the log-likelihood of the model calculated (for linear models) as:
n log( ) = − ⋅ log(σˆ 2 ) (3.3) l 2
RSS and σˆ 2 = (3.4) n where RSS is the residual sum of squares.
Models were ranked according to their ∆i scores (calculated as the difference between their AICc score and that of the model with the lowest AICc) and relative likelihood of models was determined as:
⎛ 1 ⎞ exp⎜− ∆i ⎟ ⎝ 2 ⎠ wi = (3.5) R ⎛ 1 ⎞ ∑exp⎜− ∆ r ⎟ r=1 ⎝ 2 ⎠ where R is the set of all models for comparison. Models were compared and their relative support used solely to infer which parameters explained the data most convincingly and, thus, which (if
23 Analysis of ungulate dynamics any) parameters should be used to stratify movement data sets for further analyses (in particular, for analyses of the relationship between track encounters and density). All of the factors examined are likely to affect animal movements in some way, so here, AIC was effectively used as a magnitude of effects estimator (sensu Guthery et al., 2005).
3.2.2 Estimation of deer density using a correction factor
The correction factor used was derived by Gerow et al. (2005) to estimate combined densities of red, roe and sika deer from encounter rates of their tracks. Plots were randomly selected in south- eastern Primorye Krai (Olginski and Lazovski Raions), in oak/deciduous forests and mixed conifer/deciduous forests. During winter the plot boundary was traversed and tracks were recorded to estimate the number of animals entering and leaving the plot during the previous 24 hours. Plot size and shape were chosen to minimize the chance that deer within the plot would go undetected (i.e. not cross the plot boundary during the previous 24h period). Expert assessments of the density of animals within the plot were then regressed on the number of tracks encountered.
A log-log plot was used to ensure homoscedasticity and the regression (and associated confidence intervals) were used to derive the correction factor. The formula derived for the combined density of red, roe and sika deer, Dˆ , is (Gerow et al., 2005):
Dˆ = x ⋅ exp(0.56 ± 0.11) (3.6) where x is the combined encounter rate of paths of the three species. The upper and lower 95% confidence intervals are given by using the upper and lower values of the exponent.
In practice, there are several ways in which equation 3.6 may be applied to field data consisting of multiple samples (transect segments) for the study area and period in question.
Different methods are available to calculate both the mean and its associated confidence intervals.
Firstly, all transect segments could be considered to be sections of a single sample; in that case, we can apply the equation exactly as written, calculating a single overall mean estimate of
24 Analysis of ungulate dynamics density. Secondly, we might consider each transect segment to be a single sample. In this case, we can use equation 3.6 to generate an estimate of density for each sample. We can then find the mean of these estimates. Finally, because the transect segments are of different lengths, we may wish to find a weighted mean of the estimates from each. This assumes that longer segments are likely to be closer to the true encounter rate and, thus, give a better estimate of mean density in the area. In fact, the weighted mean gives the same overall estimate of density as when the samples are combined to give an overall mean. In general, we believe that weighting by transect length is the best method and we discuss this approach (together with other forms of weighting) in Section 3.2.4, below.
3.2.3 Confidence intervals for density estimation
Deriving confidence intervals associated with mean estimated densities is a problematic issue.
Some authors (e.g. Smirnov, 1973) have suggested that track encounters should be well described by a Poisson distribution. If this were the case, then given certain properties of Poisson distributed data (for example, that the variance is approximately equal to the mean), confidence intervals would be reasonably straightforward to estimate. However, there are several reasons to believe that track encounters will not conform to a Poisson distribution. In particular, the potential for multiple crossings of a single path (see further in Section 3.3.3), as well as the possible non-independence of paths (e.g. Chelintsev, 1995), are both likely to cause deviations from the Poisson distribution. One consequence of this is that the distribution of estimates of density generated by independent transects is unknown and unlikely to conform well to a known distribution. Furthermore, sample size for some areas in some years is also low, with the result that the central limit theorem (leading to approximate normality of estimates when sample size is high) is unlikely to apply. Owing to these complications, there is no tractable method for estimating confidence intervals about the mean estimate of density. For that reason, we used bootstrapping (Efron & Tibshirani, 1991, 1993) to determine estimates for confidence intervals.
25 Analysis of ungulate dynamics
Bootstrapping is a flexible procedure that uses computational power to reduce the number of assumptions inherent in many other statistical approaches (Efron & Tibshirani, 1991). The procedure may be conducted parametrically (by repeated re-sampling from the type of distribution from which the experimental data are presumed to have been drawn) or non- parametrically (by repeated re-sampling from the available data set). The latter approach makes no assumptions about the form of the distribution from which the data have been taken and so is particularly appropriate for constructing confidence intervals for the estimates of ungulate density. Four different methods for bootstrapping confidence intervals have been recommended by Efron & Tibshirani (1993). Of these the BCA (“bias-corrected and accelerated”) approach is generally believed to be the most accurate (Efron, 2003). ‘Bias-correction’ refers to adjustments that are made to account for the discrepancy between the proportion of B bootstrap samples (see further below) that lie below the mean and the proportion that lie above the mean (an indicator of bias). ‘Acceleration’ refers to an adjustment made for heteroscedasticity in the data. Details of the construction of confidence intervals by BCA can be found in Efron & Tibshirani (1993).
Here we give a brief overview with specific reference to bootstrapping confidence intervals for the mean ungulate density, D.
We assume that N transect segments each give rise to an estimate of total deer density,
ˆ ˆ D , and that these estimates form a vector, Dn (n = 1, 2, … N), with N elements. The arithmetic
ˆ mean of the estimates is D . Bootstrapping involves re-sampling with replacement from Dn to
*b produce B bootstrap replicates of the set of estimates, denoted Dˆ n (b = 1, 2, … B). From each of these replicates, we can calculate a mean, D *b . The simplest way to create a 95% confidence interval about the overall mean D , is known as the percentile method. A 95% confidence interval is constructed assuming that 2.5% of the distribution at each tail is beyond the confidence interval (this uses an α-level of 0.025, therefore). For percentile confidence intervals, the B
26 Analysis of ungulate dynamics values of D *b are ordered and the estimate of D corresponding to Bα is selected as the lower confidence limit, whilst that corresponding to B(1 – α) is selected as the upper confidence limit.
For example, if B = 1000 and α = 0.025, then the 25th lowest value of D will be the lower confidence limit and the 975th lowest estimate will be the upper confidence limit. As noted above, the BCA approach improves on this by correcting the values of α used to account for both bias and heteroscedasticity. Specifically, two further parameters are calculated: z0 is the bias- correction and a is the acceleration. Bias-correction is given by (Efron & Tibshirani, 1993):
⎛ #(D *b < D) ⎞ −1⎜ ⎟ z0 = Φ ⎜ ⎟ (3.7) ⎝ B ⎠ where # indicates the number of values of D *b that conform to the given condition (i.e. the number that are less than the overall estimated mean) and Φ-1(x) indicates the inverse function of a standard normal cumulative distribution function (i.e. the standardised number of standard deviations giving the cumulative probability x. Note that if exactly half of the bootstrapped estimates of density are less than the mean density, there is no bias and z0 = 0).
The acceleration is determined by a jackknife procedure, whereby i resampled sets of the original set of estimates, each of size N-1, are generated by sequential deletion of the N elements.
The ith jackknifed replicate is thus equal to the original set of estimates, with the ith element removed. The mean, Di , of each replicate is calculated and the mean of all means is denoted
N D = D / N . The acceleration is then given by (Efron & Tibshirani, 1993): (•) ∑i=1 i
N 3 ∑ {[D(•) − Di ] } a = i=1 (3.8) N 3/ 2 6 D − D 2 {}∑i=1[](•) i
The two values determined by equations 3.7 and 3.8 are then used to adjust the α-values used for determination of confidence limits in the percentile method. Specifically, α1 and α2 are used for the lower and upper limits, respectively, and are calculated by:
27 Analysis of ungulate dynamics
⎡ z + z (α ) ⎤ α = Φ z + 0 1 ⎢ 0 (α ) ⎥ ⎣⎢ 1− a(z0 + z )⎦⎥ (3.9) ⎡ z + z (1−α ) ⎤ α = Φ z + 0 2 ⎢ 0 (1−α ) ⎥ ⎣⎢ 1− a(z0 + z )⎦⎥ where Φ(x) represents the number of standard deviations of a standardised normal curve associated with the cumulative probability x, and z(c) is equivalent notation for cumulative probability c.
Efron and Tibshirani (1993) suggest that accurate bootstrapping of confidence intervals requires a large number of bootstrap replicates. For all BCA bootstrapping reported here, we used B = 5000. As we used a weighted mean for estimating overall density, we also drew bootstrap samples from a weighted pool, with both length and number of crossings used to make up the bootstrap samples and find the bootstrap means.
3.2.4 Stratification and weighting of density estimates
Our analyses in Section 2 indicated that within a given broad habitat zone, species may not be distributed uniformly between either drainage basins or forest types. For this reason, estimates of density were derived in three different ways, as follows: (i) using weightings by segment length alone; (ii) using weighting by segment length and drainage basin size (equivalent to stratification by drainage basin); and (iii) using weighting by segment length and forest type (stratification by forest type). The difference between these approaches is summarised by the following equations, which indicate how mean estimated density for a given habitat zone, Dˆ , was derived in each case. First, for the simple case of weighting by transect length:
T ˆ ∑ Dt .St ˆ t=1 D = T (3.10) ∑ St t=1
28 Analysis of ungulate dynamics
ˆ where T is the total number of transect segments surveyed in the area during the time period, Dt is the point estimate of density resulting from segment t (calculated by equation 3.6), and St is the length of segment t.
Where estimates of density were stratified by drainage basin size, equation 3.10 was used
ˆ to calculate a new parameter, Db , the estimated density within the drainage basin for the given period, based on the T transect segments conducted in that basin. Overall density for the habitat zone was then calculated using:
β ˆ ∑ Db .Ab ˆ b=1 D = β (3.11) ∑ Ab b=1 where β is the total number of drainage basins in the habitat zone in which surveys were conducted during the time period, and Ab is the area of drainage basin b. Clearly, both approaches
(described by equations 3.10 and 3.11) required similar modifications to the way that bootstrap and jackknife means were calculated for use in equations 3.7 and 3.8. Where stratification by drainage basin was used (equation 3.11), bootstrap and jackknife means were also calculated using that stratification. Finally, for stratification by forest type, data were grouped using the seven vegetation categories shown in Table 2.2. Density estimation was equivalent to that
ˆ illustrated by equation 3.11, except that Db was defined as the density within a forest type, Ab was the total area dominated by that forest type within the habitat zone, and β was the number of different forest types present within the zone.
3.2.5 Estimation of density using the FMP formula
The derivation of the FMP formula has been described in detail by Chelintsev (1995). All theory presented here is derived from that paper. In brief, it is assumed that an animal’s daily travel path
(of length L) can be broken down into a large number (m) of moves which are effectively linear.
29 Analysis of ungulate dynamics
Each move has length Mi. A transect segment (of length S and any shape) can similarly be broken down into t component parts, each of length Tj. Any move is assumed to lie at an angle, α, to a given section of transect.
The probability, P(mi,tj,α), that a given move (mi) crosses a given section of transect (tj) at angle α is therefore calculated as:
M iT j sin(α) P(m ,t ,α) = (3.12) i j A
Note that the top part of this equation is the area of a parallelogram formed by mi and tj, whilst the bottom (A) is the study area. Thus, the probability is the ratio of the area within which the move must start (in order to cross the transect section) to the whole study area, and is thus the probability that a randomly located move starts close enough to the transect section to cross it.
Given an equal probability of travel in any direction (i.e. any angle, α, between the move and transect section), the average probability of a crossing for any value of α is given by integrating equation 3.12 for the interval of 0 to 2π, and dividing the result by 2π. As the integral of |sin(α)| from 0 to 2π is 4, this yields:
2M iT j P(m ,t ) = (3.13) i j πA
Given a density of animals in the study area of D = N/A and summing the probability given by equation 3.13 for all m sections of the movements of all N animals in the area, it is possible to show that the estimated density is given by:
π ⋅ x Dˆ = (3.14) 2SLˆ where x is the number of tracks encountered, S is the length of a transect (or transect segment) and Lˆ is the estimated daily travel distance of the species monitored. This is the FMP equation.
30 Analysis of ungulate dynamics
Here, error in the estimated density may arise from two sources, both error in x and error in Lˆ . In this case, however, the resultant variance in Dˆ is derived by the multiplicative rule of error propagation:
2 2 ⎛σ σ ˆ ⎞ σ 2 = Dˆ ⎜ x + L ⎟ (3.15) Dˆ ⎜ ˆ ⎟ ⎝ x L ⎠
The above derivation applies to situations in which each path (and each move within a path) is randomly located. Track encounters in such situations are likely to be well explained by a
Poisson distribution and, hence (using a property of Poisson distributions), variance in the estimated track encounter rate will be equal to the mean encounter rate itself. However, these relationships are complicated by two factors: the non-independence of multiple crossings of a single path, and the non-independence of multiple paths when animals travel together.
Chelintsev (1995) discussed the derivation of error calculations for such circumstances in some detail. Unfortunately, his resultant formula for variance depends on several parameters that may not be known in empirical surveys of animal tracks. These include estimates of the number of times that each path is crossed and estimates of average group sizes. As with estimates derived using the correction factor, the uncertainty surrounding these parameters and, by extension, the form of the resultant distribution, means that determining confidence intervals about mean estimates of density is most accurately performed using the BCA bootstrap procedure (Section
3.2.3). Consequently, this method was used to generate confidence intervals for mean estimates of density produced by the FMP formula. As with estimates based on the correction factor, each transect segment from a given time period and area was assumed to represent an independent estimate of density. Mean estimates and associated confidence intervals were again calculated in three ways: first by weighting in proportion to the length of the transect segment and then, also, using stratification by either drainage basin area or by area of forest type (Section 3.2.4).
31 Analysis of ungulate dynamics
3.2.6 Estimation of density using simulations
Estimating density using simulations requires several steps. First, it is necessary to determine a suitable sample of movement data with which to estimate densities. Methods for analysing available movement data in order to identify suitable samples are presented in Section 3.2.1, above. Next, track encounter probabilities must be estimated by simulating transects through a survey area containing a given number of movement paths. If animals are distributed randomly within an area of habitat, it is expected that mean encounter rates of individual paths will increase linearly with density and that the number of encounters of individual paths (either one or more times) will conform to a Poisson distribution. It was necessary to test both of these predictions and to determine the relationship between transect (or transect segment) length and the distribution of multiple encounters of a single path (assuming the path is encountered at least once). Finally, the most probable density given any encounter rate on a transect of given length can be estimated. To do this, it was assumed that the total number of track encounters, x, is given by:
Y x = ∑ ni (3.16) i=1 where Y is the total number of unique tracks encountered and n is the number of times that each of those unique tracks is encountered. For any density, the most probable value of x will be the expectation of x, E(x), given by:
E(x) = E(Y) × E(n) (3.17)
If Y increases linearly with density for a given transect length and n is constant for a given transect length, then E(x) will also increase linearly with density. Thus, where x is known and Y and n can be predicted, the most probable density ( Dˆ ) leading to x can be estimated. That value was taken to be a point estimate of density. As with the previous approaches, estimates arising from independent transect segments were then bootstrapped using the BCA technique, in order to determine confidence intervals about a weighted mean.
32 Analysis of ungulate dynamics
Unique path encounter probabilities, p(Y), and probabilities of multiple encounters with unique paths, p(n), were determined by simulation. The simulated survey area was 2,500 km2 (50
× 50 km). Movement paths recorded in the field were converted into schematics, each comprising m straight line moves. These were read into the model as m+1 sets of coordinates
(x1,y1 – x2,y2; x2,y2 – x3,y3; … xm,ym – xm+1,ym+1). To simulate the required density of paths, a given number of movement paths were picked at random (from a set of paths appropriate for the particular analysis) and randomly placed in the survey area, ensuring that the entire path was within the area. Transects of a given length were then designated randomly and compared to each move of each path to determine whether they crossed the section. Encounter rates were expressed per km of transect.
Pilot tests were run using all of the red deer movement paths. A range of path densities from 0.25 km-2 to 10 km-2 and a range of transect lengths from 100 m to 5 km, were simulated to ensure that encounter rates with unique paths increased linearly with both path density and transect length. For each density and transect length, 100,000 replicate simulations were performed, with path and transect locations randomised for each replicate. Thereafter, simulations used only relatively low path densities (1 km-2) and were performed using subsets of the movement paths available for each species. Relatively low path densities were used as simulations of low densities required fewer comparisons (between transects and path sections) than when high densities were used. Subsets of the movement paths available for a species were used where analyses indicated that one or more factors had a substantial bearing on the characteristics of paths collected under different circumstances (see results, Section 3.3.1).
3.3 Results
3.3.1 Movement data
Detailed records of 280 daily (24-hour) movements of individuals or groups of animals were collected during the winters of 1999/2000 to 2003/4. These included records of the movements
33 Analysis of ungulate dynamics of four ungulate species, in two areas (Lazovski Zapovednik and SAZ). Records are summarised in Table 3.1, and their main features (length and tortuosity) are shown in Fig. 3.1. No data on daily movements of moose or musk deer are available from this study. However, observations of musk deer in SAZ suggest that the mean 24-hour travel distance for males and females is approximately 1.5 km (Zaitsev, 1991). This figure was used for analysing musk deer survey data but moose are not considered further in this section.
Although sample sizes are small for Lazovski Zapovednik, the data appear to reflect quite different movement patterns to those indicated for SAZ. In particular, both red deer and roe deer show much longer average movements in Lazovski Zapovednik than SAZ, whilst wild boar move much smaller distances in Lazovski Zapovednik. Tortuosity of movement is similar in the two areas for these three species, indicating similar patterns of movement despite the different distances. By contrast, sika deer have similar mean movement lengths but apparently dissimilar tortuosity in the two areas. The differences are less marked in this species and may reflect the smaller sample sizes. However, given the general differences apparent from Fig. 3.1, as well as the limited data available from Lazovski Zapovednik, further analyses of dynamics in SAZ were conducted using only the data from SAZ.
Within SAZ, tortuosity was remarkably consistent among movement records (note the narrow confidence intervals about the mean in Fig 3.1) for each species. Furthermore, for species for which the most data were available, tortuosity and length of movements were significantly negatively correlated (red deer, Pearson’s r = -0.213, p < 0.05; wild boar, r = -0.347, p < 0.001), suggesting that distance travelled is a good general parameter characterising movement. By contrast to tortuosity, distance moved in 24 hours was relatively variable, especially for sika deer and wild boar. This factor is particularly important in influencing estimates of density generated from track encounter rates. Consequently, we analysed these data further, in order to investigate the impact of different factors on distance moved.
34 Analysis of ungulate dynamics
Table 3.1 24-hour movement data collected
Species Number of records from: Lazovski SAZ Zapovednik
Red deer 7 90 Roe deer 9 62 Sika deer 14 10 Wild boar 3 85
5000 (a)
4000
3000
Length (m) 2000
1000
0 RE (n = 7, 90) RO (n = 9, 62) SD (n = 14, 10) WB (n = 3, 85)
(b) 3.5
) 3 -1 ºm (
2.5 y 2
1.5 Tortuosit
1
0.5
0 RE (n = 7, 90) RO (n = 9, 62) SD (n = 14, 10) WB (n = 3, 85) Species and sample sizes
Figure 3.1. Mean length (a) and tortuosity (b) for paths of the four different species in Lazovski Zapovednik (filled bars) and SAZ (open bars): RE, red deer; RO, roe deer; SD, sika deer; WB, wild boar. Error bars show 95% confidence interval. Figures in parentheses show sample sizes for Lazovski and SAZ, respectively.
35 Analysis of ungulate dynamics
Factors that might be expected to affect travel distance include snow depth, habitat type, quality of mast crop, time of year and size of the travelling unit (whether a solitary animal or multiple animals). Unfortunately, the data do not provide an even representation over a range of values for each of these parameters. Furthermore, a full analysis of the importance of all factors is impossible without larger sample sizes (numbers of 24-hour movement records). Sample sizes currently available restrict the potential for sub-dividing movement records on the basis of more than one or two parameters. For sika deer, we reasoned that sample size was so small, that dividing the data for further analyses (for example, for estimation of densities from transects conducted during different periods of winter, or from transects conducted in different habitats) would render the mean distance unacceptably sensitive to outlying values of distances moved under those conditions. Consequently, we did not subdivide the sika deer movement data for further analyses.
To discern which parameters might be of greatest importance in dictating travel distance for the other three species, we used AICc to compare a range of simple, one- or two-factor models to explain the distance moved by red deer, roe deer and wild boar. Models were designated a priori and were restricted by the range of possible causal parameter values for which data were available. All possible one- and two-factor models were assessed, except where a factor had no contrasting variable values. Results of the model comparisons are given in Table 3.2.
The comparison of models indicated that for red deer, no factor explained much of the observed variance in travel distance (which was, in any case, very limited). Time of year did feature in all of the best supported models and, as such, we divided the red deer movement data into subsets from early and late winter for further analysis. We note, however, that this is likely to bring only a very slight improvement to the accuracy of density estimates. Models were more successful in explaining variation in roe deer movements, with time of year alone explaining over
50% of observed variance and group size providing additional explanatory power. Effect of
36 Analysis of ungulate dynamics
Table 3.2 Comparison of simple, single factor models for the travel distances of three species
2 Species Model variables K AICc ∆i wi R
Red deer Time of year 3 -131.45 0.00 0.279 0.048 Time of year, individual or group 4 -130.17 1.28 0.148 0.058 Time of year, snow deptha 4 -129.32 2.13 0.096 0.049 Time of year, mast qualityb 4 -129.28 2.17 0.095 0.048 Time of year, habitat typec 4 -129.26 2.19 0.094 0.048 Individual or group 3 -128.67 2.78 0.070 0.018 Snow depth 3 -127.51 3.94 0.039 0.005 Mast quality 3 -127.11 4.34 0.032 0.001 Habitat type 3 -127.04 4.41 0.031 0.000 Snow depth, individual or group 4 -126.94 4.50 0.029 0.023 Habitat type, individual or group 4 -126.49 4.96 0.023 0.018 Mast quality, individual or group 4 -126.48 4.97 0.023 0.018 Habitat type, mast quality 4 -125.60 5.85 0.015 0.008 Habitat type, snow depth 4 -125.37 6.08 0.013 0.006 Snow depth, mast quality 4 -125.32 6.13 0.013 0.005
Roe deer Time of year, individual or group 4 -95.64 0.00 0.873 0.585 Time of year 3 -90.42 5.22 0.064 0.532 Time of year, habitat type 4 -89.21 6.43 0.035 0.540 Time of year, snow depth 4 -88.74 6.90 0.028 0.537 Habitat type, snow depth 4 -52.16 43.48 0.000 0.164 Habitat type 3 -49.98 45.66 0.000 0.102 Habitat type, individual or group 4 -49.00 46.64 0.000 0.120 Snow depth, individual or group 4 -47.73 47.91 0.000 0.102 Snow depth 3 -46.10 49.54 0.000 0.044 Individual or group 3 -45.45 50.19 0.000 0.033
Wild boar Time of year, habitat type 4 150.96 0.00 0.585 0.188 Time of year, mast quality 4 153.11 2.15 0.200 0.167 Habitat type 3 155.39 4.43 0.064 0.122 Habitat type, snow depth 4 155.77 4.81 0.053 0.140 Habitat type, individual or group 4 156.97 6.00 0.029 0.128 Habitat type, mast quality 4 157.04 6.08 0.028 0.127 Time of year, individual or group 4 158.38 7.42 0.014 0.114 Time of year 3 159.66 8.69 0.008 0.077 Snow depth, mast quality 4 159.97 9.00 0.006 0.097 Mast quality 3 160.12 9.16 0.006 0.071 Time of year, snow depth 4 161.61 10.65 0.003 0.079 Mast quality, individual or group 4 161.71 10.74 0.003 0.078 Individual or group 3 165.22 14.25 0.000 0.014 Snow depth 3 165.74 14.78 0.000 0.008 Snow depth, individual or group 4 166.13 15.16 0.000 0.029 a Categorical variable indicating shallow or deep snow. For red deer, the threshold was set at 45cm. For roe deer, the threshold was 25cm. b Categorical variable indicating quality of mast crop, either acorn or pine nut dependent on the dominant trees in the habitat in which data were collected. No roe deer movement data have yet been collected in poor mast years. c Movement data have so far been collected only in the Oak and Korean pine habitat zones.
37 Analysis of ungulate dynamics group size cannot be applied currently to refine density estimates because such data were not reported in the track count surveys. In future, however, it would be beneficial to record such information. As with red deer, we based analyses of roe deer densities on subsets of the movement data for early and late winter. Finally, for wild boar, the model based on both time of year and habitat type received markedly more support than competing models. Consequently, the wild boar movement data were divided into four subsets (defined by these two variables) for further analysis.
3.3.2 Estimating density: comparison of weighting approaches
Three different weighting methods (by segment length alone, or by segment length in conjunction with stratification by either drainage basin area or area of forest type) were used to generate estimates of density from the survey data. We begin by comparing the predictions made using these three weighting approaches in conjunction with the correction factor estimator.
Table 3.3 shows the main features of predicted density using the correction factor to estimate combined density of red, roe and sika deer. Typically, estimates derived using the three weighting approaches were highly similar for each habitat zone, with no strong tendency for one method to produce consistently higher or lower results than another, or to have consistently larger confidence intervals than the others. However, an examination of overall correlations between the three different weighting approaches (Table 3.4) suggests some of the limitations of the method involving post-stratification by forest type. Although correlations between the methods are generally high (Pearson’s r > 0.86 in most cases), this is not the case for correlations between estimates derived for the Korean pine-deciduous habitat using post-stratification by forest type, and those derived for the same habitat using the other two weighting approaches (Pearson’s r <
0.63 in both cases). The reasons for this can be seen by looking at the time-series of predictions made (Fig. 3.2), and are largely attributable to a single prediction (see Fig. 3.2c, 1994). This
38 Analysis of ungulate dynamics
Table 3.3 Comparison of combined red, roe and sika deer density estimates derived using the correction factor in combination with different weightings (SL, segment length; DB, drainage basin area; FT, forest type area). Figures in parentheses show one standard error.
Mean estimated density (km-2): Mean CI proportionsa: whole last 5 Habitat zone Weighting lower upper period years only
Oak-birch SL 6.29 (± 0.76) 11.21 (± 1.15) 0.29 (± 0.03) 0.51 (± 0.08) SL + DB 6.59 (± 0.81) 9.46 (± 0.92) 0.31 (± 0.02) 0.45 (± 0.04) SL + FT 6.14 (± 0.74) 10.51 (± 1.09) 0.30 (± 0.03) 0.52 (± 0.08) Korean pine- deciduous SL 3.26 (± 0.24) 5.61 (± 0.75) 0.27 (± 0.01) 0.40 (± 0.03) SL + DB 3.27 (± 0.22) 5.39 (± 0.63) 0.27 (± 0.02) 0.41 (± 0.04) SL + FT 3.22 (± 0.34) 5.17 (± 0.78) 0.31 (± 0.02) 0.44 (± 0.03) Spruce-fir SL 0.98 (± 0.16) 2.80 (± 0.35) 0.48 (± 0.03) 0.87 (± 0.09) SL + DB 0.98 (± 0.16) 2.80 (± 0.35) 0.48 (± 0.03) 0.87 (± 0.09) SL + FT 0.93 (± 0.14) 2.33 (± 0.33) 0.49 (± 0.03) 0.78 (± 0.09) a Proportional size of confidence interval is given as deviation divided by mean. Note that upper confidence intervals are generally larger than lower confidence intervals as (i) the latter are bounded by zero when bootstrapping; and (ii) the former tend to be exaggerated when distributions are clumped.
estimate of 12.8 km-2 (CI: 12.1 - 14.3) contrasts starkly with those for the same year made using no stratification or stratification by drainage basin area: 2.9 km-2 (2.1 - 4.5) and 4.0 km-2 (2.7 -
7.2), respectively. Predictions for this year and habitat are clearly varied, due to a number of short transect segments on which the tracks of large herds of deer were encountered. However, the prediction made using post-stratification by forest type stands out as an anomalous result. A further note of caution regarding this approach to weighting data is illustrated by Fig. 3.2d. For this figure, the vegetation code associated with a single transect from the Korean pine-deciduous habitat in 1994 was altered. Specifically, a transect segment designated as running through oak forest (a relatively rare forest type, accounting for less than 5% of the Korean pine-deciduous zone), was recoded to northern pine (which dominates closer to 50% of the habitat zone; see Fig.
2.1 also), in order to see what effect this would have. The consequences of this minor alteration were substantial, reducing the predicted density for the year and habitat from almost 13 km-2 to
39 Analysis of ungulate dynamics just 3.0 km-2 (2.0 - 5.0) (Fig 3.2d), a prediction much more in line with those derived using the alternative weighting approaches. In addition, this slight adjustment increased the correlation coefficients between predictions derived using stratification by forest type, and those derived using no stratification or stratification by drainage basin area, respectively, to r = 0.92 and r =
0.81.
The findings above illustrate several points regarding the best methods for density prediction. First, in contrast to the concerns raised in Section 2, which suggested that ungulates are far from uniformly distributed between drainages and vegetation types, the generally high correlations between predictions made using different methods are reassuring. These correlations suggest that the distribution of survey effort between different drainages and forest types is broadly representative of the relative areas of these different features within SAZ. Secondly, and perhaps most importantly, our findings illustrate the extreme sensitivity of predictions made using stratification by forest type, to the designation of dominant vegetation type along transects. By comparison to defining the boundaries of drainage basins or major habitat zones (a process which is assisted by major geographical features such as watersheds, and physical features such as altitude), defining the boundaries of different forest types is relatively subjective. These boundaries are neither static in time nor, typically, are they clearly demarcated by abrupt
Table 3.4 Correlations between combined red, roe and sika deer densities predicted using the three different weighting approaches
Weighting: Habitat Weighting SL + DB SL + VT
Oak-birch SL 0.913 0.983 SL + DB - 0.864 Korean pine-deciduous SL 0.915 0.615 SL + DB - 0.626 Spruce-fir SL 1.000 0.961 SL + DB - 0.961
40
16 16 (a) (c)
12 12
8 8
) 4 4 -2
0 0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
16 16 (b) (d)
Estimated density (km 12 12
8 8
4 4
0 0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
Year
Figure 3.2 Estimates of combined red, roe and sika deer density in the Korean pine-deciduous habitat, derived using the correction factor method and: (a) weighting by transect segment length only; (b) weighting by segment length and drainage basin area; (c) weighting by segment length and forest type (unaltered data set); (d) weighting by segment length and forest type (single data point recoded to alter vegetation designation - see text for further details). Error bars show confidence intervals.
Analysis of ungulate dynamics transitions. Furthermore, some areas do not correspond to any of the seven main forest types used in our analyses and, consequently, a small proportion of data points had to be excluded from analyses based on forest type. Overall, these findings (and especially those illustrated by Fig. 3.2) cast doubt on the merits of post-stratification by forest type and we do not consider that method further.
Finally, although our results illustrate a high degree of similarity between predictions made using unstratified data and those derived using data stratified by drainage basin, we suggest that the differences between these approaches could be important. In particular, stratification by drainage basin tends to produce more conservative estimates, especially for more recent years when ungulate densities have reached relatively high levels (see Table 3.3). More importantly, outliers predicted using the unstratified data are often less extreme when stratification by drainage basin is used (see, for example, 1982 in Fig. 3.2a,b), and this is reflected in slightly lower variance associated with mean estimates over either the whole period or, more strikingly, over the past five years (Table 3.3). For these reasons, and because our spatial analyses (Section 2) indicated some degree of heterogeneity in ungulate densities between basins, we recommend that stratification by drainage basin is used. Consequently, further results presented in this section were all derived using that weighting method.
3.3.3 Parameters for density estimation by the FMP formula and simulation methods
For the FMP method, estimates of density were made using equation 3.14, which requires estimates of total length of transect segments, travel distance and numbers of path intercepts.
Based on the findings from Section 3.3.1, data on movements were divided into subsets as appropriate, with mean travel distances used as indicated in Table 3.5. As discussed in Section
3.2.3, each transect segment was treated as an independent sample for estimates made using the
FMP approach. For this reason, uncertainty in each estimate (arising from variance in travel distances) is unimportant relative to uncertainty between estimates (arising from spatial and
42 Analysis of ungulate dynamics temporal heterogeneity in ungulate distributions). Overall estimates of density will have confidence limits dictated by the variance between estimates, and it is sufficient to use mean distances to calculate the expected estimate associated with each transect segment. Consequently, variation in travel distance (as given in Table 3.5) was unimportant for the estimation of densities; it is shown only for clarity.
For the simulations, pilot tests indicated that, as expected, path encounters increased linearly with density, such that doubling the number of paths per unit area led to doubling the rate with which unique paths were encountered. Consequently, further simulations were only conducted by varying transect length (as transect length was an important predictor of multiple encounters of the same path). Simulations were conducted using the subsets of movement data indicated in Table 3.5.
In general, the approach used to estimate density is that described by equations 3.16 and
3.17. The simulations were used to derive formulae predictive of E(Y) and E(n), as defined in equation 3.15. The first of these describes the relationship between path density, transect length and numbers of encounters with unique paths. Simulations indicated that for red deer tracks in
Table 3.5 Estimates of daily travel distances used for calculations based on the FMP formula. Confidence intervals are given for information only.
Travel distance, km Species Conditions Sample size Mean 95% confidence interval
Red deer Early winter 27 1.52 1.30 - 1.74 Red deer Late winter 63 1.29 1.18 - 1.40 Roe deer Early winter 11 2.19 1.63 - 2.75 Roe deer Late winter 51 0.89 0.79 - 0.99 Sika deer All 10 2.78 1.50 - 4.06 Musk deer All - 1.50 Wild boar Early winter, OB habitat 6 3.63 0.86 - 6.39 Wild boar Late winter, OB habitat 36 3.00 2.42 - 3.59 Wild boar Early winter, KD habitat 8 7.13 3.89 - 10.36 Wild boar Late winter, KD habitat 35 4.40 3.57 - 5.22
43 Analysis of ungulate dynamics early winter, the mean number of unique paths encountered path-1 km-2 km-1, λ = 0.559. Note that the units of λ are path-1 km-2 km-1, indicating that it is a function both of the number of paths per km2, and that it depends on the transect length (in km). For any given density (D) and transect length (S), the expected number of unique paths encountered by a transect is (Fig. 3.3a):
E(Y ) = λDS (3.18)
Rates of encounter of unique paths made by roe deer, sika deer and wild boar were also determined and the mean encounter rates for each species are given in Table 3.6.
The second variable to be predicted, E(n), describes the relationship between transect length and multiple encounters of a single path. As transect length increases, so the probability that a path, once encountered, will be repeatedly crossed, also increases. Obviously, above a certain transect length (corresponding to the widest chord of a path), numbers of crossings of a given path will not increase. Thus, the relationship between E(n) and transect length is asymptotic and is well described by a Michaelis-Menton function (Fig. 3.3b) of the form:
aS E(n) = 1+ (3.19) b + S where a and b are constants for a given set of movement paths, and S is transect length. Once again, parameters were determined for the movement data for each species, or the relevant subsets, as described above. Parameters are summarised in Table 3.7.
The parameters in Table 3.6 and 3.7 were used (with equation 3.17) to predict expected numbers of track encounters on a transect of given length at a high density of track abundance.
Actual encounter rates on any transect were then used to interpolate, providing a point estimate of density. Point estimates of density for a given time period and area were bootstrapped to provide confidence intervals about the mean estimated density.
44 Analysis of ungulate dynamics
(a)
10.00
1.00
0.10
encounteredtransect by a Mean number of unique paths paths of unique number Mean 0.01 0.1 1 10
(b) 2.0
1.8
1.6
1.4 are crossed
1.2
Mean frequency with which 1.0 individual paths, once encountered, encountered, once paths, individual 012345 Transect length, km
Fig. 3.3 Estimating parameters for density estimation from simulations. The example given is for red deer in early winter (N = 27 daily movement records). (a) Number of unique paths encountered by a transect of length S = 1km, when path density is D =1km-2 was estimated as the gradient of the relationship illustrated (in this case, λ = 0.5592). (b) Parameters of the function relating mean number of encounters per path encountered to transect length were solved by least squares fitting of equation 3.19 to simulated data.
45 Analysis of ungulate dynamics
Table 3.6 Mean encounter rates of unique ungulate paths determined by simulation
Species Conditions Estimated mean (λ) for 1 km transect, when density is 1 km-2
Red deer Early winter 0.559 Late winter 0.503 Roe deer Early winter 0.596 Late winter 0.353 Sika deer All 0.819 Wild boar Oak-birch, early winter 1.639 Oak-birch, late winter 1.111 Korean pine-deciduous, early winter 2.651 Korean pine-deciduous, late winter 1.395
Table 3.7 Parameters underlying multiple encounter rates of unique paths, as determined by simulation. See main text for further details.
Species Conditions Parameter estimates a b
Red deer Early winter 0.807 0.212 Late winter 0.698 0.233 Roe deer Early winter 1.475 0.244 Late winter 0.676 0.198 Sika deer All 1.359 0.415 Wild boar Oak-birch, early winter 0.671 1.748 Oak-birch, late winter 0.964 0.884 Korean pine-deciduous, early winter 1.011 1.142 Korean pine-deciduous, late winter 1.251 0.633
3.3.4 Comparison of estimators
We began by comparing density estimates produced by the FMP and simulation methods (Fig.
3.4). Clearly, the estimates produced by the two methods were very similar. A line through the origin with a gradient of unity (indicating an exact match between the two methods) had an R2 >
0.995 in each case. Owing to these similarities and to its relative simplicity, estimates produced using the FMP formula were used for further analyses.
46 Analysis of ungulate dynamics
Combined red deer, roe deer and sika deer density was estimated using the correction factor and FMP methods. In the latter case, estimates were derived independently for each deer species and these were summed for each transect segment. Combined totals were then bootstrapped. Comparisons of point estimates are shown in Fig. 3.5. In all habitats and across the full range of densities, the correction factor produced estimates of density in the order of 1.6 times as high as those produced by the FMP formula.
3.3.5 Final estimates of density
In the previous section, we showed that estimates of density produced by the FMP and simulation methods were highly similar. Consequently, final estimates of the density of each species over time were produced using the FMP formula. Specifically, we used the travel distances given in
Table 3.5 and the BCA bootstrapping method for determining confidence intervals. Estimates of density were determined for all species except moose (for which no data on travel distance are available from SAZ). All estimates are shown in Fig. 3.6. Red deer are clearly the most abundant ungulate in SAZ, followed by roe and musk deer. Sika deer are restricted to the southern, coastal, low altitude areas, whilst wild boar are generally the least abundant of the species analysed. Musk deer show the least consistency in patterns of abundance, possibly owing to the lack of information concerning their movements. More detailed information on differences in movements between years may well improve our understanding of musk deer dynamics.
3.4 Discussion
Our results suggest that relatively simple approaches can be used to convert track encounter rates into estimates of absolute density in SAZ. The most complex and time-consuming of the conversion methods was the simulation approach but the results suggest that estimates derived using the FMP formula are extremely similar, and that this much simpler, more tractable
47 Analysis of ungulate dynamics
10.0 (a) 4.0 2.0
8.0 3.0 1.5
6.0 2.0 1.0 4.0
1.0 0.5 2.0
0.0 0.0 0.0 0.0 2.0 4.0 6.0 8.0 10.0 0.0 1.0 2.0 3.0 4.0 0.0 0.5 1.0 1.5 2.0
6.0 (b) 3.0 0.5
0.4 4.0 2.0
) 0.3 -2 km
( 0.2 2.0 1.0
0.1
0.0 0.0 0.0 0.0 2.0 4.0 6.0 0.0 1.0 2.0 3.0 0.0 0.1 0.2 0.3 0.4 0.5 simulations simulations
g 1.0 (c)
0.8
0.6
0.4
estimates derived usin 0.2 y
0.0 0.0 0.2 0.4 0.6 0.8 1.0 Densit
1.5 0.6 0.1 (d)
1.0 0.4
0.5 0.2
0.0 0.0 0.0 0.0 0.5 1.0 1.5 0.0 0.2 0.4 0.6 0.0 0.1 Density estimates derived using the FMP formula (km-2)
Figure 3.4 Comparisons of population density estimates derived using the FMP formula and the simulation approach, for oak-birch habitat (left), Korean pine-deciduous habitat (centre) and spruce-fir habitat (right). Panels show: (a) red deer, (b) roe deer, (c) sika deer and (d) wild boar. Estimates derived using data stratified by drainage area. Broken lines show expected relationship if estimates were identical.
48 Analysis of ungulate dynamics 3.0 (a) 2.5
2.0
1.5
1.0
0.5
0.0 0 5 10 15
3.0 (b) 2.5
2.0
1.5
1.0
0.5
0.0 0123456
estimate FMP to estimate factor correction of Ratio 3.0
(c) 2.5
2.0
1.5
1.0
0.5
0.0 0.0 0.5 1.0 1.5 2.0 2.5
Combined deer density (km-2) derived using the FMP formula Figure 3.5. Comparison of methods for predicting combined densities of red deer, roe deer and sika deer in (a) oak-birch, (b) Korean pine-deciduous, (c) spruce-fir habitat. Open circles are individual data points (for one year), broken line indicates a ratio of unity, expected if the two methods produce matching results.
49 18 8 Analysis3 of ungulate dynamics (a) 6 12 2 4
6 1 2
0 0 0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
8 7 3
(b) 6 6
) 5
-2 2 4 4 3 1 2 2 1 0 0 0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 2.0 1.0 1.0
Estimated density (km (c) 0.8 0.8 1.5 0.6 0.6 1.0 0.4 0.4 0.5 0.2 0.2
0.0 0.0 0.0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
3.0 12 6
(d) 2.5 9 2.0 4
1.5 6
1.0 2 3 0.5 0.0 0 0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 4 1 0.6
(e) 3 0.4
2 0.2 1
0 0 0.0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
Year Figure 3.6. Estimates of population density in oak-birch habitat (left), Korean pine- deciduous habitat (centre) and spruce-fir habitat (right), (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer and (e) wild boar. Estimates derived using the FMP formula, with BCA bootstrapping for confidence intervals. Data stratified by drainage area.
50 Analysis of ungulate dynamics approach can be used instead of simulations. Thus, the major problems with density estimation are those concerned with obtaining accurate estimates of daily travel distance (and the factors affecting this parameter), together with designing accurate, unbiased and correctly stratified survey methodologies (see further in Sections 5 and 7).
Overall, the estimates suggest that (of the species examined) densities are highest in the coastal oak-birch areas, typically lower in the mid-elevation Korean pine-deciduous area, and lowest in the spruce-fir forests that dominate the western macroslope of the Sikhote-Alin
Mountains within SAZ. Red deer were the most abundant species, with an average density in
SAZ in recent years of around 1.5 to 3.0 km-2. Roe deer were next most abundant, occurring at densities of nearer 1 to 2.5 km-2. Neither sika deer nor wild boar are very abundant at all, both occurring at about 1 per 8 or 9 km2 overall. Musk deer appear to be present at an average density of about 1 km-2 but this must be regarded as a very preliminary estimate, pending further information on musk deer daily movements.
Comparisons between methods using stratified and unstratified data showed that stratification by forest type is not a viable approach, as results are far too sensitive to this relatively subjective classification. Owing to the difficulties inherent in demarcating forest types, estimation of the area dominated by each forest type is also subject to errors that may be propagated by extrapolation. Furthermore, forest types form a mosaic in a way that is very distinct from features with a more geographical basis. It is likely that animals will often move between elements of the mosaic in a way that they would not move between drainage basins, for example. Less favoured forest types may be used extensively, if they are often found between patches of preferred types. Thus, the value of forest type as a stratification or weighting factor, is dependent on the precise configuration of the mosaic in any area. By contrast, estimates derived using the other weighting approaches were generally in very good agreement. This suggests that within each major habitat zone, the transect system is currently well designed (in terms of effort in km km-2) to reflect the relative size of different drainages. Nevertheless, including weightings
51 Analysis of ungulate dynamics by drainage basin size might have some influence over final estimates and this is the weighting approach that we recommend.
That the correction factor tended to overestimate density may be due to a combination of factors. First, data used to determine the correction factor came from different study areas in
Primorye Krai (Gerow et al., 2005). We have determined that the movement of animals can be markedly different, even between relatively proximal areas (see Section 3.3.1) and, potentially, among different habitats. It is likely that grouping data from different areas can obscure substantial variation in the relationships between track encounters and density in those different areas. Secondly, the data used to derive the correction factor came from areas of relatively low density (typically less than 2 km-2, with associated track encounter rates less than 1.5 km-1)
(Gerow et al., 2005). Had data been available from areas of higher density, the relationship may have appeared to be rather different. Finally, that insufficient data were available to determine correction factors independently for different species is likely to have reduced the utility of the correction factor substantially. Movement distances differ markedly between the three species
(Fig. 3.1) and, consequently, the three are likely to show very different relationships between track encounters and density. That the correction factor is currently unable to account for this variation greatly limits its utility.
Although the FMP formula is easy to apply, determining confidence intervals associated with mean estimates is relatively complex. However, comparisons between BCA and standard confidence intervals suggest that these can often be markedly different and, thus, the extra effort required to determine BCA intervals is likely to be worthwhile. Routines for determining these intervals are increasingly available for standard statistical software (e.g. Efron & Tibshirani,
1993) but they can also be derived reasonably easily by anyone familiar with programming.
Despite the close agreement between density estimates derived by the FMP and simulation methods, limitations of this study continue to restrict our confidence in the estimates of density produced. The first of these is the finer-scale heterogeneity in densities of ungulates.
52 Analysis of ungulate dynamics
Although we have assessed correlations between encounter rates and forest types (Section 2), it is possible that there may be relationships between the habitats used by ungulates and those through which transects were run. At the extreme, if all transects were run through valley bottoms and all ungulates concentrate in valley bottoms during winter, our estimates of density would be substantially inflated. The second limitation on estimating density arises from limits to our understanding of the factors underlying movement patterns. In this chapter, we reported on a simplistic analysis of pairs of variables important in influencing travel distance. The most important factor influencing travel distance among species appeared to be time of year. Other factors are also likely to be important but, without additional data on 24-hour movements, it is difficult to identify these effects. We note that group size also appeared to be an important factor and we strongly suggest that future surveys collect data on the numbers of animals responsible for each set of tracks encountered. Such data will be helpful for improving the accuracy of density estimation by the FMP formula and will also provide useful data on group size distributions.
Kuzyakin and Lomanov (1986) have shown that in more favourable areas, moose move shorter distances during the day than in less favourable environments, presumably because they need not travel so far in order to find browse. It seems likely that this would also apply to the species we studied. It is also interesting to note that snow depth did not receive strong support as a factor affecting travel distance. Previously, this factor has been shown to have a strong effect on ungulate movements (e.g. Mysterud, 1999; Parker et al., 1984). It may be that over-riding factors and interactions between variables mask the effects of this parameter; only with larger sample sizes, recorded in a greater variety of snow depth conditions, will it be possible to tease out the relative importance of all putative factors. Collecting additional data on animal 24-hour movements is crucially important. It is likely that determining predictive models for the distances moved in different areas and at different times would substantially increase the accuracy of density estimates determined on the basis of movement.
53 Analysis of ungulate dynamics
4. TEMPORAL ANALYSES OF UNGULATE POPULATION
DYNAMICS
4.1 Background
In this section, we concentrate on two aspects of the temporal dynamics of ungulates. First, we examine changes in track encounter rate within years. This is important largely in relation to standardising the monitoring protocol but also for detecting intra-annual movements of ungulates between different habitat areas. Secondly, we assess between-year variation in ungulate density.
Long-term datasets on the abundance of ungulates are increasingly available and a number have been subjected to rigorous analyses of their population dynamics. Several of these are summarised in Table 4.1. Evidently, ungulate dynamics may be influenced by a combination of density dependence and stochastic variation in the environment (Gaillard et al., 1998; Sæther,
1997), as well as by competition and predation. In particular, density dependent effects were found to be important in 27 of the 30 analyses listed in Table 4.1, and were important factors in all of the most elaborate, individual-based studies (e.g. Coulson et al., 2001; Coulson et al., 2000;
Forchhammer et al., 2001). In spite of this, density dependence remains difficult to demonstrate with survey data and, consequently, controversial (e.g. Shenk et al., 1998). Similarly, climatic effects were found to be important in a large proportion (22 of 30) of the analyses listed in Table
4.1. The long-term data from SAZ, comprising large numbers of surveyed transects each year, present an important opportunity to assess new ways of determining the role of density dependence in ungulate dynamics. Analyses of factors important in ungulate dynamics will also contribute information from an ecosystem with very different climate and species composition to the vast majority of previous analyses (which have used data from Europe or North America, see
Table 4.1).
54
Table 4. Analytical approaches used to assess long-term population dynamics of ungulates and their major influences1
Species Data set details Analytical approach2 Factors influencing dynamics Reference (and direction of influence)
Caribou Aerial or ground counts of 8 Regression Population density (-) Skogland (1985) (Rangifer tarandus) populations Severe weather (-) 1970 – 1981 Norway Greater kudu Detailed counts, including Regression and partial Preceding population biomass Owen-Smith (1990) (Tragelephus individual recognition correlation of population density (-) strepsiceros) 1974 – 1984 change and survival on Preceding annual rainfall (+) Kruger NP, RSA putative influences Soay sheep Detailed counts, including Key factor analysis of Population density (-) Clutton-Brock et al. (1991) (Ovis aries) individual tagging mortality acting at each life 1959 – 1968 & 1985 – 1990 stage and regression of Hirta, St Kilda, U.K. mortality rates against log (population density) White-tailed deer Aerial counts 3rd degree polynomial fitted Relative wolf (Canis lupus) Messier (1991) (Odocoileus virginianus) 1975 – 1986 to population estimates, in density (-) Superior National Forest, order to derive conservative USA estimates of population growth. Pearson partial correlations to identify contributions of different factors Moose Skeletal remains As above Wolf predation (-) Messier (1991) 1959 - 1968 Population density (-) Aerial counts 1969 – 1986 Isle Royale NP, USA Caribou Triannual aerial counts Comparative study of areas Wolf predation (-) Seip (1992) 1984 – 1989 with an without high wolf Southeastern BC, Canada predation (Continued overleaf)
Species Data set details Analytical approach2 Factors influencing dynamics Reference (and direction of influence)
Elk Mark-recapture censuses As above Population density (-) Dennis and Taper (1994) 1963 – 1985 Grand Teton NP, USA Moose Meta-analysis of 27 North Regression of population Population density (-) Messier (1994) American studies of moose- growth against population Predator density (-) wolf interactions size; curve fitting for functional and aggregative responses of predators Wild boar Winter track counts Logistic regression (to look Population density (-) Markov (1997) 1988 – 1996 for density dependent growth) Autumn and winter Sverdlosk Oblast, Russia and multiple regression (to temperatures (+) look at the effects of climatic Snow cover (-) factors) Moose Skeletal remains Visual analyses of population Predator density (-) McLaren and Peterson (1994) 1959 - 1981 trends Aerial counts 1982 – 1994 Isle Royale NP, USA European bison Archival data and hunting Regressions of density and Population density (-) Jedrzejewska et al. (1997) (Bison bonasus) statistics 1798 – 1940 population growth against Political instability (-) Track counts and ad-hoc extrinsic factors; multiple Annual temperature (+) sightings 1946 – 1993 regressions; PLR Density of other ungulates (-) Białowieża Primeval Forest, randomisation tests for Poland and Belarus density dependence Moose As above As above Population density (-) Jedrzejewska et al. (1997) Political instability (-) Annual temperature (+) Density of other ungulates (-) Wolf density (-) (Continued overleaf)
Species Data set details Analytical approach2 Factors influencing dynamics Reference (and direction of influence)
Roe deer As above As above Population density (-) Jedrzejewska et al. (1997) Political instability (-) Annual temperature (+) Lynx (Lynx lynx) density (-) Wild boar As above As above Population density (-) Jedrzejewska et al. (1997) Annual temperature (+) Acorn crop in preceding year (+) Snow cover (-) Political instability (-) Wildebeest Point counts along transects Key factor analysis of Population density (-) Mduma et al. (1999) (Connochaetes taurinus) every 2 weeks through the mortality acting at each life Dry season grass biomass (+) dry season stage and regression of 1960 – 1998 mortality rates against log (population density) Soay sheep Detailed counts, including Logistic regression with fixed Population density (+) Milner et al. (1999) individual tagging effects, and logistic NAO index3 (-) 1959 – 1968 & 1985 – 1996 regression with fixed and Hirta, St Kilda, U.K. random effects Red deer Annual counts and individual Structured demographic Population density (-) Albon et al. (2000) marking accounting as a method of 1971 – 1997 key factor analysis Rum, U.K. Saiga antelope Aerial surveys Linear regression with Population density (-) Coulson et al. (2000) (Saiga tartarica) 1976 – 1996 weather covariates; models Mean December-January Betpak-dala, Khazakhstan selected using AIC4 temperature lagged by 1 year (+) Soay sheep Detailed counts, including As above Population density (-) Coulson et al. (2000) individual tagging Mean December-April 1985 – 1998 temperature lagged by Hirta, St Kilda, U.K. 2 years (+) (Continued overleaf)
Species Data set details Analytical approach2 Factors influencing dynamics Reference (and direction of influence)
Red deer Annual counts and individual As above Population density (-) Coulson et al. (2000) marking Previous year’s population 1971 – 1997 density (-) Rum, U.K. Winter temperature lagged by 2 years (+) Soay sheep Detailed counts, including Age-structured Markov Interactions between: Coulson et al. (2001) individual tagging and mark- modelling and comparisons Population density (-) recapture with actual trajectories NAO index (-) 1986 – 1996 Sex-ratio Hirta, St Kilda, U.K. Soay sheep Detailed counts, including Generalised linear models Population density in the winter Forchhammer et al. (2001) individual tagging and mark- differentiated using AIC preceding a cohort’s recapture birth (-) 1985 – 1996 NAO index in the winter Hirta, St Kilda, U.K. preceding a cohort’s birth (-) Mule deer Roadside count index DO analysis of 12 Ricker- Population density (-) Peek et al. (2002) (Odocoileus hemionus) 1964 – 1989 type models including a Z-scored6 precipitation in June South-central Oregon, USA density independent model, and August (+) selected using both AIC and Forage biomass (+) SIC5 Elk Aerial censuses DT analysis using SIC to Population density (-) Taper and Gogan (2002) 1964 – 1995 select between various Ricker Spring precipitation (+) Northern Yellowstone, USA and Gompertz models with Spring precipitation squared (+) up to 2 terms influencing intercept, slope and error, respectively. (Continued overleaf)
Species Data set details Analytical approach2 Factors influencing dynamics Reference (and direction of influence)
Ibex Annual total counts Parametric bootstrapping to Population density (-) Sæther et al. (2002) (Capra ibex) 1920 – 1990 estimate all parameters in a θ- February – April precipitation (-) Swiss NP, Switzerland logistic regression; weather factors used as covariates of an error term. Elk Annual aerial surveys Generalised linear modelling Population density (-) Hebblewhite, Pletscher & 1985 – 2000 with log-change in population Presence of fencing along Paquet (2002) Banff NP, Canada size as the response variable. highway (+) Snow depth (-) Rate of predation by wolves (-) Caribou Hunting records AIC used to compare multi- Cold and snowy winters (+/- in Forchhammer et al. (2002) 1908 – 1957 or 1989 order autoregressive models populations at different Western and Southern incorporating NAO values locations; lagged) Greenland and population size Population size (-, delayed in some populations) Musk oxen Counts during military sledge As above Warm snowy winters (-, delayed) Forchhammer et al. (2002) (Ovibos moschatus) patrols Population size (-, delayed in 1961 – 1989 some populations) Northeastern Greenland Zebra Aerial counts plus shorter- Comparative fitting of density Population density (-) Georgiadis, Hack & Turpin (Equus burchelli) term, smaller-scale dependent and density- Mean annual rainfall (+) (2003) monitoring of individuals independent, stage and sex 1985 – 2000 structured matrix models to Laikipia District, Kenya time-series data. Ibex Annual Autumn census by Bulmer’s R and R* tests, plus Population density (-; although Jacobson et al. (2004) direct sighting DO analysis of Ricker and weak support from tests 1956 – 2000 Gompertz models, compared for density dependence) Gran Paradiso NP, Italy using AIC. Snow cover (-)
Analysis of ungulate dynamics
Notes from Table 4.1
1 Data from many long-term ungulate studies have been analysed repeatedly. Here, I present only those analyses that have employed novel techniques or presented new findings. I omit studies that have assessed environmental or population effects on one or more proxy for population performance (e.g. body weight, fecundity) but have not assessed influences at a population level. 2 see main text for further details. 3 NAO values are an index of the North Atlantic Oscillation; higher values indicate worse (wetter and windier) winter weather. 4 Akaike Information Criterion. 5 Schwartz Information Criterion (Schwarz, 1978). 6 Z-scores achieved by subtracting the mean and dividing by the standard deviation for the month in question.
In this section, we analyse long-term dynamics in three ways. First, we establish overall trends during the study period. These are determined for each major habitat area separately, and for the reserve as a whole. Using these, it will be possible to determine the overall trajectories of the studied species and, also, to see if these have been similar among the different habitat zones.
Secondly, we assess evidence for density dependence in the data, using various approaches to see if each population shows signs of density dependent regulation. Finally, we analyse the time- series of abundances in more detail, to determine whether the data show support for the effects of other environmental correlates in dictating population growth.
A variety of methods have been developed to examine the influence of density dependent processes in time-series data (e.g. Bulmer, 1975; Dennis & Taper, 1994; Pollard et al., 1987;
Vickery & Nudds, 1984) and these methods have been tested and compared on several occasions
(e.g. Shenk et al., 1998; Slade, 1977; Vickery & Nudds, 1984). Owing to the need to use serially- autocorrelated data for detecting density dependence (Eberhardt, 1970), there is considerable concern over the potential for Type I error resulting from many of the tests, especially where observation error (or sampling error) is large relative to process error (or stochastic variation in population density) and where long data sets are available (Shenk et al., 1998). However, the observation that many populations exist for long periods and yet remain finite is evidence of the
60 Analysis of ungulate dynamics ubiquity of density dependence (Royama, 1977) and, consequently, some authors have observed that estimating the size of negative autocorrelations in time series data remains interesting in its own right (Langton et al., 2002). In particular, estimating the magnitude of such negative autocorrelations may be interesting, when it also permits estimates of the contribution to growth rates of other environmental correlates.
Due to the concerns over the use of tests for density dependence, we employ two methods to assess evidence for its impact on the population growth of ungulates in SAZ. First, we use the tests of Bulmer (1975) to analyse whether density dependence is strongly illustrated by any of the populations. In contrast to many alternatives, Bulmer’s R* test has been shown to have low Type
I error rates for a wide range of conditions but, also, to lack power (Shenk et al., 1998). As such, it represents a very conservative test for the role of density dependence in a tested population.
Our second approach is motivated by the fact that previous tests developed to assess evidence for density dependence in population processes have all been designed on the basis that only one estimate of density is available for each year. As a result, these tests have been limited by an inability to confront the role of observation error (error in the annual estimates) explicitly. By contrast, the data from SAZ are based on large numbers of independent samples (surveyed transect segments) conducted annually. We have already shown that non-parametric bootstrapping can use these independent samples to derive confidence intervals around annual estimates (Section 3). Similarly, non-parametric bootstrapping presents an opportunity to determine how often observed characteristics of the data that indicate density dependence could have been produced if the underlying processes were density independent. As such, multiple annual samples provide the means for controlling for Type I error (false rejection of the null hypothesis that dynamics are density independent), the major flaw of the majority of existing tests of density dependence.
Our final set of temporal analyses uses a method employed in a large number of the studies in Table 4.1; this is the stochastic population modelling approach of Dennis & Taper
61 Analysis of ungulate dynamics
(1994) (the “DT approach” in Table 4.1). The DT approach permits analysis of the influence of various factors underlying population growth, by determining which of these factors are important for predicting the observed time-series of population size. Dennis & Taper’s (1994) approach has been used to analyse several long-term datasets on ungulate abundance (e.g. Dennis
& Taper, 1994; Jacobson et al., 2004; Taper & Gogan, 2002). It has also been modified to include weather covariates (Dennis & Otten, 2000) (the “DO approach” in Table 4.1) and this approach has been applied to indices of ungulate abundance (Peek et al., 2002). The DT approach now seems to be the main method for assessing factors important to the long-term population dynamics of a broad range of taxa, e.g. house mice (Mus domesticus) (Choquenot &
Ruscoe, 2000), common wasps (Vespula vulgaris) (Barlow et al., 2002), merlin (Falco columbarius) (Wiklund, 2001).
4.2 Methods
4.2.1 Within-year variation in track encounters
As in Section 2, where subdividing data spatially led to small sample sizes, subdividing data temporally also leads to small sample sizes, which confound inferences about the effect of time of year on track encounter rate. Again, however, patterns can be assessed for individual years and pooled across years to see if they occur consistently. To determine whether consistent patterns exist in survey results within years, we divided the encounter rate data into months. Very few surveys have been conducted in October, so for each biological year, we used data from the six months from November to April. We then used the approach summarised in equation 2.1 to determine whether average encounter rates for each month differed consistently from annual average encounter rates.
62 Analysis of ungulate dynamics
4.2.2 Linear trend analysis
Linear trend analysis is intended to give a very general indication of overall trajectories of the different surveyed species, over long periods. To determine these trajectories, we used a modification of the bootstrapping approach (described in Section 3.2.3) for linear regression. For those species for which we have estimates of movement (red deer, roe deer, sika deer, musk deer and wild boar), the raw data were estimates of density derived in Section 3.3.5, using the FMP formula with weighting by transect length and stratification by drainage basin area, as well as daily movement model averaging for red deer and wild boar. For the other species (moose), the raw data consisted of track encounter rates. For each year (and habitat where appropriate), the raw data consisted of n samples (each from an independent transect). From these, we generated B bootstrap samples, each also of size n. Each bootstrap sample was post-stratified by drainage basin area to give an average density (or encounter rate), D *b , for each year. Linear regression
b b was used to determine the slope (β1* ) and intercept (β0* ) for each bootstrap sample and the
ˆ ˆ mean slope ( β1 ) and mean intercept ( β 0 ) over all B bootstraps were used to indicate the mean trend for that species.
To generate confidence intervals about the linear trends, each bootstrap estimate of slope
b b (β1* ) and intercept (β0* ) was used to generate a prediction for the density (or encounter rate) associated with each year. The 95% confidence limits for each year were then calculated as described in Section 3.2.3 (equations 3.7 – 3.9). Trend analysis was conducted for each species in each of the three main habitat zones and then for each species for the whole of SAZ combined. In the latter case, bootstrap samples from each year were generated by sub-sampling from each of the three habitat zones and adjusting the year’s mean estimate according to the relative areas of each habitat zone. Clearly, for those species for which we do not have good estimates of travel distance, this assumed that track encounter rate and density were related by the same function in all zones. In Section 5, we discuss the annual survey effort required to allow trends to be detected
63 Analysis of ungulate dynamics over five year periods. Early on in the monitoring of SAZ, survey effort in many years was insufficient for that purpose and, consequently, it is likely that trends will not be detected accurately. By contrast, surveys in recent years have generally been adequate for the detection of trends (Section 5). For these reasons, we split the study period into four subsections for trend analysis. These were: 1962 - 1982; 1983 - 1992; 1993 - 1997; and 1998 - 2002.
4.2.3 Detecting density dependence
The derivation and statistical basis of Bulmer’s tests for density dependence have been discussed in detail elsewhere (Bulmer, 1975; Pollard et al., 1987; Shenk et al., 1998; Slade, 1977; Vickery
& Nudds, 1984). Here we present only a brief outline of the methods. The main approach is to calculate a statistic, R (or R*, see further below), which has been assessed by simulation and shown to be indicative of density dependence. The calculated statistic is compared to a critical value to determine whether the null hypothesis (that the data were produced by a density independent process) can be rejected. For a time-series of length q, it is assumed that the annual logged estimates of population size are denoted xt (i.e. x1, x2 … xq). Bulmer (1975) defines the following parameters:
q−1 2 U = ∑(xt+1 − xt ) t=1
q 2 V = ∑(xt − x) t=1
R = V /U (4.1)
The distribution of the R statistic was examined by simulation, and Bulmer suggested that critical values of the R statistic should be calculated as:
Rcrit = 0.25 + (q - 2)RL (4.2)
For α = 0.05, RL is given as 0.0366 and significance (rejection of the null hypothesis of density independence) is assumed where R < Rcrit.
64 Analysis of ungulate dynamics
Bulmer (1975) also noted that the presence of observation error in the estimates of xt will tend to exaggerate the appearance of a density dependent signal in the data. This is a well- recognised problem (e.g. Eberhardt, 1970) that arises because overestimates of population size in any year will generally lead to underestimates of the change in population size between that and the following year. Similarly, underestimates will lead to exaggerated corresponding changes.
Thus, smaller estimates of population size will be correlated with larger estimates of change and vice versa, leading to the appearance of density dependence, even where this plays no role in the underlying process. To remedy this, Bulmer (1975) defined additional parameters as:
q−2 W = ∑(xt+2 − xt+1 )(xt − x) t=1
R* = W /V (4.3)
The distribution of R* was also determined by simulation and the test was assumed to be significant when R* < R*crit, where, for α = 0.05, this is given by:
13.7 139 613 R * = − + − (4.4) crit q q 2 q 3
Bulmer’s R test has been shown to have high Type I error rates but can indicate the possibility of a density dependent signal, whilst the R* test has been shown to be highly conservative, having generally low power (Shenk et al., 1998). One of the limitations of
Bulmer’s tests (in keeping with all other tests developed to assess the influence of density dependence in time-series data) is that they were developed for application to data consisting of a single annual estimate of population size. As the data from SAZ comprise multiple independent estimates for each year, the possibility arises to develop a test that explicitly accounts for observation error. Our test draws on approaches discussed by Dennis & Taper (1994) and Pollard et al. (1987) but is novel, in that it uses non-parametric bootstrapping of multiple annual samples, in order to determine the significance of an apparent density dependent signal.
65 Analysis of ungulate dynamics
There is little consensus regarding the best type of underlying model when testing for density dependence in vertebrates. Due to its analytical tractability, many authors (e.g. Pollard et al., 1987) have used a Gompertz-type model, in which population growth is logarithmically dependent on population size. Dennis & Taper (1994) noted that, by contrast, a Ricker model (a standard logistic growth model, in which population growth depends on absolute population size) allows for stronger density dependence, and is therefore preferable. The Ricker approach was used by Peek et al. (2002). In practice, however, the two processes (Ricker and Gompertz) can lead to very similar dynamics (e.g. see Fig. 4.1); consequently, some authors have suggested examining both possibilities (Jacobson et al., 2004) and that is the approach that we take. Using the notation given above, the Ricker and Gompertz models, respectively, are described by the following autoregressive processes:
xt+1 = r + xt + βN t + σZ t (4.5)
xt+1 = r + βxt + σZ t (4.6) where r and β are constants and Zt is a normally distributed random number, with a mean of zero and a standard deviation of one. Values of Zt are assumed to be uncorrelated between years. In either case, three different models can be distinguished:
r = 0, β = 0 (Ricker) or β = 1 (Gompertz) (model 1)
r ≠ 0, β = 0 (Ricker) or β = 1 (Gompertz) (model 2)
β ≠ 0 (Ricker) or β ≠ 1 (Gompertz) (model 3)
Model (1) is a random walk, model (2) is a random walk with drift (an exponential growth or decline model, with mean growth rate r) and model (3) is a density dependent population model
(with a carrying capacity of -r / β for the Ricker process, or exp[r / (1 - β)] for the Gompertz process). We now discuss the detection of either of these density dependence processes. For brevity, our discussion focuses on the Gompertz model but is readily adapted to the Ricker model
66 Analysis of ungulate dynamics also, by noting the effects of the different values of β associated with each model (see models 1 to
3, above). 4.0 (a) 3.5 t
N 3.0
2.5
2.0
1.5
1.0 Population density, 0.5
0.0 010203040
Time, t
0.25
t (b) d 0.20
0.15
0.10 0.05
0.00
-0.05
-0.10 Log-changein population density, 01234
Population density, N t
Figure 4.1. Sample simulations of populations following a Ricker process (solid lines) or a Gompertz process (broken lines): (a) a single time-series for each process; (b) best fit regressions showing the mean relationships between population growth and population size (Ricker shown with linear regression, Gompertz with logarithmic regression). For both processes, initial population density, N1 = 1, carrying capacity, K = 3, and process error, σ = 0.07. Additional parameters: Ricker, r = 0.3, β = -0.1; Gompertz, r = 0.22, β = -0.8.
A common approach to testing for Gompertz density dependence, is to regress dt on xt.
This regression has slope b = β - 1 and intercept r. The mean squared residual is equivalent to σ.
In both models 1 and 2, defined above, β = 1 and, hence, we might expect that a regression of density independent data would have a slope of b = 0. However, two processes can affect this.
Firstly, stochasticity can lead to slopes that are different from zero, although this will be increasingly unlikely in longer data sets. Secondly, and more importantly, the consequences of
67 Analysis of ungulate dynamics observation error (discussed above) will invariably lead to a negative slope. The key requirement of a test for density dependence is to determine whether a slope of b could have been produced merely as a consequence of stochasticity and sampling error, or whether it is likely to reflect a clear density dependent process. As we already have estimates of the amount of sampling error inherent in our data, we can use a combination of simulations and bootstrapping to determine the frequency with which slopes less than or equal to the observed slope could be generated by density independent processes. This is effectively a modified form of the randomisation test of
Pollard et al. (1987), adapted to include a known distribution of sampling error.
Once again, we consider the case of a time-series of length q, consisting of annual estimates of population size, Nt. As we explicitly incorporate the availability of multiple annual estimates, we assume that each overall annual estimate (Nt) is the arithmetic mean (or weighted arithmetic mean if the data are stratified) of i annual estimates, n1,q, n2,q, … ni,q. As above, we define xt = ln(Nt), and annual changes in these values are given by dt = xt+1 - xt. Given an actual time-series of data, Nt (hereafter referred to as the test data set), the test requires the following steps:
(i) Determine the coefficients of the regression of dt on xt, analysed by each of the three models given above. For clarity, we term these coefficients σ1 (for model 1), σ2 and r2 (for model
2) and σ3, r3 and b3 (for model 3).
(ii) Beginning with N'1 = N1, simulate a random data set (N'1, N'2, … N'q), based on either model (1) (using the value of σ1) or model 2 (using the values of σ2 and r2). Note that if N1 = 0, the simulated set should be conditioned on the first non-zero estimate of Nt.
(iii) For each year, populate an array of independent samples that would have led to the simulated annual estimate. These will take the values n'i,q = ni,q · N't / Nt (where ni,q are the i independent samples from year t of the test data set).
(iv) Non-parametrically bootstrap the independent samples (n'i,q) for each year, to produce a bootstrapped set of the simulated annual estimates, N*t.
68 Analysis of ungulate dynamics
ˆ (v) By taking logs of N*t (denoted x*t), estimate b * for this bootstrap.
By repeating the bootstrap process B times and the simulation of a data set G times, we
ˆ can estimate the probability p(I) = #( b* ≤ b3 ) / B·G, where # indicates the absolute number of times that the given condition is satisfied. In this way, it is possible to estimate the overall probability, given the actual distribution of sampling errors, that a slope as negative as that observed could have been produced by a density independent process. Preliminary assessments showed that some slopes (b3) calculated from test data sets were extremely sensitive to individual data points. For that reason, all parameters for each test data set were calculated after having removed the data point that contributed the most to the negative value of b3. This conservative estimate of the slope for each test data set was termed b(j). Using b(j) instead of b3 affected the outcome of only one test, where the removal of a single data point vastly altered the value of b3
(see further in Section 4.3.3). Overall, evidence suggests that this modified-Pollard test has low
Type I error rates, except where survey error is extremely high, but that test power is high only when density dependence is strong (P.A. Stephens, unpublished data). Consequently, we use α =
0.10 as our significance threshold.
4.2.4 Time-series analysis
Analyses of most data sets to account for the factors underlying density dependent changes in population estimates (whether they are due to a density dependent population growth process, or to autocorrelations in sampling error) can tell us little about the environmental factors that affect population growth. More thorough analyses of time-series data aim to determine which intrinsic and extrinsic factors are likely to underlie the time-series of observed population size (or indices of population size). Many methods exist for such analyses but here, we focus on the stochastic
69 Analysis of ungulate dynamics population modelling approach of Dennis and colleagues (Dennis & Otten, 2000; Dennis &
Taper, 1994).
Dennis & Taper (1994) presented their analytical approach based on an underlying
Ricker process (equation 4.5). The approach can be modified for use with a Gompertz process
(Jacobson et al., 2004) but here, we follow Dennis and colleagues, and build on the notation given in equation 4.5, above. Dennis & Otten (2000) extended this to incorporate density independent environmental correlates of population growth. In general, the extended model can be written as:
xt+1 = xt + r + βN t + c1E1 + c2 E2 + ... + ci Ei + σZ t (4.7) where c1, c2, … ci are constants, and E1, E2, … Ei are environmental correlates, such as weather indices, forage biomass, predator abundance, etc. It is possible to identify a range of competing hypotheses based on equation 4.2, according to whether the various constants differ from zero.
Maximum likelihood estimates of the constants may be obtained using linear regression.
Specifically, multiple linear regression is conducted using dt as the response variable, with Nt and
E1 to Ei as the independent variables (note that a Gompertz process would use xt rather than Nt as the independent population size variable). This yields coefficients equivalent to maximum likelihood estimates of r (the intercept), β (the coefficient of Nt) and c1 to ci (the coefficients of E1
2 to Ei, respectively). Error (σ ) is given by the mean sum of squared residuals. Lagged density dependence may also be incorporated by including βlNt-l terms, for a density dependent lag of order l+1. Competing models can be compared using AIC (see further below) and, thus, the ‘best model’ or set of models will indicate support for the importance of various constants from the full
(or global) model (equation 4.7).
Having assessed the extent of support for density dependence acting within the populations (see Sections 4.2.3 and 4.3.3), the aim of our time-series analyses was to determine which other factors are important for explaining annual changes in population size. For this reason, we included both an intercept (equivalent to r in equation 4.7) and an autoregressive term
70 Analysis of ungulate dynamics
(βNt or βxt) in all models. Whether or not there is strong evidence for density dependence, the autoregressive term also accounts for serial autocorrelation in survey error, allowing remaining variation to be accounted for by other factors in the model. Our choice of whether to use a Ricker or a Gompertz process as the underlying model was guided by regressions of dt on Nt and xt. The autoregressive metric (Nt or xt) that explained the greater amount of variation in dt (i.e. had the higher R2 value) was then used in all models of that population.
Models including various combinations of factors were compared using AIC (equations
3.2-3.5). As data sets were small (40 data points at best but less where shorter time periods were considered, lag terms were included or data were missing), AICc was used in all cases. Model comparisons were run using the statistical software package R (http://www.r-project.org/) and
AIC values were taken directly from the model output. AICc was then calculated as shown in equation 3.1. Models can be considered to have strong support if their AICc value is within two units of that of the best model (Anderson et al., 2000). Models with low AICc values may, nevertheless, be rejected if they do not conform to prior biological understanding. For example, if a covariate is initially assumed to have a positive effect on population growth but features in models as a negative influence, it is likely that the model fit is an artefact of spurious regression
(a relationship between two variables that is due to chance, rather than to any biologically meaningful process). In these cases, such models were removed from the set of strongly supported models (or ‘confidence set’). Where confidence sets included a variety of candidate models, average models were obtained by multi-model averaging (Burnham & Anderson, 2002).
Specifically, a weighted average of the models’ predictions is calculated using weightings obtained by formula 3.5, calculated only for the group of models of interest. Model averaging permitted large sets of models to be condensed to a single model indicating the approximate effect sizes of well-supported parameters. Only strong effects, typically occurring in several models within the confidence set, were still visible in average models.
71 Analysis of ungulate dynamics
4.2.5 Putative factors influencing population growth
In model selection, the prior determination of candidate model sets is extremely important
(Burnham & Anderson, 2002). Candidate models were discussed during meetings at the
Zapovednik offices in Terney during September 2004. Although not all correlates were thought likely to affect all species, here we describe factors likely to affect one or more of the ungulates surveyed in SAZ, together with the derivation of appropriate indices. Where parameters are identified, this is done in light of the general aim to predict log population change from year t to year t+1, dt. The following sets of factors were thought likely to have an impact on population growth in one or more species. “Global model” refers to the full set of factors included in models for a given species in a given habitat zone.
Density dependence. For ungulates, it is possible that density dependence is more complex than first-order lags and several of the studies listed in Table 4.1 show evidence for higher order lags. All global models included lags of up to three orders. This required using Nt,
Nt-1 and Nt-2 (or xt, xt-1 and xt-2), as predictors for dt. The choice of scale (absolute or logarithmic) was determined as described in the previous section.
Mast abundance. Mast is an important food resource for ungulates in SAZ, especially wild boar. As discussed in Section 1.3, indices of both oak and Korean pine mast abundance have been collected annually in SAZ. As a predictor variable, we used the categorical index, Mt, for the predominant mast type in the habitat analysed (oak in the oak-birch habitat zone, and
Korean pine in the Korean pine-deciduous zone). The exception to this was wild boar. Biologists in SAZ have observed that wild boar depend largely on oak mast but, in years when oak mast fails, a good crop of pine nuts can alleviate problems of food shortage. Consequently, some biologists assess wild boar dynamics in relation to a modified mast index, equivalent to the oak mast in all but three years when this failed completely; in those years, the mast index is modified upwards, according to the quality of the pine mast. As wild boar dynamics in oak-birch and
Korean pine-deciduous habitats were analysed together (see further below), all three mast indices
72 Analysis of ungulate dynamics
(oak, pine and the alternative, amalgamated index) were compared for this species, in order to see which was most informative. Note that a good mast in year t is expected to improve the condition of animals emerging from the biological winter of year t and, consequently, to increase recruitment (and, hence, population change, dt) from t to t+1. Mast index values are shown in
Fig. 4.2a-c.
Predator abundance. Tigers in the case of red deer, sika deer and wild boar, and lynx
(Felis lynx) in the case of roe deer (and possibly musk deer), are significant predators.
Abundance indices are available for both: estimates of absolute tiger numbers are available for each year, and lynx tracks (of less than 48 hours old) are recorded on the winter transect counts.
The latter can be expressed as tracks km-1, to give an approximate relative index of the likely level of predation from year to year. Tiger abundance was highly non-stationary throughout the study period. Consequently, we used log-change in tiger population size from t to t+1 as our index of tiger abundance. Lynx abundance is relatively stationary. Again, however, abundance in both the previous winter and the current winter could be argued to be the relevant index for looking at effects on population growth. In practice, fluctuations in predator populations are likely to be slow and, consequently, we smoothed the index by using an average of these two values (i.e. Lynx = [Lynx (t) + Lynx (t+1)] / 2). Predator indices are shown in Fig. 4.2d,e.
Competitor abundance. Different species are likely to compete to different extents with other members of their guild and other species that exploit the same resources. In addition to competition between the larger ungulates, wild boar may compete (at least for mast) with small rodents. Where C was the abundance of a competitor, we used Ct as our index of competition.
Abundance indices for ungulates were the densities calculated in Section 3 of this report. For small rodents, trapping has been conducted every year since 1965 (E. Smirnov, unpublished data).
Numbers of rodents trapped per 100 trap nights have been recorded for three species: the Korean field mouse, Apodemus peninsulae; the northern red-backed vole, Clethrionomys rutilus; and the grey red-backed vole, C. rufocanus. Although trapping success has shown a more dramatic
73 Analysis of ungulate dynamics increase for the mouse than for the voles since monitoring began, all three species tend to show highs in similar years (Fig. 4.2). As trapping is conducted in the summer preceding the ungulate winter survey, we used as our index of competition, the combined trap success for all three species in the year from which change was measured, i.e. year t. The Z-scored index of rodent abundance (see further below) is show in Fig. 4.2f.
Winter severity. Two aspects of winter weather conditions were deemed particularly important. These were snow cover (which limits access to resources) and temperature (which dictates demand for resources). These might act independently, or in concert. Consequently, we compared models containing any one of four different indices of winter weather. The indices were winter snow (WS, total precipitation for October to March in biological year t), winter temperature (WT, mean temperature for October to March in biological year t), a combined winter conditions index [defined as WC = Z(WT) – Z(WS), where Z(x) is the Z-score for x (see further below)], and the winter North Pacific Oscillation Anomaly (WNPO). WNPO data are available from the USA’s National Centre for Atmospheric Research website
(http://www.cgd.ucar.edu:80/cas/climind) and have been shown to have a strong influence on elk dynamics in parts of North America (Hebblewhite, 2005). On that continent, higher NPO indices are associated with poorer conditions in winter but in the Russian Far East, higher NPO values are associated with milder winters with less snow. Although correlations with winter variables from the Melnichnoye and particularly the Terney weather stations are not strong, the NPO index was used to provide a broader indication of winter weather, in contrast to these very localised measures. Note that all winter weather variables (from year t) were assumed to affect the condition in which ungulates emerge from winter and, consequently, their reproductive success
(and population growth) from t to t+1.
Spring conditions. Weather conditions during April and May can have an important effect on survival of newborn young, especially for the smaller species. If snowy conditions
74
(d) 20 (a) 5 1.2 (g) 4 0.9 16
3 0.6 12
2 0.3 8
Oak mast index index mast Oak 1 0 of reports Number 4 Log (population change) Log (population 0 -0.3 0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 (e) (b) 5 8 (h) 48 ) -1 4 40 6 32 3 4 24 2 16 Illegal entries Pine mast index mast Pine Pine mast index mast Pine 2 1 8 Abundance (tracks km (tracks Abundance 0 0 0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 (f) (c) 3 3 (i) 10 2 8 1 2 0 6
Total abundance Total -1 Estimated protection Alternative mast index 1 -2 4 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 Year Year Year
Fig. 4.2. Covariates used in time-series models (excluding weather and ungulate competitor covariates): (a) oak mast; (b) pine mast; (c) alternative mast index (note reduced number of categories); (d) tiger population growth; (e) lynx abundance; (f) rodent abundance (Z-scored); (g) reports of poaching; (h) incidences of illegal entry; (i) expert assessments of efficacy of protection.
Analysis of ungulate dynamics persist, warm springs could also be problematic, reducing the mobility of some species. We incorporated both spring precipitation and mean temperature from April and May (at the start of the biological year t+1) as model covariates.
Summer conditions. Both summer temperatures and precipitation might be important for vegetative productivity and, hence, might be expected to affect the condition in which animals enter winter and, thus, recruitment in the following year. Our indices were for June to September in the biological year t (i.e. the summer preceding the winter of biological year t).
Human impacts. At times, poaching of animals from within SAZ may have had an effect on ungulate population dynamics. To examine this, we used several indices of human impact that may correlate with either poaching or hunting pressure. These were: annual reports of poaching in SAZ, RP; annual numbers of illegal entries into SAZ, IE; and an expert assessment of the efficacy of protection of SAZ, EP. The latter index was the average of five independent, year by year assessments, given by Zapovednik employees familiar with the enforcement history in SAZ.
Time series of these factors are shown in Fig. 4.2g-i.
In addition to the specific seasonal weather variables discussed above, annual mean temperature was also used as a broader climatic index. Climatic variables are shown in Fig. 4.3.
All parameters (including autoregressive parameters) were Z-transformed to remove the effect of scale. This allows the magnitude of effects to be compared more easily. In general,
Z(x) = (x − x) / s , where Z(x) is the Z-score for a given value of x, x is the mean of all x, and s is the standard deviation of x.
The factors listed summarise the full range of correlates designated a priori, for which data exist to compare population models. Not all factors were included in the global model for any population. Our general approach was to include three autoregressive terms (for density dependence and lagged density dependence), together with spring and summer weather indices, in
76
(a) (d) (g) -20 14 18 C 12 17 -16 ure, 10 t 16 -12 8 15 empera 6 t -8 C °
er 14 t 4 n i -4 2 13
ean w 0 0 12
M Mean summer temperature, ° 1962 1972 1982 1992 2002 index anomaly NPO Winter 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
(b) 350 (e) 10 (h) 950 300 m 250 8 750 200 6 150 550 100 4 350 50 0 2 150 Summer precipitation, m Summer precipitation, Winter precipitation, mm precipitation, Winter
1962 1972 1982 1992 2002 Mean spring temperature, °C 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
(c) 5 (f) 350 (i) 7 300 3 5 250 1 200 3
-1 150 1 100 -3 -1 50
Winter conditions index conditions Winter -5 0 -3 Spring precipitation, mm Spring precipitation, 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 Annual mean temperature, °C Year Year Year
Fig. 4.3. Weather covariates used in time series analyses. Note that in each case, the solid line represents Melnichnoye (used for analyses of population in the spruce-fir zone) and the broken line represents Terney (used for analyses of data from the oak-birch and Korean pine-deciduous zones). The exception is (d), the winter NPO anomaly index, which is independent of habitat zone.
Analysis of ungulate dynamics the global models for all populations. To these were added relevant predators (tigers for the larger ungulates, but lynx for roe deer and musk deer) and relevant mast crops (only musk deer were thought likely to be completely unaffected by mast crops). All of the larger deer were included as competitors in global models for any other large deer. Whilst this competition might not be direct, an array of indirect effects are possible, including foraging disturbances and interactions with predators (for example, predator dilution). Rodents were also included as a competitor in the wild boar global models. Musk deer were deemed unlikely to compete with rodents or other ungulates and so no competitors were included in the musk deer global models.
In addition to these factors, winter weather variables and human impact variables were also included in global models. To avoid the potential for over fitting that arises from having highly correlated parameters, a maximum of one winter weather parameter and one human impact variable was included in any one model. Thus, although all winter weather variables were included in the global model, these were never included in any candidate model in combination.
Similarly, whilst all three human impact factors were included in the set of candidate models, only one (at most) was ever used in any given candidate model. For clarity, further details of the models compared are given in the results section.
4.2.6 Selection of data sets for density dependent and time-series analyses
Although Dennis and colleagues (Dennis et al., 1998) have developed their approach for use on metapopulation data (see also Langton et al., 2002), they caution that this approach can lead to a rapid inflation of the number of estimated parameters. This will be even more pronounced when environmental correlates are included. In addition, trend analyses (Section 4.3.2) showed that for most species, populations had markedly different trajectories in the different habitat zones of
SAZ. Amalgamating data for the whole of SAZ often led to less pronounced trends, obscuring some of the detail evident amongst the different zones. Furthermore, it seems likely that different factors may be important in different parts of SAZ (for example, mast crops are only expected to
78 Analysis of ungulate dynamics be important in the habitat zone in which the masting species predominates). For these reasons, we chose to analyse populations of each species separately for each zone. The exception to this was wild boar, which exist in relatively low numbers in both the oak-birch and Korean pine- deciduous zones. Boar are also known to move large distances between zones in search of food.
Consequently, average density of wild boar over the two zones was used for analysis.
Analysing longer data sets is preferable, as multi-parameter models can be treated with greater confidence when applied to larger data sets. Where possible therefore, full data sets were used for analyses of the role of density dependence. However, for time-series analyses, we had one very clear reason to divide the data set temporally. This was that important sections of the oak-birch zone only received formal protection from 1980 onwards. These areas are known to be important for many of the ungulate species and, consequently, had the potential to influence populations throughout SAZ (either by recruitment or migration). Indeed, Fig. 3.11 suggests that the dynamics of several species may have been different before and after 1980, seemingly in all zones of SAZ. Consequently, for time-series analyses, all populations were divided into the two periods, 1962 - 1979 and 1980 - 2002. The exception to this was musk deer, which are relatively rare in the oak-birch zone and showed no sign of a change in dynamics after 1980 in either the spruce-fir or Korean pine-deciduous zones. For both of those zones, time-series analyses were conducted for musk deer for the entire period, 1962 - 2002.
Finally, analyses of the importance of density dependent and independent factors affecting population growth depend critically on good quality data. For this reason, we elected not to analyse data on moose (which are very sparse and, given current levels of survey effort, unreliable; see further in Section 5). Other species were analysed only in the zones in which they were abundant (where population data are likely to be more reliable). Specifically, red deer and roe deer were analysed for all three zones, sika deer were analysed in the oak-birch zone only, musk deer data from the oak-birch zone were not analysed, and wild boar were analysed only in the oak-birch and Korean pine-deciduous areas. Several species occurred in certain habitat zones
79 Analysis of ungulate dynamics in very low numbers during one of the two studied time periods. In particular, sika deer were largely absent from the oak-birch zone until 1980, whilst roe deer were present in the Korean pine-deciduous and spruce-fir zones in very low numbers prior to that point. Consequently, no analyses were possible for these species in those habitats, during the first period. A small number of conspicuous outliers were removed from remaining data sets. These included data points with confidence intervals which overlapped with neither of their neighbouring data points, and which also lay outside the confidence intervals of their neighbouring data points. Specifically, these included: red deer, oak birch zone, 1987 and spruce-fir zone, 1979; roe deer, Korean pine- deciduous zone, 1994; sika deer, oak-birch zone, 1984; musk deer, Korean pine-deciduous zone,
1982 and spruce-fir zone, 1993.
4.3 Results
4.3.1 Within-year variation in track encounters
Relative track encounter rates for the months of November to April are shown in Fig. 4.4.
Relative monthly encounter rates differ substantially from unity in only a very few cases.
However, where temporal patterns are visible from the figure, a tendency for encounter rates to decline from early winter to late winter is the most common pattern (approximately half of the cases illustrated). That there are no corresponding increases in encounter rate in other areas, suggests that this is not a consequence of movement between areas; however, we return to this point in the discussion (Section 4.4). A reduction in travel distance over winter seems likely from the daily movement data (Section 3.3.1) but other factors may confound attempts to determine the magnitude of such declines. As a result, it is not possible to establish whether or not reductions in travel distance are the sole cause of observed declines in encounter rate, or whether mortality during the season or some other cause is implicated.
80 Analysis of ungulate dynamics 3 3 3 (a) 2 2 2
1 1 1
0 0 0 Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr 3 3 3 (b) 2 2 2
1 1 1
0 0 0 Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr
3 (c) 2
1
0 Nov Dec Jan Feb Mar Apr 3 3 3 (d) 2 2 2
1 1 1
0 0 0 Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr
3 3 (e) 2 2
1 1
0 0 Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr 3 3 3 (f) 2 2 2
1 1 1 Encounter rate relative mean, averaged annual to over all years was present species that and surveyed
0 0 0 Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr Nov Dec Jan Feb Mar Apr
Month
Figure 4.4. Relative encounter rates over winter. Oak-birch habitat (left panels), Korean pine-deciduous (middle panels) and spruce-fir (right panels) for: (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer, (e) moose, (f) wild boar. Broken lines indicate a ratio of one, at which encounter rates in a given month are equal to the average for the year. Some larger confidence intervals are truncated.
81 Analysis of ungulate dynamics
4.3.2 Linear trend analysis
Linear trends and associated confidence intervals were generated for each species in each habitat
(Fig. 4.5). Confidence intervals for each period, including those for the five year periods, are typically narrow, indicating that survey effort is currently sufficient to give a good indication of trends on these timescales. There are exceptions, however, especially for species in habitats in which they occur relatively infrequently (such as red deer in spruce-fir habitats, for example) and, in particular, where the mean trend suggests that a species population density remained fairly constant during the period. Beyond these observations, it is difficult to generalise about the trends illustrated in Fig. 4.5. In the oak-birch zone, red deer and roe deer appear to have followed similar trajectories, increasing initially but decreasing in recent years. This contrasts with sika deer, which have increased rapidly in the oak-birch zone in the last decade. That red deer and roe deer seem to have increased in the Korean pine-deciduous and spruce-fir zones in the last decade, could indicate either improving conditions in those areas, or population movement in response to a decline in conditions in the oak-birch zone. Wild boar in both the oak-birch and Korean pine- deciduous zones have followed fairly similar trajectories to red deer and roe deer in the oak-birch zone, suggesting that similar factors are affecting the dynamics of the three species. Musk deer show the least consistency in trends, possibly as a result of the limited data available on their movements (see Section 3). Sharp discontinuities between musk deer trends in the different periods are also a product of highly varying predictions between sequential years (for example, between the final year of one period and the first year of the following period). Finally, moose appear to have declined in the spruce-fir zone, the only zone in which they were sighted with any regularity. A suggestion that they may be recovering slightly now is undermined by wide confidence intervals. These are unsurprising, given the survey effort required to assess moose dynamics with confidence (see further in Section 5).
The overriding trends in SAZ are more easily interpreted when the study areas are combined (Fig. 4.6). From these results, it is readily apparent that only moose have shown a
82 Analysis of ungulate dynamics
(a) 10 4.0 2.0 8 3.0 1.5 6 2.0 1.0 4 2 1.0 0.5 0 0.0 0.0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 (b) 5.0 4.0 2.0 4.0 3.0 1.5 3.0 2.0 1.0 2.0 1.0 0.5 1.0 0.0 0.0 0.0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
)
-1 (c) 1.6 1.2
0.8
0.4 0.0 1962 1972 1982 1992 2002 (d) 0.8 4.0 5.0 0.6 3.0 4.0 3.0 0.4 2.0
) or track encounter rate (km rate encounter track or ) 2.0
-2 0.2 1.0 1.0 0.0 0.0 0.0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
(e) 0.25 Density (km 0.20 0.15 0.10 0.05 0.00 1962 1972 1982 1992 2002
(f) 2.4 0.6 0.15 2.0 0.5 0.12 1.6 0.4 0.09 1.2 0.3 0.06 0.8 0.2 0.4 0.1 0.03 0.0 0.0 0.00 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002
Year
Figure 4.5. Linear trends during four periods (1962-82; 1983-92; 1993-97; 1998-2002). Oak-birch habitat (left panels), Korean pine-deciduous (middle panels) and spruce-fir (right panels) for: (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer, (e) moose, (f) wild boar. Solid lines show the mean trend from 5,000 bootstrapped regressions. Broken lines indicate the 95% confidence intervals for predictions. All panels show trends in density except for moose (e), which show trends in encounter rate. Trends for sika deer and moose are shown only for the primary habitats in which they occur.
83 Analysis of ungulate dynamics
)
-1
4.0 2.5 0.4 (a) 2.0 (b) (c) 3.0 0.3 1.5 2.0 0.2 1.0 1.0 0.5 0.1
0.0 0.0 0.0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 2.5 (d) 0.08 0.8 (f) ) or encounter rate (km (e) 2.0 -2 0.06 0.6 1.5 0.04 0.4 1.0 0.02 0.2 0.5 0.0 0.00 0.0 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 1962 1972 1982 1992 2002 Density (km
Year Figure 4.6. Linear trends during four periods (1962-82; 1983-92; 1993-97; 1998-2002) averaged over all habitats (weighted by area): (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer, (e) moose, (f) wild boar. Solid lines show the mean trend from 5,000 bootstrapped regressions. Broken lines indicate the 95% confidence intervals for predictions. All panels show trends in density except for moose (e), which show trends in encounter rate.
general decline throughout the study period, but that wild boar, musk deer and, to a lesser extent, red deer, have all declined in recent years. In the case of the wild boar, this decline is disturbingly abrupt. Sika deer is the only species that has shown an uninterrupted increase over recent years.
4.3.3 Density dependence
The results of Bulmer’s R and R* tests are shown in Table 4.2. Two-thirds (8 out of 12) of the populations tested gave positive results of the R test but none of the R* tests gave positive results.
These findings are presented mainly for comparative purposes and accord with what is known about the two tests. Given the potential for Type I error in the R test, the non-significant results are perhaps more interesting than the significant results. In particular, that the R tests gave non- significant results for red deer, roe deer and sika deer in the oak-birch zone, as well as roe deer in the spruce-fir zone is suggestive that, in the oak-birch zone in particular, some process may be regulating all of the deer species at a level beneath the natural carrying capacity of the
84 Analysis of ungulate dynamics environment. That none of the R* tests gave significant results is unsurprising, given the notoriously low power of this test, and we hesitate to conclude from this finding that there is no evidence for density dependence in the population processes of the ungulates studied.
The modified-Pollard test was run using G = 250 simulated density independent data sets
(125 each of random walk and stochastic exponential growth or decline) and B = 400 bootstraps of each data set, giving 100,000 estimates of bˆ * . Random walk models and stochastic exponential models gave similar results, and we present combined results. The proportion of all
ˆ density independent models yielding b* ≤ b( j) for each tested data set is shown in Table 4.3.
Overall, half (6 of 12) of the tested populations showed evidence for either Ricker-type,
Gompertz-type, or both types of density dependence. Once again, there was no evidence for
Table 4.2 Bulmer’s R and R* tests for density dependence. Parameters as in main text. † denotes significant values (p ≤ 0.1; none of the R* tests yielded significant results).
Species Habitat q-1 U V W R Rc R* R*c
Red deer Oak-birch 41 17.60 39.01 0.59 2.22 1.68 0.02 -0.62 Korean pine-deciduous 40 9.62 6.86 -2.11 0.71 1.64 † -0.31 -0.64 Spruce-fir 36 43.74 31.81 11.91 0.73 1.49 † 0.37 -0.75 Roe deer Oak-birch 40 15.39 27.54 -0.75 1.79 1.64 -0.03 -0.64 Korean pine-deciduous 40 54.09 71.34 5.48 1.32 1.64 † 0.08 -0.64 Spruce-fir 25 16.94 39.11 -2.25 2.31 1.09 -0.06 -1.31 Sika deer Oak-birch 29 35.65 78.13 2.87 2.19 1.24 0.04 -1.04 Musk deer Korean pine-deciduous 40 23.02 17.51 -6.34 0.76 1.64 † -0.36 -0.64 Spruce-fir 37 23.87 20.85 -2.90 0.87 1.53 † -0.14 -0.72 Wild boar Oak-birch 40 40.75 50.72 -9.74 1.24 1.64 † -0.19 -0.64 Korean pine-deciduous 40 146.41 70.84 5.67 0.48 1.64 † 0.08 -0.64
85 Analysis of ungulate dynamics
Table 4.3 Modified-Pollard test for density dependence. Parameters as in main text. † denotes significant values (p ≤ 0.1).
Ricker Gompertz Species Habitat bb(j) p(I) bb(j) p(I)
Red deer Oak-birch -0.141 -0.126 0.288 -0.245 -0.200 0.498 Korean pine-deciduous -0.476 -0.441 0.208 -0.739 -0.687 0.021† Spruce-fir -1.044 -0.777 0.089† -0.728 -0.610 0.268 Roe deer Oak-birch -0.198 -0.170 0.269 -0.283 -0.227 0.710 Korean pine-deciduous -0.440 -0.321 0.344 -0.380 -0.310 0.526 Spruce-fir -0.573 -0.312 0.477 -0.294 -0.157 0.966 Sika deer Oak-birch -1.844 -0.268 0.336 -0.268 -0.133 0.959 Musk deer Korean pine-deciduous -1.092 -0.910 0.215 -0.795 -0.656 0.091† Spruce-fir -0.430 -0.396 0.396 -0.672 -0.626 0.175 Wild boar Oak-birch -1.218 -1.026 0.025† -0.469 -0.406 0.707 Korean pine-deciduous -6.106 -5.283 0.018† -0.987 -0.922 0.091†
density dependent regulation of red, roe or sika deer in the oak-birch zone, although wild boar showed evidence of Ricker-type density dependence in this zone. Time-series for red deer showed evidence of density dependence in both the Korean pine-deciduous zone and spruce-fir zone, by at least one method. Roe deer gave no significant results, suggesting either that density dependence is too weak to be detected in the studied populations of this species, or that competition with other ungulates is currently the over-riding regulatory factor for roe deer.
Finally, it is interesting to note that the removal of the most extreme point from each test data set generally made little difference to the slopes (typically reducing their absolute magnitude by between 10 and 20%). The exception to this was the data set for sika deer in the oak-birch zone.
Removing a single outlying data point from this data set reduced the slope of the regression of dt on Nt by over 80%, preventing the test from giving a significant result. This finding suggests caution in the analysis of data sets subject to large sampling errors, and supports the removal of outliers when conducting the modified Pollard test.
86 Analysis of ungulate dynamics
4.3.4 Time-series analysis
Variables used in the models are set out in Table 4.4. The actual variables considered within the global model for any population are shown in Appendix 4A, together with hypothesised directions of effects, given prior biological knowledge. Given the relatively small sample sizes, models were restricted to contain a maximum of four parameters (in addition to the intercept and error term). Higher numbers of parameters would have certainly led to overfitted models. Even with four parameters, there was a danger of overfitting but fewer parameters would have greatly limited the insights that could be gained from this analyses, showing only the most dominant effects.
The best-supported models for each population are shown in Appendix 4B. Populations varied from sika deer in the oak-birch zone, 1980-2002, for which a single model received substantially higher support than any alternative, to roe deer in the oak-birch habitat, 1980-2002, where 20 models received good support (based on AIC alone). There was also substantial variation among populations, in terms of the amount of variation in population growth that was explained by selected models. Models selected for roe deer in the Korean pine-deciduous zone,
1980-2002, typically explained over 80% of variation in population growth rates, whilst in the spruce-fir zone during the same period, models selected for roe deer explained only 30 to 46% of variation in population growth rates.
Typically, the set of models selected for a given population all contained two or three common variables, together with one or two additional variables that varied among models.
Those variables that appeared consistently in all of the models selected for a population are likely to be among the most important effects influencing that population. Other variables that did not appear consistently among models were often associated with one another however, and frequently highly correlated (such as different indices of the severity of winter). For each
87
Table 4.4. Summary of variables used in time-series analyses. Further details on which variables were included in models of the different populations are given in the appendices to this Section
Variable Description Variable Description
Dependent variable dt Log change in population size from year t to year t+1 Predators Density dependence Tig Log (change in tiger population from t to t+1)
Nt Absolute population density in winter of year t Lynx Lynx abundance averaged between winters of biological years t and t+1
Nt-1 Absolute population density in winter of year t-1
Nt-2 Absolute population density in winter of year t-2 Weather variables xt Logarithm of population density in winter of year t WT Mean winter temperature in winter of biological year t xt-1 Logarithm of population density in winter of year t-1 WS Total winter precipitation in winter of biological year t xt-2 Logarithm of population density in winter of year t-2 WC Winter conditions index in winter of biological year t VT Mean spring temperature in spring of biological year t+1 Competitors VP Total spring precipitation in spring of biological year t+1 Red Red deer abundance in winter of biological year t ST Mean summer temperature in spring of biological year t+1 Roe Roe deer abundance in winter of biological year t SP Total summer precipitation in spring of biological year t+1 Sika Roe deer abundance in winter of biological year t AT Annual mean temperature in biological year t Rdnt Rodent abundance in summer of biological year t WNPO Winter NPO index for winter of biological year t
Mast indices Human impact variables Oak Oak mast abundance in summer of biological year t RP Reports of poaching for biological year t+1 Pine Pine mast abundance in summer of biological year t IE Illegal entries for biological year t+1 AltMast Alternative mast index in summer of biological year t EP Estimated efficacy of protection for calendar year t+1
Analysis of ungulate dynamics population, models (shown in Appendix 4B) that were clearly contrary to prior hypotheses and, hence, did not receive good biological support, were excluded from the confidence set.
Remaining models were then averaged. The results of this process are shown in Table 4.5.
The process of model averaging permits all of the major influences on each population to be illustrated within a single model formulation. All variables were Z-transformed prior to analysis, so the size of coefficients also gives an indication of the strength of an effect, relative to a change in the underlying parameter of a given number of standard deviations. First order autoregressive terms were included in all models and generally (though not always) had large effects relative to other factors. All were negative, as would be expected from data with survey error. We will not comment further on these here. More interesting were the small number of populations that seemed to be affected by higher order density dependence. Positive second or third order lags (associated with the estimated populations in years t-1 and t-2) are usually associated with populations in which growth is limited by a shortage of reproductively mature females. Such lags are seen in red deer in the oak-birch zone, 1962-1980, roe deer in the spruce- fir zone, 1980-2002, musk deer in the Korean pine-deciduous zone, 1962-2002 and sika deer in the oak-birch zone, 1980-2002. In three of these cases (red deer, roe deer and sika deer), the populations considered appear to have been undergoing near-exponential increases and, thus, positive lagged density dependence is unsurprising. By contrast, musk deer do not appear to have been increasing, suggesting that the population was limited by some extrinsic factor.
The effects of competition feature in models of several populations. In the later period
(1980-2002), there is evidence of competition among all of the larger deer in the oak-birch zone with, in particular, negative effects of red deer and sika deer on one-another, reinforcing the findings of our spatial analyses (Section 2.3.1). In the spruce-fir zone during that period, red and roe deer also showed positive responses to the numbers of sika deer in the oak-birch zone.
Although this is unlikely to be a direct effect, it might suggest that whatever factor underlies the
89
Table 4.5 Summary of best models describing dynamics of each population, determined using the methods of Dennis & Otten (2000). Parameters are summarised in Table 4.4.
Population (models in the confidence set a) Multi-model average b R2
Red deer, Oak-birch habitat, 1962-1979
1 - 3 dt = 0.08 - 0.17 Nt + 0.23 Nt-1 + 0.22 Oak - 0.32 WS - 0.19 AT 0.71
Red deer, Oak-birch habitat, 1980-2002
1 - 7 dt = - 0.04 Nt - 0.27 Roe - 0.05 Sika - 0.02 ST + 0.06 EP 0.50
Red deer, Korean pine-deciduous, 1962-1979
1 - 3 dt = - 0.03 - 0.39 xt - 0.06 ST - 0.06 AT - 0.32 WS - 0.26 RP 0.78
Red deer, Korean pine-deciduous, 1980-2002
1, 3 - 5, 7 dt = 0.04 - 0.19 xt - 0.15 WS + 0.03 VP - 0.01 ST - 0.08 SP 0.82
Red deer, Spruce-fir, 1962-1979
1 - 3 dt = - 0.25 - 0.32 xt + 0.31 WNPO + 0.10 VP - 0.50 RP 0.77
Red deer, Spruce-fir, 1980-2002
1 - 3, 5 dt = 0.19 - 0.67 xt + 0.26 Sika + 0.02 WNPO + 0.05 ST 0.55
Roe deer, Oak-birch habitat, 1962-1979
1 - 11 dt = 0.07 - 0.12 Nt + 0.24 Oak + 0.05 Red - 0.30 WS + 0.08 WC - 0.15 VT + 0.10 ST 0.55
Roe deer, Oak-birch habitat, 1980-2002
1, 4, 5, 7, 8, 12 - 14, 16, 19, 20 dt = - 0.01 - 0.41 Nt - 0.04 Nt-2 - 0.01 Sika - 0.01 WS + 0.01 VP - 0.01 ST - 0.02 SP + 0.04 EP 0.49
Roe deer, Korean pine-deciduous, 1980-2002
3 - 5 dt = 0.13 - 0.55 xt - 0.28 Lynx - 0.40 WS + 0.10 VT + 0.04 AT 0.84 (Table continues …)
Population (models in the confidence set a) Multi-model average b R2
Roe deer, Spruce-fir, 1980-2002
1 - 7, 10 dt = 0.08 - 0.95 xt + 0.07 xt-2 + 0.27 Red + 0.16 Sika + 0.04 AT - 0.07 EP - 0.06 IE 0.34
Sika deer, Oak-birch habitat, 1980-2002
1 dt = 0.38 - 0.96 xt + 0.60 xt-1 - 0.30 Red + 0.24 ST 0.77
Musk deer, Korean pine-deciduous, 1962-2002
1, 3, 6, 7, 9 dt = 0.02 - 0.34 Nt + 0.43 Nt-1 - 0.23 WC + 0.03 VT + 0.39 ST + 0.30 AT + 0.11 EP 0.51
Musk deer, Spruce-fir, 1962-2002
1 - 12 dt = 0.11 - 0.47 xt - 0.02 WS + 0.01 WC - 0.01 VT + 0.01 VP - 0.03 ST - 0.01 IE 0.50
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1962-1979
4 dt = 0.12 - 0.61 xt 0.45
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1980-2002
1 - 6 dt = - 0.07 - 0.58 xt + 0.07 AltMast + 0.11 WT + 0.09 WC - 0.04 SP + 0.07 AT + 0.40 EP 0.50
a Numbers of models in the confidence set refer to model numbers in the summary of all models in Appendix B. Some models reported in that summary were excluded for reasons given in the Appendix. b Average models clearly contain more parameters than any one model reported in Appendix B. Parameters are not shown, however, where the magnitude of their coefficients is less than 0.01.
Analysis of ungulate dynamics rapid increase in sika deer in the oak-birch zone also accounts for the increasing utilisation of the spruce-fir zone by red and roe deer. Intriguingly, roe deer show positive effects of red deer in two areas. Although the dominant interactions between these species tend to be negative, roe deer may benefit where red deer maintain paths through deep snow (Danilkin, 1995). Whether such an effect underlies our results is difficult to determine but might form the basis of an interesting behavioural study.
Oak mast featured as a factor in models of only a few populations, including red deer, roe deer and wild boar (see Table 4.5). In the case of wild boar (in the more recent period), the alternative mast index appeared to be more informative than the index of oak mast alone, underlining the importance of pine nuts to boar in years of low acorn availability. Pine mast alone did not feature as a positive effect in selected models but whether this reflects its relative unimportance, or the difficulty of accurate estimation of pine mast quality, it is currently impossible to say. In general, mast indices may be too coarse to capture the variation among years adequately, or they may become more revealing if reduced to fewer categories (to reflect more drastic differences between years). Predators also appeared in very few population models, with only lynx remaining as a strong negative influence on the growth of roe deer in the Korean pine-deciduous zone, 1980-2002. No other model for roe deer was as informative as for that population (note the lower R2 values in Table 4.5); it may be that survey error inhibited the accurate identification of influential factors in other roe deer populations, for which it seems likely that lynx are also important predators. That tigers did not emerge as an important factor for any of the populations may be associated with the relatively low impacts of tigers as predators
(see Section 6 and Miquelle et al., 2005). Alternatively, it may be that log-growth in the tiger population is a poor predictor of the impact that they have on prey populations during any biological year. Unfortunately, due to the highly non-stationary nature of tiger dynamics during the study period, absolute abundances of tigers are prone to spurious regressions with ungulate populations, and so could not be incorporated into our analyses.
92 Analysis of ungulate dynamics
Many relationships between weather variables and ungulate dynamics are possible, especially given the broad array of weather variables considered in our analyses. Winter weather variables appear in most of the averaged models in Table 4.5, typically with negative effects of cold snowy winters. These relationships are most pronounced for red and roe deer. Two curious exceptions to this general pattern are worth noting. First, musk deer in the Korean pine- deciduous zone seem to show a substantial negative reaction to milder, less snowy winters. It is possible that movement in these small deer is inhibited by warmer winters, when snow is softer and they may regularly break through the crust. More puzzling, is that all of the top models for wild boar prior to 1980 (many of which had high R2 values, indicative of high explanatory power; see Appendix 4B), contained parameters suggesting that milder winters with less precipitation inhibited population growth. These associations were rejected as potentially spurious, but it might be instructive to consider whether there could be biological support for such patterns, perhaps indirectly through an interaction between colder winters and food availability in spring, for example. Few other weather variables had strong influences on any populations and the consequences of given weather variables often varied between zones or periods. Such patterns may suggest non-linear effects and it may be beneficial to include non-linearities in subsequent, more detailed analyses of any specific population. One interesting feature of selected models for red deer, was that there appeared to be negative impacts of higher summer or annual temperatures in the oak-birch and Korean pine-deciduous zones, whilst increased temperatures led to population increases in the spruce-fir zone. This might suggest that rising summer temperatures are leading to a gradual northward shift in red deer in SAZ.
Finally, human impact factors appeared in a large number of models, suggesting that effective protection may be important for many of the ungulates in SAZ. The strongest effects were seen among red deer and wild boar but all species apart from sika deer showed some relationship with one of the indices of protection or poaching pressure. An unexpected relationship is that shown by musk deer in the Korean pine-deciduous zone, where the population
93 Analysis of ungulate dynamics appears to decline in response to increasingly effective protection. It is possible that musk deer
(which are one of the primary targets of poachers, due to the highly valued musk glands of males, e.g. Yang et al., 2003) have moved into the central belt, away from the oak-birch zone in more recent years, in response to increasing poaching pressure in that area (which, since receiving formal Zapovednik designation, may have been perceived as a potential haven for this prized species).
4.4 Discussion
In this section, we have demonstrated a seasonal decline in the rate at which tracks of several ungulate species are encountered, with important implications for winter surveys of ungulates.
We have also assessed the longer term, temporal dynamics of ungulates in SAZ, shedding further light on the trajectories of different populations in the area, their interactions, and the factors that affect their growth. Importantly, we have used the data from SAZ to provide evidence for the role of density dependent effects in several populations. Whilst the influence of density dependence on population dynamics is generally accepted to be widespread, evidence for this is notoriously difficult to derive. That we have done so here, underlines the value of rigorously collected, long term data sets, such as that from SAZ.
4.4.1 Within-year variation in track encounters
Seasonal declines in track encounter rates suggest that consistency in the timing of surveys is crucial for providing data that are comparable from one year to the next. In Section 3.3.1, we assessed the effect of time of year on the movement of ungulates. Models based on time of year received some support for red deer and strong support for roe deer (Table 3.2). With the limited
24-hour movement data available, it is currently difficult to interpret the importance of time of year as a factor underlying decreasing track encounters over winter. It is likely that changes in encounter rate throughout the sampling period are partially attributable to changes in movement
94 Analysis of ungulate dynamics behaviour but, at least for red deer, the measured decrease in daily travel distances is not sufficient to account for the magnitude of observed declines in track encounters. Declines in track encounters may also reflect changes in density, due either to mortality or migration. That no commensurate increases in encounter rate were seen in any part of SAZ suggests that migration is unlikely to account for the observed patterns. Although it is possible that, as winter progresses, ungulates move to some part of SAZ that is not surveyed thoroughly, radio-tracking data do not provide evidence of large-scale movements during the winter seasons. Fall migrations occur in October and November, and red deer remain within small winter home ranges until late April (Myslenkov and Miquelle, unpubl. data). As more data (especially radio-tracking data) on ungulate daily movements become available, it should become possible to determine whether changes in distribution or travel distance are likely to affect track encounter rates.
Randomised survey routes in areas that are rarely surveyed would also help to establish whether seasonal changes in ungulate distributions play a role in the observed declines in track encounter rates over winter.
4.4.2 Linear trend analyses
Linear trend analyses must be interpreted with some caution, owing to the influence of the placement of period boundaries. Our choice of period boundaries was motivated solely by the aim of establishing trends over five-year periods when survey effort was high, and longer periods
(of ten or twenty years) when survey effort was lower. Bootstrapping led to generally narrow confidence intervals for the more numerous species but, given the importance of outliers for sika deer at least (as determined by subsequent analyses, see Section 4.3.3), could have been supplemented with jackknifing to generate confidence intervals even more robust to erroneous data points.
These concerns aside, the trend analyses revealed some important patterns in the trajectories of ungulate populations in SAZ. There were strong similarities between the trends of
95 Analysis of ungulate dynamics several populations, suggesting that these populations respond to similar factors, and providing additional support for the accuracy of density estimation, at least as a temporally-relative measure. In particular, red deer and roe deer showed very similar trajectories in all three zones of
SAZ. In the oak-birch zone, their pronounced increases from the early 1960s to the early 1990s, were followed by general declines over the next decade, most marked in the red deer population of that zone. The same pattern was seen in wild boar in all zones of SAZ and is in contrast to the almost exponential increase of sika deer in the oak-birch zone over the last decade of this data set.
These trends add weight to the developing picture of strong competition between sika and red deer, which was further emphasised by the results of the time series analyses. The most disturbing pattern evident from the trend analyses, is the abrupt and widespread decline in wild boar numbers over the last decade. Time-series analyses suggested that wild boar may be negatively affected by recent reductions in effective protection within SAZ. Although boar are among the rarest ungulates in SAZ, they are surprisingly frequently encountered, suggesting that they will be highly vulnerable to opportunistic poachers. This situation is likely to be exacerbated by the fact that boar are concentrated in the Oak-birch zone along the coast, closest to centres of human population and most accessible to hunters.
4.4.3 Density dependence
The results of our tests for density dependence are important for several reasons. Perhaps the most significant, is the development of a robust and relatively powerful approach to testing for density dependence. Although we have not developed a formal inferential framework here, additional work (P.A. Stephens, unpublished data) shows that the test could be substantially more powerful than existing alternatives (e.g. see Shenk et al., 1998). Previous tests have tended to consider only data sets consisting of a single annual estimate, but it seems likely that a large proportion of long term data sets contain far more information about the structure of survey error than this would imply. Our test is novel in permitting the structure of that error to be mapped on
96 Analysis of ungulate dynamics to simulated data sets and, by using bootstrapping, to determine whether the error was sufficient to have generated the observed properties of autoregression. The majority of existing tests show an increase in power with increasing sample size (number of years) but the benefits of this are undermined by the rapid increases in Type I error rates that also result (Shenk et al., 1998;
Vickery & Nudds, 1984). Crucially, there is no reason why our test should be vulnerable to such increases in Type I error, rendering it increasingly useful with longer data sets. Several authors have discussed the robustness of tests for density dependence in relation to the ratio of within- year CV (coefficient of variation) to between-years CV (Forchhammer et al., 2002; Freckleton et al., in prep.; Shenk et al., 1998). Generally, if within-year CV is small relative to between-years
CV, then census error is minor and tests for density dependence should be robust to census error
(Forchhammer et al., 2002). However, when samples are drawn from an intractable distribution with a significant proportion of zeros, CV estimation is invalid; in these cases, bootstrapping offers the only powerful method for assessing the consequences of error.
Overall, half of the populations examined showed some evidence for direct density dependence using our bootstrapped test. That the other populations did not show such evidence could arise either because density dependence in the species is relatively weak, or because their populations are currently held at levels below where intraspecific competition depresses growth rate. Several authors have noted that ungulates and other large mammals tend to exhibit ‘ramped’ transient dynamics, meaning that there is very little density regulation up to a relatively high proportion of the potential carrying capacity of the environment, above which density acts strongly to inhibit population growth (Fowler, 1981, 1987; McCullough, 1992). Interspecific competition, in particular, can obscure the effects of direct density dependence and it is noticeable that roe deer, which appear to experience negative impacts from red deer and sika deer in various areas (Table 4.5), showed no sign of direct density dependence in any zone of SAZ. Sika deer also showed no sign of direct density dependence. That this was the case is perhaps unsurprising, given the nature of an expanding population that is new to the environment, and evidenced by the
97 Analysis of ungulate dynamics near-exponential increase in sika deer numbers over the past decade. Until the last decade, the species was rare and it exists presently only in the oak-birch zone, where it is still not abundant
(little more than 1 km-2 by the end of the study period). We predict, however, that as the population continues to grow towards a density more like that of red deer in the oak-birch zone
(which have, at times, exceeded 6 to 7 km-2), direct density dependence will be detectable in this population.
4.4.4 Time-series analysis
Our time series analyses represent the first formal attempts to assess a full range of parameters that could affect the dynamics of ungulate populations within SAZ. Proponents of model selection theory place a strong emphasis on a priori model design, generally assuming that there will be good prior reasons for the inclusion or rejection of certain parameters (e.g. Burnham &
Anderson, 2002). Unfortunately, reality is often different in that, of a large number of putative influences, there is little reason to assume that one may be of greater importance than another.
Our study is an example of this situation: we had no strong reasons to select one particular weather covariate, one human impact index or, indeed, one autoregressive order, over potential alternatives. Similarly, although we could have minimised the number of competitive species terms within candidate models, there is little to suggest that roe deer might compete more with red deer than sika deer, for example. The consequence of these problems is that, even using our strategy of permitting a maximum of one winter weather covariate and one human impact factor in any one candidate model, large numbers of models were compared for each data set. AIC provides a powerful means of balancing the conflicting goals of simplicity and goodness of fit
(Johnson & Omland, 2004; Stephens et al., 2005) and, using this in conjunction with a limit of four parameters in any one model, we minimised the risks of substantial overfitting.
Nevertheless, the danger of overfitting remains because, with 20 or more parameters appearing in the different candidate models (albeit never in the same one), it was highly probable that, even by
98 Analysis of ungulate dynamics chance, one parameter or more would fit the data well (see Ginzburg & Jensen, 2004, for example). This is not a problem unique to our study. Assessing a 25 year time series of mule deer abundance, Peek et al. (2002) assessed models with up to seven covariates and an autoregressive term, generating a very large number of models that could be fitted to the data.
More spectacularly, Lubow & Smith (2004) compared models with from 12 to 70 parameters to explain a 23 year time series of data on the population dynamics of the Jackson elk herd, finding a best-supported model with 25 parameters. This approach stands in contrast to the observation that a model with 10 parameters could fit almost any 25 year time series (Ginzburg & Jensen,
2004). One way to overcome these problems, is to use model averaging (Burnham & Anderson,
2002). Using this technique, only parameters that consistently appear with the same sign in the set of best models will appear to have a strong influence in the multi-model average.
Consequently, the remainder of our discussion is based on averaged models derived by this process (Table 4.5).
Populations varied greatly in the degree to which selected models explained observed dynamics. Given the many potential sources of error in converting track counts into annual estimates of density, it is pleasing that biologically meaningful models described several populations (including the sika deer population, four red deer populations and one roe deer population) very well. Poorer model fits for musk deer, wild boar and some lower-density roe deer populations may be a consequence of overwhelming observation error in the data on these populations, which inhibits meaningful interpretation of the underlying processes. Low density, substantial aggregative behaviour and, in the case of musk deer, limited information about their movements, may well underlie the noise in these data sets. In most cases, more intensive study would be required to generate data of a quality that would permit detailed analyses of the factors affecting growth among these populations. Whether such intensive studies would be worthwhile depends strongly on the goals of the Zapovednik monitoring system and, in particular, whether time-series analysis is a priority. An alternative explanation for poorer model fits, is that the
99 Analysis of ungulate dynamics dynamics of these species are too complex to be captured by the simplistic linear models we used in our analyses. As these were the first time-series analyses conducted using the data on ungulates in SAZ, their findings may be viewed as preliminary. More detailed studies conducted in the future could incorporate non-linearities (especially among weather variables, as discussed in Section 4.3.4) and interactions among covariates.
We have commented on the detailed findings of our time-series analyses in Section 4.3.4.
Here, we comment more broadly on three important processes assessed in that section: lagged density dependence, impacts of weather, and impacts of protection from human depredations.
Overall, density dependence, including lagged density dependent terms, emerged as an important process for many populations, in keeping with many other studies of ungulates (see Table 4.1).
The positive effects of previous population sizes for growing populations are unsurprising. For example, sika deer attain sexual maturity between months 16 and 18 after birth (Danilkin, 1995) and, consequently, where reproductive potential is the limiting factor for population growth, population at time t is likely to have less of a bearing on population growth from time t to t+1, than population size at time t-1. That this emerged as the strongest example of lagged density dependence, whilst other tests showed no support for the action of direct density dependence, is compelling support for this explanation. By contrast, the musk deer population did not appear to be increasing throughout the study period, and musk deer showed evidence of direct (Table 4.3) as well as delayed (Table 4.5) density dependence. Alternative explanations for lagged density dependence often invoke interactions with other trophic groups (Forchhammer et al., 2002; Post et al., 2002; Stenseth et al., 1998), especially where there is strong coupling between trophic groups (Bjornstad et al., 2001); delayed climatic effects (Forchhammer et al., 2001) including carry-over effects from poor nutritional status of cohorts (Beckerman et al., 2002; Berryman,
1992); differential effects of density on age or sex classes (Gaillard et al., 1998; Mysterud et al.,
2002); and the impacts of territoriality (Erb et al., 2001). At present, it is hard to say which of these is most likely to affect musk deer.
100 Analysis of ungulate dynamics
For most of the populations analysed, winter weather covariates typically had the strongest effects of any of the weather covariates. In general, these effects were in the expected directions but the apparent benefits of colder, snowier winters for wild boar before 1980 are perplexing and may merit further consideration. In Section 3.3.1, we showed that wild boar are the only species for which existing data show a strong influence of snow depth on daily travel.
The effect was most striking in the Korean pine-deciduous zone, where boar daily movement distances were much greater in shallower snow. It seems likely that deep snow inhibits both boar movement and boar foraging to a greater degree than it inhibits these behaviours in the deer species. It would be surprising, therefore, if wild boar were positively affected by colder, snowier winters. Negative effects of severe winters have been seen in studies of wild boar in other parts of Russia (Markov, 1997) and Europe (Jedrzejewska et al., 1996). For all of these reasons, we rejected the possibility of positive effects of winter severity, as most likely arising from spurious regressions.
Finally, we noted above that human impact variables appeared in the averaged models for many (over half) of the studied populations, including at least one model of each species.
Deriving indices that accurately reflect human impacts within the Zapovednik is complex and there may be no way to quantify the exact level of illicit practices that are inevitably conducted in a way to avoid detection. Nevertheless, our analyses suggest that human impacts may be important variables affecting the dynamics of all the ungulates of SAZ. Recent declines in numbers of boar (possibly in response to reductions in anti-poaching measures) are disturbing and point to the necessity of maintaining the high level of protection with which the Zapovednik system is associated.
101
Appendix 4A
The following table summarises the variables used in global models for each population studied by time-series analysis (see further in Sections 4.2.4, 4.2.5, 4.2.6 and 4.3.4). General hypothesised effects are noted in the table, indicating where a variable is likely to have a positive effect (↑), a negative effect (↓), or where it could affect changes in population size in either way (-). Typically, where models received good support but included variables that did not conform to prior hypothesised effect directions, they were rejected (see further in Appendix 4B). No prior hypotheses were made about the effects of lagged density dependence, as these depend on the stage of population development and other aspects of the interaction of a species with its environment. Although the dominant effects of competitors are likely to be negative, other effects are possible, especially for roe deer, for example, which can benefit from the presence of larger ungulates if this results in paths being kept open through deep snow (Danilkin, 1995). Consequently, we did not automatically reject models that suggested positive interactions between species. Similarly, sika deer (which are essentially limited to the oak-birch zone) were included as potential factors in red deer and roe deer analyses after 1980, even in other zones. Some biologists believe that sika deer displace other deer from favoured habitats, so the effects in these other zones may be complex. Finally, the dominant effects of human impact factors are also given. These effects may also vary between zones, especially where, for example, increases in human pressure in more accessible areas drive populations into less accessible areas. Again, therefore, models which did not conform to the hypothesised effects given here for human impact variables, were not automatically rejected.
Table 4A.1 Variables included in the time-series analyses for each population. Abbreviations for zone are: OB, oak-birch habitat; KD, Korean pine-deciduous habitat; SF, spruce-fir habitat. Variable codes are as summarised in Table 4.4
Species Red deer Red deer Red deer Red deer Red deer Red deer Roe deer Roe deer Roe deer Roe deer Sika deer Musk Musk Wild boar Wild boar deer deer Zone OB OB KD KD SF SF OB OB KD SF OB KD SF OB&KD OB&KD Period Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Post-1980 Post-1980 Post-1980 Full Full Pre-1980 Post-1980
Variable
Nt ↓ ↓ ↓ ↓ ↓
Nt-1 - - - - -
Nt-2 - - - - - xt ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ xt-1 ------xt-2 ------
Red ↓ ↓ ↓ ↓ ↓ Roe ↓ ↓ ↓ ↓ ↓ ↓ Sika ↓ --↓ -- Rdnt ↓ ↓
Oak ↑ ↑ ↑ ↑ ↑ ↑ ↑ Pine ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ AltMast ↑ ↑
Tig ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ Lynx ↓ ↓ ↓ ↓ ↓ ↓ (Table continues …)
Species Red deer Red deer Red deer Red deer Red deer Red deer Roe deer Roe deer Roe deer Roe deer Sika deer Musk Musk Wild boar Wild boar deer deer Zone OB OB KD KD SF SF OB OB KD SF OB KD SF OB&KD OB&KD Period Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Post-1980 Post-1980 Post-1980 Full Full Pre-1980 Post-1980
Variable
WS ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ WT ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ WC ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ VT ------VP ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ST ------SP ------AT ------WNPO ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑
RP ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ IE ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ EP ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑
Appendix 4B
The following table summarises the best-supported models selected by time-series analysis for each population. The best-supported model (with lowest AIC value) and those within two AIC units of it are shown. In two cases (roe deer in Korean pine-deciduous habitat, 1980-2002 and wild boar in oak-birch and Korean pine-deciduous habitats, 1962-1979) no model in the top set (within two AIC units of the best model) made biological sense (for reasons given in the Comments column). In these cases, the best biologically-supported model and those within two AIC units of it are also shown.
Table 4B.1 Best-supported models selected by time-series analysis of each population. Some models were rejected from the confidence set for reasons given in the Comments column
2 Model (number: structure) nKAICc ∆AICc wi R Comments
Red deer, Oak-birch habitat, 1962-1979
01: dt = 0.06 + 0.18 Nt-1 + 0.33 Oak - 0.33 WS - 0.30 AT 17 6 -39.83 0.00 0.40 0.78
02: dt = 0.08 + 0.25 Oak - 0.29 WS - 0.19 AT 18 5 -39.52 0.31 0.35 0.64
03: dt = 0.12 - 0.66 Nt + 0.63 Nt-1 - 0.37 WS 17 5 -38.87 0.96 0.25 0.70
Red deer, Oak-birch habitat, 1980-2002
01: dt = - 0.00 - 0.53 Roe + 0.25 EP 20 4 -18.86 0.00 0.22 0.52
02: dt = - 0.00 - 0.28 Nt - 0.34 Roe 20 4 -18.58 0.27 0.19 0.51
03: dt = - 0.00 - 0.49 Roe 20 3 -17.82 1.04 0.13 0.41
04: dt = - 0.00 - 0.51 Roe - 0.21 ST 20 4 -17.76 1.10 0.13 0.49
05: dt = - 0.00 - 0.51 Roe - 0.21 Sika 20 4 -17.74 1.12 0.13 0.49
06: dt = - 0.00 - 0.20 Nt - 0.41 Roe + 0.18 EP 20 5 -17.31 1.54 0.10 0.56
07: dt = - 0.00 - 0.53 Roe - 0.15 ST + 0.20 EP 20 5 -17.07 1.78 0.09 0.55
Red deer, Korean pine-deciduous, 1962-1979
01: dt = - 0.03 - 0.39 xt - 0.13 ST - 0.25 RP 16 5 -39.66 0.00 0.47 0.80
02: dt = - 0.03 - 0.39 xt - 0.13 AT - 0.28 RP 16 5 -38.90 0.76 0.32 0.79
03: dt = - 0.03 - 0.39 xt - 0.24 RP 16 4 -38.03 1.64 0.21 0.72
Red deer, Korean pine-deciduous, 1980-2002
01: dt = 0.07 - 0.34 xt - 0.27 WS - 0.17 SP 22 5 -53.68 0.00 0.26 0.81
02: dt = 0.07 - 0.35 xt - 0.37 WS + 0.14 VP + 0.13 RP 22 6 -52.78 0.90 0.17 0.83 Possible spurious relationship with reports of poaching
03: dt = 0.07 - 0.37 xt + 0.08 Sika - 0.25 WS - 0.16 SP 22 6 -52.38 1.29 0.14 0.83
04: dt = 0.07 - 0.41 xt + 0.11 Roe - 0.26 WS - 0.15 SP 22 6 -52.05 1.62 0.12 0.83
05: dt = 0.07 - 0.35 xt - 0.29 WS + 0.07 VP - 0.14 SP 22 6 -52.01 1.67 0.11 0.83
06: dt = 0.07 - 0.36 xt - 0.26 WS - 0.16 SP - 0.07 EP 22 6 -51.76 1.92 0.10 0.83 Possible spurious relationship with efficacy of protection
07: dt = 0.07 - 0.34 xt - 0.27 WS - 0.06 ST - 0.18 SP 22 6 -51.74 1.94 0.10 0.83 (Table continues …)
2 Model (number: structure) nKAICc ∆AICc wi R Comments
Red deer, Spruce-fir, 1962-1979
01: dt = - 0.25 + 0.60 WNPO - 0.71 RP 11 4 -7.05 0.00 0.52 0.79
02: dt = - 0.25 - 0.61 xt - 0.50 RP 11 4 -5.66 1.38 0.26 0.76
03: dt = - 0.25 - 0.72 xt + 0.46 VP 11 4 -5.33 1.72 0.22 0.75
Red deer, Spruce-fir, 1980-2002
01: dt = 0.19 - 0.71 xt + 0.32 Sika 19 4 -21.14 0.00 0.31 0.56
02: dt = 0.19 - 0.72 xt + 0.34 Sika + 0.18 ST 19 5 -20.47 0.67 0.22 0.61
03: dt = 0.19 - 0.49 xt 19 3 -20.13 1.01 0.19 0.45
04: dt = 0.19 - 0.68 xt + 0.27 Roe 19 4 -19.90 1.24 0.17 0.53 Possible spurious relationship with roe deer
05: dt = 0.19 - 0.80 xt + 0.40 Sika + 0.15 WNPO 19 5 -19.20 1.94 0.12 0.59
Roe deer, Oak-birch habitat, 1962-1979
01: dt = 0.07 + 0.33 Oak - 0.43 WS - 0.25 VT + 0.24 ST 17 6 -15.20 0.00 0.15 0.64
02: dt = 0.07 + 0.34 Oak - 0.33 WS 17 4 -14.85 0.35 0.13 0.42
03: dt = 0.07 + 0.34 Oak - 0.36 WS + 0.23 ST 17 5 -14.82 0.38 0.13 0.53
04: dt = 0.07 + 0.33 Oak - 0.40 WS - 0.24 VT 17 5 -14.69 0.51 0.12 0.52
05: dt = 0.07 - 0.45 Nt + 0.30 Red + 0.37 WC - 0.32 VT 17 6 -14.05 1.15 0.09 0.62
06: dt = 0.07 + 0.22 Red + 0.39 Oak - 0.39 WS - 0.30 VT 17 6 -13.79 1.41 0.08 0.61
07: dt = 0.07 - 0.32 Nt + 0.33 WC 17 4 -13.49 1.71 0.06 0.37
08: dt = 0.07 - 0.42 Nt + 0.32 Red - 0.36 WS - 0.32 VT 17 6 -13.46 1.74 0.06 0.60
09: dt = 0.07 - 0.20 Nt-1 + 0.32 Oak - 0.35 WS + 0.30 ST 17 6 -13.43 1.77 0.06 0.60
10: dt = 0.07 - 0.20 Nt + 0.26 Oak - 0.36 WS + 0.25 ST 17 6 -13.34 1.87 0.06 0.60
11: dt = 0.07 - 0.32 Nt + 0.40 WC - 0.25 VT 17 5 -13.33 1.87 0.06 0.48 (Table continues …)
2 Model (number: structure) nKAICc ∆AICc wi R Comments
Roe deer, Oak-birch habitat, 1980-2002
01: dt = - 0.01 - 0.40 Nt 22 3 -31.29 0.00 0.09 0.44
02: dt = - 0.01 - 0.41 Nt - 0.16 Nt-2 - 0.19 Oak + 0.19 EP 22 6 -31.09 0.20 0.08 0.63 Possible spurious relationship with oak mast
03: dt = - 0.01 - 0.43 Nt - 0.18 Oak + 0.19 EP 22 5 -31.03 0.26 0.08 0.57 Possible spurious relationship with oak mast
04: dt = - 0.01 - 0.38 Nt - 0.15 Nt-2 22 4 -31.00 0.29 0.08 0.50
05: dt = - 0.01 - 0.43 Nt + 0.13 EP 22 4 -30.40 0.89 0.06 0.49
06: dt = - 0.01 - 0.40 Nt - 0.12 Oak 22 4 -30.21 1.07 0.05 0.48 Possible spurious relationship with oak mast
07: dt = - 0.01 - 0.42 Nt - 0.12 ST 22 4 -30.20 1.08 0.05 0.48
08: dt = - 0.01 - 0.41 Nt - 0.15 Nt-2 + 0.13 EP 22 5 -30.03 1.26 0.05 0.55
09: dt = - 0.01 - 0.37 Nt - 0.15 Nt-2 - 0.13 Oak 22 5 -29.95 1.34 0.05 0.55 Possible spurious relationship with oak mast
10: dt = - 0.01 - 0.40 Nt - 0.19 Oak - 0.13 WS + 0.20 EP 22 6 -29.91 1.37 0.04 0.61 Possible spurious relationship with oak mast
11: dt = - 0.01 - 0.48 Nt - 0.17 Oak - 0.14 SP + 0.23 EP 22 6 -29.82 1.46 0.04 0.61 Possible spurious relationship with oak mast
12: dt = - 0.01 - 0.38 Nt - 0.11 WS 22 4 -29.80 1.49 0.04 0.47
13: dt = - 0.01 - 0.49 Nt - 0.16 SP + 0.18 EP 22 5 -29.77 1.52 0.04 0.54
14: dt = - 0.01 - 0.42 Nt - 0.11 Sika 22 4 -29.75 1.54 0.04 0.47
15: dt = - 0.01 - 0.42 Nt - 0.14 Sika - 0.16 Oak 22 5 -29.45 1.83 0.04 0.54 Possible spurious relationship with oak mast
16: dt = - 0.01 - 0.43 Nt - 0.09 SP 22 4 -29.43 1.86 0.04 0.47
17: dt = - 0.01 - 0.42 Nt + 0.09 IE 22 4 -29.43 1.86 0.04 0.47 Possible spurious relationship with illegal entries
18: dt = - 0.01 - 0.45 Nt - 0.20 Oak + 0.12 VT + 0.22 EP 22 6 -29.41 1.87 0.03 0.60 Possible spurious relationship with oak mast
19: dt = - 0.01 - 0.39 Nt + 0.09 VP 22 4 -29.35 1.94 0.03 0.46
20: dt = - 0.01 - 0.40 Nt - 0.15 Nt-2 - 0.11 Sika 22 5 -29.29 2.00 0.03 0.53 (Table continues …)
2 Model (number: structure) nKAICc ∆AICc wi R Comments
Roe deer, Korean pine-deciduous, 1980-2002
01: dt = 0.13 - 0.66 xt - 0.32 Lynx - 0.42 WS + 0.26 RP 20 6 -31.46 0.00 0.64 0.87 Possible spurious relationship with reports of poaching
02: dt = 0.13 - 0.52 xt - 0.22 Pine - 0.34 Lynx - 0.44 WS 20 6 -30.26 1.19 0.36 0.86 Possible spurious relationship with pine mast
03: dt = 0.13 - 0.54 xt - 0.27 Lynx - 0.38 WS + 0.20 VT 20 6 -28.71 2.74 0.16 0.85
04: dt = 0.13 - 0.54 xt - 0.27 Lynx - 0.44 WS 20 5 -27.45 4.00 0.09 0.81
05: dt = 0.13 - 0.60 xt - 0.34 Lynx - 0.42 WS + 0.17 AT 20 6 -26.87 4.59 0.07 0.84
Roe deer, Spruce-fir, 1980-2002
01: dt = 0.06 - 1.12 xt + 0.80 Red 16 4 0.07 0.00 0.15 0.35
02: dt = 0.06 - 1.04 xt + 0.72 Sika 16 4 0.15 0.08 0.14 0.34
03: dt = 0.06 - 0.43 xt 16 3 0.33 0.26 0.13 0.19
04: dt = 0.29 - 1.01 xt + 0.62 xt-2 13 4 0.82 0.75 0.10 0.46
05: dt = 0.06 - 1.53 xt + 1.13 Red + 0.39 AT 16 5 0.88 0.81 0.10 0.46
06: dt = 0.06 - 0.98 xt - 0.64 EP 16 4 1.02 0.95 0.09 0.31
07: dt = 0.06 - 0.52 xt - 0.34 IE 16 4 1.11 1.05 0.09 0.30
08: dt = 0.06 - 1.33 xt + 0.83 Sika + 0.37 RP 16 5 1.38 1.31 0.08 0.44 Possible spurious relationship with reports of poaching
09: dt = 0.06 - 1.11 xt + 0.89 Sika - 0.32 Pine 16 5 1.57 1.50 0.07 0.43 Possible spurious relationship with pine mast
10: dt = 0.06 - 1.04 xt + 0.64 Sika - 0.29 IE 16 5 1.91 1.85 0.06 0.42
Sika deer, Oak-birch habitat, 1980-2002
01: dt = 0.38 - 0.96 xt + 0.60 xt-1 - 0.30 Red + 0.24 ST 16 6 -23.66 0.00 1.00 0.77 (Table continues …)
2 Model (number: structure) nKAICc ∆AICc wi R Comments
Musk deer, Korean pine-deciduous, 1962-2002
01: dt = 0.04 - 0.68 Nt + 0.65 Nt-1 + 0.63 ST 22 5 -3.99 0.00 0.19 0.54
02: dt = - 0.01 - 0.43 Nt + 0.63 ST + 0.48 RP 23 5 -3.43 0.56 0.14 0.50 Possible spurious relationship with reports of poaching
03: dt = - 0.01 - 0.56 WC + 0.73 AT 23 4 -3.39 0.60 0.14 0.43
04: dt = - 0.10 - 0.40 Nt-2 + 0.48 VP + 0.54 ST + 0.61 RP 22 6 -2.47 1.52 0.09 0.58 Possible spurious relationship with reports of poaching
05: dt = 0.03 - 0.69 Nt + 0.49 Nt-1 + 0.62 ST + 0.27 RP 22 6 -2.41 1.58 0.08 0.58 Possible spurious relationship with reports of poaching
06: dt = - 0.07 + 0.03 Nt-2 - 0.59 WC + 0.79 AT 22 5 -2.28 1.71 0.08 0.50
07: dt = 0.04 - 0.78 Nt + 0.68 Nt-1 + 0.21 VT + 0.65 ST 22 6 -2.20 1.78 0.08 0.58
08: dt = 0.03 - 0.65 Nt + 0.60 Nt-1 + 0.20 Lynx + 0.64 ST 22 6 -2.08 1.91 0.07 0.57 Possible spurious relationship with lynx
09: dt = 0.06 + 0.92 Nt-1 + 0.69 ST + 0.88 EP 22 5 -2.01 1.98 0.07 0.50
10: dt = - 0.05 - 0.64 Nt + 0.32 Nt-2 + 0.59 ST + 0.50 RP 22 6 -1.99 2.00 0.07 0.57 Possible spurious relationship with reports of poaching
Musk deer, Spruce-fir, 1962-2002
01: dt = 0.11 - 0.46 xt 36 3 -49.33 0.00 0.16 0.48
02: dt = 0.11 - 0.44 xt - 0.10 ST 36 4 -48.32 1.00 0.10 0.50
03: dt = 0.11 - 0.47 xt - 0.09 IE 36 4 -48.30 1.03 0.10 0.50
04: dt = 0.11 - 0.48 xt - 0.08 VT 36 4 -48.00 1.33 0.08 0.50
05: dt = 0.11 - 0.47 xt + 0.08 VP 36 4 -47.93 1.40 0.08 0.50
06: dt = 0.11 - 0.48 xt - 0.08 WS 36 4 -47.90 1.43 0.08 0.49
07: dt = 0.11 - 0.47 xt + 0.08 WC 36 4 -47.85 1.48 0.08 0.49
08: dt = 0.11 - 0.45 xt + 0.12 WC - 0.13 ST 36 5 -47.76 1.56 0.07 0.53
09: dt = 0.11 - 0.45 xt - 0.11 WS - 0.12 ST 36 5 -47.46 1.86 0.06 0.52
10: dt = 0.11 - 0.46 xt + 0.06 EP 36 4 -47.42 1.91 0.06 0.49
11: dt = 0.11 - 0.47 xt + 0.05 WT 36 4 -47.39 1.94 0.06 0.49
12: dt = 0.11 - 0.50 xt - 0.12 WS + 0.12 VP 36 5 -47.38 1.94 0.06 0.52 (Table continues …)
2 Model (number: structure) nKAICc ∆AICc wi R Comments
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1962-1979
01: dt = - 0.08 + 0.34 xt-1 - 0.86 WC 13 4 -10.37 0.00 0.70 0.69 Possible spurious relationships with winter weather variables
02: dt = - 0.10 + 0.42 xt-1 + 0.24 Oak - 0.86 WC 13 5 -8.72 1.65 0.30 0.76 Possible spurious relationships with winter weather variables
03: dt = 0.12 - 0.40 xt + 0.37 WS 15 4 -8.03 2.34 0.22 0.57 Possible spurious relationships with winter weather variables
04: dt = 0.12 - 0.61 xt 15 3 -7.83 2.54 0.20 0.45
05: dt = - 0.10 + 0.38 xt-1 + 0.18 AltMast - 0.88 WC 13 5 -7.53 2.84 0.17 0.73 Possible spurious relationships with winter weather variables
06: dt = - 0.07 + 0.72 xt-1 - 0.38 Rdnt - 0.77 WC 11 5 -7.46 2.90 0.16 0.85 Possible spurious relationships with winter weather variables
07: dt = 0.12 + 0.60 WS 15 3 -7.41 2.96 0.16 0.44 Possible spurious relationships with winter weather variables
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1980-2002
01: dt = - 0.07 - 0.48 xt + 0.32 WC + 0.38 EP 22 5 -12.52 0.00 0.29 0.50
02: dt = - 0.07 - 0.60 xt + 0.31 WT + 0.40 EP 22 5 -11.88 0.64 0.21 0.49
03: dt = - 0.07 - 0.67 xt + 0.24 AltMast + 0.33 WT + 0.33 EP 22 6 -11.08 1.44 0.14 0.55
04: dt = - 0.07 - 0.53 xt - 0.28 SP + 0.42 EP 22 5 -11.02 1.51 0.14 0.47
05: dt = - 0.07 - 0.74 xt + 0.29 AltMast + 0.37 AT + 0.45 EP 22 6 -10.63 1.89 0.11 0.54
06: dt = - 0.07 - 0.63 xt + 0.30 AT + 0.50 EP 22 5 -10.56 1.97 0.11 0.46
Analysis of ungulate dynamics
5. SURVEY PROTOCOL
5.1 Background
Although winter transect counts have been employed in SAZ for over four decades, a rigorous analysis of the power of this approach to monitoring large ungulates, together with its associated error, has not previously been conducted. Such an analysis is necessary to focus attention on the aims and possibilities of the survey and, ultimately, to guide ongoing development of the survey protocol. In this section, we present an analysis of the current survey design, with an emphasis on two aspects of design: minimising zero counts and determining required total survey effort.
Following Hayward et al. (2002), we began by assessing the length of transect segments required to reduce the proportion of zero counts (i.e. instances when no tracks of a given species are recorded along an entire transect segment). The importance of zero counts depends on the type of analysis to which the data are subject. However, for many analyses (particularly those which rely on distributional assumptions) zeros can pose a significant hindrance. This is especially the case where it is desirable to conduct parametric statistical analyses that rely on normality in data. Large numbers of zeros can substantially skew data away from normality and cannot be transformed to a normal distribution. The result is that zero counts are problematic in surveys, as they increase the need to amalgamate transect segments for meaningful analysis, reducing the potential for finer-scale analysis. Secondly, we explored the relationship between mean track encounter rate and the total length of transects (the “survey effort”) required annually to approximate the mean track encounter rate. This allowed us to estimate the error associated with estimates of the density of different species, as a function of annual survey effort. Finally, we also conducted a power analysis to determine the amount of error in annual estimates that can be tolerated, if abundance trends of given magnitude are to be detected. By combining this power analysis with our estimates of the relationship between error and survey effort, we were able to identify the survey effort required to detect trends for each of the ungulate species in SAZ.
112 Analysis of ungulate dynamics
5.2 Methods
5.2.1 Zero counts and the length of transect segments
To assess the relationship between transect segment length and the probability with which zero tracks were encountered, we relied on the results of our simulations (Section 3.2.6). These showed that the probability with which zero, one or more unique movement paths are encountered along a transect can be predicted using a Poisson probability distribution of the form:
(λ ⋅ D ⋅ S)Y P(Y ) = e−(λ⋅D⋅S ) (5.1) Y! where Y is the number of unique paths encountered, D is the density of animals making tracks, S is transect segment length and λ is the mean rate at which animal paths are encountered when
S = 1 km and D = 1 km-2. Using this equation, it is possible to predict transect segment lengths required to keep the proportion of zeros below some threshold, again as a function of density. We did this for each species and, where appropriate (as dictated by the findings in Section 3.3.1), combinations of relevant conditions (see estimates of λ in Table 3.6).
5.2.2 Survey effort and associated error
To determine the relationship between survey effort and uncertainties in density estimation, we assessed the field data. Specifically, we examined how increases in field data sample sizes led to increases in the accuracy with which the mean encounter rate was approximated. To do this, we used areas and years for which the most data had been collected (i.e. those years in which at least
50 transects had been conducted). By re-sampling with replacement, we effectively bootstrapped the mean track encounter rates on these samples but, rather than being interested in achieving a consistent mean, we were interested in the total length of samples required in order to provide a good approximation of the mean. For example, 51 transects were conducted in Korean pine- deciduous habitat in 1967. Fig. 5.1 shows ten bootstraps of the mean encounter rate of red deer,
113 Analysis of ungulate dynamics obtained by sequentially adding random transects to a sample. It is apparent that even with very large samples (as much as 3,000 km of transects) there remains some variation in the mean encounter rate. However, it is also evident that while variation initially declines rapidly as total survey length increases, that decline soon becomes very gradual. In the case illustrated (red deer with a mean encounter rate of approximately 1.44 km-1), increases in survey effort beyond approximately 500 km bring very little gain in terms of a more accurate approximation of the mean.
4.0
3.5
) 3.0 -1 km ( 2.5
2.0
1.5
1.0
Mean encounterrate 0.5
0.0 0 500 1000 1500 2000 2500 3000 Sample effort (km)
Figure 5.1. Ten bootstraps (black lines) of the relationship between sample effort (kms of transect) and precision of mean encounter rate. The actual mean for the sample is illustrated by the red line.
One way to summarise the increase in accuracy as sample size increases, is to assess the relationship between coefficient of variation (CV; the ratio of standard deviation of estimates to the mean estimate) and sample effort (Hayward et al., 2002). To do this, we derived 100 bootstraps as detailed above, for each case where at least 50 transects had been conducted in one of the three major habitats during any biological year. Mean CV was calculated for each category of known mean encounter rate (categories were designated to the nearest 0.2 km-1) and each
114 Analysis of ungulate dynamics category of sample effort (designated to the nearest 20 km), over all bootstrap samples within those categories.
5.2.3 Power analyses and required survey effort
The amount of survey effort required annually depends on the specific aims of the survey. For example, if the aim of the survey is to detect trends in ungulate abundance, then the magnitude of trends that should be detected, the period over which they should be detected, and the area within which they should be detected (i.e. at the level of the drainage basin, the habitat zone, or the entire reserve), will all affect the required survey effort. As the detection of trends is a common aim of vertebrate monitoring (Thompson et al., 1998), we decided to analyse power with respect to that aim. We assumed that there would be limited utility in trying to detect trends in ungulate abundance within individual drainages, as populations will likely move among drainages
(especially the smaller basins) in response to temporal heterogeneity in resources. However, as most ungulate populations occur in only one or two of the three major habitat zones in SAZ, it seems likely that detection of abundance trends at the level of the habitat zone will be useful.
Short term trends (i.e. those lasting a few years) may result from normal fluctuations in the environment, such as from a series of poor mast crop years. However, if only long term trends are deemed to be of interest, there is a danger that substantial changes in abundance could be well underway before they are detected. As a compromise, we assumed that it would be useful to detect trends in abundance over periods of five years.
Our analysis assumed that trend will be examined using regression methods by testing for a significant slope coefficient based on a t-test of the null hypothesis that slope is zero
(Gerrodette, 1987; Thompson et al., 1998). Although other statistical approaches could be employed, we based our analysis on this method because its applicability for monitoring vertebrate populations has been thoroughly assessed in recent literature (see review in Thompson et al., 1998). We used Monte Carlo simulations to determine how CV of density estimates and
115 Analysis of ungulate dynamics alpha (probability of a Type I error) influenced power. Specifically, we generated 300,000 simulations of track indices over a 5-year monitoring horizon to estimate power to detect an annual change in density estimates of -10%, or -20%. The analyses assumed that declines were of the exact magnitude tested (10% or 20% per annum) but that measurements of abundance were subject to error dictated by the sampling CV. Thus, our simulations included observation error
(inaccuracies in estimation) but no process error (inaccuracies in the actual population trend).
5.3 Results
5.3.1 Zero counts and the length of transect segments
We assessed the transect segment lengths required to produce certain proportions of zero counts.
The results of this analysis are summarised in Fig. 5.2. Clearly, target transect lengths are highly dependent on three factors: the daily movement behaviour of the species, its local population density and the acceptable proportion of zero counts. In general, however, it appears that for low density species (in the order of 0.5 km-2), a low proportion of zero counts will only be achieved by creating long transect segments, typically of 7 to 10 km, or even longer. By contrast, for moderate densities (of 1 to 2 km-2), transects of 3 to 6 km should be sufficient, whilst with ungulate densities of over 2 km-2 zero counts should be rare even with transect segments of 3 km or less (Fig. 5.2). Given equal densities, zero counts are most problematic for roe deer in late winter, as these have the shortest daily travel distances of the species considered. However, as this species is one of the more abundant, zero counts should generally pose less of a problem.
5.3.2 Survey effort and associated error
Relationships between CV of estimates and survey effort (total km y-1) were generated for each species in each of the three main habitat zones in which they occur. Results were all qualitatively similar but some sample results are illustrated in Fig. 5.3. In general, bootstrapping demonstrated the expectation that CVs were lower for higher mean encounter rates. The qualitative similarities
116 Analysis of ungulate dynamics
10 10 10 (a) (b) (c) 8 8 8 6 6 6
4 4 4
2 2 2
0 0 0 012345012345012345
10 10 10 (d) (e) (f) 8 8 8
6 6 6
4 4 4 2 2 2 0 0 0 012345012345012345
10 10 10 (g) (h) (i) 8 8 8 Required transectsegment length(km) 6 6 6 4 4 4
2 2 2
0 0 0 012345012345012345 -2 Density of tracks in the environment (km ) Figure 5.2. Transect lengths required to produce less than 50% zeros (bottom line in each panel), 25% zeros (middle lines) and 10% zeros (top lines) for: (a) red deer in early winter; (b) red deer in late winter; (c) roe deer in early winter; (d) roe deer in late winter; (e) sika deer; (f) wild boar in oak-birch habitat, early winter; (g) wild boar in oak-birch habitat, late winter; (h) wild boar in Korean pine-deciduous or spruce-fir habitat, early winter; (i) wild boar in Korean pine-deciduous or spruce-fir habitat, late winter.
between results allow us to make some general recommendations across species, habitats and
densities. Specifically, it appears that CV in mean encounter rate declines very rapidly as survey
effort is increased up to 250 km y-1 and that significant gains are made up to approximately 500
km y-1. Increasing the survey effort beyond 500 km y-1 appears to bring marginal improvement in
accuracy in most cases (especially those where encounter rate is high), however, whilst in other
cases (e.g. moose in areas of low density), significant improvements would only be made through
substantial increases in survey effort (such as increasing the survey by a further 500 to 1,000 km
y-1). This issue can be examined in more detail using a power analysis, as shown in the next
section.
117 Analysis of ungulate dynamics
2.0 2.0 (a) (d) 1.6 1.6
1.2 1.2
0.8 0.8
0.4 0.4
0.0 0.0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
2.0 2.0 (b) (e) 1.6 1.6
1.2 1.2
0.8 0.8 0.4 0.4
0.0 0.0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
2.0 2.0 (c) (f) 1.6 1.6 Coefficient of variationin mean encounter rate
1.2 1.2
0.8 0.8
0.4 0.4
0.0 0.0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
Survey effort (km y-1)
Figure 5.3. Sample relationships between encounter rate CV and survey effort: (a) red deer in Korean pine-deciduous habitat (dashed lines show encounter rate categories: 0.5, 1.3 and 2.1 km-1, top to bottom); (b) red deer in oak-birch (top to bottom: 0.3, 2.7, 4.7 km-1); (c) wild boar in oak-birch (top to bottom: 0.1, 0.9, 1.9 km-1); (d) roe deer in oak-birch (top to bottom: 0.1, 1.7, 3.5 km-1); (e) sika deer in oak-birch (top to bottom: 0.1, 0.9, 1.9 km-1); (f) moose in spruce-fir (top to bottom: 0.1, 0.3 km-1).
5.3.3 Power analyses and required survey effort
The relationship between power to detect a trend and CV of density estimates is shown in Fig.
5.4. Clearly, larger CVs in density estimates can be tolerated where it is only necessary to detect more pronounced trends, and where the existence of trends will be accepted on the basis of
118 Analysis of ungulate dynamics
1.0
(a)
0.8
0.6
0.4
α = 0.25 α = 0.20 0.2 α = 0.10
α = 0.05 0.0
0.0 0.2 0.4 0.6 0.8 1.0
1.0
(b) 0.8
Power to detect trend
0.6
0.4 α = 0.25 α = 0.20
0.2 α = 0.10
α = 0.05
0.0 0.0 0.2 0.4 0.6 0.8 1.0
CV of density estimates
Figure 5.4. Relationship between power to detect trends in abundance and CV of density estimates: (a) 10% annual decline over 5 years; (b) 20% annual decline over 5 years. Solid lines show relationships for given α levels. Broken horizontal lines show points yielding 80% power, whilst broken vertical lines show acceptable CVs of density estimates associated with 80% power, for each α level.
119 Analysis of ungulate dynamics weaker evidence (higher α). Broken lines in Fig. 5.4 show threshold values of CV that can be tolerated whilst still achieving 80% power to detect trends. These depend on the α level employed but CVs are in the order of 10 to 20% for detection of a 10% annual decline, and 20 to
40% for detection of a 20% annual decline, given the range of α levels assessed (0.05 ≤ α ≤ 0.25).
Determining the amount of survey effort required annually to achieve tolerable CVs in density estimates is complex, as this depends on the density of the surveyed species. As a general guide, we derived recommendations based on track encounter rates in the habitat zone in which each species is most common, but designed to reflect the encounter rate experienced in relatively poor years (i.e. years of relatively low abundance in relation to recent records). These recommendations are summarised in Table 5.1, which should also clarify our approach.
5.4 Discussion
Our analyses have demonstrated that the adequacy of survey effort is contingent on several factors, some of which can be controlled by survey design criteria. In this way, our results highlight the importance of setting clear objectives to guide winter transect counts in SAZ. At present, these objectives are not widely known or clearly stated. One possible reason for this, is that the purpose of the winter transect count is far broader than simply collecting data on ungulates. Nevertheless, monitoring will become most effective when clear objectives are defined for SAZ, so that the survey can be designed to meet all of those objectives adequately. In the absence of precise objectives, we can make only general recommendations related to common goals of ungulate monitoring (but see further in Section 7). Hence, the results of our analyses should be revisited following a rigorous exercise to set specific objectives for winter track counts in SAZ.
In the absence of clear objectives and associated decisions regarding spatial and temporal scales of interest, habitats of interest, necessary precision, and priorities regarding species of interest, we can outline several broad conclusions from our analysis. First, our results suggest
120 Analysis of ungulate dynamics
Table 5.1 Recommended annual survey effort based on the assumed goal of detecting change in the dominant habitat zone during periods of relatively low abundance.
Species Parameter RE RO SD MU MOa WB
Main habitat zone OB OB OB SF SF OB Mean annual encounter rates (tracks km-1) in that habitat since 1990: Minimum 1.65 1.40 0.27 0.48 0.00 0.16 Maximum 6.31 3.55 2.63 3.52 0.09 2.08 Approximate lower quartile 2.39 1.80 0.55 1.32 0.00 0.33
Approximate survey effort (km y-1) required to detect trend at lower quartile of encounter rate: to achieve 10% CV 400 720 2100 600 1500 to achieve 20% CV 90 200 500 150 360 to achieve 30% CV 40 100 230 70 160 to achieve 40% CV 20 60 130 40 90
a It is unlikely that trends in moose abundance could be detected over 5 years, given their very low abundance at present. Consequently, required survey effort for moose was not calculated.
that CVs of 20% or less should be achievable for all species except moose, by conducting no more than 500 km of transects each year, in each habitat zone. This figure may appear high.
However, if we assume that sika deer will continue to increase in abundance, then it seems likely that less effort will be required. As an approximate guideline, 250 to 350 km per year in each habitat zone should be adequate to detect declines of 10% per annum with 80% probability for most species, assuming an α level of 0.20. From Fig. 5.3, it is evident that for most scenarios, increases in total survey effort above this range will bring only incremental improvements in accuracy and, consequently, will only be necessary to answer questions that demand high levels of precision. Interestingly, it is common practice for managers of hunting leases in the Russian
Federation to aim for approximately 250 km of representative transects when surveying game
(D.G. Pikunov, pers. comm.). In recent years, the target of 250 to 350 km of transects per year has been achieved consistently for the oak-birch and Korean pine-deciduous areas, although the
121 Analysis of ungulate dynamics spruce-fir area has frequently dropped below the target. Whether further effort should be invested in the spruce-fir area depends on the ultimate goals of the ungulate survey.
The incidence of transects producing zero results is another issue that depends on the ultimate aim of the track surveys. For many statistical purposes, a low incidence of zeros is desirable. In that case, individual transects of 6 to 10 km should ensure that relatively few zeros are recorded for most species, although this result is confounded by highly aggregative behaviour
(a problem that survey design cannot overcome). The average length of a transect segment (that part of a transect within a given habitat type) is currently just over 3 km. Small increases in the lengths of these could substantially decrease the proportion of zeros for several species.
Unfortunately, required transect lengths are greatly affected by the density of the species surveyed and for some species (e.g. wild boar in some areas), only very long transect segments would ensure that zero counts are rarely recorded. Geographic conditions (the spatial extent of habitat patches) may also limit transect lengths. Finally, efforts to achieve desired survey length should keep in mind other principles of sampling, such as maintaining dispersion of sample locations and implementing some level of randomisation in placement of transects.
122 Analysis of ungulate dynamics
6. TIGER-PREY RELATIONSHIPS
6.1 Background
A central motivation for this study of the long-term dynamics of ungulates in SAZ was the importance of ungulates as prey for Amur tigers. In this section, we concentrate on that predator- prey relationship, by assessing the prey requirements of tigers and the potential impact of tigers on prey. Field data on kill rates and prey preferences from the Amur tiger project are currently being analysed (Goodrich and Miquelle, unpublished data). These will allow more detailed analyses of prey requirements and should also permit more precise predictions of the impacts on different prey species. In this section, however, we restrict ourselves to theoretical predictions of intake and impact, using published data on the allometry of metabolic rates, and simple modelling approaches to estimate likely impacts.
There are three principal approaches to estimating the prey requirements of predators.
Although currently unavailable (as discussed above) and difficult to collect, field data on kill rates provide the best source of data specific to a given system. A second approach uses empirically- based allometric relationships between body mass and metabolic rate, together with estimates of assimilation efficiency, to predict the amount of meat that a predator must consume to meet its daily requirements. Finally, data from similar systems can be used to provide general estimates of actual kill rates or quantities consumed. Here, we use both of the latter sources to estimate likely intake rates of Amur tigers.
Estimating the likely impact of large predators on prey is far more complex and controversial than estimating prey requirements (Eberhardt, 1997, 1998; Eberhardt et al., 2003;
Eberhardt & Peterson, 1999; Messier, 1991, 1994) but is correspondingly more important for understanding system dynamics and for developing management plans. The challenge of predicting predator impacts results from several factors. First, few systems are simple enough to permit the analysis of the effects of a single predator on a single prey. In particular, human
123 Analysis of ungulate dynamics exploitation of both predators and (largely ungulate) prey is often a confounding factor (Eberhardt et al., 2003). Secondly, and perhaps most importantly, an understanding of the impact of predation relative to other effects on prey population growth, requires age specific information on mortality and reproduction, together with information on the status of stressors other than predation (for example, forage condition, climate and social interactions).
Simpler systems could be assessed through modelling interactions but this can also be complicated by the fact that carnivorous mammals often show some form of social regulation, such that territory sizes are rarely a straightforward response to prey availability. For the wolf at least, Fuller (1989) provided evidence that territories may expand, contract, disappear, or be established in response to changes in prey availability or distribution, but the rate at which these changes occur is unclear. Such complexities in the relationship between predator and prey densities can confound attempts to model the impacts of predators on prey.
In this section, we use two modelling approaches to examine the possible impacts of tigers on their prey in SAZ. First, we use an energetic balance model that assumes that densities of tigers and their prey will tend towards long-term equilibria determined by the productivity of the prey and the numerical response of the tigers. Secondly, we use a simulation model that permits the inclusion of stochasticity in prey availability. For the reasons detailed above, this approach requires certain assumptions about the territorial responses of tigers to prey density. For both methods, we consider a single prey system, using red deer as the primary prey species (due to their dominance in the tiger diet, Miquelle et al., 1996). However, our results should also be applicable to a multi-prey-species system.
6.2 Methods
6.2.1 Estimating the requirements of tigers
Energy requirements of tigers were first calculated on the basis of field metabolic rates (FMR), themselves based on body mass. Approximate mean body masses of Amur tigers were taken
124 Analysis of ungulate dynamics from field data and were: females, 120kg; males, 180kg. The most comprehensive assessments of
FMR across a range of taxa are those conducted by Nagy and colleagues (1987; 1994; 1999).
Overall for 79 species of mammals, Nagy et al. (1999) estimated the relationship between body mass (M, in grams) and FMR (in kJday-1) as:
FMR = 4.82 M 0.734 (6.1)
Although sample size was much smaller, Nagy et al. (1999) also estimated the relationship from data on seven species of Carnivora, as:
FMR = 1.67 M 0.869 (6.2)
To convert these estimates of energy use into estimates of required consumption, it is also necessary to know the energy content of meat, the typical meat content of prey, and the assimilation efficiency of predators. Estimates of the energy content of ungulate meat vary (e.g.
7.9MJkg-1, Davison et al. 1978; 5.2MJkg-1, Gorman et al. 1998), as do estimates of assimilation efficiency by carnivores. We used an intermediate figure of 6.5MJkg-1 and, accounting for a potential loss in the urine, we used an approximation of 85% utilisation of ungulate meat
(Davison et al., 1978; Gorman et al., 1998; Litvaitis & Mautz, 1976) . We also assumed that 90% of juvenile (up to 6 months) live weight and 75% of the live weight of older animals (over 6 months) was consumed (e.g. Ackerman et al., 1986; Fuller, 1989; Glowacinski & Profus, 1997;
Hornocker, 1970). Finally, to convert estimates of requirements into an estimate of actual numbers of animals consumed also requires estimates of the body mass of prey species. Average masses of ungulates common in the Sikhote-Alin area are given in Table 6.1. Estimates of consumption rates of wild tigers are also available from the literature (Sunquist et al., 1999) and we used these for comparison with predictions from allometric relationships (equations 6.1 and
6.2).
125 Analysis of ungulate dynamics
Table 6.1 Ungulate body masses
Species Mean mass (kg) and (sample size) Source males females
red deer 224 (9) 149 (12) Bromley & Kucherenko (1983) roe deer 43 (2) 30 (1) A. Myslenkov, unpublished data sika deer 117 (5) 73 (12) Bromley & Kucherenko (1983) wild boar 144 (7) 131 (5) Bromley & Kucherenko (1983)
6.2.2 Estimating the impacts of tigers
We used two modelling techniques to estimate potential impacts. For the first of these, we compared the relationship between prey productivity and prey density, with that between predator requirements and predator density. These are linked by empirically-based relationships between predator density and prey density (hereafter, “numerical responses”), permitting the point of equilibrium to be estimated. Consequently, we termed this the “energy balance” approach. Four steps are required to construct this model: estimation of the tiger numerical response; estimation of prey productivity curves; estimation of tiger requirement curves; and comparison of productivity and requirements, in order to estimate equilibria. As stated previously, the model was designed using data on red deer, as these are the principle prey of tigers in SAZ.
Data on the tiger numerical response were collated from thirteen field studies of
(primarily Bengal) tigers. It has been suggested that some wild carnivores show Type I (i.e. linear) numerical responses to prey availability (e.g. wolves, Canis lupus, Eberhardt, 1997;
Eberhardt & Peterson, 1999). However, given the strong territoriality and social intolerance of tigers (Smith et al., 1987), a Type II (or asymptotic) numerical response may be expected. To determine which type of response best explained the data, we fitted two different linear (Type I) responses and two asymptotic (Type II) responses, and compared their explanatory power using
2 AICc (see Section 3.2.1) and R . The linear models included an ordinary least squares fit and a least squares bisector (LSB, e.g. Ricker, 1973). The LSB model may be used where it is
126 Analysis of ungulate dynamics explicitly acknowledged that both axes (in this case, estimates of prey density and estimates of tiger density) may be subject to similar levels of error. To obtain an LSB fit, least squares regression is used to regress each axis on the other (i.e. tiger density on prey density and prey density on tiger density) and the LSB model is the bisector of these two regressions. The asymptotic models were two commonly used variants that allow a range of speeds of progression to the asymptote. These were an inverse curve of the form y = a + b / x and a Michaelis-Menton curve of the form y = ax / (b + x), where a and b are constants in both cases.
Next, we estimated the relationship between deer density and productivity, allowing for habitats with a range of carrying capacities (in the absence of predation) of from 2 to 20 km-2.
Demographic parameters for red deer (e.g. Clutton-Brock et al., 1982; Houston, 1982) suggested an approximate mean population growth rate of r = 0.3 in the absence of density constraints.
Density dependence in large ungulates is typically of a nonlinear or ramped form, with a plateau of relatively constant growth and a ramp of density dependent decline in growth (Fowler, 1981,
1987; McCullough, 1992). Consequently, density dependence was assumed to act only above a threshold at 0.6K, where K is the ‘carrying capacity’ of the environment. Beyond that point, we assumed that mean potential population growth declined linearly from r = 0.3 to r = 0, at K. Due to the low productivity of the system, we also assessed predator-prey equilibria where maximum potential population growth of the prey population was r = 0.25. We assumed that an adult female represents a red deer of approximately typical weight and, therefore, that the production of
1 km-2 red deer raised to adulthood each year would represent biomass production of approximately 150 kg km-2 y-1; we combined this with predicted growth rates to produce biomass production curves. As this simple model did not account for gender of tigers, we used the estimate of daily consumption from Sunquist et al. (1999), in combination with the numerical response, to determine how tiger off-take would vary with prey density. Clearly, this approach assumes that the sex ratio remains constant throughout the range of prey densities considered.
127 Analysis of ungulate dynamics
For the simulation model, we generated a simple population simulation of red deer occupying 5,000 km2 of the Russian far East. Prey dynamics were essentially a stochastic version of those used in the energy balance model, with density dependence acting negatively and linearly on mean population growth above 0.6 K. Environmental stochasticity was incorporated by drawing an “environmental condition” parameter from a uniform distribution. The impact of environmental stochasticity was varied to achieve two scenarios: a moderately stochastic scenario
(population coefficient of variation, CV = 0.15) and a highly stochastic scenario (CV = 0.40).
Parameters used for tigers are summarized in Table 6.2. Predator dynamics were linked to prey availability through energetic constraints on survival and reproduction. Because estimation of functional responses is problematic (Marshal & Boutin, 1999), energetic constraints were modelled using a simple depletion approach (Sutherland, 1996). Specifically, we assumed that during each time step, tigers could remove all required prey (red deer) from the environment down to some critical threshold density (below which predation is no longer energetically viable).
Tiger consumption rates were the same as those used for the equilibrium model. Tigers that could not obtain their requirements during any time step were assumed to die or disperse. Social tolerance, reproductive behaviour, dispersal behaviour and presence of transient animals were all modelled on the basis of empirical data (e.g. Kerley et al., 2003, Goodrich, unpubl. data) (see also
Miquelle et al., 2005).
6.3 Results
6.3.1 Requirements of tigers
Energetic requirements were calculated according to the two allometric relationships given in equations 6.1 and 6.2. Estimates of meat consumption were also taken from Sunquist et al.
(1999). These were converted into estimates of daily kill rates, as shown in Table 6.3. Clearly, the Sunquist et al. (1999) estimate is approximate, given that it is an estimate for tigers in general,
128 Analysis of ungulate dynamics
Table 1. Life-history parameters used in the tiger-prey simulation model
Parameter Value Sources
Survival Maximum age 25 (Danilkin, 1995) Background survival rate1 0.95 (females > 1yr) (Kerley et al., 2003) 0.90 (males > 1yr) 0.75 (cubs < 1yr)
Fecundity and birth Age at first reproduction 4 yrs (Danilkin, 1995; Kerley et al., 2003)
Annual probability of female 0.553 (Kerley et al., 2003) reproduction Mean (± SD) litter size2 2.38 (± 1.15) (Danilkin, 1995; Kerley et al., 2003) Sex ratio at birth (males per offspring) 0.41 (Kerley et al., 2003)
1 Background survival rates reflect mortality from causes other than food limitation. The figures used were selected to reflect mortality in the absence of anthropogenic causes. Survival rates are expressed as annual equivalents. 2 Litter sizes in the model were drawn from normal distributions described by these parameters but were reduced if food was limiting. 3 The territories of male and female tigers are known to overlap. However, it was assumed that one male could mate with no more than three females in any one year.
and is not broken down by gender. However, it is reassuring that for both genders, that estimate falls within the range of estimates from the two allometric approaches. Consequently, the two allometric approaches were used as low and high estimates for each gender. Simplifying the diet to its three dominant components (which together represent approximately 93% of prey eaten), equivalent numbers of ungulate prey killed annually were derived from those estimates (Table
6.4). These show that a male tiger may be expected to kill between 14 and 25 red deer annually, together with 2 to 4 sika deer and 6 to 11 wild boar. A female tiger may be expected to kill between 10 and 18 red deer, 2 or 3 sika deer and 4 to 8 wild boar annually. Obviously, these figures are highly approximate and will depend on the relative availability of prey within a tiger’s range, pregnancy or the presence of cubs and, potentially, on individual differences in prey preferences. Nevertheless, as an approximate guide to the frequency of kills and potential impact on prey populations, they are informative. Intermediate values suggest that male tigers should
129 Analysis of ungulate dynamics kill approximately every 11 or 12 days, whilst solitary females should kill once every 16 to 17 days. Obviously, if a high number of young prey are taken, kill frequencies will be rather higher.
Table 6.3 Estimated daily kill rates by tigers
Equivalent Kill requirement, given 85% Estimated Basis for estimate Gender meat at 6.5MJ assimilation efficiency and 25% FMR (MJ d-1) kg-1 (kg d-1) wastage of carcass (kg d-1)
Nagy et al. (1999) Male 34.7 5.3 8.4 (all mammals) Female 25.8 4.0 6.2 Nagy et al. (1999) Male 61.6 9.5 14.9 (Carnivora) Female 43.3 6.7 10.5 Sunquist et al. (1999) Not 5.5 8.7 specified
Table 6.4 Estimated annual predation by tigers
Approximate Total killed equivalent number of annually (kg) prey2 Prey Scaled proportion of Male Female Male Female Basis for estimate Species diet1 tiger tiger tiger tiger
Nagy et al. (1999) red deer 0.69 2104 1562 14 10 (all mammals) sika deer 0.05 164 122 2 2 wild boar 0.26 789 586 6 4
Nagy et al. (1999) red deer 0.69 3734 2625 25 18 (Carnivora) sika deer 0.05 292 205 4 3 wild boar 0.26 1400 984 11 8
1 Represents the relative proportions of each prey type in the diet if no other prey were taken. 2 Based on female prey masses.
6.3.2 Estimated impacts of tigers
Results of the energy balance model are shown in Fig. 6.1. The poor fit of Type I numerical response models is evident from Fig. 6.1a. A Type II numerical response model appears more
130 Analysis of ungulate dynamics
likely from Fig 6.2b and this was confirmed by a comparison using AICc and other diagnostics, which provided the best support for the two asymptotic models and suggested that the Michaelis-
Menton model was best supported by observed data (Table 6.5). Given the small difference in the AICc values of the three best-supported models, model averaging (as discussed in Section
4.3.4) could be used to derive predictions of the tiger numerical response. However, owing to the frequency with which Michaelis-Menton curves can be used to describe natural phenomena, as well as to the similarities between the average model and the Michaelis-Menton function (P.A.
Stephens, unpublished data), we chose to use the fitted Michaelis-Menton function as our model.
Table 6.5 Comparison of tiger numerical response models
2 Model Form K AICc ∆i wi R
Least squares linear y = ax + b 2 -33.21 1.45 0.21 0.333 LSB y = ax + b 2 -30.94 3.72 0.07 0.003 Inverse y = a + b / x 2 -33.76 0.90 0.28 0.395 Michaelis-Menton y = ax / (b + x) 2 -34.66 0.00 0.44 0.484
Fig. 6.1c shows an example of how the energy balance model works. Production and demand curves are contrasted and, where they meet is assumed to be the predator-prey equilibrium. This is intuitive as, if the prey population drops below the equilibrium, the predator population will also reduce, such that production outstrips demand and the system returns to the equilibrium point. Similarly, should fluctuations take the prey population above the equilibrium, the predator population would increase, increasing demand, and pressuring the system back toward equilibrium. Using this approach, we solved equilibria for a range of initial prey carrying capacities, under two scenarios of prey population growth rate (average maximum growth rate, r
= 0.30 and r = 0.25) (Fig. 6.1d). Predictions are similar and show that the highest reductions in prey population are likely when prey are relatively scarce. Increasing prey density leads to a reduction in the impact of tigers, due to the tiger’s Type II numerical response (a likely result of
131 Analysis of ungulate dynamics social constraints on tiger density, rather than constraints of prey availability). If we assume
(very approximately) that prey densities in the more productive areas of SAZ are currently in the order of 1000 kg km-2 (equivalent in biomass terms to approximately 6 to 7 red deer km-2), then the results of the equilibrium model suggest that, in the absence of tiger predation, prey biomass could be closer to 1200 to 1350 kg km-2.
The results of the simulation model of tiger predation are shown in Fig. 6.2. Using existing estimates of prey biomass and tiger density, we derived territory size of tigers based on the assumption that each territory of an adult resident tigress contains 3.3 tigers (a female, a third of a male, 1-3 cubs or a young daughter; and one transient) (Fig. 6.2a). Using the predicted territory sizes, simulation models of predation suggested that the proportion by which prey populations were reduced below K by tigers was typically in the range of 18-25% and never exceeded 30% (Fig. 6.2b). Tiger impact on prey decreased with higher prey density due to constraints on tiger density imposed by territoriality (see Fig. 6.2a), except when stochasticity was high. In this case, tigers were better able to limit prey when initial prey abundance was high, as this reduced the possibility of prey becoming so scarce that tigers could not hunt effectively.
6.4 Discussion
Estimating the impact of large mammalian predators on prey is a problematic and contentious issue (Eberhardt et al., 2003; Messier, 1994; Van Ballenberghe & Ballard, 1994). Our analyses have illustrated a number of the complexities involved in such analyses but, nevertheless, have provided a number of useful and informative results. Among these are estimates of the likely number of kills made by individual tigers, an examination of the tiger’s type of numerical response, together with fitting of explanatory models, and estimation of the likely effect of tiger predation on prey populations.
132 Analysis of ungulate dynamics
0.20
) (a)(a) C -2 A 0.15 B
0.10
0.05 Tiger density(km
0.00 0 2000 4000 6000 8000 Prey density (kg km-2)
0.20 (b)
) (b) -2 0.15
0.10
0.05 Tiger density (km
0.00 0 2000 4000 6000 8000 Prey density (kg km-2) 200 (c)
) (c) B
-2
100 A
0 Production orProduction
requirements (kg km (kg requirements -100 0123456 Deer density (km-2) 0.40
0.30 (d) (d) A 0.20 B 0.10 Proportional reduction Proportional below carrying capacity carrying capacity below 0.00 02468101214161820 Deer carrying capacity in the absence of predation (km-2)
Figure 6.1. The energy balance model: (a) Tiger numerical response (A, regression of tiger density on prey density; B, regression of prey density on tiger density; C, least squares bisector; open circles show empirical data); (b) Michaelis-Menton fit to tiger numerical response; (c) sample production (A) and requirement (B) curves when deer carrying capacity K = 5 km-2; (d) predicted impact of tiger predation on prey population size, as a function of prey carrying capacity in the absence of predation (A, deer maximum population growth, r = 0.25; B, r = 0.3). See text for further details.
133 Analysis of ungulate dynamics
600 (a)
500
) 2 400
300
200
Territory size (km 100
0 0 1000 2000 3000 4000 5000 6000 7000 8000
Prey biomass density (kg km-2) 0.50 (b)
0.40
0.30 C
0.20 B A
reduced by tiger predation predation reduced by tiger 0.10
by whichProportion population is
0.00 012345678910 Red deer carrying capacity in the absence of predation (km-2) Figure 6.2. Tiger-prey simulation models: (a) Empirically derived relationship between territory size and prey availability (based on 3.3 tigers per territory). Territory Area, –0.7764 A = 22270 B , F11 = 42.5, p < 0.001. (b) predicted impact of tiger predation on prey population size, as a function of prey carrying capacity in the absence of predation (A, no environmental stochasticity; B, moderate stochasticity (prey population coefficient of variation, CV = 0.15); C, high stochasticity (CV = 0.35)).
134 Analysis of ungulate dynamics
Our estimates of the annual kill rate of tigers are quite varied (Table 6.3), owing to substantial differences in the two allometric predictions of FMR given by Nagy et al. (1999).
Given the estimates of intake rate from Sunquist et al. (1999), it seems likely that kill rates will be towards the low end of our predictions (Table 6.4), and that Nagy et al.’s (1999) allometric relationship based on carnivores rather over-estimates the requirements of tigers. This could be due to the low sample size available for predicting the allometry of carnivore requirements but, also, could arise because at least two of the larger Carnivora assessed by Nagy et al. (1999), are wolves and African wild dogs (Lycaon pictus). We have speculated elsewhere (Miquelle et al.,
2005) that in contrast to tigers, social, cursorial hunters have very much higher than expected energy requirements. This seems to fit with available evidence on the intake rates (Gorman et al.,
1998) and densities (Carbone & Gittleman, 2002) of social, cursorial carnivores, and may explain why Nagy et al.’s (1999) allometric relationship for energy requirements leads to over-estimates for tigers. It will be useful to compare our estimates to field data on kill rates, when these are available. Should it be possible to parameterise matrix models of population growth for other prey species in SAZ, our estimates will also permit a more detailed investigation of the likely impact of tiger predation on individual species.
Our analysis of the tiger numerical response provides strong evidence of a Type II form, presumably owing to regulation by social constraints when prey densities are higher, rather than prey availability. The two asymptotic models examined were evidently better supported than simpler, Type I models and, the complexities of estimating the underlying data notwithstanding, the Michaelis-Menton model provided a surprisingly good fit to the data (R2 = 0.48).
The precise predictions of the models of tiger impact on prey populations are sensitive to a number of underlying assumptions, including the potential growth rate of the prey population, the variation in territory size with prey availability, and the nature of stochasticity experienced by the prey population. Nevertheless, the two methods both predicted that within the range of densities seen in SAZ, it is likely that tiger predation could be reducing prey populations by about
135 Analysis of ungulate dynamics
20 to 30% below their expected size in the absence of predation. This impact is substantially lower than has been estimated for other carnivores, especially for wolves (Eberhardt et al., 2003;
Miquelle et al., 2005; Van Ballenberghe & Ballard, 1994). That all of our modelled scenarios suggested that tiger impacts would be reduced at higher prey densities accords with estimates from the high ungulate biomass systems of the Indian subcontinent, where off-take has been estimated at less than 10% (Schaller, 1967; Stoen & Wegge, 1996). In particular, our energy balance model, which predicted 10% depletion when K = 20 km-2 deer (equivalent to a prey biomass density of 3000kg km-2), is in close agreement with these estimates.
136 Analysis of ungulate dynamics
7. GENERAL DISCUSSION
Our study was driven by three principal motivations: (i) the importance of gaining accurate knowledge regarding densities of ungulates in SAZ and the utility of the survey protocol; (ii) the broader contribution that our analyses can make to the field of estimating animal population density from indirect sign; and (iii) the importance of understanding ungulate dynamics in SAZ, in order to inform management of the Amur tiger. We divided our approach into five inter- related objectives and we have presented each, with an associated discussion, in the previous sections. Our aim in this section is to bring together our main findings in light of these three original motivations, and provide some specific recommendations for continued monitoring of ungulates in SAZ.
7.1 Ungulate densities and the utility of the survey protocol
In Section 3, we provided support for the extensive work already existing in Russian literature that, by comparison to other approaches, the FMP equation represents an easily applied and accurate method for translating track encounter rates into estimates of density. An advantage of our work is the use of a non-parametric bootstrapping method to generate confidence intervals about density estimates derived using the FMP. Given reliable data on track encounter rates and suitable, accurate estimates of daily travel distances, ungulate densities (with appropriate confidence intervals) can be identified fairly accurately. Two questions arise from this investigation: how reliable are the underlying data (and, hence, how accurate are our mean estimates) and how can the ranges be narrowed (giving greater precision of estimates)?
137 Analysis of ungulate dynamics
7.1.1 Accuracy of data
Considering the issue of accuracy, two lines of evidence give us confidence in the quality of the underlying data. First, fieldworkers must differentiate recent tracks from tracks over 24 hours old
– a classification certain to have some error. However, comparisons of fieldworker estimates of tracks made in the last 24 hours, with counts made of tracks known to have been made on the same day (which can be differentiated with a much higher level of accuracy) show high correlations (Miquelle and Aramilev unpubl.). Second, accurate density estimates depend on whether survey routes are representative of the survey area. Again, our analyses of different approaches to post-stratification of the data (see Sections 3.2.4 and 3.3.2) provide indications that the coverage provided by survey routes within SAZ is indeed highly representative. In particular, although small numbers of data points can be affected by the type of stratification used
(encouraging the use of relatively broad scale and strictly objective stratification approaches), the majority of data points are unaffected, regardless of whether the data are unstratified, or are stratified by drainage basin or forest formation (see Fig. 3.3). This suggests that survey routes within each drainage or forest type are generally in proportion to their area.
In spite of the foregoing observations, there remain many ways in which the accuracy of mean estimates can be improved. Here, we focus on four important issues.
Independent validation of ungulate densities. Independent validation of density estimates is essential if we are to have real confidence in the track count approach. Therefore, it is necessary to collect data by some other method, in order to generate independent estimates of density. In Section 1.1 we referred briefly to some of the problems involved with alternative methods of censusing ungulates in SAZ. However, both aerial counts (Myslenkov & Voloshina,
2005) and direct observation combined with distance sampling (Zaumyslova, 2005) have been used in SAZ. Aerial counts, combined with development of a sightability model (which requires capture and marking individuals of each of the key ungulate species) (Samuel et al., 1987) would provide an expensive but effective approach for validation of the track count method. Training
138 Analysis of ungulate dynamics forest guards and scientific staff of the reserve to collect distance sampling data could also provide a means of verification for the WTC data in those areas where patrols are regular and scientific investigations are conducted (i.e., where adequate sampling is possible). Although these suggested methods need not be conducted regularly (data from a very few years would probably be sufficient to indicate the accuracy of the WTC), in the years when they were conducted, all would require a considerable increase in the manpower devoted to surveying. This is unavoidable.
Representative surveys and bias reduction. A second issue affecting data quality is the placement of survey routes and, in particular, whether routes are representative of the distribution of habitats within SAZ. Ideally, survey design would include randomly placed transects to estimate ungulate densities. Clearly the existing transect system is largely confined to more accessible areas at lower altitude and in valley bottoms, thus raising the question of bias in survey results. Our comparisons of different types of stratification provide support for the representative layout of survey routes, but only in relation to the total area directly surveyed by those routes.
Whether these routes are representative of SAZ as a whole, could be determined in two ways.
First, GIS could be used to assess whether certain landscape features and habitats are over- or under-represented in surveys. Under-represented features could then be surveyed to determine whether they support very different ungulate densities to those in surveyed areas, thus revealing whether survey route placement is a source of bias. A second approach would compare density estimates from the current survey routes to estimates derived from similar levels of survey effort along randomised transects. Either test for bias need be conducted for only a few years in order to give an indication of the quality of current WTC practices. However, tests would require a substantial increase in resources dedicated to surveying during those years. Whether that is worthwhile, strongly depends on the purpose of surveying within the Zapovednik. If surveys are designed to generate accurate estimates of ungulate abundance then additional effort, aimed at reducing bias by surveying under-represented areas, is likely to be important.
139 Analysis of ungulate dynamics
Improved estimates of ungulate daily travel distances. A third, related issue, provides an alternative to the use of randomised transects. If density estimates are to be derived using the
FMP formula, as we suggest, then increasing the precision of density estimates (even when used as a relative measure between years) depends on the availability of good estimates of 24-hour movement data for each species. Gathering additional data on animal movements will have two benefits. First, it will permit an improved understanding of the relationship between animal movements and environmental conditions (including habitat, snow depth, time of year, mast crop, etc.). As we discussed in Section 3, this is extremely important for generating good estimates of density, whether absolute or relative (among habitats or years). Without a large library of travel distances from different conditions, it will be extremely difficult to identify relationships between environmental factors and movement distances. Collecting movement data using telemetry in a variety of areas within SAZ could have further benefits. In particular, analysing mapped data on animal movements may allow estimation of the relative use of different areas and habitat types among species. This will have important implications for the stratification of survey effort and will provide an alternative to conducting large numbers of randomised survey routes, through potentially difficult terrain.
Dealing with multiple track crossings (“nabrods”). A fourth issue affecting both accuracy and precision of density estimates is that of multiple crossings, where tracks are so confused that fieldworkers have been unable to discern the number of animals that have made them. These instances are recorded as “nabrods”. Although only about 2% of all track encounters are nabrods, for highly grouped species (such as wild boar and sika deer) these may account for 10% or more of animal tracks. To convert track data into estimates of animal abundance, either relative or absolute, it is essential that these records of “nabrod” be converted to some value. Consequently, interpretation of these records will significantly affect density estimates and their accuracy. In this study, we converted data based on estimates of average group size for each species. However, we believe that accuracy could be greatly increased if
140 Analysis of ungulate dynamics fieldworkers made the extra effort to record actual values instead of simply “nabrod.” We recommend that fieldworkers on winter transects follow a protocol of going around nabrods in ever increasing circles until they are able to derive an estimate of animal number. Although there will be error in such estimates, the error is less than an estimate based on mean group size.
Therefore, in future surveys, we recommend that fieldworkers be trained in reporting track number to the best of their ability, to avoid all records of nabrods.
7.1.2 Precision of estimates
The second major aspect of the survey protocol that was considered in this study is that of precision. The survey effort required to increase precision is the explicit focus of Section 5. In that section we showed that, for the more abundant species, current levels of survey effort (in terms of kilometres surveyed per year) are sufficient to detect declines of 10% per year with 80% probability, assuming an α level of 0.20 and five years of decline. For less abundant species, it is unlikely that accurate data could be obtained. However, here we consider two ways that the other species could be surveyed more precisely, so that smaller trends could be detected more easily.
Habitat zones and stratification. Throughout this study, we have followed the existing system of classifying SAZ into three broad habitat zones and typically performing analyses for each zone separately. There is some evidence, however, that substantial differences exist within different parts of the oak-birch zone, and that this zone might reasonably be further divided. In particular, Figs. 2.1 and 2.2 suggest that the four coastal oak-birch drainages (Abrek,
Blagodatnoe, Khuntami and Inokov) differ substantially from the three inland oak-birch drainages
(Lianovaya, Kuruma and Kunaleyka), with the former dominated by oak forests, whilst birch/aspen forests predominate in the latter. For most of the ungulates, analyses of encounter rates within these drainage basins do not show clear differences between the two sets of drainages. However, sika deer show a marked tendency to aggregate in the coastal drainages, and other species show similar, though subtler, differences. It is likely that, in the future, a four zone
141 Analysis of ungulate dynamics system of analysis would be more informative for interpreting the survey data. Should this zoning system be implemented for survey purposes, it may be that further stratification of survey data by drainage basin will become unnecessary, thereby obviating the complications that this additional step introduces to data analysis. Emerging methods which combine survey data with habitat variables to develop associations between density and habitat type also promise to improve understanding of variance and, potentially, to increase precision. We recommend that the relevance of these methods (e.g. Hedley & Buckland, 2004) to SAZ should be considered.
Appropriate survey effort. In Russia, there is a tendency to think of sampling effort in terms of percentage of the area sampled. Biologists often refer to the 10% rule in sampling, which suggests that sampling 10% of the study area is usually adequate. In this report, we do not comment on what proportion of the area is sampled but, instead, consider only the absolute number of kilometres surveyed. There are two reasons for this. First, determining what proportion of an area is surveyed by counting tracks along 1 km of transect is far from straightforward, requiring an estimate of perpendicular movement of animals relative to the survey line. This will vary among species and between different environmental conditions
(depending on how these affect movement). Consequently, surveying 10% of an area will require different amounts of total survey effort depending on the species studied, habitat traversed and time of year. As a result, it is often easier to talk about survey effort in terms of the objective measure of kilometres travelled. Secondly, when it is possible to determine the kilometres of survey route required to survey 10% of an area, it does not automatically follow that this is an adequate level of survey effort. The abundance of the species and its spatial distribution
(clumped or not) both significantly influence the adequacy of a survey. Most important, however, adequacy depends on the goals of the survey and can only be determined if the questions to be answered by the survey are clearly established at the outset.
142 Analysis of ungulate dynamics
7.2 Estimating animal density from sign
In Section 1.1, we discussed the importance of methods to estimate densities of animals indirectly from their sign. As we noted there, a very wide array of methods for estimating densities from sign is available but the field remains highly contentious (e.g. Carbone et al., 2001; Carbone et al., 2002; Jennelle et al., 2002; Sadlier et al., 2004; Webbon et al., 2004). Two problems are common to many approaches to estimating abundance from sign. These include the difficulties of quantifying variance in estimates and, commonly, a lack of calibration of the relationship between sign abundance and animal abundance. Our study can provide improvements in both areas. First, the FMP formula has, hitherto, been little known outside Russia and we have found no instances of similar methods being applied within the English-language ecological literature. Our talk at the Society for Conservation Biology international conference in New York, August 2004, generated considerable interest in the FMP formula, together with a recognition of its application to other methods based on randomised encounters (particularly that of camera trapping). In many wildlife studies, data on animal movements are collected in addition to attempts to estimate abundance. When such data are available, the FMP formula presents a further method by which densities may be estimated, providing the opportunity for checking density estimates against those produced by an alternative method. The emphasis that we place on using nonparametric bootstrapping to generate confidence intervals from transect data is also important for many studies in which estimates of density are made from multiple samples. Most formal methods for estimating the variance associated with density estimates rely on parametric methods which, in turn, rely on tractable distributions and relatively large sample sizes (e.g. Buckland et al., 1993).
In practice, many wildlife studies, especially those of species occurring at low density, generate data which meet neither of those requirements. In these cases, as in our study, the use of nonparametric bootstrapping is likely to be invaluable for quantifying error.
143 Analysis of ungulate dynamics
7.3 Ungulate dynamics and tiger conservation
The third major motivation for this study was the importance of understanding ungulate dynamics in SAZ, and their relation to Amur tigers. Our analyses have shown that, by comparison with other parts of the geographic range of tigers, SAZ (and, by extension, the Russian Far East) has extremely low densities of prey, highlighting the vital importance of protecting existing prey populations. Moreover, whilst the ungulates of SAZ have tended to increase over the course of the monitoring period reported here, recent years have seen disturbing evidence of a downturn, especially for red deer and wild boar, the two key prey species of the tiger (Fig. 4.6). The reasons for this decline are unclear but the evidence suggests that predation by tigers is not a primary factor driving these changes. For the red deer, several lines of evidence developed in the preceding chapters suggest that warmer temperatures and recent increases in numbers of sika deer may be leading to reduced numbers of red deer in the coastal basins and increases in the spruce- fir zone. Given (i) the tiger’s evident adaptability to different prey complexes throughout its range (Sunquist et al., 1999), and (ii) the dominance of sika deer in Lazovski Zapovednik, where tigers are present at densities at least as high as SAZ, the potential for a gradual replacement of red deer by sika deer in SAZ is cause for limited concern (at least, from the perspective of tiger prey availability). The apparent decline of wild boar is more disturbing. Given that our results indicate the tigers limit at least some prey species to a much lesser extent than other carnivores, and that there is no evidence that tigers regulate prey numbers, it is important to consider the other factors that are impacting prey numbers. For instance, the temporal analyses suggest that the decline in wild boar numbers may be associated with reduced efficacy of protection within
SAZ. Hence, changes in management approaches to reduce impacts of humans in the
Zapovednik (and specifically to reduce poaching) may result in positive responses of prey populations.
It is perhaps disappointing that our time-series analyses (Section 4) did not provide a clearer picture of the factors driving the dynamics of each species. As we noted there, however,
144 Analysis of ungulate dynamics our analyses are the first of their kind for this system and our findings must, as a result, be viewed as preliminary. There is considerable opportunity for studying each species in more detail (for example, assessing the role of nonlinear interactions with variables) but whether this will produce greater insights into the dynamics of species is currently unclear. One limitation on the type of time-series analyses we used is the need for accurate data on population densities. We have discussed methods by which accuracy may be improved but, again, whether implementing those methods is worthwhile depends on the goals of the monitoring programme. Clearly, if informative analysis of the dynamics of individual species is a stated goal of the monitoring programme, then improving accuracy of density estimates must become a key aim of developing the WTC protocol.
More broadly, our work on ungulate dynamics leads to questions on the goals and design of the Zapovednik system. Most of the species studied showed evidence of the importance of climatic factors affecting their dynamics. In keeping with global trends, a warming trend is visible even from a cursory look at Fig. 4.3 g,i. Changing temperatures will have impacts on many species that SAZ currently protects, and may already be having an impact on some of the species studied in this report (red deer, sika deer and moose). Protected area networks that function within a context of shifting wildlife distributions will be of considerable importance if current trends accelerate.
Finally, it is also clear that a fixed system of monitoring will provide much more detailed information on relatively common species, whilst even the detection of trends among rarer species can be difficult, given limited resources and manpower. Clearly, if conserving those rarer species is an important aspect of Zapovednik policy, management systems must be in place to identify and prioritise species of concern, diverting resources towards their study where necessary.
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7.4 Specific recommendations
Our work has suggested a variety of improvements that could be made to the monitoring work conducted in SAZ. The goals of monitoring within the Zapovednik system are not for us to designate. However, we suggest goals and make recommendations that we believe will better define and enhance the ungulate monitoring conducted in SAZ.
• Review strategies for protecting ungulates. Ungulates are at very low densities in SAZ
relative to other systems across Asia that support tigers. There is some evidence of
declining ungulate densities in recent years and this may be linked to the level of
protection that they receive. It is essential to safeguard and enhance these remaining prey
populations, in order to promote the stability of the tiger population.
• Use a four-zone classification of SAZ for ungulate monitoring. As discussed elsewhere,
these zones would include the coastal zone (dominated by oak forests), the inner-coastal
zone (dominated by birch-aspen forests), the central zone (dominated by Korean pine-
deciduous forests) and the montane zone (dominated by spruce-fir forests).
• Define an overall goal for monitoring ungulates. This should specify whether monitoring
will produce only an index of relative abundance, or estimates of absolute abundance
also. It should also specify the units of interest (both species and zones) and whether
trend detection is important. If trend detection is important, the magnitude of trends and
the time periods over which these should be detected must also be defined. As an
example, we suggest that the goal be defined as follows: Ungulate monitoring in SAZ will
provide estimates of the absolute abundance in winter of ungulates in the four major
habitat zones. At least 1000 km of surveys will be conducted annually, distributed
equally over the four zones. The aim of this will be to give the maximum power to detect
trends in numbers of the more abundant species in the habitats most important to that
species.
146 Analysis of ungulate dynamics
• Recognise limitations and adapt to priorities and changing conditions. It is vital that the
limitations of the monitoring be recognised including, in particular, that density estimates
are associated with considerable uncertainty, and that species at lower abundance, with
shorter daily travel distances and with highly clumped behaviour will be subject to
greater uncertainty, such that trends are harder to detect with confidence. The monitoring
protocol should also be adaptable to changing priorities and to changes in conditions
(such as increasing or decreasing densities of certain species) . This adaptability may
require a core monitoring program to assure the integrity of a long-term data base,
alongside sampling that is more flexible in response to recognised monitoring needs.
• Validate the relationships between track counts and density estimates. Independent
estimates of density must be generated using alternative methods, in order to indicate
how accurately density is estimated by current methodologies. Field data for an
independent estimate of density would be collected for a limited number of years to
achieve validation but not become part of the long-term monitoring work. In particular,
we recommend the use of distance sampling or aerial surveys combined with the
development of sightability models.
• Assess bias in transect network. Assess bias in the transect network using GIS analyses
of survey route placement and by comparing results of randomly placed transects to the
existing network within a number of basins of the reserve. If a significant bias is
detected, there are two alternatives to address this bias: (i) if the bias is stable and
predictable across all areas and all conditions, apply a simple correction factor; (ii) if the
bias is not stable and is difficult or impossible to predict, relocate transects to
approximate a random sampling effort.
• Improve data base on daily travel distances. Daily travel distances must be collected for
each species during the time frame in which surveys are conducted, as there is evidence
147 Analysis of ungulate dynamics
that travel distance drops in late winter (Sections 3 and 4). Data on travel distances must
also be collected across the range of environmental parameters that are likely to affect
movements.
• Collect data on the numbers of animals that made each set of tracks encountered. To
collect data not only on the number of sets of tracks of each species encountered on
transects but, also, on the number of these that were made by single animals or groups of
various sizes, is likely to be awkward, especially from the point of view of data storage.
Nonetheless, our analyses showed that size of the travelling group may be important in
dictating the travel distance of some species. Consequently, collecting such data will be
helpful for improving the accuracy of density estimates. The data could also be useful for
determining group size distributions, which will have important implications for error
calculations and other aspects of understanding demography of the studied species.
• Eliminate the recording of “nabrods“. Eliminate records of “nabrod” in SABZ the data
set by training all observers to circle nabrods and report actual numbers of tracks to the
best of their ability.
7.5 Concluding remarks
In conclusion, this has been an extremely beneficial collaboration between all four organisations involved. The exchange of ideas and integration of scientific literatures that has resulted is an important outcome that is easy to overlook. Using the data from SAZ to develop a new approach to detecting density dependence in time-series of ecological data, and propagating the use of the
FMP formula outside Russia have been two developments of substantial significance. Despite the intensity, consistency and rigour with which WTC data have been collected in SAZ, our analyses were often limited by the quality of the underlying data. Analyses cannot improve the data retrospectively and there is no substitute for increased intensity of survey effort (and expense) for accurately estimating the densities of species within an area. However, whether such increases in
148 Analysis of ungulate dynamics effort and expense are necessary depends critically on the goals of the Zapovednik monitoring programme. It is vital that these goals are clearly defined, in order that resources can be allocated, and surveys designed, accordingly.
149 Analysis of ungulate dynamics
REFERENCES
Abernathy, K. (1994) The establishment of a hybrid zone between red and sika deer (Genus Cervus). Molecular Ecology, 3, 551-562. Ackerman, B.B., Lindzey, F.G. & Hemker, T.P. (1986). Predictive energetics model for cougars. In Cats of the World: Biology, Conservation and Management (eds S.D. Miller & D.D. Everett), pp. 333-352. National Wildlife Foundation, Washington. Albon, S.D., Coulson, T.N., Brown, D., Guinness, F.E., Pemberton, J.M. & Clutton-Brock, T.H. (2000) Temporal changes in key factors and key age groups influencing the population dynamics of female red deer. Journal of Animal Ecology, 69, 1099-1110. Anderson, C.R. & Lindzey, F.G. (1998) Results of line intercept probability sampling of mountain lion tracks along the west face of the Bighorn mountains, March 8, 1998. Wyoming Cooperative Fish & Wildlife Research Unit, Laramie. Anderson, D.R., Burnham, K.P. & Thompson, W.L. (2000) Null hypothesis testing: problems, prevalence, and an alternative. Journal of Wildlife Management, 64, 912-923. Barlow, N.D., Beggs, J.R. & Barron, M.C. (2002) Dynamics of common wasps in New Zealand beech forests: a model with density dependence and weather. Journal of Animal Ecology, 71, 663-671. Barnes, R.F.W. (2001) How reliable are dung counts for estimating elephant numbers? African Journal of Ecology, 39, 1-9. Becker, E.F. (1991) A terrestrial furbearer estimator based on probability sampling. Journal of Wildlife Management, 55, 730-737. Becker, E.F., Spindler, M.A. & Osborne, T.O. (1998) A population estimator based on network sampling of tracks in the snow. Journal of Wildlife Management, 62, 968-977. Beckerman, A., Benton, T.G., Ranta, E., Kaitala, V. & Lundberg, P. (2002) Population dynamic consequences of delayed life-history effects. Trends in Ecology and Evolution, 17, 263- 269. Berryman, A.A. (1992) On choosing models for describing and analyzing ecological time-series. Ecology, 73, 694-698. Bjornstad, O.N., Sait, S.M., Stenseth, N.C., Thompson, D.J. & Begon, M. (2001) The impact of specialized enemies on the dimensionality of host dynamics. Nature, 409, 1001-1006. Bromley, G.F. & Kucherenko, S.P. (1983) Ungulates of the southern Far East of Russia. Nauka Publishing, Moscow, Russia (in Russian). Buckland, S.T., Anderson, D.R., Burnham, K.P. & Laake, J.L. (1993) Distance Sampling: Estimating Abundance of Biological Populations. Chapman and Hall, London. Bulmer, M.G. (1975) The statistical analysis of density dependence. Biometrics, 31, 901-911. Burnham, K.P. & Anderson, D.R. (2002) Model Selection and Multimodel Inference: a Practical Information-Theoretic Approach. 2nd edn. Springer-Verlag, New York. Carbone, C., Christie, S., Conforti, K., Coulson, T., Franklin, N., et al. (2001) The use of photographic rates to estimate densities of tigers and other cryptic mammals. Animal Conservation, 4, 75-79. Carbone, C., Christie, S., Conforti, K., Coulson, T., Franklin, N., et al. (2002) The use of photographic rates to estimate densities of cryptic mammals: response to Jennelle et al. Animal Conservation, 5, 121-123. Carbone, C. & Gittleman, J.L. (2002) A common rule for the scaling of carnivore density. Science, 295, 2273-2276. Caughley, G. (1977) Analysis of Vertebrate Populations. John Wiley & Son, Brisbane. Chelintsev, N.G. (1995) Mathematical principles of winter censuses of mammals. Byulleten Moskovskogo Obschestva Ispytatelei Prirody, 100, 3-19 (in Russian).
150 Analysis of ungulate dynamics
Choquenot, D. & Ruscoe, W.A. (2000) Mouse population eruptions in New Zealand forests: the role of population density and seedfall. Journal of Animal Ecology, 69, 1058-1070. Clutton-Brock, T.H., Guinness, F.E. & Albon, S.D. (1982) Red Deer: Behavior and Ecology of Two Sexes. University of Chicago Press, Chicago, USA. Clutton-Brock, T.H., Price, O.F., Albon, S.D. & Jewell, P.A. (1991) Persistent instability and population regulation in Soay sheep. Journal of Animal Ecology, 60, 593-608. Collie, J.S. & Sissenwine, M.P. (1983) Estimating population size from relative abundance data measured with error. Canadian Journal of Fisheries and Aquatic Sciences, 40, 1871-1879. Coulson, T., Catchpole, E.A., Albon, S.D., Morgan, B.J.T., Pemberton, J.M., et al. (2001) Age, sex, density, winter weather, and population crashes in Soay sheep. Science, 292, 1528- 1531. Coulson, T., Milner-Gulland, E.J. & Clutton-Brock, T. (2000) The relative roles of density and climatic variation on population dynamics and fecundity rates in three contrasting ungulate species. Proceedings of the Royal Society of London Series B, 267, 1771-1779. Danilkin, A.A. (1995) Capreolus pygargus. Mammalian Species Accounts, 512, 1-7. Davison, R.P., Mautz, W.W., Hayes, H.H. & Holter, J.B. (1978) The efficiency of food utilization and energy requirements of captive female fishers. Journal of Wildlife Management, 42, 811-821. De Young, C.A., Heffelfinger, J.R., Coughlin, S.P. & Beasom, S.L. (1988) Accuracy of track counts to estimate white-tailed deer abundance. Proceedings of the Annual Conference of the Southeastern Association of Fish and Wildlife Agencies, 42, 464-469. Dennis, B., Kemp, W.P. & Taper, M.L. (1998) Joint density dependence. Ecology, 79, 426-441. Dennis, B. & Otten, M.R.M. (2000) Joint effects of density dependence and rainfall on abundance of San Joaquin kit fox. Journal of Wildlife Management, 64, 388-400. Dennis, B. & Taper, M.L. (1994) Density dependence in time series observations of natural populations: estimation and testing. Ecological Monographs, 64, 205-224. Diefenbach, D.R., Conroy, M.J., Warren, R.J., James, W.E., Baker, L.A. & Hon, T. (1994) A Test of the Scent-Station Survey Technique for Bobcats. Journal of Wildlife Management, 58, 10-17. Dunn, W.C., Donnelly, J.P. & Krausmann, W.J. (2002) Using thermal infrared sensing to count elk in the southwestern United States. Wildlife Society Bulletin, 30, 963-967. Eberhardt, L.L. (1970) Correlation, regression, and density dependence. Ecology, 51, 306-&. Eberhardt, L.L. (1997) Is wolf predation ratio-dependent? Canadian Journal of Zoology, 75, 1940-1944. Eberhardt, L.L. (1998) Applying difference equations to wolf predation. Canadian Journal of Zoology, 76, 380-386. Eberhardt, L.L., Garrott, R.A., Smith, D.W., White, P.J. & Peterson, R.O. (2003) Assessing the impact of wolves on ungulate prey. Ecological Applications, 13, 776-783. Eberhardt, L.L. & Peterson, R.O. (1999) Predicting the wolf-prey equilibrium point. Canadian Journal of Zoology, 77, 494-498. Efron, B. (2003) Second thoughts on the bootstrap. Statistical Science, 18, 135-140. Efron, B. & Tibshirani, R. (1991) Statistical data analysis in the computer age. Science, 253, 390- 395. Efron, B. & Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York. Erb, J., Boyce, M.S. & Stenseth, N.C. (2001) Population dynamics of large and small mammals. Oikos, 92, 3-12. Forchhammer, M.C., Clutton-Brock, T.H., Lindstrom, J. & Albon, S.D. (2001) Climate and population density induce long-term cohort variation in a northern ungulate. Journal of Animal Ecology, 70, 721-729.
151 Analysis of ungulate dynamics
Forchhammer, M.C., Post, E., Stenseth, N.C. & Boertmann, D.M. (2002) Long-term responses in arctic ungulate dynamics to changes in climatic and trophic processes. Population Ecology, 44, 113-120. Formozov, A.N. (1932) Formula for quantitative censusing of mammals by tracks. Russian Journal of Zoology, 11, 66-69 (in Russian). Fowler, C.W. (1981) Density dependence as related to life history strategy. Ecology, 62, 602-610. Fowler, C.W. (1987). A review of density dependence in populations of large mammals. In Current Mammalogy (ed H. Genoways), pp. 401-441. Plenum Press, New York. Frantz, A.C., Schaul, M., Pope, L.C., Fack, F., Schley, L., et al. (2004) Estimating population size by genotyping remotely plucked hair: the Eurasian badger. Journal of Applied Ecology, 41, 985-995. Freckleton, R.P., Sutherland, W.J. & Watkinson, A.R. (in prep.) Census error and the detection of density-dependence. Fuller, T.K. (1989) Population dynamics of wolves in north-central Minnesota. Wildlife Monographs, 1-41. Gaillard, J.M., Festa-Bianchet, M. & Yoccoz, N.G. (1998) Population dynamics of large herbivores: variable recruitment with constant adult survival. Trends in Ecology & Evolution, 13, 58-63. Garant, Y. & Crete, M. (1997) Fisher, Martes pennanti, home range characteristics in a high density untrapped population in southern Quebec. Canadian Field-Naturalist, 111, 359- 364. Georgiadis, N., Hack, M. & Turpin, K. (2003) The influence of rainfall on zebra population dynamics: implications for management. Journal of Applied Ecology, 40, 125-136. Gerow, K.G., Miquelle, D.G. & Aramilev, V.V. (2005). Monitoring Tiger Prey Abundance in the Russian Far East. In Statistics: a Guide to the Unknown (eds R. Peck, G. Casella, G.W. Cobb, R. Hoerl, D. Nolan, R. Starbuck & H. Stern), pp. 105-118. Duxbury, Belmont, CA. Gerrodette, T. (1987) A power analysis for detecting trends. Ecology, 68, 1364-1372. Ginzburg, L.R. & Jensen, C.X.J. (2004) Rules of thumb for judging ecological theories. Trends in Ecology & Evolution, 19, 121-126. Glowacinski, Z. & Profus, P. (1997) Potential impact of wolves Canis lupus on prey populations in eastern Poland. Biological Conservation, 80, 99-106. Gorman, M.L., Mills, M.G., Raath, J.P. & Speakman, J.R. (1998) High hunting costs make African wild dogs vulnerable to kleptoparasitism by hyaenas. Nature, 391, 479-481. Gromyko, M.N. (2005). Physical-geographic characteristics of Sikhote-Alin Zapovednik. In Tigers in Sikhote-Alin Zapovednik: Ecology and Conservation (eds D.G. Miquelle, E.N. Smirnov & J.M. Goodrich), pp. 14-18. PSP, Vladivostok (in Russian). Guthery, F.S., Brennan, L.A., Peterson, M.J. & Lusk, J.J. (2005) Information theory in wildlife science: critique and viewpoint. Journal of Wildlife Management, 69, 457-465. Haroldson, B.S., Wiggers, E.P., Beringer, J., Hansen, L.P. & McAninch, J.B. (2003) Evaluation of aerial thermal imaging for detecting white-tailed deer in a deciduous forest environment. Wildlife Society Bulletin, 31, 1188-1197. Havens, K.J. & Sharp, E.J. (1998) Using thermal imagery in the aerial survey of animals. Wildlife Society Bulletin, 26, 17-23. Hayward, G.D., Miquelle, D.G., Smirnov, E.N. & Nations, C. (2002) Monitoring Amur tiger populations: characteristics of track surveys in snow. Wildlife Society Bulletin. Hebblewhite, M. (2005) Predation by wolves interacts with the North Pacific Oscillation (NPO) on a western North American elk population. Journal of Animal Ecology, 74, 226-233. Hebblewhite, M., Pletscher, D.H. & Paquet, P.C. (2002) Elk population dynamics in areas with and without predation by recolonizing wolves in Banff National Park, Alberta. Canadian Journal of Zoology, 80, 789-799.
152 Analysis of ungulate dynamics
Hedley, S.L. & Buckland, S.T. (2004) Spatial models for line transect sampling. Journal of Agricultural, Biological and Environmental Statistics, 9, 181-199. Hornocker, M.G. (1970) An analysis of mountain lion predation upon mule deer and elk in the Idaho Primitive Area. Wildlife Monographs, 21, 1-39. Houston, D.B. (1982) The Northern Yellowstone Elk: Ecology and Management. Macmillan Publishing Co., New York. IUCN (2002) 2002 IUCN Red List of Threatened Species. http://www.redlist.org, Downloaded 10 June 2003. Jacobson, A.R., Provenzale, A., Von Hardenberg, A., Bassano, B. & Festa-Bianchet, M. (2004) Climate forcing and density dependence in a mountain ungulate population. Ecology, 85, 1598-1610. Jedrzejewska, B., Jedrzejewski, W., Bunevich, A.N., Milkowski, L. & Krasinski, Z.A. (1997) Factors shaping population densities and increase rates of ungulates in Bialowieza Primeval Forest (Poland and Belarus) in the 19th and 20th centuries. Acta Theriologica, 42, 399-451. Jedrzejewska, B., Jedrzejewski, W., Bunevich, A.N., Milkowski, L. & Okarma, H. (1996) Population dynamics of wolves Canis lupus in Bialowieza primeval forest (Poland and Belarus) in relation to hunting by humans, 1847-1993. Mammal Review, 26, 103-126. Jennelle, C.S., Runge, M.C. & MacKenzie, D.I. (2002) The use of photographic rates to estimate densities of tigers and other cryptic mammals: a comment on misleading conclusions. Animal Conservation, 5, 119-120. Johnson, J.B. & Omland, K.S. (2004) Model selection in ecology and evolution. Trends in Ecology & Evolution, 19, 101-108. Karanth, K.U. (1999). Counting the tiger's prey, reliably. In Riding the Tiger: Tiger Conservation in Human-Dominated Landscapes (eds J. Seidensticker, S. Christie & P. Jackson), pp. 104-105. Cambridge University Press, Cambridge, UK. Karanth, K.U. & Nichols, J.D. (1998) Estimation of tiger densities in India using photographic captures and recaptures. Ecology, 79, 2852-2862. Karanth, K.U., Nichols, J.D., Kumar, N.S., Link, W.A. & Hines, J.E. (2004) Tigers and their prey: predicting carnivore densities from prey abundance. Proceedings of the National Academy of Sciences of the United States of America, 101, 4854-4858. Karanth, K.U. & Stith, B.M. (1999). Prey depletion as a critical determinant of tiger population viability. In Riding the Tiger: Tiger Conservation in Human-Dominated Landscapes (eds J. Seidensticker, S. Christie & P. Jackson), pp. 100-113. Cambridge University Press, Cambridge, UK. Karanth, K.U. & Sunquist, M.E. (1992) Population-Structure, Density and Biomass of Large Herbivores in the Tropical Forests of Nagarahole, India. Journal of Tropical Ecology, 8, 21-35. Kerley, L.L., Goodrich, J.M., Miquelle, D.G., Smirnov, E.N., Quigley, H.B. & Hornocker, M.G. (2003) Reproductive parameters of wild female Amur (Siberian) tigers (Panthera tigris altaica). Journal of Mammalogy, 84, 288-298. Kucherenko, S.P. (2001) Amur tigers at the turn of the century. Okhota i okhotnichie khozyaistvo, 4, 20-24 (in Russian). Kuzyakin, V.A. (1983). Results of modelling winter transect counts. In Scientific Proceedings: Winter Transect Counts of Game Animals, pp. 193-229. Central Research Laboratory of Glavokhota, Moscow (in Russian). Kuzyakin, V.A. & Lomanov, I.K. (1986). Factors affecting daily travel distance of moose in the European part of the Russian Federation. In Scientific Proceedings: Winter Transect Counts of Game Animals, pp. 5-21. Central Research Laboratory of Glavokhota, Moscow (in Russian).
153 Analysis of ungulate dynamics
Langton, S.D., Aebischer, N.J. & Robertson, P.A. (2002) The estimation of density dependence using census data from several sites. Oecologia, 133, 466-473. Litvaitis, J.A. & Mautz, W.W. (1976) Energy utilization of three diets fed to a captive red fox. Journal of Wildlife Management, 40, 365-368. Lomanov, I.K. (2000) Winter transect count of game animals for large territories: results and prospects. Zoologichesky Zhurnal, 79, 430-436 (in Russian). Lubow, B.C. & Smith, B.L. (2004) Population dynamics of the Jackson elk herd. Journal of Wildlife Management, 68, 810-829. Mandujano, S. & Gallina, S. (1995) Comparison of deer censusing methods in tropical dry forest. Wildlife Society Bulletin, 23, 180-186. Markov, N.I. (1997) Population dynamics of wild boar, Sus scrofa, in Sverdlovsk oblast and its relation to climatic factors. Russian Journal of Ecology, 28, 269-274. Marques, F.F.C., Buckland, S.T., Goffin, D., Dixon, C.E., Borchers, D.L., et al. (2001) Estimating deer abundance from line transect surveys of dung: sika deer in southern Scotland. Journal of Applied Ecology, 38, 349-363. Marshal, J.P. & Boutin, S. (1999) Power analysis of wolf-moose functional responses. Journal of Wildlife Management, 63, 396-402. McCullough, D.R. (1992). Concepts of large herbivore population dynamics. In Wildlife 2001: Populations (eds D.R. McCullough & R.H. Barrett), pp. 967-984. Elsevier Science Publishers Ltd., London. McLaren, B.E. & Peterson, R.O. (1994) Wolves, moose, and tree rings on Isle Royale. Science, 266, 1555-1558. Mduma, S.A.R., Sinclair, A.R.E. & Hilborn, R. (1999) Food regulates the Serengeti wildebeest: a 40-year record. Journal of Animal Ecology, 68, 1101-1122. Messier, F. (1991) The significance of limiting and regulating factors on the demography of moose and white-tailed deer. Journal of Animal Ecology, 60, 377-393. Messier, F. (1994) Ungulate population models with predation: a case study with the North American moose. Ecology, 75, 478-488. Milner, J.M., Elston, D.A. & Albon, S.D. (1999) Estimating the contributions of population density and climatic fluctuations to interannual variation in survival of Soay sheep. Journal of Animal Ecology, 68, 1235-1247. Miquelle, D.G., Smirnov, E.N., Merrill, T.W., Myslenkov, A.E., Quigley, H.B., et al. (1999). Hierarchical spatial analysis of Amur tiger relationships to habitat and prey. In Riding the Tiger: Tiger Conservation in Human-Dominated Landscapes (eds J. Seidensticker, S. Christie & P. Jackson), pp. 71-99. Cambridge University Press, Cambridge, UK. Miquelle, D.G., Smirnov, E.N., Quigley, H.B., Hornocker, M.G., Nikolaev, I.G. & Matyushkin, E.N. (1996) Food habits of Amur tigers in Sikhote-Alin Zapovednik and the Russian Far East, and implications for conservation. Journal of Wildlife Research, 1, 138-147. Miquelle, D.G., Stephens, P.A., Smirnov, E.N., Goodrich, J.M., Zaumyslova, O.Yu. & Myslenkov, A.E. (2005). Tigers and Wolves in the Russian Far East: Competitive Exclusion, Functional Redundancy and Conservation Implications. In Large Carnivores and the Conservation of Biodiversity (eds J.C. Ray, J. Berger, K.H. Redford & R. Steneck), pp. 179-207. Island Press, New York. Mirutenko, V.S. (1986). Reliability of the analysis of route surveys of game animals. In Issues of Game Animal Censuses, pp. 21-28. Central Research Laboratory of Glavokhota, Moscow (in Russian). Mooty, J.J., Karns, P.D. & Heisey, D.M. (1984) The relationship between white-tailed deer track counts and pellet-group surveys. Journal of Wildlife Management, 48, 275-279. Murdie, G. & Hassell, M.P. (1973). Food distribution, searching success and predator-prey models. In The Mathematical Theory of the Dynamics of Biological Populations (eds M.S. Bartlett & R.W. Hiorns), pp. 87-101. Academic Press, London.
154 Analysis of ungulate dynamics
Myslenkov, A.E. & Voloshina (2005). Results of aerial surveys of ungulates in Sikhote-Alin reserve. In Results of protection and research of the Sikhote-Alin natural landscape. Papers presented at the International Science and Management Conference devoted to the 70th anniversay of the Sikhote-Alin State Reserve, Terney, Primorksiy Region, September 20-23, 2005 (eds I.V. Potikha, D.G. Miquelle, M.N. Gromyko, E.A. Pimenova, L.P. Khobtoneva, O.Yu. Zaumyslova, N.E. Labetskaya & L.V. Ivanova), pp. 255-261. Primpoligraphkombinat, Vladivostok (in Russian). Mysterud, A. (1999) Seasonal migration pattern and home range of roe deer (Capreolus capreolus) in an altitudinal gradient in southern Norway. Journal of Zoology, 247, 479- 486. Mysterud, A., Coulson, T. & Stenseth, N.C. (2002) The role of males in the dynamics of ungulate populations. Journal of Animal Ecology, 71, 907-915. Nagy, K.A. (1987) Field metabolic rate and food requirement scaling in mammals and birds. Ecological Monographs, 57, 111-128. Nagy, K.A. (1994) Field bioenergetics of mammals: what determines field metabolic rates? Australian Journal of Zoology, 42, 43-53. Nagy, K.A., Girard, I.A. & Brown, T.K. (1999) Energetics of free-ranging mammals, reptiles, and birds. Annual Review of Nutrition, 19, 247-277. Nowak, R.M. (1999) Walker's Mammals of the World. 6th edn. Johns Hopkins University Press, Baltimore. Noyes, J.H., Johnson, B.K., Riggs, R.A., Schlegel, M.W. & Coggins, V.L. (2000) Assessing aerial survey methods to estimate elk populations: a case study. Wildlife Society Bulletin, 28, 636-642. Ogutu, J.O. & Dublin, H.T. (1998) The response of lions and spotted hyaenas to sound playbacks as a technique for estimating population size. African Journal of Ecology, 36, 83-95. Owen-Smith, N. (1990) Demography of a large herbivore, the greater kudu Tragelaphus strepsiceros, in relation to rainfall. Journal of Animal Ecology, 59, 893-913. Parker, K.L., Robbins, C.T. & Hanley, T.A. (1984) Energy expenditures for locomotion by mule deer and elk. Journal of Wildlife Management, 48, 474-488. Patterson, B.R., Quinn, N.W.S., Becker, E.F. & Meier, D.B. (2004) Estimating wolf densities in forested areas using network sampling of tracks in snow. Wildlife Society Bulletin, 32, 938-947. Peek, J.M., Dennis, B. & Hershey, T. (2002) Predicting population trends of mule deer. Journal of Wildlife Management, 66, 729-736. Pikunov, D.G., Abramov, V.K., Korkisko, V.G., Nikolaev, I.G. & Belov, A.I. (2000) Full range survey of the Far Eastern Leopard and Amur tiger in Southwestern Primorski Krai. Report to WWF, WCS and Tigris Foundation, Vladivostok. Pollard, E., Lakhani, K.H. & Rothery, P. (1987) The detection of density-dependence from a series of annual censuses. Ecology, 68, 2046-2055. Post, E., Stenseth, N.C., Peterson, R.O., Vucetich, J.A. & Ellis, A.M. (2002) Phase dependence and population cycles in a large-mammal predator-prey system. Ecology, 83, 2997-3002. Rabe, M.J., Rosenstock, S.S. & de Vos, J.C. (2002) Review of big-game survey methods used by wildlife agencies of the western United States. Wildlife Society Bulletin, 30, 46-52. Ricker, W.E. (1973) Linear Regressions in Fishery Research. Journal of the Fisheries Research Board of Canada, 30, 409-434. Royama, T. (1977) Population persistence and density-dependence. Ecological Monographs, 47, 1-35. Sadlier, L.M.J., Webbon, C.C., Baker, P.J. & Harris, S. (2004) Methods of monitoring red foxes Vulpes vulpes and badgers Meles meles: are field signs the answer? Mammal Review, 34, 75-98.
155 Analysis of ungulate dynamics
Sæther, B.E. (1997) Environmental stochasticity and population dynamics of large herbivores: a search for mechanisms. Trends in Ecology & Evolution, 12, 143-149. Sæther, B.E., Engen, S., Filli, F., Aanes, R., Schroder, W. & Andersen, R. (2002) Stochastic population dynamics of an introduced Swiss population of the ibex. Ecology, 83, 3457- 3465. Samuel, M.D., Garton, E.O., Schlegel, M.W. & Carson, R.G. (1987) Visibility bias during aerial surveys of elk in Northcentral Idaho. Journal of Wildlife Management, 51, 622-630. Schaller, G.B. (1967) The Deer and the Tiger: a Study of Wildlife in India. The University of Chicago Press, Chicago, USA. Schwarz, C.J. & Seber, G.A.F. (1999) Estimating animal abundance: Review III. Statistical Science, 14, 427-456. Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics, 6, 461-464. Seip, D.R. (1992) Factors limiting woodland caribou populations and their interrelationships with wolves and moose in Southeastern British Columbia. Canadian Journal of Zoology, 70, 1494-1503. Shenk, T.M., White, G.C. & Burnham, K.P. (1998) Sampling-variance effects on detecting density dependence from temporal trends in natural populations. Ecological Monographs, 68, 445-463. Skogland, T. (1985) The effects of density-dependent resource limitations on the demography of wild reindeer. Journal of Animal Ecology, 54, 359-374. Slade, N.A. (1977) Statistical detection of density dependence from a series of sequential censuses. Ecology, 58, 1094-1102. Smirnov, E.N. & Miquelle, D.G. (1999). Population dynamics of the Amur tiger in Sikhote-Alin Zapovednik, Russia. In Riding the Tiger: Tiger Conservation in Human-Dominated Landscapes (eds J. Seidensticker, S. Christie & P. Jackson), pp. 61-70. Cambridge University Press, Cambridge, UK. Smirnov, V.S. (1973). Mathematical derivations of game animals abundance surveys. In Methods for the Census of Game Animals in Forested Areas, pp. 13-29. Proceedings of Oksky State Reserve, Ryazan, Russia (in Russian). Smith, J.L.D., McDougal, C.W. & Sunquist, M.E. (1987). Female land tenure systems in tigers. In Tigers of the World: the Biology, Biopolitics, Management and Conservation of an Endangered Species (eds R.L. Tilson & U.S. Seal), pp. 97-109. Noyes Publications. Stenseth, N.C., Chan, K.S., Framstad, E. & Tong, H. (1998) Phase- and density-dependent population dynamics in Norwegian lemmings: interaction between deterministic and stochastic processes. Proceedings of the Royal Society of London Series B-Biological Sciences, 265, 1957-1968. Stephens, P.A., Buskirk, S.W., Hayward, G.D. & Martinez del Rio, C. (2005) Information theory and hypothesis testing: a call for pluralism. Journal of Applied Ecology, 42, 4-12. Stephens, P.A., d'Sa, C.A., Sillero-Zubiri, C. & Leader-Williams, N. (2001) Impact of livestock and settlement on the large mammalian wildlife of Bale Mountains National Park, southern Ethiopia. Biological Conservation, 100, 307-322. Stoen, O.G. & Wegge, P. (1996) Prey selection and prey removal by tiger (Panthera tigris) during the dry season in lowland Nepal. Mammalia, 60, 363-373. Sunquist, M.E., Karanth, K.U. & Sunquist, F. (1999). Ecology, behaviour and resilience of the tiger and its conservation needs. In Riding the Tiger: Tiger Conservation in Human- Dominated Landscapes (eds J. Seidensticker, S. Christie & P. Jackson), pp. 5-18. Cambridge University Press, Cambridge, UK. Sutherland, W.J. (1996) From Individual Behaviour to Population Ecology. Oxford University Press, Oxford, UK. Taper, M.L. & Gogan, P.J.P. (2002) The Northern Yellowstone elk: density dependence and climatic conditions. Journal of Wildlife Management, 66, 106-122.
156 Analysis of ungulate dynamics
Thompson, W.L., White, G.C. & Gowan, C. (1998) Monitoring Vertebrate Populations. Academic Press, San Diego, USA. Turchin, P. (1998) Quantitative Analysis of Movement. Sinauer Associates, Sunderland, MA. Van Ballenberghe, V. & Ballard, W.B. (1994) Limitation and regulation of moose populations: the role of predation. Canadian Journal of Zoology, 72, 2071-2077. Van Sickle, W.D. & Lindzey, F.G. (1991) Evaluation of a cougar population estimator based on probability sampling. Journal of Wildlife Management, 55, 738-743. Vickery, W.L. & Nudds, T.D. (1984) Detection of density-dependent effects in annual duck censuses. Ecology, 65, 96-104. Walter, M.J. & Hone, J. (2003) A comparison of 3 aerial survey techniques to estimate wild horse abundance in the Australian Alps. Wildlife Society Bulletin, 31, 1138-1149. Wasser, S.K., Davenport, B., Ramage, E.R., Hunt, K.E., Parker, M., et al. (2004) Scat detection dogs in wildlife research and management: application to grizzly and black bears in the Yellowhead Ecosystem, Alberta, Canada. Canadian Journal of Zoology, 82, 475-492. Webbon, C.C., Baker, P.J. & Harris, S. (2004) Faecal density counts for monitoring changes in red fox numbers in rural Britain. Journal of Applied Ecology, 41, 768-779. Wiklund, C.G. (2001) Food as a mechanism of density-dependent regulation of breeding numbers in the merlin, Falco columbarius. Ecology, 82, 860-867. Williams, B.K., Nichols, J.D. & Conroy, M.J. (2002) Analysis and Management of Animal Populations. San Diego, CA, Academic Press. Wilson, G.J. & Delahay, R.J. (2001) A review of methods to estimate the abundance of terrestrial carnivores using field signs and observation. Wildlife Research, 28, 151-164. Yang, Q.S., Meng, X.X., Xia, L. & Feng, Z.J. (2003) Conservation status and causes of decline of musk deer (Moschus spp.) in China. Biological Conservation, 109, 333-342. Zaitsev, V.A. (1991) The Musk Deer of Sikhote-Alin: Ecology and Behaviour. Nauka, Moscow (in Russian). Zaumyslova, O.Yu. (2000). Long term population-dynamics of ungulates in the Sikhote-Alin Reserve from winter transect count data. In Analysis of Long-Term Monitoring Data of Nature Components in Nature Reserves in the Russian Far East (ed A.A. Astafiev), pp. 70-79. Dalnauka, USAID, Vladivostok (in Russian). Zaumyslova, O.Yu. (2005). Ungulate population dynamics in the coastal zone of the Sikhote-Alin Reserve. In Results of protection and research of the Sikhote-Alin natural landscape. Papers presented at the International Science and Management Conference devoted to the 70th anniversay of the Sikhote-Alin State Reserve, Terney, Primorksiy Region, September 20-23, 2005 (eds I.V. Potikha, D.G. Miquelle, M.N. Gromyko, E.A. Pimenova, L.P. Khobtoneva, O.Yu. Zaumyslova, N.E. Labetskaya & L.V. Ivanova), pp. 191-202. Primpoligraphkombinat, Vladivostok (in Russian). Zaumyslova, O.Yu., Puzachenko, J.G. & Puzachenko, A.J. (2001) Wild boar population dynamics in Sikhote-Alin Reserve. Unpubl. report.
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