Assessing estimators of feral goat (Capra hircus) abundance
John Paul Tracey
A thesis submitted in fulfillment of the requirements for the Degree of Master of Applied Science (Resource Management) Division of Health, Design and Science University of Canberra June 2004 © 2004 John P. Tracey
For Lisa, Kirk, Jaydan, Jack and Alana
Usted es mi amor y mi fuerza
Summary
(1) Reliable measures of population abundance are essential for managing wildlife effectively. Aerial surveys provide a rapid and efficient means of surveying large mammals and many techniques have been developed to adjust for the inability to count all animals within transects. The probability of detection varies according to a range of factors which are important to consider when estimating density. Standardised survey methods developed in flat country are not readily transferable to steep terrain due to safety, access and difficulties delineating transect widths. Other methods have logistic constraints and must adhere to various other assumptions.
(2) Density estimators are seldom examined using actual population size, hence their ability to correct for true bias is unknown. Studies that compare techniques are difficult to interpret because of the uncertainty of adherence to their respective assumptions. Factors influencing detection probability, estimators that correct for bias, the validity of their assumptions and how these relate to true density are important considerations for selecting suitable methods. The aim of this study was to obtain accurate and reliable methods for estimating the density of feral goats by improving predictions of detection probability, investigating the assumptions of aerial surveys, and examining the accuracy of 15 density estimators by comparing with total counts of feral goats.
(3) Group size, vegetation and observer were the most important factors influencing the probability of observing a group of goats during aerial surveys. However, different approaches to analysing these data influenced the significance of variables and the predicted probabilities. Goat colour, type of helicopter, site and rear observer experience in hours were also found to be significant (P<0.05) when using likelihood equations based on all animals in the population rather than only those in the sample. The slope of the terrain was also shown to significantly (P=0.014) affect the probability of detection.
(4) Indices are commonly used in wildlife management for their simplicity and practicality, but their validity has been questioned because of variable probability of detection. Results of this study suggest aerial survey indices are useful in monitoring a
i range of medium-sized mammal species across space and time if differences in detection probability between species, group size, vegetation and observer are considered and their effects are standardised.
(5) An assumption of most sampling regimes that is fundamental but rarely examined is that animals are not counted more than once. In this study the behavioural responses of feral goats to helicopters were investigated as a basis for estimating the probability that goats were recounted. No long-term consequences were evident in feral goat behaviour of responses to helicopters. However, helicopter surveys were found to alter the structure of 42% of groups observed, with 28% of groups merging with others and 14% splitting into separate groups. Therefore, group size estimated from the air should not be considered as biologically important, and when estimating density, researchers should also avoid using group sizes determined from independent ground observations to correct group sizes determined from aerial surveys. Goats were also more likely to flush further when helicopters were within 150 m, which is close to or within standard helicopter strip widths. Substantial movement occurred between transects and 21% of goats were estimated to be available for recounting in adjacent transects.
(6) Different detection probabilities between groups of goats may be particularly relevant when using double-counting, where multiple observers are ‘capturing’ and ‘recapturing’ animals in the same instant. Many analyses test and adjust for this ‘unequal catchability’ assumption in different ways, with the approaches of Huggins and Alho allowing prediction of unique probability values for a range of co-variates. The approach of Chao attempts to correct for skewed distributions in small samples. The Horvitz-Thompson approach provides a useful basis for estimating abundance (or density) when detection probability can be estimated and is known to vary between observations according to a range of independent variables, and also avoids errors associated with averaging group size.
(7) After correcting for recounting, the Alho estimator applied to helicopter surveys was the most accurate (Bias = 0.02) and reliable of all techniques, which suggests that estimates were improved by taking into account unconditional detection probability and correcting individual observations according to their characteristics. The positive bias
ii evident in the Chao (Bias = 0.28) and Petersen (Bias = 0.15) aerial survey estimators may have been a result of averaging detection probability across all observations. The inconsistency and inaccuracy of the ground-based area-count technique emphasises the importance of other assumptions in density estimation, such as representative sampling and availability bias. The accuracy of index-manipulation-index techniques was dependent on the indices used. Capture-recapture estimates using mustering showed slight negative bias (Bias = -0.08), which was likely a result of increased probability of re-capture (i.e. trap happy). Ground-based capture-resight estimates were labour intensive and positively biased (Bias = 0.13), likely due to underestimating the area sampled, or overestimating the number of unmarked individuals with each sample.
(8) Helicopter survey using double-counting is recommended for estimating the density of feral goats in steep terrain. However, consideration of recounting under intensive sampling regimes and adjustments for the factors that influence unconditional detection probability is required.
iii
Acknowledgments
Sincere thanks to my supervisors Peter Fleming and Jim Hone who provided guidance and encouragement throughout this study and to Glen Saunders for his on-going support. Thanks also to Greg Jones, Matthew Gentle and Ryan Breen for assistance with field work, friendship and ‘flehmen’ brew, and to many others who spent long hours collecting data. I greatly appreciate the efforts of Brian Lukins and Barry Kay for support in the office, Ken England, Glen Walker and Richard Mason for their assistance in aerial surveys, and Matt Hollingdale and Mark Rogers for reliable and safe helicopter piloting. Gavin Melville provided sound advice and assistance with data analysis, especially with the coding of Alho’s maximum likelihood equations, and deriving the variance estimate for the Horvitz- Thompson estimator. The statistical advice and assistance of Remy van de Ven and Steve McLeod is also gratefully acknowledged. Ann Tracey, Bruce Mitchell and Michelle Walter provided editorial comments. Peter Worsley and Ian McGowen assisted with spatial data. Mike, Ant and Chris Martin, Donald and Doug Arnott, and Kevin Cluff kindly provided access to their land. Jenni Tarleton and Corinne King assisted with line drawings and figures. Funding for this project was provided by the Bureau of Rural Sciences (National Feral Animal Control Program - Natural Heritage Trust), Wildlife and Exotic Disease Preparedness Program and NSW Agriculture.
v Contents
Summary ...... i Certificate of Authorship of Thesis...... iv Acknowledgments...... v List of Figures ...... ix List of Tables...... xi CHAPTER 1: INTRODUCTION 1.1 Importance of estimating abundance...... 1 1.1.1 Why estimate feral goat density in Australia? ...... 2 1.2 Sampling design and sources of error ...... 3 1.2.1 Sampling intensity...... 3 1.2.2 Sources of error ...... 3 1.2.3 Accuracy and precision...... 5 1.2.4 Stratification...... 5 1.3 Review of techniques...... 6 1.3.1 Capture-recapture methods ...... 6 1.3.2 Distance sampling methods...... 9 1.3.3 Removal methods ...... 10 1.3.4 Aerial survey methods...... 12 1.4 Aims of the study...... 14 CHAPTER 2: GENERAL METHODS 2.1 Study Site ...... 16 2.2 Total counts ...... 17 2.3 Aerial survey...... 18 2.3.1 Double-counting...... 21 2.3.2 Transect width and flying height...... 22 2.4 Notation...... 23 CHAPTER 3: FACTORS INFLUENCING DETECTION PROBABILITY IN AERIAL SURVEYS 3.1 Introduction...... 25 3.2 Methods...... 27 3.2.1 Variables for the detection probability model ...... 27 vi 3.2.2 Distance to the mid-point of the transect ...... 29 3.2.3 Analyses ...... 32 3.3 Results ...... 34 3.4 Discussion...... 44 CHAPTER 4: BEHAVIOURAL RESPONSES OF FERAL GOATS DURING HELICOPTER SURVEYS 4.1 Introduction...... 48 4.2 Methods...... 51 4.2.1 Behavioural observations ...... 51 4.2.2 Analyses ...... 53 4.3 Results ...... 56 4.4 Discussion...... 62 4.4.1 Helicopter distance ...... 62 4.4.2 Prior activity and responses of goats...... 63 4.4.3 Herd responses...... 64 4.4.4 Sex and age response differences...... 65 4.4.5 Habituation or aversion?...... 66 4.4.6 Helicopter type...... 67 4.4.7 Other variables ...... 68 4.4.8 Conclusion ...... 69 CHAPTER 5: TESTING ASSUMPTIONS IN AERIAL SURVEY USING GROUND OBSERVATIONS 5.1 Introduction...... 70 5.2 Methods...... 71 5.2.1 Ground observations...... 71 5.2.2 Verifying colour ratios ...... 73 5.2.3 Delineating transect boundaries...... 73 5.2.4 Probability animals are available for recounting...... 74 5.3 Results ...... 77 5.3.1 Assumption 1: All animals are counted within the designated strip...... 77 5.3.2 Assumption 2: Transect boundaries are accurately delineated...... 79 5.3.3 Assumption 3: Animals are not counted more than once...... 80
vii 5.4 Discussion...... 84 5.4.1 Assumption 1: All animals are counted within the designated strip...... 84 5.4.2 Assumption 2: Transect boundaries are accurately delineated...... 87 5.4.3 Assumption 3: Animals are not counted more than once...... 88 CHAPTER 6: AERIAL SURVEYS AS INDICES 6.1 Introduction...... 90 6.2 Methods...... 91 6.3 Results ...... 92 6.4 Discussion...... 96 6.4.1 Feral goats ...... 98 6.4.2 Macropodoids ...... 98 6.4.3 Conclusion ...... 99 CHAPTER 7: DENSITY ESTIMATION AND KNOWN NUMBERS 7.1 Introduction...... 101 7.2 Methods...... 107 7.2.1 Aerial survey ...... 107 7.2.2 Area count technique...... 111 7.2.3 Ground-based capture-recapture...... 112 7.2.4 Index-manipulation-index ...... 113 7.2.5 Comparison of estimates...... 113 7.3 Results ...... 114 7.3.1 Aerial survey ...... 114 7.3.2 Area count technique...... 115 7.3.3 Ground-based capture-recapture...... 117 7.3.4 Index-manipulation-index ...... 118 7.4 Discussion...... 119 CHAPTER 8: GENERAL DISCUSSION...... 124 References...... 129
viii List of Figures
Figure 2-1: Helicopter survey in the Coolah Tops showing surveying height, strip width, calibrating markers, observer seating position and distance unavailable beneath the helicopter...... 20
Figure 3-1: Parameters for estimating the distance (cd and cu) from observers to the midpoint of the transect...... 29 Figure 3-2: Predicted relationship between group size and unconditional detection
probability (pd) of feral goat groups for three vegetation types...... 36 Figure 3-3: Relationship between mean unconditional detection probability of feral goat groups and vegetation cover (%)...... 37
Figure 3-4: Estimates of pd for vegetation types...... 37
Figure 3-5:Predicted relationship for detection probability (pd) and rear observer hours ...39
Figure 3-6: Unconditional detection probability (pd) estimates for mixed, light, coloured and dark groups of feral goats...... 40 Figure 3-7: Relationship between slope and mean detection probability of feral goats...... 41
Figure 3-8: Relationship between relative slope (Cd and Cu, degrees) and mean detection probability of groups of feral goats...... 42
Figure 3-9: Relationship between mean detection probability (pc) of feral goat groups and
distance from observers to the mid-point of the transect (cd and cu)...... 43 Figure 3-10: Relationship between distance (c) to the mid-point of the transect and degree slope at varying survey heights...... 44 Figure 4-1: The relationship between the percentage of feral goats displaying alert behaviour and horizontal distance (m) from the helicopter...... 58 Figure 4-2: The relationship between the distance (m) moved by feral goats and horizontaldistance (m) from the helicopter...... 59 Figure 4-3: Percentage of feral goats alert relative to their activity before disturbance by a helicopter...... 60 Figure 4-4: Mean distances moved by feral goats relative to their activity before disturbance from a helicopter...... 60
ix Figure 4-5: The relationship between density (goats km-2) and the percentage of goat groups that displayed alert behaviour in response to helicopters, recorded by ground- based observers...... 61
Figure 5-1: Representation for calculating the perpendicular distance goats moved (dp) from the transect during aerial surveys...... 75 Figure 5-2: Percentage of feral goat groups observed moving and standing from the air and ground...... 77 Figure 5-3: Percentage of feral goat groups observed from the air and ground in four vegetation communities ...... 78 Figure 5-4: Percentage of light, coloured and dark feral goats observed from helicopters and in ground musters...... 78 Figure 5-5: The probability that a group of goats (y) will move x distance perpendicular to the transect direction...... 81 Figure 5-6: Contrast of white (4) and dark (1) goats in the Coolah Tops...... 86 Figure 6-1: Detection probabilities for six sympatric medium-sized mammals using double- count helicopter surveys...... 93 Figure 6-2: Corrected and uncorrected indices of eastern grey kangaroos and common wallaroos observed during helicopter surveys...... 94 Figure 6-3: Relative changes in corrected and uncorrected indices of eastern grey kangaroos (a) and common wallaroos (b) between sampling periods...... 95 Figure 7-1: Bias associated with five estimators of feral goat density for eight sites where known numbers were obtained and average bias...... 114 Figure 7-2: Bias associated with five estimators of feral goat density for eight sites where
known numbers were obtained after correcting for recounting (pa = 0.21)...... 115 Figure 7-3: Bias associated with ground-based area counts using estimators uncorrected (Area count) and corrected (Petersen and Chao) for detection probability...... 117 Figure 7-4: Bias associated with a Petersen capture-recapture technique using mustering and a survival-modified estimator using re-sightings from ground observations to estimate the density of feral goats on four sites...... 118 Figure 7-5: Bias for index-manipulation-index estimates using six indices on two sites with known numbers...... 119
x List of Tables
Table 2-1: Notation for parameters and statistics used for capture-recapture models (after Seber 1982; Pollock et al. 1990) and for equations used to derive the probability of recounting...... 24 Table 3-1: Variables included in log-linear and logistic regression modelling for
theresponse to unconditional detection probability (pd) of groups of feral goats...... 28 Table 3-2: Notation for parameters and statistics for estimating the distance from observers to the midpoint of the transect...... 30 Table 3-3: Analysis of deviance for the logistic regression model predicting unconditional
detection probability (pd)...... 35
Table 3-4: Predicted unconditional detection probabilities (pd) for individual observers using a weighted average of observer sightings...... 38 Table 4-1: Variables included in step-wise multiple regression and analyses of variance for predicting alert responses caused by a helicopter ...... 55 Table 4-2: Significance values using an analysis of variance following step-wise multiple regression for alert scale, alert and distance moved models...... 57
Table 5-1: Predicted probabilities (pm) of groups of goats, once available for sampling, moving to additional transects...... 82 Table 6-1: Variables affecting conditional detection probability of six sympatric medium sized mammals in helicopter surveys using binomial linear modelling...... 92 Table 7-1: Notation for parameters and statistics used for the Horvitz-Thompson estimator...... 109 Table 7-2: The final fixed effects model of the main determinants of detection probability
(pc) from area counts...... 116
xi
CHAPTER 1
INTRODUCTION
1.1 Importance of estimating abundance
Measures of abundance are vital for the management of wildlife populations (Hone 1994; Krebs 1999). Most valuable information about a species relies on some measure of population size, including measuring rates of increase (e.g. Southwell and Pickles 1993) and rates of decline (e.g. Martin 1985; Borner et al. 1987), monitoring changes in endangered species (e.g. Pardon et al. 2003), assessing impacts of animals on vegetation (e.g. Maas 1997; Choquenot 1994; Kessler 2002; Courchamp et al. 2003), measuring the effects of predation (e.g. Choquenot et al. 1997), measuring the success of management regimes (e.g. Saunders and Bryant 1988; Fleming et al. 2000), and determining rates of disease transmission (e.g. Pech and Hone 1988; McCallum et al. 2001).
Abundance can be considered in three ways: as population size, the number of animals in a population, as absolute density, the number of animals within a unit area, or as a density index, some correlative of absolute density (Caughley 1980; Southwell 1989). Many questions posed to wildlife managers can be resolved using relative measures of density. These usually rely on indices of abundance that relate in some form to changes in the actual population. Some examples include the number of kangaroos (Macropus spp.) per km (Southwell 1989), birds observed in a 20 minute search (Griffioen and Clarke 2002), rabbits (Oryctolagus cuniculus) per spotlight km (Caley and Morley 2002), active warren entrance counts for rabbits (Ballinger and Morgan 2002), number of quoll (Dasyurus maculatus) tracks per sand-plot (Körtner et al. 2003), faecal counts per km (Landsberg et al. 1994), and feral goats (Capra hircus) shot per hour (Parkes 1990).
The nature of the relationship between index and density is traditionally considered positively linear, i.e. increasing proportionally to density and passing through the origin (Caughley 1980). Although indices are most applicable where linearity can be assumed, those that display a non-linear relationship can be sufficient in some situations (Southwell 1989; Krebs et al. 2001). In practice, the relationship of many indices with actual density is 1 Chapter 1: Introduction rarely examined (Anderson 2001) and is likely to vary because of a range of factors independent of density, including changes in observer efficiency (Bart and Schoultz 1984) and different probabilities of detecting animals in time and space (MacKenzie and Kendall 2002). However, relative measures of density can be more precise, practical and cost effective than absolute measures (e.g. Ruscoe et al. 2001; Caley and Morley 2002). In some cases actual measurement of population size is essential for answering important biological questions. These include any studies that relate some explicit level of density to changes in survival, behaviour, reproduction, emigration, immigration or other ecological issues, for example, density-dependent economic models (Saunders and Robards 1983; Hone 1990), threshold densities for endangered species (Humphrey 1988), sustained yield harvesting (Bayliss 1989; Lundie-Jenkins et al. 1999) and many disease transmission models (Anderson 1981).
1.1.1 Why estimate feral goat density in Australia?
Feral goats are widely dispersed throughout Australia’s arid and semi-arid rangelands and patchily distributed but abundant in higher rainfall environments, particularly in the eastern tablelands of New South Wales (West and Saunders 2003). Appropriate management of goats for commercial use (Toseland 1992; Ramsay 1994), weed control (Vere and Holst 1979; Holst 1993), reducing environmental impacts (Harrington 1982; Reeves 1992), recreational hunting (Voyer et al. 2003), or for containment of endemic and exotic disease (Williams and Henzell 1992) requires reliable measures of abundance and distribution. In particular, outbreaks of exotic diseases such as foot and mouth disease will require rapid risk assessment and subsequent containment of potential vectors including feral goats (Animal Health Australia 2003). Investigation of cost-effective, accurate and widely applicable means for estimating population densities of feral goats is therefore required. Other introduced ungulates particularly feral pigs (Sus scrofa), deer (chital [Axis axis], sambar [Cervus unicolour], rusa [C. timorensis], hog [Axis percinus], red [C. elaphus], fallow [Dama dama]) and horses (Equus caballus) may also represent a significant, although unquantified risk in the event of exotic or endemic disease outbreaks. Survey techniques and methods for estimating population abundance, similar to those discussed here, may also be of relevance for these species.
2 Chapter 1: Introduction
1.2 Sampling design and sources of error
1.2.1 Sampling intensity
As it is unrealistic in most situations to census an entire wildlife population, a subset or sample from the population needs to be taken (Lancia et al.1996b; Krebs 1999). Consequently the problem arises of determining what sort of sample, from those available, will produce the best measure (Underwood 1997), and how large that sample needs to be (McCallum 2000). This will depend on the hypotheses of interest and the desired level of precision. Estimating sample sizes usually requires data from published sources, similar surveys or some prediction of current parameters (Eberhardt 1978), including variance or density. However, in many cases greater variance can be accepted than first thought desirable, for example, large variance between samples can be tolerated when detecting large differences between means. The difficulties are in predicting the variance within samples and the expected magnitude of the difference between treatments (e.g. Tracey et al. 2001). For the majority of populations, the variance of counts on sampling units increases linearly with density (Caughley and Sinclair 1994). Therefore the sample size should be proportional to the size of the population, and a greater number of samples are required in areas of higher density. This principle can be applied where a preliminary indication of density can be approximated. If a study area can be ranked into sections of high and low density, sampling can be stratified accordingly, which will increase precision (Krebs 1999) (Section 1.2.4). However, when sampling populations of extremely low density, increased effort may be required to detect the animals. If animals are not evenly distributed across the study site or stratum, which may be particularly important for highly gregarious species such as goats, greater sampling effort will be required (Caughley 1980).
1.2.2 Sources of error
In an ideal situation all individuals are seen within sample areas. In these cases simple random sampling (e.g. selecting trapping grids for Great Basin pocket mice [Perognathus parvus], Skalski 1994), stratified random sampling (e.g. aerial surveying of caribou [Rangifer tarandus], Siniff and Skoog 1964; or sampling shellfish, Iachan 1985) and
3 Chapter 1: Introduction systematic sampling (e.g. helicopter surveys of horses, Walter and Hone 2003) will all allow a selection of samples that are representative and produce an estimate that is unbiased. The only error in this case is random sampling error, which simply occurs when sample units have more or fewer animals than the mean (Jolly 1969; Short and Bayliss 1985). However, in nearly all cases, including the examples above, not all individuals are observed or captured within a sample. The proportion of animals that are counted therefore needs to be estimated and counts adjusted to estimate the actual number (Caughley 1974). This proportion is termed ‘detection probability’ (p) (Lancia et al. 1996b). The proportion of animals that are not counted within sample units is described as visibility bias (1-p) (e.g. Choquenot 1995a). The term ‘bias’ in this thesis is used as the bias associated with density or abundance. Hence visibility bias is different from random sampling error, which occurs even when all animals are counted within sample areas. Detection probability is consistent under different conditions and can be estimated using capture-recapture theory (e.g. Choquenot 1995a,b, Section 1.3.1), line transect (e.g. Pople et al. 1998a, Section 1.3.2), double sampling (e.g. Jolly 1969; McCallum 1999), radio telemetry (e.g. Packard et al. 1985) or colour marking (Bear et al. 1989).
Some authors have made the distinction between perception bias and availability bias (e.g. Marsh and Sinclair 1989a,b) or used other terminology (Bayliss 1986; Jachman 2002). Marsh and Sinclair (1989a) define perception bias as a measure of those animals potentially visible to observers that are not seen, and availability bias as a measure of those animals not available to observers because they are concealed by other animals, impenetrable vegetation, or for marine mammals, turbid water (Marsh and Sinclair 1989a). This concept, first identified by Bayliss (1986), is particularly useful where there is a clear separation between those animals potentially visible and those animals that are never available to observers. Dugongs (Dugong dugon) and other marine fauna that float on the water’s surface (Bayliss 1986) or seals and penguins that haul out on ice (Southwell et al. 2002) are good examples. However, in aerial surveys of terrestrial mammals the distinction between those potentially visible and those that are never available is unclear, and all animals are usually considered to be potentially available with distinct differences in the probability of detecting them (e.g. Choquenot 1995a,b). There are various models proposed to examine the effects of individuals or groups displaying unequal detection probabilities (Chapman
4 Chapter 1: Introduction
1952; Leslie et al. 1953; Otis et al. 1978; Caughley 1980) and adjust for them (Chao 1987; Huggins 1989; Steinhorst and Samuel 1989; Marques and Buckland 2003). Hence in this thesis the term ‘detection probability’ is used, denoted by p collectively, but different detection probabilities are distinguished according to the way in which each was estimated using subscripts (Section 2.4).
1.2.3 Accuracy and precision
Accuracy is a measure of how close a population estimate is to the true population size, and can be measured by bias ([Estimate-Known]/Known) or mean squared error (sample variance + [bias]2) (Burnham et al. 1985; Lancia et al. 1996b). If an estimate equals the actual population size it is unbiased (Lancia et al 1996b). By this definition the accuracy of an estimate can only be measured when the true population size is known. Some estimates of bias can be achieved by investigating factors that consistently cause density to be over- or under-estimated (e.g. Caughley et al. 1976; Southwell 1996). In most cases, estimates are assumed accurate and unbiased and only precision is estimated. Accuracy is desirable in many population studies (Section 1.1) but may have less importance than repeatability, consistency and precision (Southwell 1989; Cairns 1999; Pople 1999b), depending on project outcomes.
Precision is a measure of how close population estimates are to each other, or how close they are to an expected value based on repeated samples, and is measured by a variance (Lancia et al. 1996b). A measure of precision can be obtained by replicating sampling units. In general, the larger number of sampling units the more precise the estimate (Snedecor and Cochran 1967).
1.2.4 Stratification
To avoid high sampling rates and low precision a study area can be separated into sections or strata, of high and low density (Snedecor and Cochran 1967; Seber 1982; Krebs 1999), for example, animals are likely to be more abundant in their preferred habitat. If totals are estimated separately for each habitat then combined, estimates would be considerably more precise than if the area was sampled as a whole unit (Caughley 1977). Southwell and 5 Chapter 1: Introduction
Fletcher’s (1988) study of whiptail wallabies (Macropus parryi), which have highly specific habitat requirements, provides a good example where stratification can significantly improve precision with reduced sampling effort. Ideally density is homogeneous within strata but different between strata (Snedecor and Cochran 1967). However, the exact placement of strata is not critical and even approximate stratification will improve estimates (Caughley 1980; Krebs 1999). Although it is normal practice to consider stratification before surveying commences, precision can also be improved by post stratification procedures (Caughley 1977; McCallum 2000).
1.3 Review of techniques
1.3.1 Capture-recapture methods
A substantial amount of literature is available on capture-recapture theory (Cormack 1968; Otis et al. 1978; White et al. 1982; Seber 1986; Burnham et al. 1987; Pollock et al. 1990; Lebreton et al. 1992; Seber 1992; Buckland et al. 2004). Although the underlying principles are simple, there are many complex models available that test and correct for assumption violations (e.g. Chapman 1952; Leslie et al. 1953; Eberhardt 1969; Pollock et al. 1990).
In capture-recapture experiments multiple samples (>2) are taken from a population. Individuals are marked and released on one or multiple occasions. A capture history can then be used to estimate the population size. If all animals are uniquely marked, assumptions can be tested to validate estimates and other demographic parameters can be estimated, including survival and recruitment (e.g. Burnham et al. 1987). However, without additional information true survival rates cannot be distinguished from emigration or true recruitment from immigration (Pollock et al. 1990). Capture-recapture models can be classified into those for open (Pollock et al. 1990) or closed (Otis et al. 1978) populations. An open population is one where additions, by births or immigration, and deletions, by deaths and emigration, can occur during the study (Jolly 1963, 1965). A closed population is one where additions or permanent deletions do not occur, i.e. the population has constant size throughout the study. It is also possible to combine closed and open models (Pollock
6 Chapter 1: Introduction
1982; Kendall et al. 1995).
Models that assume populations are closed rely on fewer assumptions and are less complex. The capture-recapture technique on a closed population was first used by John Graunt in 1662 to estimate the human population of London (Graunt 1662, cited in Buckland et al. 2000), then in wildlife ecology by Petersen in 1896 (Le Cren 1965) and Lincoln (1930), and later described by Seber (1982). The Petersen method is commonly used in wildlife investigations and provides the basis for more detailed capture-recapture models. In its simplest form, n1 animals are captured, marked and released and n2 animals are re-captured in a second sample, of which m2 are marked. Population size (N) is then estimated using the concept that the ratio of marked animals (m2) in the second sample (n2) is equal to the ratio of the total number of marked animals (n1) in the population:
m2 n1 = n Nˆ 2 Rearrangement gives the estimator:
n1n2 Nˆ = m2 where the symbol ^ implies an approximated value.
This model has been slightly modified to overcome the small bias associated with the statistical properties of ratios (Chapman 1951; Bailey 1951, 1952). Where the number of re-captures is not decided beforehand a binomial approximation is used (Bailey 1951, 1952):
n (n +1) Nˆ = 1 2 m2 +1 with variance (Seber 1982:61):
7 Chapter 1: Introduction
2 ˆ n1 (n2 +1)(n2 − m2 ) var(N) = 2 (m2 +1) (m2 + 2)
These estimators assume that:
1. the population is closed to additions and deletions, 2. all animals are equally likely to be captured in each sample, and 3. marks are not lost and are not overlooked (Otis et al. 1978).
For closed populations, which can be simply achieved if samples are taken close together, the most important assumption is that all animals are equally likely to be captured in each sample. Violation of this assumption may be viewed in two parts; (1) ‘individual heterogeneity’, where probability of captures varies between individuals (resulting in negative bias), and (2) ‘trap response’, where the probability of capture depends on an animal’s prior history of capture (resulting in negative bias if animals are trap-happy and positive bias if animals are trap-shy) (Pollock et al. 1990).
Various models have been developed to test (Chapman 1952; Leslie et al. 1953; Eberhardt 1969) and account for (Otis et al. 1978; White and Burnham 1999) differences in capture or detection probability (p). These examine changes in p over time; differences in response to the capture technique; differences between individuals; or a combination of these (Schnabel 1938; Pollock 1974; Otis et al. 1978; Pollock et al. 1990). These models can only be effectively examined where more than 3 samples are taken (Krebs 1999).
The contributions of Chao (1987, 1988) improved density estimation (cf. Druhan 1993; Davis et al. 2003) where relatively few samples are taken (but > 5), heterogeneity is high and capture probability is low (cf. the Jack-knife estimator, Burnham 1972; Burnham and Overton 1978). Cormack (1981, 1993) used log linear modelling (Knoke and Burke 1980) to examine the effects of covariates on unequal capture probabilities for open models. Other approaches investigate covariates in closed models (Pollock et al. 1984), and also provide likelihood equations for adjusting for those individuals that do not occur in the sample (Huggins 1989, 1991; Alho 1990; Chapter 3).
8 Chapter 1: Introduction
1.3.2 Distance sampling methods
Line transect sampling and point sampling are commonly used in wildlife management and extensive reviews are available (Burnham et al. 1980; Seber 1982; Buckland et al. 1993, 2000, 2001, 2004; Barry and Welsh 2001). These methods use the distances that animals are observed from a transect line or point to estimate their probability of detection. The underlying concept is that the detection of animals decreases from the transect line or point and can be predicted. Although sighting distances (r) have been used to estimate detection functions they are unreliable (Hayes and Buckland 1983) hence perpendicular distances (x), calculated using sighting angle (; x = r sin ()) are preferred. The use of this technique requires the fulfillment of four assumptions (Buckland et al. 1993), in descending order of importance:
1. all animals located directly on the line, or at the point, are detected, 2. animals are detected at their initial location and movement from the transect does not result in counting these animals twice, 3. distances are measured exactly, and 4. sightings are independent events.
However, an additional assumption implicit in distance sampling but under-emphasised in previous reviews (e.g. Buckland et al. 1993), is that distances to animals are uniformly distributed (Barry and Welsh 2001). An approach proposed by Melville and Welsh (2001) overcomes this ‘uniformity assumption’ by using calibration data, which has been shown to improve estimates of abundance where animals are not homogeneously distributed across the study area (Melville and Welsh 2001; Welsh 2002). Melville and Welsh (2001) applied this model to estimate the abundance of devils claw (Martynia annua), an agricultural and environmental weed, and found it produced estimates that were more accurate and precise than other distance sampling approaches.
Other techniques can be used to estimate the distance function without confounding with spatial distribution and tests are available for spatial randomness (Cowling 1998). For example, the application of capture-recapture in distance sampling provides a way of
9 Chapter 1: Introduction examining and adjusting for the assumption that all animals are detected on the line (Zahl 1989; Alpizar-Jara and Pollock 1996 ; Manly et al. 1996; Borchers et al. 1998a,b; Chen and Lloyd 2000; Okamura et al. 2003) and could be used to provide a detection function independently. These approaches could also include modelling of additional variables (e.g. group size, Otto and Pollock 1990; or time of day, Ramsay et al. 1987). Covariates besides distance have also been included in conventional line transect models (Borchers et al. 1998a,b; Marques and Buckland 2003). The approach of Borchers et al. (1998a) emphasised the importance of including factors that cause heterogeneity in detection probability, and also allowed inclusion of the likelihoods of Huggins (1989, 1991) and Alho (1990) to allow for estimates of unconditional probabilities. Other studies (Hone 1986, 1988; White et al. 1989; Southwell and Weaver 1993; Southwell 1994; Anderson and Southwell 1995) that have applied and assessed distance sampling methods are reviewed in Chapter 7.
1.3.3 Removal methods
The application of removal methods is most applicable where wildlife is being harvested or controlled (Caughley 1980; Lancia et al. 1996b; Krebs 1999; Quinn and Deriso 1999). Three methods commonly used are: change-in-ratio (Kelker 1940), index-manipulation- index (Eberhardt 1969) and cumulative catch (Leslie and Davis 1939) methods.
The change-in-ratio method can be used where a population can be classified into two or more classes, e.g. according to coat colour, sex or age or where species are closely related (Chapman 1955), and a known number of animals has been removed from or added to one class (Caughley 1980). Kelker (1940, 1944) first applied this technique to estimate deer density after removing males through hunting. Estimates of abundance and variance are given by Paulik and Robson (1969), who provide equations where large (>500) and small (<100-200) samples are taken.
Index-manipulation-index is a method used to estimate population abundance when standardised indices are collected before and after the removal or addition of a known number of animals (Eberhardt 1982; Caughley 1980). The technique is not new (e.g. faecal
10 Chapter 1: Introduction counts of red deer, Riney 1957), but was described with an improved variance estimate by Eberhardt in 1982. The notation of Caughley (1980) is used in this thesis for estimating population size (N) before a removal (C) and Eberhardt’s (1982) variance estimate:
I C Nˆ = 1 I1 − I 2
2 ≈ ’ 2 ≈ q ’ 1 1 with a variance of V (Nˆ ) ≈ Nˆ ∆ ÷ ∆ + ÷ from which the standard error (s.e.) of Nˆ is « p ◊ « I1 I 2 ◊
s.e.(Nˆ ) = V (Nˆ ) where,
N population size before removal
I1 index before
I2 index after
C number removed
p proportion removed, (I1 – I2) / I1
q proportion of those remaining, 1 – p.
This method is most appropriate when a large proportion of the population is removed or added, and indices before and after have a constant relationship to population size (Eberhardt 1982). To remove bias, the technique used to obtain the index should also be independent of the removal method. Variance estimates can be calculated from single count and repeated count indices (Eberhardt 1982). Index-manipulation-index has been applied to a variety of animals and situations (feral goats, Maas 1997; Pople et al. 1998b : feral pigs, Saunders 1988; Choquenot 1995a: feral donkeys [Equus asinus] and buffalo [Bubalis bubalus], Bayliss and Yeomans 1989a,b: foxes [Vulpes vulpes], Thompson and Fleming 1994: wild dogs [Canis lupus ssp.], Fleming 1996, 1997). In the semi-arid rangeland of New South Wales (Maas 1997) and Queensland (Pople et al. 1998b), aerial survey indices
11 Chapter 1: Introduction taken before and after helicopter shooting provided estimates of feral goat abundance similar to those using the double-count technique.
The cumulative catch method (Leslie and Davis 1939) relies on a decline of catch-per-unit- effort with time and is restricted to situations where removals are large enough to detect a change in effort. Krebs (1999) suggests that the approaches of Leslie (Leslie and Davis 1939) and Ricker (1975) be applied to check underlying assumptions. The assumption of equal catchability also applies to this method (Otis et al. 1978; White et al. 1982), and if catchability becomes reduced, this can produce negatively biased estimates of density (Schnute 1983). Studies of feral goats on Raoul Island (Parkes 1984) and mainland New Zealand (Parkes 1990) indicated a declining trend in the numbers of goats killed per hunter day. In these studies a relationship with cumulative kill was not presented and catch-effort was used as an index. Maas (1997) found the cumulative catch method provided pre- reduction estimates of feral goat density consistent with those using aerial double-counting (Section 2.3.1) and index-manipulation-index methods. The cumulative catch technique has also been applied to an eradication campaign of feral goats in New Zealand, providing estimates of goat density before removal and during the control operation (Brennan et al. 1993)
Removal methods may also be used to assist in the estimation of other ecological parameters. For example, catch-effort can be used to investigate the cost-effectiveness of control of pests (Choquenot 1988; Taylor and Katahira 1988; Bayliss and Yeomans 1989b; Hone 1990), or changes in density from removal can be used to investigate competition (Paine 1992; Laska and Wootton 1998). Assumptions of removal methods to estimate density have been investigated and several improved estimators have been proposed (e.g. Pollock et al. 1985; Udevitz and Pollock 1995; Chen et al. 1998).
1.3.4 Aerial survey methods
Aerial surveys are effective for estimating densities of wildlife over large areas (Caughley et al. 1976; Caughley and Grigg 1981; Bear et al. 1989). However, bias associated with aerial counts is widely accepted and may cause significant under-estimates of population
12 Chapter 1: Introduction size (Goddard 1967; Caughley 1974; Bodie et al. 1995).
In Australia, aerial surveys are used for monitoring the abundance of macropodoids more than any other species (Caughley et al. 1983; Grigg et al. 1985; Southwell 1989; Pople 1999a; Cairns et al. 2000), principally for setting harvest quotas (Grigg et al. 1999; Lundie- Jenkins et al. 1999; Gilroy 1999). Application to other species has typically occurred on a smaller scale (e.g. Saunders 1988; Maas 1997; Choquenot 1994; Fleming et al. 2000; Walter and Hone 2003; cf. Bayliss and Yeomans 1989b) or whilst surveying for kangaroos (e.g. Caughley and Grice 1982; Southwell et al. 1993). In practice, most applications of aerial survey do not attempt to estimate bias, but instead use the underlying counts, or apply previously derived correction factors (31 of 35 studies reviewed in Table 4 of Southwell 1989; Choquenot 1990, 1991; Southwell et al. 1993; Pople et al. 1996). Variable detection probability due to a range of factors can seriously compromise the validity of these estimates for comparing abundance in space and time (Anderson 2001).
Various methods can be used to correct for visibility bias in aerial surveys including double-counting, distance sampling and regression techniques. Double-counting (Section 2.3.1) has been applied to feral goats in semi-arid environments (Maas 1997; Pople et al. 1998b); feral livestock in the Northern Territory (Bayliss and Yeomans 1989a), feral horses and donkeys (Graham and Bell 1989; Black 2000; Walter and Hone 2003), feral pigs (Choquenot 1995a), magpie geese (Anseranas semipalmata, Bayliss 1989), marine fauna (Bayliss 1986; Marsh and Sinclair 1989a,b) and kangaroos (Choquenot 1995b). Distance sampling techniques have been used for feral goats (Pople et al. 1998b; Southwell 1996) and a range of other species (e.g. feral pigs, Hone 1988: kangaroos, Pople et al. 1998a: seals and penguins, Southwell et al. 2002: horses, Walter and Hone 2003). Other techniques have included; multiple regression using various independent variables (Caughley et al. 1976; Bayliss and Giles 1985; Hone 1986; Hone and Short 1988), and comparison with ground counts (e.g. Short and Bayliss 1985; Short and Hone 1988) and aerial photographs (Dexter 1990).
13 Chapter 1: Introduction
1.4 Aims of the study
Few methods for estimating density have been trialled in higher rainfall, more productive environments. Southwell (1996) attributed this to the decreased safety of aerial surveying in steep terrain and reduced visibility. Fixed-wing aircraft are the standard for broad-scale aerial surveys (Clancy 1999) but are unsuitable in steeper country. Walked line transects have been suggested as an alternative (Grigg and Pople 1999), but are constrained by cost (Clancy et al. 1997; Pople et al. 1998a). The inability to assess macropod density efficiently in this type of terrain has prevented commercial harvesting in New South Wales east of the Great Dividing Range (K. England, NSW NPWS, pers. comm. 2002), despite some evidence that densities are higher than in the western division (Tracey and Fleming unpublished data). In rugged terrain, line transect sampling has the added difficulty of accurately recording distances using struts, poles or markers (e.g. Southwell et al. 2002). There are also cost and logistical constraints to the methods described and managers require techniques that are low cost, practical and repeatable, and that reflect real abundance. Investigation of alternative methods is required.
Density estimators are rarely examined using true population size. Studies that compare techniques are difficult to interpret due to the uncertainty of abiding by their respective assumptions (Buckland et al. 1993). Advances in analysis techniques, despite being theoretically convincing, do not necessarily provide improved estimates when applied to real populations (e.g. Druhan 1993). For example, there is a diversity of adjustments that can be made for fine-tuning capture-recapture and line transect estimators, but this may have less importance than other underlying assumptions (e.g. recounting, Linklater and Cameron 2002: attention to repeatability and precision, Cairns 1999: or assumptions about dispersion, Melville and Welsh 2001). Further attention must be given to matching improvements in density estimation procedures to an adherence of their assumptions and to how well they estimate true density.
Factors influencing detection probability, estimators that correct for bias, the validity of their assumptions and how these relate to true density are important considerations for selecting suitable methods. The aim of this study was to obtain accurate, precise and
14 Chapter 1: Introduction practical methods of estimating the density of feral goats by:
1. Examining the probability of detecting feral goats from aerial surveys using a range of analysis techniques and investigating the conditions where this is variable (Chapter 3).
2. Investigating the behavioural responses of feral goats to helicopters (Chapter 4), and examining their influence on the assumptions of aerial surveys (Chapter 5).
3. Establishing a method to quantify bias in aerial surveys associated with recounting animals (Chapter 5).
4. Testing the validity of aerial surveys to monitor feral goats and other medium- sized mammal populations over time and between sites (Chapter 6).
5. Assessing the accuracy of a variety of density estimators using known populations of feral goats including five aerial survey estimators using strip counts and the double-count technique; two capture-recapture estimators based on a novel ground-based area count technique; two capture-recapture estimates using tagged animals and re-sightings from ground observations; and six index- manipulation-index estimators (Chapter 7).
15
CHAPTER 2
GENERAL METHODS
2.1 Study Site
This project was undertaken across seven sheep and cattle grazing properties adjacent to the Coolah Tops National Park from 1996 to 2003. Eight study sites were selected at the junction of the Warrumbungle and Liverpool Ranges, between 20 and 50 km north east of Coolah (149°58 E; 32°0 S), New South Wales. The region is very productive, supporting between 2.5 to 6.0 dry sheep equivalents ha-1, has high rainfall (739 mm average annual rainfall, s.e. =23.2, n=55 years landholder records) and is derived from basalt (Banks 1998).
The region has medium to high elevation (620 m to 1190 m) and topography is rugged encompassing a diverse arrangement of gorges, creeklines, narrow ridge tops and plateaux. Southern sites have north to south flowing river valleys providing a dominance of eastern and western aspects. Northern sites are steeper (up to 48°) with a greater representation of northern and southern aspects.
Six vegetation types were variously dispersed across the region, corresponding to increasing levels of vegetation cover based on the classifications of Specht (1970) and Beadle (1981). Grassland and woodland were most common and comprised 48% and 27% of the study area respectively. Open woodland (14%), shrubby woodland (7%), forest (3%) and shrubland (1%) were also present. Grassland consisted of a diversity of native and introduced grasses and herbs ---native: wallaby grass [Danthonia spp.], red grass [Bothriochloa macra] and weeping rice grass [Microlaena stipoides]) and introduced: phalaris [Phalaris aquatica], white clover [Trifolim repens], subterranean clover [T. subterraneum] and lucerne [Medicago sativa], with annual species causing marked changes in plant species composition with season. St. Johns Wort (Hypericum perforatum) was also prevalent in certain sections, particularly in northern sites.
The overstorey communities consisted mainly of Eucalyptus melliodora, E. laevopinea, E. bridgesiana, E. goniocalyx and Angophora floribunda. Tall stands of Casuarina
16 Chapter 2: General methods cunninghamiana and E. viminalis occurred commonly along creeklines. Shrubland and shrubby woodland communities comprised moderate to dense shrub layers of oleander wattle (Acacia neriifolia), lemon bottlebrush (Callistemon pallidus), dogwood (Cassinia quinquefaria), sticky daisy bush (Olearia elliptica), blackthorn (Bursaria spinosa), sweet briar (Rosa rubiginosa) and blackberry (Rubus fruticosus).
2.2 Total counts
To assess the accuracy of different survey techniques for estimating goat density, considerable efforts were made to ensure actual numbers of goats were obtained in eight study sites. Sites were selected on the basis of discrete movements between feral goat groups. Total counts were obtained by repeated mustering campaigns immediately after surveys were conducted, followed by intensive and systematic searches by helicopter and ground teams. Mustering was achieved using a helicopter and ground teams of up to 10 people on foot, motorbikes and horses. In six of these sites, goats were semi-domesticated and were frequently mustered for shearing, drenching and vaccination, and marking of kids. Searching by helicopter for those animals that escaped mustering involved the driving and counting of individuals and groups. Subsequent searching on foot was thorough and achieved by non-intrusive observations and systematic searches by ground teams. This accounted for individuals that broke away from groups while mustering as well as groups that avoided mustering altogether. At the other two sites, final counting also included aerial shooting from a helicopter to ensure feral goats were not counted twice, followed by ground verification.
Pollock and Kendall (1987) considered a total ground count was probably the best technique to estimate bias in aerial surveys. Previous studies have used other methods to obtain total numbers of animals (e.g. drive counts, Short and Hone 1988; Hone and Short 1988: ground counts from a vehicle, Short and Bayliss 1985). Drive counts are achieved by a team of observers that are evenly spaced along a line ‘driving’ animals within a defined area. Counts are made of animals that move from or into the area by observers on the boundary, and of animals that move from ahead of the ‘drivers’ back through the line (Lancia et al. 1996b). Short and Hone (1988) applied this technique to kangaroos and emus
17 Chapter 2: General methods
(Hone and Short 1988) and suggested the accuracy of drive counts depend on the behaviour of the animals, the vegetation and terrain of the study area, the number of people participating, and the opportunities for the animals to move from the counted area without being detected. They concluded that their drive counts were accurate for kangaroos as vegetation was predominantly open and terrain was flat (Short and Hone 1988). Lancia et al. (1996b) suggested drive counts should only be considered an index of density and that most researchers miss an unknown proportion of animals, which could be as high as 20- 30% (McCullough 1979, cited in Lancia et al. 1996b). The total counts in this study were considered reliable because the populations selected were the subject of an intensive four- year study, which involved detailed ground observations, capture and radio tracking, and all known and observed radio collared, tagged, ear marked and accompanying unmarked goats within these areas were accounted for during intensive searching.
2.3 Aerial survey
Helicopter aerial surveys were a major component of this study and the methods presented here are relevant to chapters 3, 4, 5, 6 and 7. Thirty-four surveys were flown in Hughes 500 and Bell Jet Ranger (206B) helicopters over the Coolah Tops study area between 1997 and 2002. This allowed 306 hours of aerial observation and 9719 observations of groups of medium-sized mammals (4536 of eastern grey kangaroos [Macropus giganteus], 3359 of feral goats, 1088 of wallaroos [M. robustus], 511 of swamp wallabies [Wallabia bicolor], 131 of red-necked wallabies [M. rufogriseus] and 94 of feral pigs). Observers were positioned in the right front and both rear seats in the Hughes 500 (Figure 2-1), and in the left front and both rear seats of the Bell Jet Ranger. Hence double count estimates could be calculated from observations from the right-hand side of the Hughes 500 and the left-hand side of the Bell Jet Ranger. Where observers were seated on the same side, care was taken to ensure counters were not directly influenced by each other. There was no audio communication between observers whilst counting and seating arrangement prevented any visual cues between observers. To reduce the influence of ‘perspex hazing’, where the sun may reduce visibility (Pople et al. 1998a,b), and to maximise sightability, the doors of the helicopter were removed during all counts.
18 Chapter 2: General methods
Observers on the same side counted onto a continuously running multi-track tape recorder using two handheld microphones, which allowed groups of animals to be recorded as having been seen by one or both observers (Caughley and Grice 1982). The single side rear observer counted onto a separate single-track tape recorder. Where there was uncertainty whether a group was seen by both observers (<0.1% of observations) it was treated as two separate groups. Each group of animals was recorded in one of six different types of vegetation following the classification previously described (Section 2.1) with an additional ‘edge’ category for those animals observed on the ecotone between woodland and open grassland.
To eliminate errors when estimating group size, goats were counted in units of less than four (Trick and Pylyshyn 1994) or occasionally five, onto a tape recorder, which were later summed to obtain a count for each group. Where extremely large numbers were seen in short periods, observers would obtain a minimum count using this technique rather than an estimate. ‘Groups’ of goats in this context were considered sighting entities rather than biologically meaningful groups or herds.
19
Figure 2-1: Helicopter survey in the Coolah Tops showing surveying height, strip width, calibrating markers, observer seating position and distance unavailable beneath the helicopter.
20 Chapter 2: General methods
2.3.1 Double-counting
The double count method (Caughley and Grice 1982) uses multiple observers and is an adaptation of the Petersen mark-recapture estimate (Seber 1982). The double count method was first used combining aerial counts with ground counts (Henny et al. 1977; Magnusson et al. 1978; Grier et al. 1981). Later the technique in which two observers count simultaneously from the same aircraft was described and used by Caughley and Grice (1982). Further refinements were proposed by Choquenot (1995a,b), who took account of visibility bias in different habitats.
Goat groups recorded as seen by one or both observers were identified as follows (Caughley and Grice 1982):
S1 the number of groups seen by the first observer but missed by the second
S2 the number of groups seen by the second observer but missed by the first, and B the number of groups seen by both observers N population size
(S + B)(S + B) Nˆ = 1 2 B This equation can be modified to allow the Bailey (1951) correction;
(S + B +1)(S + B +1) Nˆ = 1 2 −1 B +1 and to provide an estimate of detection probability;
t
ƒ nk pˆ = k 2Nˆ where n is the total number of groups seen (B+S1+S2) in the kth sample.
21 Chapter 2: General methods
2.3.2 Transect width and flying height
Transects were fixed at 100 m wide and delimited by right-angled poles attached to either side of the helicopter. For calibration the helicopter hovered over two stationary objects 100 m apart and the delimiting poles were adjusted to assist observers counting equal transect boundaries. Consideration was also given to the 60 m (30 m each side) directly underneath the helicopter that was not available for sampling to ensure a 100 m effective width was sampled on either side of the helicopter (Figure 2-1). Hence the pole was in fact calibrated for sighting out to 130 m from the centre of the helicopter. Due to the difficulty of using fixed markers in variable terrain extra training was required to abet scanning out to 100 m but not beyond. This was achieved by calibrating prior to every survey, and individual training during surveys by regularly identifying of features on the transect boundary. To test whether observers did scan equal transect boundaries animals close to the line were recorded as inside or outside by all observers (Chapter 6). Those groups recorded as outside by either observer were assumed outside the transect area.
The helicopter maintained a constant height of 150 ft (46m) above ground level (AGL) where possible throughout the surveying (Figure 2-1). During preliminary surveys a transect width of 150 m and a flying height of approximately 30 m was trialled for consistency with those established for surveying in the western division of New South Wales (Choquenot 1995a,b; Choquenot et al. 1997; Maas 1997; Fleming et al. 2000). However, it was impossible to maintain this height in the Coolah Tops where sections of tall eucalypt forest exceeded 20 m. Although unquantified, it also quickly became evident that our ability to search from the transect line rapidly diminished beyond 100 m. Although intuitively this would support line transect estimators, the nature of the terrain inhibited observers accurately delineating multiple transect widths. Therefore a 100m transect width was selected and applied throughout this study. The differences in survey height and transect width were a result of more structured and higher canopy layers.
2.3.3 Sampling and standardisation
The sampling rate was approximately 40% for seasonal surveys and 60% where known
22 Chapter 2: General methods numbers of goats were obtained. Transects were selected at random without replacement, with equal probability; ran east-west perpendicular to the orientation of the major valley systems; and were between 6 and 14 km in length. Although a constant speed of 45 knots (~85 km hr-1) was intended throughout the surveying, actual speed calculated from start and finish waypoint and transect times fell between 32 and 64 knots (85 km hr-1) and hence was included as a factor in the detection probability model (Chapter 3). This was exacerbated during high winds when transects flown into the wind were frequently at slower speeds. To standardise other factors all counts were made during the first and last three hours of daylight at a temperature of less than 25ºC and above 5ºC. Cloud cover was 4 octals or less. The distinction was also made between high cirrus cloud, which had little influence on visibility and low cumulus cloud.
2.4 Notation
For consistency, notation in this study follows Seber (1982) and Pollock et al. (1990) (Table 2-1). Additional parameters are included for the double-count technique (following Caughley and Grice 1982) and for estimating the probability of recounting. Subscripts for detection probability (p) denote analysis methods, or differentiate recounting probability values. Additional notation used for other equations is defined when needed.
23 Chapter 2: General methods
Table 2-1: Notation for parameters and statistics used for capture-recapture models (after Seber 1982; Pollock et al. 1990) and for equations used to derive the probability of recounting.
Symbol Description M number of marked animals in the population. N the total number of animals in the population.
mi the number of marked animals in the sample in the ith sample (i = 1, …, k).
ni the number of animals captured in the ith sample (i = 1, …, k). unconditional probability of detecting an animal or group within a sample,
pd estimated using the double count technique with likelihood equations of Alho (1990). probability of detecting an animal or group within a sample estimated using the
pc double count technique, conditional on being observed by either observer (Petersen estimate). detection probability estimated using known locations of animals from ground pg observations. probability that an animal, once available for aerial observation, becomes available pa for recounting in another transect. probability that an animal or group, once available for aerial observation, moves pmx into x additional transects.
psx probability of sampling transect x. the distance an animal moves from its initial position until it has stopped moving dm in response to the helicopter, or is out of sight of the observer.
dp the perpendicular distance moved by animals in response to the helicopter. direction moved by animals in response to the helicopter from grid north (0-360 θm degrees). the perpendicular distance an animal or group moves in relation to east-west θp transects.
S1 the number of groups seen by the first observer but missed by the second.
S2 the number of groups seen by the second observer but missed by the first. B the number of groups seen by both observers.
24
CHAPTER 3
FACTORS INFLUENCING DETECTION PROBABILITY IN AERIAL SURVEYS
3.1 Introduction
Detection probabilities and related bias are known to vary considerably with: vegetation cover (Caughley et al. 1976; Steinhorst and Samuel 1989; Choquenot 1995a,b; Southwell 1996); position of animals in relation to the aircraft (Bodie et al. 1995), activity (Gasaway et al. 1985; Barnes et al. 1986; Samuel et al. 1992), group size (Samuel and Pollock 1981; Steinhorst and Samuel 1989; Maas 1997; Pople et al. 1998b), colours (Mahood 1985; Jachmann 2002), and gender and age composition of groups (Downing et al. 1977; Gasaway et al. 1985; Samuel et al. 1992; Bodie et al.1995), varying lighting (Bodie et al. 1995) and weather conditions including cloud cover (Short and Bayliss 1985), snow depth (Steinhorst and Samuel 1989) and time of day (Bayliss and Giles 1985; Short and Hone 1988), and survey variables such as altitude (Bayliss and Giles 1985), speed and transect width (Caughley 1974; Caughley et al. 1976; Shupe and Beasom 1987). Further advances in aerial survey analyses allow adjustments for a range of these covariates (e.g. Huggins 1989; Alho 1990), and hence may be of increasing importance in aerial surveys of wildlife.
Previous studies have evaluated detection probabilities over a range of influencing factors and using various methods. Bayliss and Yeomans (1989a), using regression analysis for aerial surveys of buffalo and other feral livestock, found a significant relationship between detection probability and vegetation but not for observers or group size. Mean group size was used in the estimation of detection probability, which may also have resulted in positive bias (Drummer and MacDonald 1987). Where larger groups have a higher probability of being seen than smaller groups, mean group size is likely to be overestimated but the mean number of groups per unit area underestimated (Cook and Martin 1974). This effect is particularly important for populations with highly variable aggregations.
Where a significant relationship exists between group size and detection probability, it can be used to correct underlying counts from the aerial survey. Samuel and Pollock (1981) applied a sighting function for group size in this way and used ground counts to estimate
25 Chapter 3: Factors influencing detection probability in aerial surveys detection probability. This was adapted from a similar but more restrictive approach proposed by Cook and Martin (1974).
Choquenot (1995a,b) tested for the effects of vegetation, site, survey and species on visibility bias using analyses of variance (ANOVA) with transects as replicates. This technique relies on an adequate number of observations for estimating bias within each replicate (i.e. transect). Despite methods to take account of unbalanced sample sizes (e.g. a weighted mean, Snedecor and Cochran 1967), small sample sizes can still result in estimation error, and do not allow for a completely balanced analysis. As a result, such analysis is also unconducive to testing a multitude of factors. If transects were substantially shorter than those flown in Choquenot’s (1995a,b) studies (20-30 km long) these problems would be exacerbated.
Pople et al. (1998b) used a log-linear modelling approach that included the underlying counts in sightings by each observer and by both observers, rather than detection probability as the response variable for testing the effects of observer pair, vegetation and group size. This approach was based on conventional generalised linear models (GLM) (Crawley 1993), which are reviewed in a capture-recapture context by Cormack (1993).
Alho (1990) introduced a conditional logistic estimator of detection probability that is an extension of the work by Pollock et al. (1984) and is similar although independently derived to the method of Huggins (1989, 1991). This technique uses capture-recapture data and individual sighting covariate information. In comparison to the approach by Pollock et al. (1984) and Pople et al. (1998b) this method allows estimation of the unconditional probability of sighting. Capture-recapture estimators rely on estimating probability from those animals seen or captured, i.e. the estimation of a probability conditional on groups being observed or captured in the sample. Alho (1990) used conditional capture data (Seber 1982) and also allowed the use of independent variables without grouping. Data from a dual registration system for Finnish occupational diseases was used to demonstrate this model, which included type of diagnosis and age as independent variables (Alho 1990).
26 Chapter 3: Factors influencing detection probability in aerial surveys
This chapter contains an investigation of the effects of 19 variables (Table 3-1) on the detection probability of feral goats using multiple observers and two alternative approaches described by Alho (1990) and Pople et al. (1998b), as well as probability predictions for the significant variables.
3.2 Methods
3.2.1 Variables for the detection probability model
For a summary of all variables refer to Table 3-1. Groups of goats were identified as having been seen by one or both observers because it was impossible to distinguish whether individual goats had been seen or not. Where there was uncertainty whether a group was seen by one or both observers (<0.1% of observations) they were treated as independent groups. Each group of goats was recorded in one of five different types of vegetation (Section 2.1), and in one of four activities; moving, standing, lying, or hiding. The number of light, coloured and dark animals, and the gender composition of each group (males, females, kids and combinations) were also recorded.
Degree slope and aspect of the terrain for observations was calculated by plotting the location of each group using GPS-determined waypoints, start and finish times of each transect and overlaying slope and aspect layers in a geographic information system. To test the potential effect of hazing, groups were identified as having been observed whilst looking ‘into’ or ‘away’ from the sun. The effects of other factors such as group size, observer pairings, the experience of observers expressed as observer hours, the type of helicopter (Hughes 500 or Bell Jet Ranger), speed, aspect, time of day, site, survey, direction travelled and interactions between factors were also investigated (Table 3-1).
27 Chapter 3: Factors influencing detection probability in aerial surveys
Table 3-1: Variables included in log-linear and logistic regression modelling for
theresponse to unconditional detection probability (pd) of groups of feral goats.
Variable Description Group size Number of individuals counted in units of 5 or fewer. (0-154) Vegetation Open grassland, edge, woodland, shrubby woodland and forest. (5) Observer Pair Front and rear observers included as a pair in analysis. (7) Groups separated into 4 colour categories: mixed, all light, all coloured, and all Colour dark. (4) Helicopter Two types of helicopter used for surveying; Hughes 500 or Bell Jetranger. (2) Site Three sites surveyed in the Coolah Tops: North, South, East. (3) Hours of surveying experience for each observer, calculated for each Observer hours observation. (Rear 0-80; Front 24-160) Rear observer Hours of surveying time for the rear observer for each observation. (0-80) hours Aspect Orientation from true north for each observation. (8) Degree slope calculated for each observation using a digital elevation model and Slope geographic information system. (0-45) Dstance (m) from observers to the mid-point of the transect. (60-170) Distance (c) (Figure 3-1) Direction The direction the helicopter is moving: east-west or west-east. (2) travelled Time of day First three hours after sunrise (AM) or last three hours before sunset (PM). (2) Direction travelled in relation to the time of day and observer position; 'into' or Sun 'away' from the sun (2) Activity Main activity of each group; moving, standing, lying down or hiding. (4) Sex of goat Males, Females, Females and kids or Mixed (4) Speed (km/hour) calculated for each transect from GPS determined waypoints Speed and start and finish times. (59-118) Survey Consecutive surveys 1997-2000. (34) Survey set Series of surveys for each time period. (9)
28 Chapter 3: Factors influencing detection probability in aerial surveys
3.2.2 Distance to the mid-point of the transect
Whilst surveying in rugged terrain, observers are closer to the area scanned when viewing uphill, than when viewing downhill. To test whether this affects the probability of detecting a group of goats the distance (c) from observers to the midpoint of the transect was derived using degree slope, aspect of the terrain and the observer position (Figure 3-1). This distance (c) was not an estimate of the actual distance to individuals or groups of animals within the 100m strip. However, these equations provide a basis for correcting distance data in other studies, and also allow investigation of whether viewing downhill or uphill effects the probability of detection. If observers are viewing south then they observe downhill (denoted by subscript d) on southern aspects and uphill (subscript u) on northern aspects and vice versa when viewing north. The formulas and notation (Table 3-2) for calculating distance (c) are given below.
Figure 3-1: Parameters for estimating the distance (cd and cu) from observers to the midpoint of the transect.
29 Chapter 3: Factors influencing detection probability in aerial surveys
Table 3-2: Notation for parameters and statistics for estimating the distance from observers to the midpoint of the transect.
Symbol Description
area unavailable for sampling beneath the helicopter. Calculated as 30 m, each side, for a a flat surface at a flying height of 46m.
A angle opposite a
b flying height (46m)
B angle opposite b
degree slope
c distance from observers to the area scanned.
C slope (degrees) relative to observer, aspect and flight direction Cu= 90-; Cd = 180-Cu
distance to the mid point of the transect scanned by observers (50 m), or distance to d animals observed if measured (Chapter 4), or if applying distance sampling techniques.
Distance (cd and cu)
The sighting angle is calculated at the midpoint of the 100 m strip scanned by observers, and assumes observers scan the 100 m width despite variable terrain.
Step 1. Determine A for a flat surface
a 30m tan A = = b 45.72m ≈ 30 ’ A = tan −1 ∆ ÷ « 46 ◊ A = 33.27 0
30 Chapter 3: Factors influencing detection probability in aerial surveys
Step 2. Determine Bd and Bu
Bd + A + Cd =180
Bd =180 − Cd − A B 180 C A u = − u −
Step 3. Determine ad and au
ad b = [Sine theorem] sin A sin Bd ≈ ’ ∆ b ÷ ad = ∆ ÷×sin A « sin Bd ◊ ≈ ’ ∆ b ÷ au = ∆ ÷×sin A sin B « u ◊
Step 4. Determine distance cd and cu
[As two sides (b; {a + d}) and the included angle (C) are known we can use the cosine theorem: cos C = (a2 + b2 - c2)/2ab]
2 2 2 2 (ad + dd ) + b − cd cosCd = 2(ad + d d )b 2 2 2 cosCd (2(ad + dd )b) = (ad + d d ) + b − cd 2 2 2 2 cd = (ad + d d ) + b − cd
2 2 cd = (ad + d d ) + b ) − cosCd (2(ad + dd )b) c = (a + d )2 + b2 ) − cosC (2(a + d )b) u u u u u u
31 Chapter 3: Factors influencing detection probability in aerial surveys
Step 5. Determine sighting angle d and u
[Sine theorem a/sin A = b/sin B = c/sin C]
cd b = [Sine theorem] sin Cd sin θ d b sin θ = d ≈ ’ cd ∆ ÷ « sin Cd ◊
−1 b θ d = sin ≈ c ’ ∆ d ÷ « sin Cd ◊
−1 b θ u = sin ≈ c ’ ∆ u ÷ « sin C ◊ u
Distance (c) was calculated as 92m for a flat surface, and ranged between 60 and 170 m when calculated for each observation.
3.2.3 Analyses
3.2.3.1 Log-linear modelling approach
The effects of observer pair, observer hours, site, survey, group size, colour, vegetation, slope, relative slope, type of helicopter, speed, facing, and 1st and 2nd order interactions were initially tested using log-linear modelling following the approach of Pople et al. (1998b). In log-linear modelling all factors were treated as response variables, i.e. this analysis displayed associations between variables but no distinction was made between independent and dependent variables (Knoke and Burke 1980). The procedure used was typical of generalised linear modelling (Crawley 1993) and followed a step-wise progression from the maximal (full) model through a series of simplifications and deletions to the minimal adequate model. The maximal model contained all factors, interaction terms and covariates. Higher-order interactions were progressively removed if they were not significant (P<0.05) using an analysis of deviance, i.e. the measure of discrepancy to assess the goodness of fit between the data and the model, measured by the logarithm of the ratio
32 Chapter 3: Factors influencing detection probability in aerial surveys of two log-likelihoods and an approximate Chi-square statistic (Crawley 1993).
3.2.3.2 Logistic regression
The effects of factors on detection probability were also investigated using logistic regression, which may be viewed as a non-linear transformation of the linear regression. Although either method should produce a reliable result when investigating the significance of factors, logistic regression provides estimates of the predicted probabilities (Selvin 1995), including likelihood equations to correct for conditionality (Alho 1990). In the logistic regression analysis the response (dependent) variable was in a binary form i.e. 0 or 1, and a distinction was made between the dependent and independent variables. Continuous and discrete independent variables were included (Selvin 1995), e.g. group size was included as a continuous independent variable (ranging from 1 to 200 individuals), and type of helicopter was included as a discrete independent variable. Underlying the response variable was the detection probability (pd). This logistic regression model explored the relationship of a set of independent variables on this probability (Selvin 1995). The response variable was the observation status of a group of goats, i.e. seen or not seen for each of two observers. Therefore each group appeared twice in the data with one of the following detection patterns:-
Group Observer Detected 1 Front 1 1 Rear 1 2 Front 1 2 Rear 0 3 Front 0 3 Rear 1
In this example, group 1 was seen by both observers, group 2 by the forward observer only and group 3 by the rear observer only. Without adjustment, only the conditional probabilities can be modelled as no information is available for groups that are not seen by either observer (Seber 1982). However, Alho (1990) provides likelihood equations for
33 Chapter 3: Factors influencing detection probability in aerial surveys unconditional probabilities, and this is the approach has been taken in this study. The models were fitted sequentially whereby, at each step, the factor causing the largest change in likelihood was included in the model (Alho 1990). A similar approach has also been suggested by Huggins (1989, 1991) and follows the contributions of Pollock et al. (1984) and Chao (1987,1988).
Prior to testing the factors influencing detection probability, the size of each group was taken as the larger of the two observer counts, as this was more likely to reflect the true group size. To provide improved explanations as to why goat groups were seen or not seen, predictions of unconditional sighting probabilities (pd) were estimated for the most significant factors. Probabilities on the logit scale were then re-transformed. To remove the effects of other factors, average covariate values were employed and factor levels equally balanced. However, owing to a large imbalance for ‘site’ and ‘colour’, the most numerous categories were used for these factors.
3.3 Results
Initial log-linear modelling revealed that only group size, vegetation, and observer pair were significant (P-chi<0.01). Further analysis using logistic regression supported these results but revealed that other factors were also important at various levels. The interaction with group size and vegetation, colour, helicopter, site and rear observer hours caused significant decreases in deviance (Table 3-3).
34 Chapter 3: Factors influencing detection probability in aerial surveys
Table 3-3: Analysis of deviance for the logistic regression model predicting unconditional
detection probability (pd). Response Y~ pd of groups of feral goats.
Significance Change in Change Model Deviance Probability deviance in df (Chi) Null 3390 NA NA NA + Group size 3270 120 2 <0.0001 + Vegetation 3209 61 10 <0.0001 + Group size*Vegetation 3185 24 10 <0.0001 + Observer Pair 3120 65 12 <0.0001 + Colour 3084 36 6 <0.0001 + Helicopter 3064 20 2 <0.0001 + Site 3054 10 4 <0.001 + Rear observer hours 3049 5 2 <0.01
Logistic regression analysis allowed a prediction of the relationship between unconditional detection probability for goat groups (pd) and each independent variable by averaging over the remaining covariates. Group size was the most significant factor influencing pd (Table 3-3), increasing steeply until group size of 25, after that increases were slight and the detection probability was close to 1 (Figure 3-2). After removing the intermediate category of edge habitat, a significant negative relationship between percent vegetation cover and pd was also apparent (df=3, P=0.042, Figure 3-3). Vegetation was subsequently included as a discrete independent variable to allow the inclusion of edge vegetation that had a pd estimate of 0.77 (Figure 3-4). The interaction between group size and vegetation was also significant (Table 3-3) suggesting vegetation is more important in groups of smaller size (Figure 3-2).
35 Chapter 3: Factors influencing detection probability in aerial surveys
1.0
Open grassland Woodland 0.9 Forest Detection probability (pd) 0.8
0.7
0.6
0.5 0 50 100 150 Group Size
Figure 3-2: Predicted relationship between group size and unconditional detection
probability (pd) of feral goat groups for three vegetation types. Predicted for site = Turee, rear hours = 45, colour = Mixed. These relationships were truncated at the maximum observed group size recorded in the study.
36 Chapter 3: Factors influencing detection probability in aerial surveys
0.9
0.85 Detection Probability 0.8 (pd) 0.75
0.7 y = -0.0018x + 0.8639 2 0.65 R = 0.9171
0.6 0 20 40 60 80 100 Vegetation cover (%)
Figure 3-3: Relationship between mean unconditional detection probability of feral goat groups and vegetation cover (%). Predicted for size=8, site=Turee, rear hours=45, colour=Mixed.
1 0.9 0.8 Detection 0.7 Probability 0.6 (pd) 0.5 0.4 0.3 0.2 0.1 0 Open Woodland Shrubby Edge Forest woodland
Figure 3-4: Estimates of pd for vegetation types. Predicted for size=8, site=Turee, rear hours=45, colour=Mixed.
37 Chapter 3: Factors influencing detection probability in aerial surveys
The effects of observer pair also caused a large change in deviance (Table 3-3). The weighted averages of observer sightings allowed for comparison between observers (Table
3-4), but as paired observers are used to calculate pd ‘observer pair’ was used in the overall model. Overall, pd was significantly greater (P<0.01) in the front (0.82) than in the rear (0.67), after standardising for group size (8), site (Turee) and colour (mixed). However position is confounded with observer as few observers were placed in both front and rear and more experienced observers were positioned in the front for standardisation purposes.
To test this effect independently, pd for two observers who were seated in both positions (A and B) were compared directly. Both observers had greater pd in the front (A: front 0.78 n=1341, back 0.77 n=197; B: front 0.84 n=142, back 0.72 n=296) but this effect was not significant for either observer. Observer hours was also included but was significant only for rear observers (Table 3-3, Figure 3-5).
Table 3-4: Predicted unconditional detection probabilities (pd) for individual observers using a weighted average of observer sightings. Predicted for size=8, colour=mixed, site=Turee.
Detection Observer probability (pd) A 0.78 B 0.77 C 0.75 D 0.68 E 0.66 F 0.63
38 Chapter 3: Factors influencing detection probability in aerial surveys
1.0 0.9 Detection 0.8 Probability 0.7 (pd) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 100 200 300 400 500 600 700 Rear Observer Hours
Figure 3-5: Predicted relationship for detection probability (pd) and rear observer hours, predicted for size = 8, site = Turee, colour = Mixed. This relationship was truncated at 700 hours to demonstrate the levelling out of detection probability. The maximum cumulative survey time by an observer was recorded was 160 hours.
Goat colour was significant (Table 3-3) after distinguishing groups with mixed colours from those containing only light, coloured or dark individuals. Detection probability decreased from light to dark (Figure 3-6). After standardising the effects of other factors
(group size=8, site=Turee, rear hours=45, colour=Mixed), pd was significantly higher from the Hughes (0.83) than the Bell Jet Ranger (0.66), and site was also significant (Table 3-3).
39 Chapter 3: Factors influencing detection probability in aerial surveys
1 0.9 0.8 Detection 0.7 probability 0.6 (pd) 0.5 0.4 0.3 0.2 0.1 0 Mixed Light Coloured Dark
Figure 3-6: Unconditional detection probability (pd) estimates for mixed, light, coloured and dark groups of feral goats.
Initial analysis of the effects of degree slope indicated that there was a significant negative linear relationship with detection probability (P=0.0136; Figure 3-7). The relationship with relative slope was also significant (df=1, r2=0.791, P<0.01, Figure 3-8). Mean detection probability of groups of feral goats was strongly related to the distance of observers from the midpoint of the transect (Figure 3-9) with lower detection at greater distances.
However neither slope nor relative slope was included in the final logistic regression model as these did not cause a significant change in deviance after removing the effects of other variables. Other factors that also did not contribute significantly to the model were speed, aspect, time of day, survey, sun, direction travelled, sex of goat, and activity.
40 Chapter 3: Factors influencing detection probability in aerial surveys
0.78
0.77 Detection probability (pd) 0.76
0.75
0.74
0.73
0 10 20 30 40 Slope (degrees)
Figure 3-7: Relationship between slope (degrees) and mean detection probability of feral goats. Y=-0.008x + 0.7764. r2 = 0.6051
41 Chapter 3: Factors influencing detection probability in aerial surveys
0.78
0.76 Detection probability (pd) 0.74
0.72
0.70
0.68 60 80 100 120 RelaRtievlaet ivSel Solpoepe (C) (degrees)
Figure 3-8: Relationship between relative slope (Cd and Cu, degrees) and mean detection probability of groups of feral goats.
42 Chapter 3: Factors influencing detection probability in aerial surveys
0.76
Detection 0.74 probability (pd) 0.72
0.70
0.68
40 60 80 100 120 140 160 180 Distance, c (m)
Figure 3-9: Relationship between mean detection probability (pc) of feral goat groups and
distance from observers to the mid-point of the transect (cd and cu). Y= -0.0005x2 + 0.0025x + 0.6541. r2=0.9803
For comparing of the results of the present study with previous surveys (Denny 1979; Dudzinski et al. 1982; Caughley et al. 1987; Choquenot 1995a,b; Walter 2002), the expected distances to the mid-point of the transect were plotted for different heights (Figure 3-10). As height flown increases, so will the area unsurveyed below the aircraft (Figure 3-1).
43 Chapter 3: Factors influencing detection probability in aerial surveys
500 100m (Denny 1979; Walter 2002) 450
400 76m (Caughley et al. 1987) 350 ) m
( 300 46m (This Study) e c
n 250 a t s i 200
D 30m (Choquenot 1995a,b; Dudzinski et al. 1982) 150 100 50 0 0 10 20 30 40 50 Slope (Degree)
Figure 3-10: Relationship between distance (c) to the mid-point of the transect and degree slope at varying survey heights, estimated for viewing downhill. A of 33.27, and d of 50 m were used for consistency with the present study.
3.4 Discussion
The increase in detection probability (pd) with group size (Figure 3-2) is consistent with other studies on feral goats (cf. Southwell 1996; Maas 1997; Pople et al. 1998b) and other species (e.g. sea otter [Enhydra lutris], Cook and Martin 1974; Samuel and Pollock 1981: white-tailed deer [Odocoileus virginianus], Cook and Jacobson 1979: elk [Cervus spp.], Samuel et al. 1987). However, detection probability in the current study was found to be lower than for feral goats in western New South Wales using comparable methodology (Maas 1997) and similar for feral goats in western Queensland using fixed wing aircraft (Pople et al. 1998b ). Maas (1997) reported unusually low bias (between 0.08 and 0.02) translating to a detection probability of 0.92 and 0.98 goats observed in different vegetation types. Groups of greater than 5 were observed on every occasion (Maas 1997). Possible explanations for the low probability of detection in the present study include greater sample size, and taller and more structured vegetation.
44 Chapter 3: Factors influencing detection probability in aerial surveys
Vegetation, but not group size, was found to be important for feral goats in the rangelands of Western Australia using line transect methods (Southwell 1996). Vegetation is consistently shown as an important factor in aerial surveys of wildlife (Choquenot 1995a,b; Southwell 1996; Maas 1997; Pople et al. 1998b). Although often not represented as a percentage in other studies, detection probability decreases proportionally to increasing vegetation cover (e.g. Choquenot 1995a,b; Bayliss and Yeomans 1989a) as shown here (Figure 3-3). Comparison with known proportions from ground observations provides independent evidence of this effect (Chapter 5).
As with many other wildlife sampling studies (e.g. Bart and Schoultz 1984; Graham and Bell 1989), detection probability in the current study varied considerably between observers (Table 3-4). Seating position also appeared to influence detection probability with front observers possibly having a positional advantage, but this effect may have been confounded by observer experience. The ability to detect wildlife species is likely to improve with experience, particularly in the early stages where observers become familiar with delineating strip widths and developing a search image for the target species. Steep increases in detection probability would be expected during the training phase, and these would level out with observer experience. A shoulder before levelling out may also be expected when observers ‘try too hard’ (Caughley pers. comm. cited in Beard 1999).
The predicted relationship with observer hours in this study suggests untrained observers initially counted up to half that of experienced observers, which is consistent with other studies (Beard 1999). Contrary to suggestions by Beard (1999) who recommended between 40 and 48 hours of training for fixed-wing surveys of kangaroos, detection probability continued to increase for rear observers up until the completion of the study despite over 150 hours of survey time. However, cumulative survey time was not important for front observers, who were more experienced from the outset (>50 hours surveying time), and survey time for rear observers was of secondary importance to other factors.
Differences in the probability of detecting feral goats from different helicopters has not been previously investigated and was found to be important in the current study. The Hughes 500 and Bell Jet Ranger helicopters are known to generate equivalent noise levels
45 Chapter 3: Factors influencing detection probability in aerial surveys out to 10 km (Newman et al. 1982), but produce different sounds. The Hughes 500 with 4 overhead rotor blades emits a continuous whirring noise, while the Bell Jet Ranger with 2 overhead rotor blades generates an alternating pulse or thump (pers. obs.). Analysis of alert behaviour (Chapter 4) indicates the Hughes 500 helicopter caused a greater response than the Bell Jet Ranger and increased movement is commonly assumed to increase the probability of detection (Gasaway et al.1985; Barnes et al. 1986; Samuel et al. 1987; Jachmann 2002; Chapter 5), which may explain the greater visibility from the Hughes 500.
However, the activity of goats from aerial observations was not found to influence detection probability and there may be other explanations for improved sightability from the Hughes 500. For example, the size of viewing platform in the Bell Jet Ranger was noticeably smaller for front observers, and the higher power to weight ratio of the Hughes 500 may increase the pilot’s ability to maintain the correct height over undulating country, and hence potentially improve sightability.
Despite exclusion of slope and distance (c) from the overall model, the linear relationship between detection probability and degree slope indicates steepness of the terrain may influence detection probability when slopes are greater than 20°. Detection was not found to be influenced by observing uphill or downhill. A lower probability of detection was apparent when relative slope (C) (Table 3-2; Figure 3-8) was >120° and < 70°, corresponding to an actual slope of >30° and >20° respectively. Therefore sites with steeper terrain (>20°) may experience a greater effect on detection probability than was evident here, which may be of particular relevance for aerial surveys that use distance to calculate detection probability (Buckland et al. 2001). Estimates of distance in rugged terrain could include adjustments for slope in distance calculations using the method described. For example, this approach could increase the applicability of Southwell et al.’s (2002) automated ‘sighting gun’ for collecting distance data in rugged terrain if degree slope is available and individual observations are plotted with a GPS.
The influence of the studied variables on detection probability can be used to quantify bias under different conditions and improve density estimation. For example, specific corrections can be applied to individual observations according to their characteristics,
46 Chapter 3: Factors influencing detection probability in aerial surveys including group size or vegetation (e.g. Choquenot 1995a; Southwell 1996). Predicting the effects of a combination of factors can allow correction for heterogeneity in detection probability (e.g. Steinhorst and Samuel 1989; Alho 1990). Applying an average correction across groups may otherwise overestimate the adjustment for those groups that are always detected by both observers (i.e. group sizes of feral goats >40 in this study) and underestimate those groups with low probabilities of detection. The results herewith suggest bias may be greatest during surveys with inexperienced observers or in sites or subsections with smaller group sizes and increased vegetation structure. Investigation is required to discover whether improved reliability or accuracy of density estimates can be achieved by considering these or other factors that influence detection probability (Chapter 6,7).
47
CHAPTER 4
BEHAVIOURAL RESPONSES OF FERAL GOATS DURING HELICOPTER SURVEYS
4.1 Introduction
Helicopters are widely used in the management of wildlife. This includes the monitoring of population density (e.g. Caughley 1977; Pollock and Kendall 1987; Bromley et al. 1995; Pople 1999a), recreation (e.g. Stockwell et al. 1991), for exploration (Cote 1996), harvesting (e.g. Fleming et al. 2002), or management of pests via shooting (e.g. Saunders 1993; Saunders and Bryant 1988; Hone 1990; Maas 1997) and baiting (e.g. Choquenot 1994; Fleming et al. 2000).
The ‘intrusive’ use of helicopters including harvesting, shooting, and baiting, can reduce the effectiveness of future management by targeting or removing a biased proportion of the population and/or reducing detectability (e.g. Saunders 1988; Bayne et al. 2000). The use of helicopters or fixed-wing aircraft for surveying, tourism or exploration is often assumed to be ‘non-intrusive’, but can also potentially result in short-term or long-term changes in wildlife movements (Cote 1996; Krausman and Hervert 1983; Linklater and Cameron 2002), foraging (Stockwell and Bateman 1987; Stockwell et al. 1991) and breeding behaviour (Fjeld et al. 1988). These changes in behaviour can also compromise assumptions when surveying from a helicopter (Bleich et al. 1990; Linklater and Cameron 2002). For example an alert or flight response may cause animals to hide reducing detectability; result in movement between transects resulting in recounting (e.g. Linklater and Cameron 2002); or induce movement into denser vegetation, which can compromise estimates of habitat use (e.g. Krausman and Hervert 1983).
Helicopter disturbance can also cause a range of negative impacts to wildlife including immediate physical injury (e.g. Cote 1996), increased energy expenditure (e.g. Stockwell et al. 1991), changes in physiological condition (e.g. MacArthur et al. 1979), or long-term changes in behaviour such as shifts to poorer feeding sites (Calef et al. 1976; Larkin 1996). These effects are essentially equivalent to the influence of a predator. For example, changes 48 Chapter 4: Behavioural responses of feral goats during helicopter surveys in ungulate behaviour in response to predators such as increased vigilance, altered group sizes and movement to adjacent habitat (Caro and FitzGibbon 1995; FitzGibbon and Lazarus 1995; Hunter and Skinner 1998) provide a similar basis for comparison with helicopter disturbance. Management of pest animals has been considered in terms of predator-prey theory (e.g. Hone 1990; Choquenot et al. 1999; Walter 2002), and knowledge of anti-predator or alert behaviour can improve the applicability of these models (e.g. Ives and Dobson 1987). During ‘non-intrusive’ helicopter use immediate physical injury is unlikely although severe injury has been observed during over-flights of some species (e.g. mountain goats [Oreamnos americanus], Cote 1996). Long-term changes in home range areas have seldom been investigated as a result of intrusive (Dexter 1996) or non-intrusive use, and such changes are difficult to separate from movements for other reasons, such as dispersal, migratory patterns, or in response to available resources.
Temporal changes in responses of wildlife to noise are well-known. Most animals become less responsive to sounds emitted at regular intervals, a process referred to as habituation (Thompson and Spencer 1966). This is most commonly observed in the use of acoustic devices during conflicts with agriculture (Bomford and O’Brien 1990; Koehler et al. 1990). However, habituation has not been well documented for wildlife responses to helicopters. Miller and Gunn (1980) observed decreased responsiveness of muskoxen (Ovibos moscharus) with consecutive cargo slinging by helicopters indicating short-term habituation but this varied between years.
The reverse of habituation can occur where, instead of animals becoming acclimatised to noise, they become averse to it. This has been the focus of research in aversive conditioning (e.g. Brush 1971; Galef 1982). Aversion from helicopters is usually associated with a threat, such as aerial shooting (e.g. Saunders 1988; Bayne et al. 2000). For example, a marked increase in evasive behaviour was observed for feral goats following helicopter shooting (Bayne et al. 2000). Also, Saunders (1988) found a significant decrease in the number of feral pigs observed in aerial surveys, following harassment by a helicopter where shooters aimed close to but not at feral pigs. However, Dexter (1996) investigated the effects of an intensive shooting exercise on the movements and home range use of feral pigs, but found no significant differences before and up to 4.5 days after shooting. During
49 Chapter 4: Behavioural responses of feral goats during helicopter surveys
‘non-intrusive’ helicopter flights, Calef et al. (1976) observed that caribou were more responsive in a subsequent year and suggested that animals became sensitised, rather than habituated, to aircraft as a result of frequent flights.
Wildlife responses to aircraft are usually associated with the sound they generate (e.g. Maier et al. 1998; Bayne et al. 2000). Helicopter noise consists of sound from the engine or turbine, gearbox, blade loading, rotors and turbulence interactions (Chan and Hubbard 1985; Larkin 1996). The most significant source of noise is the pulsating sound of the rotor blades, which can vary according to weather conditions, the number of blades, their tilt and speed, and the speed, activity or load of the helicopter (Larkin 1996). Hence the noise created by different models of helicopter also varies under the same conditions (True and Rickley 1977).
The responses of wildlife to noise range from slightly increasing vigilance (e.g. mink [Mustela vison] to jet aircraft, Brach 1983) to bolting over large distances for extended periods (e.g. mountain sheep [Ovis canadensis] to helicopters, Bleich et al. 1990). The severity of disturbance may vary with species (Miller and Gunn 1979), group size (Czech 1991), individual groups (Miller and Gunn 1980), sex and age (Lenarz 1974), vegetation cover (Krausman et al. 1986), season (Stockwell et al. 1991; Harrington and Veitch 1992), terrain (Cote 1996), distance from the helicopter (Calef et al. 1976; MacArthur et al. 1982; Cote 1996) or whether the helicopter is visible (Brach 1983).
An understanding of how animals respond to helicopters is important in predicting the consequences of the disturbance on the ecology and behaviour of exposed wildlife (e.g. Calef et al. 1976; Stockwell et al. 1991); when investigating the efficacy of helicopters to manage pests (e.g. Ives and Dobson 1987; Hone 1990); and in verifying bias associated with aerial survey techniques (e.g. Linklater and Cameron 2002, Chapter 5). The definitions of ‘alert behaviour’ and ‘distance moved’ in relation to helicopter wildlife disturbance used here follow reviews of Quenette (1990) and Taylor and Knight (2003). This chapter investigates the main factors that influence alert behaviour (Quenette 1990) and distance moved (Taylor and Knight 2003) for feral goats in response to helicopter surveys.
50 Chapter 4: Behavioural responses of feral goats during helicopter surveys
4.2 Methods
4.2.1 Behavioural observations
During helicopter surveys up to 12 ground-based observers located, counted and monitored the behaviour and movements of free-ranging feral goats. To reduce disturbance from ground observers, herds of goats were approached on foot as quietly as possible. All observations where goats were noticeably affected by ground observers were omitted from these analyses. Observers recorded time, location, and the number, colour, sex and age ratio, location, activity, vegetation type, and movements of goat groups and other variables (Table 4-1). Horizontal distances to the helicopter from observed goats were also recorded using line-of-sight, 1:25,000 topographic maps, grid locations and GPS. Where helicopters were not observed grid locations were taken and horizontal distances subsequently verified with simultaneous helicopter locations that were calculated from start and finish waypoints and time as previously described. All observations were conducted during aerial surveys with helicopters maintaining a fixed height (b) of 46 m above ground level. The recorded horizontal distance (a+d) was therefore directly proportional to actual distance (c) of the helicopter ( c 2 = (a + d)2 + b2 ; Figure 3-1).
Observed activities for each group included foraging (grazing and browsing), resting (lying down), standing (not alert), moving (not alert) and four classes of alert activity. Each observation was classified into the following, corresponding to an increasing level of alert response:
0 No visible response. Animals showed no sign of being disturbed and did not alter their activity.
1 Alert standing. (Stationary response). Animals did not move but were vigilant (Quenette 1990) in a standing position.
2 Alert walking. (Mild escape response). Animals walked in response to the helicopter. If already moving, the animals changed direction.
51 Chapter 4: Behavioural responses of feral goats during helicopter surveys
3 Alert moving. (Medium escape response). This is an intermediate moving category, where goats initially moved quickly but stopped soon after the helicopter passed, or if goats continued moving there was no breakdown of social cohesion evident within the group.
4 Alert bolting. (Strong escape response). Animals ran quickly from the helicopter in an alert state and continued running after the helicopter had passed. Often this category involved a breakdown of the group structure with animals moving in different directions.
Where individual animals within the same group behaved differently the activity of the majority of the group was recorded. The alert categories in this study are comparable to the classes described by Calef et al. (1976) but presented in an increasing scale and include an additional intermediate category (3 Alert moving). Calef et al.‘s (1976) ‘panic response’ where ‘individuals were out of control, colliding with each other or running into obstacles’, was not observed during ground observations. However, there were isolated cases where animals responded in this way during aerial observations (<20 from 28558 observations). For example, a female goat tripped and rolled several metres down a 20° slope; and a sheep was observed turning and colliding with a tree. There were also other cases where animals collided with each other, for example, when pushing through holes in fences.
Alert standing is synonymous with ‘vigilant’, which describes animals interrupted in their continuing activity, lifting their heads and visually scanning the environment (Quenette 1990). This definition implies animals become alert from an undisturbed activity. However, in practice without physiological information (e.g. MacArthur et al. 1979) it is difficult to separate these observations from a hiding response, which may reflect a higher level of stress. Although animals were identified as hiding separately to alert standing, these differences were largely subjective hence included in the alert standing class.
To overcome the subjective nature of these classifications alert activity was also analysed
52 Chapter 4: Behavioural responses of feral goats during helicopter surveys using a binominal model; alert (1); not alert (0). ‘Alert’ in this case included classes 1 to 4. An additional analysis investigating distance (m) moved was also conducted. The distance moved was recorded as the distance from where goats started to move (Class 2-4) in response to the helicopter, to where they stopped moving (Taylor and Knight 2003).
Defining a ‘group’ from aerial observations may be confounded by the influence of helicopters on group structure. This has been acknowledged previously by regarding groups that are observed from the air as sighting entities rather than biologically meaningful aggregations (e.g. Choquenot 1995a,b; Fleming et al. 2000) but has not been investigated. The ‘biological meaning’ of a group varies with the intention of the investigation (Martin and Bateson 1993). A group in this context has been variously considered as a cohort (O’Brien 1984a) a party (Crook 1970) or mob (Fleming, pers. comm. 2004). To examine the effects of the helicopter on group structure, ground observers recorded whether groups (1) ‘split’, where a homogenous aggregation separated into two or more spatially discrete units; (2) ‘combined’, where two or more spatially separated aggregations joined with other aggregations and behaved as one unit, or (3) remained unchanged, after they were disturbed by the helicopter. For applicability to aerial surveys only those observations of goat groups where the helicopter was less than 130 m and hence available to be seen from the air were included.
4.2.2 Analyses
The effects of 18 variables (Table 4-1) and 1st order interactions on the response of alert, alert class, and distance moved were investigated using binomial, linear and log-linear models respectively, and an analysis of variance of regression (Crawley 1993). Each model was selected as it best represented the data type of the response variable (i.e. alert: 0 or 1; alert scale and distance moved: increasing continuous variables). The procedures used were typical of GLM and followed a step-wise progression from the maximal (full) model through a series of simplifications and deletions to the minimal adequate model. The maximal model contained all continuous and discrete variables and 1st order interaction terms. Higher-order interactions were progressively removed if they were not significant (P<0.05) using an analysis of variance (Crawley 1993). Model fit was investigated using
53 Chapter 4: Behavioural responses of feral goats during helicopter surveys standard residual plots (e.g Cochran 1951). In these models, log transformations were used for distance moved, horizontal distance and group size to remove heterogeneity of variance and linearise the response. These values were retransformed when displaying regressions graphically.
To remove any potential sampling bias of animals moving into denser vegetation, ‘vegetation type’ and ‘tree cover’ were analysed separately using only observations where groups were first disturbed. Observations containing missing values were omitted for all variables, but included as a separate level (‘NA’) for ‘herd’ and ‘before activity’ to maximise available data. Significance values (P>0.05) were calculated after removing the effects of all other significant variables using analysis of variance. To reduce the confounding effects of year and helicopter type, year was included in the final analysis of variance to remove the influence of this factor. Survey hours was included as the cumulative time for seasonal surveys over a two year period. However, an additional survey was conducted 24 months later, but was excluded when analysing for survey hours.
54 Chapter 4: Behavioural responses of feral goats during helicopter surveys
Table 4-1: Variables included in step-wise multiple regression and analyses of variance for predicting alert responses caused by a helicopter. The response variables are marked with an asterisk. The number of terms for discrete variables or the range for continuous variables is listed in parentheses.
Variable Description Scale of alert activity: no visible change (0); alert standing (1); alert Alert Class* walking (2); alert moving (3); alert bolting (4). Linear model. Alert* Alert (1) or not alert (0). Binomial model. Distance goats moved (metres) after they were disturbed by the helicopter Distance Moved* (0-1200). Log-linear model. Horizontal Distance The horizontal distance from the helicopter to the focal animals. Activity before goats were disturbed by the helicopter; foraging, standing, Before activity moving, resting (4) Goat groups that move within a spatially discrete area defined by tagged Herd individuals (12) Survey Hours The cumulative hours of seasonal surveys between 1997 and 1998 (0-22). Helicopter Type Hughes 500 or Bell 206 Jetranger (2) Density of goats within the defined district calculated using the double- Density count technique (Chapter 7) Season Summer, Autumn, Winter, Spring (4) Site Turee or Birnam (2) Slope Degree slope (0° to 35°) Aspect Aspect of the terrain (8) Away Goats moving away, towards or alongside helicopter (3) Kids Groups with and without kids (2) Aspect Moved Movement of goats up, down, or along the slope (3) Habitat classification based on Specht 1970: Open grassland, Open Vegetation Type Woodland, Shrubland, Shrubby Woodland, Woodland, Forest (6). Tree Cover Percentage tree cover based on habitat classification (0-85%) Position Helicopter 'in front', 'behind' or 'beside' goats (3) Group size Instantaneous size of the goat herd (1-268). Log transformed. First three hours after sunrise or last three hours before sunset (AM or PM; Time of day 2)
55 Chapter 4: Behavioural responses of feral goats during helicopter surveys
4.3 Results
The horizontal distance to the helicopter was important in determining alert response and distance moved for all three models using analysis of variance (Table 4-2). There was a significant (P<0.0001) relationship between the percentage of alert animals observed and their distance from the helicopter, described by a negative exponential function showing a good fit to the data (Figure 4-1, y = 81.753e-0.0005x, r2=0.9816). Distance moved increased with helicopter distance (Figure 4-2, y = -22.792Ln(x) + 243.71), with goats typically moving distances of greater than 150 m when the helicopter was less than 200 m away. Distance moved did not consistently increase when the helicopter was further than 200 m away.
56 Chapter 4: Behavioural responses of feral goats during helicopter surveys
Table 4-2: Significance values using an analysis of variance following step-wise multiple regression for alert scale, alert and distance moved models.
1 2 3 Response Variables→ Alert Scale Alert Distance Moved Dependent Variables↓ log Horizontal Distance <0.0001 <0.0001 <0.0001
(F1,17 = 173.9) (F1,17 = 151.64) (F1,17 = 128.21) Before activity <0.0001 <0.0001 <0.0001
(F4,17 = 9.47) (F4,17 = 14.20) (F4,17 = 12.96) Herd 0.001 0.007 0.002
(F11,17 = 2.81) (F10,17 = 2.47) (F11,17 = 2.67) Survey Hours 0.03 NS 0.0006
(F1,17 = 4.86) (F1,17 = 11.80) Helicopter Type NS 0.04 NS
(F1,17 = 4.43) Density NS 0.001 NS
(F1,17 = 10.78) Season NS NS NS Site NS NS NS Slope NS NS NS Aspect NS NS NS Away NS NS NS Kids NS NS NS Aspect Moved NS NS NS Vegetation Type NS NS NS Tree Cover NS NS NS Position NS NS NS log Group size NS NS NS Time of day NS NS NS Multiple R 0.472 0.481 0.425
F statistic F19,596 = 8.949 F7,737 = 26.34 F7,341 = 10.41 NS: P>0.05 1Linear 2Binomial 3Log-linear
57 Chapter 4: Behavioural responses of feral goats during helicopter surveys
90
70 Alert (%)
50
30
10 0 500 1000 1500 2000 2500
Horizontal Distance (m)
Figure 4-1: The relationship between the percentage of feral goats displaying alert behaviour and horizontal distance (m) from the helicopter.
58 Chapter 4: Behavioural responses of feral goats during helicopter surveys
300
Distance Moved 200 (m)
100
0 0 500 1000 1500 2000 Horizontal Distance (m)
Figure 4-2: The relationship between the distance (m) moved by feral goats and horizontal distance (m) from the helicopter. r2 = 0.6292.
The activity of feral goats before they were visibly disturbed by the helicopter was significant in explaining whether they exhibited alert behaviour (P<0.0001), the extent of their alert response (P<0.0001) and the distance they moved from their original position (P<0.0001) (Table 4-2). More animals displayed alert behaviour when they were already moving, and fewer when resting (Figure 4-3). They were also more likely to flush over greater distances if they were previously foraging or already moving, than standing or resting (Figure 4-4).
59 Chapter 4: Behavioural responses of feral goats during helicopter surveys
100 90 80 70 60 Alert (%) 50 40 30 20 10 0 resting standing foraging moving
Figure 4-3: Percentage of feral goats alert relative to their activity before disturbance by a helicopter. Error bars show the 95% confidence intervals.
160 140 120 100 Average Flushing 80 Distance (m) 60 40 20 0 standing resting moving foraging
Figure 4-4: Mean distances moved by feral goats relative to their activity before disturbance from a helicopter. Error bars show the 95% confidence intervals.
60 Chapter 4: Behavioural responses of feral goats during helicopter surveys
Different herds varied in their responses to the helicopter, in terms of incidence (P=0.007) and extent (P=0.001) of alert activity as well as distance moved (P=0.002) (Table 4-2). Survey hours, for investigating the cumulative effects of seasonal surveys over two years, was positively correlated with the extent of alert activity (P=0.03), but negatively correlated with distance moved (P=0.0006). A greater proportion of goats displayed alert behaviour when exposed to the Hughes 500 helicopter than the Bell Jet Ranger (P=0.04); and a greater percentage of animals were alert in areas of higher densities (P=0.001; Figure 4-5, linear fit y = 0.3535x + 28.598).
60
55
50 Alert (%) 45
40
35
30
20 30 40 50 60 70 Density
Figure 4-5: The relationship between density (goats km-2) and the percentage of goat groups that displayed alert behaviour in response to helicopters, recorded by ground-based observers. r2 = 0.5819.
61 Chapter 4: Behavioural responses of feral goats during helicopter surveys
The structure of groups of goats following disturbance by the helicopter remained unchanged on 159 of 272 (58%) occasions, ‘split’ into separate distinct groups on 38 occasions (14%) and ‘combined’ with other groups on 75 occasions (28%) (n=272).
4.4 Discussion
There has been very little investigation of the alert behaviour of feral goats in response to aircraft (Bayne et al. 2000). In this section comparisons have been made with studies of other species and various responses to predators. While useful for discussing the main determinants of alert activity, different species respond differently (Klein 1973; Awbrey and Bowles 1990; Miller and Gunn 1979) and sources of disturbance vary (e.g. predators, helicopters, fixed-wing aircraft), hence these studies are considered accordingly.
4.4.1 Helicopter distance
The distance from the source of disturbance is an obvious and consistently important indicator of alert behaviour both from predators (e.g. Fitzgibbon 1989) and human activities, including helicopters (Calef et al. 1976; MacArthur et al. 1982; Harrington and Veitch 1992; Luick et al. 1994; Cote 1996). In the present study, 90% of goat groups displayed alert behaviour when the helicopter was directly overhead. This percentage decreased exponentially with helicopter distance (Figure 4-1), with an average of 20% still alert at distances of 2.5 kilometres. Occasional observations of alert behaviour were recorded up to 5km from the helicopter. A negative relationship was also evident with distance moved (Figure 4-2), but distance moved did not continue to decrease when the helicopter was further than 200 m (Figure 4-2).
Comparative studies of other ungulates were similar, suggesting alert response is low when helicopters are greater than 400 m (caribou: Calef et al. 1976; MacArthur et al. 1982; Harrington and Veitch 1992) and significant when less than 100 m (Harrington and Veitch 1991; Luick et al. 1994). For caribou, alert running (equivalent to alert category 4 of this study) was the most common response when the helicopter was less than 100 m (Harrington and Veitch 1991; Luick et al. 1994). A study of the responses of mountain goats to helicopters reported greater disturbance with 85% of animals being disturbed when 62 Chapter 4: Behavioural responses of feral goats during helicopter surveys the helicopter was within 500 m (Cote 1996).
The reason animals flush from helicopters is usually associated with noise (e.g. Cote 1996; Maier et al. 1998; pers. obs.), although most studies do not separate visual from non-visual disturbance (see Larkin 1996 for review). In some cases visual cues have been shown to be important in affecting alert activity (Brach 1983). In the present study the continuous increase in alert behaviour and helicopter distance (Figure 4-1) may indicate an auditory rather than a visual cue prompts disturbance. However sharp increases in distance moved were evident when the helicopter was 150 m or less, which is within the visual range for feral goats. These results may imply that noise initiates an initial alert response, but visual cues may cause animals to flush greater distances. Moreover, regardless of whether visual or auditory cues are used, 150 m appears to be the critical approach distance feral goats will tolerate before the animals will flush. Standardised aerial surveys use 100 m or 200 m strip widths (Choquenot 1995a; Grigg and Pople 1999) hence goats that are available for sampling are more likely to flush greater distances, which has implications for recounting animals in consecutive transects (Chapter 5).
4.4.2 Prior activity and responses of goats
The alert response of feral goat groups in this study, varied according to their prior activity. More animals displayed alert behaviour when they were moving, fewer when foraging and least reactions were observed when animals were standing and resting (Figure 4-3). Animals that were moving prior to the disturbance also flushed further than when standing or resting but greatest distances were traversed when animals were foraging (Figure 4-4). These results are consistent with the findings of Calef et al. (1976) who found caribou more reactive to a helicopter when moving or feeding than resting, but differed from McCourt et al. (1974) who reported that caribou that were resting and feeding animals reacted more strongly. The results observed in this study support Calef et al.’s (1976) work and suggest animals are increasingly responsive to helicopters when they are more active. Moving and foraging exert greater energy and increases heart rate compared with other activities (Wunder 1975; Taylor et al. 1982; Saunders et al. 1993). A more energetic state intuitively would increase the likelihood of animals detecting and responding to a threat or
63 Chapter 4: Behavioural responses of feral goats during helicopter surveys disturbance.
The presence of differences in alert activity also has implications when sampling for density estimation (Chapter 5). Animals are found to be more easily detected when moving rather than standing or resting (Chapter 5; Gasaway et al. 1985; Samuel et al. 1987). Changes in activity as a result of helicopter disturbance are also important when considering energy consumption. For example, a study of the reactions of bighorn sheep (Ovis canadensis) to recreational helicopter flights in the Grand Canyon indicated sheep decreased their time spent foraging by 17% (Stockwell and Bateman 1987; Stockwell et al. 1991). In contrast during behavioural observations of goat groups of the current study, vigilant animals were found to decrease their time spent resting rather than that spent foraging, suggesting negligible energetic costs (Reilly, Fleming and Jones, unpublished data).
4.4.3 Herd responses
Despite an equivalent number of helicopter fly-overs some herds reacted more intensely, displaying different levels of alert behaviour and flushing greater distances (Table 4-2). This was particularly evident in the analysis of the alert classification (P=0.0002, Table 4- 2). Individual and group differences in alert behaviour have also been observed in other studies. For example, Miller and Gunn (1980 ) showed there was consistent variation in the levels of responses between herds of muskoxen with one herd classified as ‘calm’, another ‘excitable’ and the other intermediate. Ungulate responses to predators also show differences between groups (Fitzgibbon 1989; Fitzgibbon and Lazarus 1995). For example, groups of gazelle (Gazella thomsoni) have been found to detect approaching cheetahs at greater distances than others (Fitzgibbon 1989). Differences in vigilant behaviour have been attributed to predation for impala (Aepyceros melampus) and wildebeest (Connochaetes taurinus), where both species had increased rates of looking and a greater proportion of time spent looking in areas with higher predation pressure (Hunter and Skinner 1998). Results presented here show that, although helicopter time was equivalent between herds, some resided closer to human activity, implying greater exposure to motorbikes, tractors and vehicles. Other herds occupied secluded areas that were seldom
64 Chapter 4: Behavioural responses of feral goats during helicopter surveys accessed by managers. Although not measured at the time, groups closer to centres of activity may have been more acclimatised to human and motorised disturbance, which would explain these differences.
4.4.4 Sex and age response differences
Studies of ungulates show that considerable differences can occur in alert behaviour within groups (Fitzgibbon and Lazarus 1995; Elgar 1989). For example, sex and age are important in determining predator responses for gazelle (FitzGibbon 1990), springbok (Antidorcas marsupialis, Bedekoff and Ritter 1994), ibex (Capra ibex ibex, Toigo 1999) and other ungulates (Burger and Gochfeld 1994). During non-invasive observations of goats of the present study, females with kids were shown to be more vigilant than other individuals (Reilly, Fleming and Jones, unpublished data), a trait that also differs with post-partum strategies of individuals (O’Brien 1984b). In the current study, groups with kids did not display a different alert response to helicopters (P>0.05, Table 4-2). This may be due to pooling the activity of all individuals within the group, or that all animals were more likely to respond to an imposed disturbance.
Although unquantified, on several occasions individuals within groups responded differently. This was particularly evident with lactating females who became alert sooner and were more vigilant, which is common amongst other ungulates (Lenarz 1974; Fitzgibbon 1990; Burger and Gochfeld 1994; Maier et al. 1998; Toigo 1999). This predominantly occurred during the early stages of alert activity (i.e. alert standing). A moving response however, nearly always resulted in movement by all group members. However, exceptions to this were evident during some aerial observations and helicopter mustering, where females with newly born and immobile young would remain standing when others moved off. This suggests helicopter surveys and aerial mustering in this study did not cause mothers to abandon their young, which has also been shown for calving caribou (Calef et al. 1976).
65 Chapter 4: Behavioural responses of feral goats during helicopter surveys
4.4.5 Habituation or aversion?
Modelling of the first two years’ data indicates cumulative survey hours were related to the extent of alert response (linear model) but not to the proportion of animals alert (binomial). In the linear model alert response was positively related to cumulative survey time, indicating an increasing aversion to the helicopter over time. However, the opposite was apparent for distance moved. These results suggest aversion or habituation to helicopters is more complex than simply increased incidence of alert activity.
The few studies that have investigated the effects of prolonged disturbance by helicopters suggest variable learning by individuals and groups (Calef et al. 1976; Miller and Gunn 1980). Miller and Gunn (1980) indicated short-term habituation varied between years and herds of muskoxen. Long-term habituation in their study was noted in one of three herds, which was also the herd considered the most ‘excitable’. The other two herds apparently increased in responsiveness with time, which was attributed to breeding activity (Miller and Gunn 1980). Maier et al. (1998) found changes in responsiveness of caribou to low flying jets were associated with season rather than sequentially.
Aversion of ungulates to helicopters is usually associated with more intrusive activities such as shooting (Saunders 1988; Bayne et al. 2000), with animals becoming less detectible following disturbance. Changes in behaviour, such as increased hiding (Bayne et al. 2000) or less movement may result in decreased detection probability. Animals in the current study appeared to alter their behaviour by moving more often (‘alert class’ model) but less distantly (‘distance moved’ model), possibly into areas that were perceived ‘safe’. During field observations of some sub-populations, goats were observed retreating to and congregating at the same locations in response to consecutive helicopter surveys, despite a 3 month time lag between sampling. The frequency of disturbance is likely to be a major mechanism affecting these behavioural changes. More frequent surveys, such as weekly or monthly, are likely to increase habituation, but equally may also increase the likelihood of long-term changes in movements, such as animals vacating their home range (e.g. Bleich et al. 1990). In the current study, intensive monitoring of ear-marked and radio-tagged goats indicated strong site fidelity with no long-term changes in movements or activity (Fleming
66 Chapter 4: Behavioural responses of feral goats during helicopter surveys and Tracey unpublished data). This suggests the changes in alert behaviour that were evident during surveys did not cause altered behaviour or movements during other periods, which is consistent with the movements of feral pigs following helicopter shooting (Dexter 1996). Non-intrusive observations of goats outside surveying periods support this, with very few occasions where individuals displayed vigilant behaviour (Reilly, Fleming and Jones unpublished data).
4.4.6 Helicopter type
A Hughes 500 helicopter was used for all surveying with the exception of the follow-up survey in 2000 where a Bell Jet Ranger was employed. Hence direct comparison of the effects of the helicopter type is confounded with time. In an attempt to remove these effects, survey hours were included in the final analysis of variance prior to helicopter type. In this analysis a greater proportion (P=0.007) of goat groups was found to exhibit alert behaviour from the Hughes 500 than the Bell Jet Ranger. However, helicopter type did not significantly affect the extent of alert behaviour in the linear model or distance moved in the log-linear model (P>0.05, Table 4-2).
The increase in alert behaviour in the binomial model caused by the Hughes 500 is consistent with increased detection evident from this helicopter (Chapter 3). Movement as an escape response is commonly suggested to increase sightability (e.g. Chapter 5; Kufield et al.1980; Gasaway et al. 1985; Samuel et al. 1987). Helicopters are usually observed to cause a greater alert response than fixed-wing aircraft (McCourt et al. 1974; Grubb and King 1991; Harrington and Veitch 1991; Watson 1993; cf. Calef et al. 1976). Behavioural responses to different models of helicopter have seldom been compared. However, Ward and Stein (1989) found reactions of geese (Branta bernicla) were significantly greater from a Bell 205 than the smaller Bell Jet Ranger (Bell 206) and Hughes 500 helicopters.
Differences in alert behaviour caused by exposure to Hughes 500 and Bell Jet Ranger helicopters have not previously been identified and these models have similar volume levels (Newman et al. 1982). This suggests that alert behaviour is not only related to loudness but that animals respond differently to different sounds or alternatively use visual
67 Chapter 4: Behavioural responses of feral goats during helicopter surveys cues (see Section 3.4 re variation in helicopter noise). The confounding affect of time also needs to be considered. The increasing extent of alert activity with survey time would imply animals respond more severely during latter surveys when the Bell Jet Ranger was used. However, the opposite was evident, indicating that the differences between the effects of the two helicopters were directly related to the type of noise rather than a developed aversion to the sound.
4.4.7 Other variables
Although unquantified, differences in flushing behaviour between species (horses, sheep, goats, pigs, macropodoids) were evident in this study and have been commonly observed elsewhere (Klein 1973; Miller and Gunn 1979; Awbrey and Bowles 1990). Group size is also often found to be important in studies of alert behaviour (McCourt and Horstman 1974; Jarman 1987; Elgar 1989; Czech 1991; Quenette 1990; Quenette and Gerard 1992; Blumstein and Daniel 2003). In most cases, alert activity is found to decrease with increasing group size, which has been attributed to the ‘many eyes’ hypothesis (Pulliam 1973). However, these studies mainly report stationary or scanning responses to predators and seldom observe animals flushing. Czech (1991) investigated flight responses of elk from logging and tourist activities and found smaller herds were less likely to move. Hence the countering effects of group size on stationary and moving animals may explain the non- significant differences evident in this study. Pooling the activity within a group would also dilute the effects of individual stationary responses. However, for caribou, Calef et al. (1976) also found group size was not important.
Flushing of animals will increase the interaction between groups, particularly in areas of higher density. Hence, the positive relationship with density (P=0.01; Figure 4-5) suggests alert groups may be increasing the alert activity of other goats within defined areas.
Season was not important in the current study despite previous evidence of this for caribou (Klein 1973; Maier et al. 1998) and bighorn sheep (Stockwell et al. 1991). Slope, ranging from 0° to 35° was not significant which is consistent with Bleich et al. (1990). Habitat, tree cover, time of day and positional variables were also not important (P>0.05) in
68 Chapter 4: Behavioural responses of feral goats during helicopter surveys predicting the occurrence or extent of alert behaviour or distance moved (Table 4-2).
4.4.8 Conclusion
This chapter assists in understanding why and how goats respond to helicopters, which is useful when considering the potential behavioural consequences of the disturbance and the implications for aerial surveys.
Results suggest helicopter surveys did not cause long-term energetic or behavioural consequences for feral goats. Although a greater number of goats were alert with cumulative survey time, these moved less distance. No changes in home range were recorded; vigilance activity outside surveying periods was minimal (Reilly, Fleming and Jones, unpublished data); groups with kids did not display a different alert response to helicopters; and post-partum females were never observed deserting their young.
Nevertheless, short-term changes in movements have implications for aerial surveys. Goats were more likely to flush when helicopters were within 150 m, which is close to or within standard helicopter strip widths commonly used in wildlife studies (Choquenot 1995a; Grigg and Pople 1999). The relationship between the distance to the helicopter and the distance moved indicates that goats do not have an equal chance of moving into or out of a transect, but are more likely to move further once they are able to be seen. Helicopter surveys were also found to alter the structure of 42% of groups observed, with 28% of groups merging with others and 14% splitting into separate groups. Therefore, group size estimated from the air should not be considered as biologically important. For estimating density, researchers should also avoid using group sizes determined from ground observations to correct group sizes determined from aerial surveys because of the afore- mentioned disturbance effect. Further implications of flushing behaviour on density estimates are discussed in the next chapter.
69
CHAPTER 5
TESTING ASSUMPTIONS IN AERIAL SURVEY USING GROUND OBSERVATIONS
5.1 Introduction
The use of strip transects to estimate actual abundance relies on various assumptions. Three key assumptions are: (1) all animals are counted within the designated strip; (2) transect boundaries are accurately delineated, and (3) animals are not counted more than once (Caughley and Sinclair 1994). When surveying wildlife from the air it is widely accepted that the first assumption is likely to be violated in most cases (e.g. Goddard 1967; Caughley 1980; Krebs 1999), hence various methods can be used to calculate the probability of detection of animals and subsequent corrections can be applied to the underlying counts. Estimates of detection probabilities usually rely on a suite of other assumptions, and have been achieved using multiple observers (e.g. Caughley and Grice 1982; Maas 1997), distance sampling (e.g. Buckland et al. 1993; van Hensbergen et al. 1996; Walter and Hone 2003), regression techniques (Caughley et al. 1976; Hone 1986), radio tagging (Rice and Harder 1977; Packard et al. 1985) or comparison with independent population estimates (Short and Bayliss 1985; Hone 1988; Hone and Short 1988; Short and Hone 1988).
With regard to assumption 1, correction factors using multiple observers have advanced in theory and application (Pollock et al. 1990; Schwarz and Seber 1999; Linberg and Rexstad 2002) and are the focus of this study. A key assumption of this technique is that observations are independent (Caughley and Grice 1982). However this assumption may be violated due to a correlated search image of observers (Caughley and Grice 1982), or when a proportion of animals are impossible to observe or are unavailable (Bayliss 1986; Marsh and Sinclair 1989a).
With regard to assumption 2, defining transect width is achieved in aerial surveys using parallel (e.g. Clancy 1999; Walter and Hone 2003) or perpendicular (e.g. Choquenot 1995a,b) poles, or markers placed on struts for fixed-wing aircraft (e.g. Clancy 1999). These boundaries are usually calibrated for each observer using fixed markers on the 70 Chapter 5: Testing assumptions in aerial survey using ground observations ground. These techniques are simple and likely to be accurate for flat country (e.g. Choquenot 1995a,b). However, delineating transect width in steeper terrain is difficult and may result in biases associated with increased transect widths when viewing downhill and decreased width when viewing uphill.
In wildlife research, aerial surveys are usually designed using standard random (e.g. Choquenot 1995a) or systematic (e.g. Walter and Hone 2003) sampling procedures. A common practice is to saturate the study area with transects running across the grain of the country and select a subset randomly without replacement (e.g. Choquenot 1995a,b; Pople et al. 1998b; Fleming et al. 2000). To reduce ferry time and therefore cost, transects are typically flown consecutively from one edge of the study site to the other. Where consecutive transects are sampled assumption 3 is likely to be violated from individuals flushing between transects. In this case most estimators will not be affected if animals have an equal chance of moving into or out of a transect. However, consistent movements into or out of transects will result in biased estimates of density (e.g. Linklater and Cameron 2002).
In this chapter the first assumption is tested using independent ground observations and mustering; the second assumption is verified using multiple observers; and the third is examined and quantified using observations of flushing behaviour and known locations of feral goats.
5.2 Methods
5.2.1 Ground observations
Ground observations in this chapter are equivalent to those described in Chapter 4, and are only summarised here. During aerial surveys ground-based observers located, counted and monitored behaviour and movements of free-ranging goats. Observers recorded the number, colour and sex ratios, location, distance from the helicopter, activity, vegetation type, movements, and other behavioural attributes of goat groups during synchronised time intervals. A sub-set of these data included records of activity (n=88), vegetation (n=82) and location (n=47) for groups known to occur within transect areas at the time surveyors were passing overhead. Hence these groups were potentially observable from the air. Field 71 Chapter 5: Testing assumptions in aerial survey using ground observations investigations were extremely labour intensive, requiring many observations (>1500 observations) as ground observers were unable to know in advance if particular goats would occur within transect areas concurrently.
Groups were confirmed as observed or not observed from the air using GPS’s, precise times and attributes of the groups (i.e. number of goats, proportion of kids and colour ratios). Additional consideration was given to the area not visible directly underneath the helicopter, previously stated to be 60 metres at flying height of 46 m (Figure 2-1). Any ground observations that coincided with ferry time, or when there was uncertainty whether a group was observed or missed were omitted.
Sample sizes were adequate for comparison between aerial and ground observations for two types of activity (moving and standing) using Chi-squared tests. Due to the potential differences in the perception of vegetation type from the air and ground, vegetation was determined from grid locations, rectified air photos and spatial queries in Arcview 3.2 (ESRI 2000). Comparisons were then made between the proportion of groups observed in four vegetation communities (open grassland, woodland, shrubby woodland, forest; using the classification adapted from Specht 1970, Chapter 2), from the air and ground.
By including only those groups that were available for simultaneous observation within transect boundaries by ground and aerial observers, the differences in detection probability could be separated from the effects of flushing caused by the helicopter. Hence, any difference in the proportions observed from the air and ground could be attributed directly to detection probability.
Ground observations were used to calculate activity and vegetation preferences, and mustered animals were used to calculate unbiased colour ratios. These were then compared to equivalent ratios estimated from aerial observations.
72 Chapter 5: Testing assumptions in aerial survey using ground observations
5.2.2 Verifying colour ratios
Extensive mustering on the study site between 1996 and 2000 resulted in the capture of 984 feral goats and allowed an unbiased determination of colour ratios. During mustering a detailed description of coat colour was recorded for each individual captured. Goats were then classified into three classes on the basis of coat colour: ‘Light’, including white, light cream and fawn; ‘Coloured’, including a mix of light to dark chocolate brown, tan, coffee, grey, or red, this often included animals with a black stripe along the back and shoulders (‘donkey cross’), which were from a mixture of genotypes such as goats from Toggenburg and Nubian breeds (Mackenzie 1993); and ‘Dark’, including individuals with a uniform coat of black or dark brown, or black with white points such as British Alpine derivatives (Mackenzie 1993). The same colour descriptions were used to classify animals observed from the air.
Chi-squared tests were used to compare the number of light, coloured and dark goats from ground mustering (n=984) and aerial observations (n=13,326). All aerial observations where colour ratios were estimated rather than counted were omitted, which allowed a direct comparison of those individuals actually observed.
5.2.3 Delineating transect boundaries
Perpendicular poles mounted on the helicopter (Choquenot 1995a) were calibrated by observers in the helicopter at 46 m AGL using fixed markers placed 100 m apart on the ground. This allowed delineation of the 100 m strip width for flat terrain. However, observers were also required to estimate 100 m in steep terrain, which involved a preliminary training process for new observers. Once poles were calibrated, ‘training’ flights were flown where observers practised counting. During these flights new observers practised identifying animals and features that were perceived to be at 100 m, which were verified by experienced observers. To examine whether front and back observers identified an equal strip width, animals were called onto tape as either being inside or outside the transect by observers on the same side of the helicopter.
73 Chapter 5: Testing assumptions in aerial survey using ground observations
5.2.4 Probability that animals are available for recounting
There have been no attempts to quantify the extent to which animals are recounted during standard wildlife surveys. In this section a method is derived using information on alert movement behaviour from ground observations and sampling rate to examine and quantify assumption 3: animals are not observed more than once. The probability that an animal or group is available for recounting (pa) was estimated using the following equation:
pa = pm1 ps1 + pm2 ps2 + ...... + pmi psi
where: pmi is the probability an animal moves to i other transects; psi is the probability of sampling transect i; and the maximum value for i is the maximum perpendicular distance moved divided by the distance between transects.
The probability of an animal moving into another transect (pmi) is dependent on the transect width, the distance between transects, the proportion of animals that move, how far they travel (dm) and in which direction they travel (θm). In this study these parameters were observed or estimated for feral goats known to occur within sampled transects. Distance
(dm) and direction (θm) moved were converted to the perpendicular distance moved in relation to east-west transects (Figure 5-1).
74 Chapter 5: Testing assumptions in aerial survey using ground observations
Figure 5-1: Representation for calculating the perpendicular distance goats moved (dp) from
the transect during aerial surveys. Notation: dp = (sinθp) dm, where dm= distance
moved; dp= perpendicular distance moved; and angle θp is calculated using
angle θm (direction moved, 0-360 degrees) and the following formulae: a. if
θm<90,then θp=90-θm; b. if 90<θm<180,then θp=θm-90; c. if 180<θm<270, then
θp=270-θm; d. if θm>270,then θp=θm-270. Direction of travel is left to right.
γ A Weibull distribution ( y = e[−(λx) ] ) was selected for describing the relationship between the probability of goats moving into another transect (y = pmi) and perpendicular distance moved (x = dp) (Evans et al. 1993). This relationship was selected over the simple exponential function as its shape could be altered according to the value. Scale () and shape () parameters were optimised using maximum log likelihood estimation in Solver© for Microsoft® Excel 2002, assuming a multinomial error structure.
75 Chapter 5: Testing assumptions in aerial survey using ground observations
The probability of sampling a transect depends upon survey design and initial sampling rate. If parallel transects are flown consecutively from one edge of the study site to the other, only animals that move in one direction were able to be recounted. However, in this study, to lessen the effects of driving animals, consecutive transects were omitted on the first pass and flown on a second pass. This complicates the calculations of pmi, as animals that move in either direction are available during the second pass. The sampling probability for this scenario was estimated by calculating separate probabilities for the first and second pass where,
≈ 2 ’ ∆ p s ÷ p s (First Pass) = p s -∆ ÷ « 2 ◊
p 2 p (Second Pass) = s s 2
On the first pass the probability of goats moving into a transect directly adjacent is 0 and probabilities of moving into >1 transect are calculated only for those animals that move one direction. On the second pass goats that moved in either direction may be available for sampling hence;
2 2 2 pa (First Pass) = 0 + pm2 ( ps − ps 2) + pm3 ( ps − ps 2) + pm4 ( ps − ps 2)
2 2 2 2 pa (Second Pass) = pm1 ( p s 2) + pm2 ( p s 2) + pm3 ( p s 2) + pm4 ( p s 2)
76 Chapter 5: Testing assumptions in aerial survey using ground observations
5.3 Results
5.3.1 Assumption 1: All animals are counted within the designated strip
5.3.1.1 Comparison of activity, vegetation and colour ratios
The proportion of goat groups observed from the air moving (0.95) and standing (0.05, n=1302) was significantly different from that expected from ground observations (n=88) (Figure 5-2, 2 = 342, df = 1, P <0.001). As perceived during aerial counts, this suggests that standing animals are less likely to be observed from the air, independent of flushing.
A greater than expected proportion of groups of feral goats was observed from the air in more open and less structured canopy cover (Figure 5-3, 2 = 103, df = 3, P < 0.001). This indicates that feral goats are less visible from the air in denser vegetation types and those types with an obvious shrub layer (forest and shrubby woodland), and are more visible in open grassland and woodland (Figure 5-3). The proportion of light to coloured and dark goats was also greater in aerial observations (Figure 5-4, 2 = 911, df = 2, P < 0.001) suggesting that light coloured goats had a greater probability of detection, or that perception of colour categories by observers was different from the air than at close range.
Ground Aerial n=88 n=1302
standing 5% standing 28%
moving 72% moving 95%
Figure 5-2: Percentage of feral goat groups observed moving and standing from the air and ground.
77 Chapter 5: Testing assumptions in aerial survey using ground observations
Ground Aerial n=82 n=1216
Forest Forest Shrubby Woodland 6% 11% Open grassland 10% 32% Open grassland Shrubby Woodland 39% 19%
Woodland Woodland 45% 38%
Figure 5-3: Percentage of feral goat groups observed from the air and ground in four vegetation communities
Ground Aerial n=984 n=13326
dark dark 11% 7%
coloured 24%
coloured light 33% 56% light 69%
Figure 5-4: Percentage of light, coloured and dark feral goats observed from helicopters and in Ground musters.
78 Chapter 5: Testing assumptions in aerial survey using ground observations
5.3.1.2 Correction factors
Unlike aerial surveys, ground observations were assumed to be independent of visibility bias because feral goats were recorded from fixed locations, over longer periods, during a range of activities, whilst in varying vegetation cover and at appropriate distances to avoid bias (i.e. <400 m), and observations were excluded where goats were disturbed by an observer. This assumption then allows verification of assumption 1 and an independent estimation of detection probability ( pˆ g ) based on the number of feral goats observed from the air (39) that were known to occur within sampled transects (45) i.e. pˆ g = 39 45 = 0.87 . This probability provides an equivalent estimator to the double count formula pˆ 1 = B (B + S 2 ) , but in this case ground observations were assumed to be unbiased. A correction factor for the aerial counts can then be estimated as the inverse of this detection probability (C.F.=1.15).
The proportions of observed feral goats that are standing or moving, are in different vegetation and are of different colour can also be used to estimate specific correction factors. However, these calculations assume no correction is necessary for categories where a greater proportion of animals was observed from the air (i.e. moving, open or woodland and light coloured) than the ground, and do not allow the flexibility of combined correction functions. Using this approach, animals that are standing have a probability of detection of 0.18 (C.F.=28/5=5.6; Figure 5-2); those in shrubby woodland have a detection probability of 0.53 (C.F.= 19/10=1.9; Figure 5-3), and for those in forest have a detection probability of 0.55 (C.F.=11/6=1.83; Figure 5-3). Differences between the observed and actual proportions of coloured goats (Figure 5-4) lead to estimates of detection probability for coloured and dark goats of 0.73 (C.F.= 33/24 = 1.38) and 0.64 (C.F.=11/7=1.57) respectively.
5.3.2 Assumption 2: Transect boundaries are accurately delineated
Although the accuracy of this assumption was not specifically examined due to logistic constraints, groups of animals of all species were identified as occurring inside or outside the transect by double count observers, which allowed a comparison of whether observers
79 Chapter 5: Testing assumptions in aerial survey using ground observations were scanning an equivalent search area. Of all the groups recorded (n=5686) only nine (0.16%) were identified as occurring inside the transect by one double count observer and outside by the other. This indicates the observers were similarly calibrated, but does not provide conclusive evidence that transect width was delineated accurately.
5.3.3 Assumption 3: Animals are not counted more than once
5.3.3.1 Do feral goats display consistent movement patterns?
Goats were found to be significantly more likely to move south if they were initially south of the helicopter (χ2 = 16.6, df=1, P<0.001) and more likely to move north when they were north of the helicopter (χ2 = 16.8, df=1, P <0.001). Combining these ratios, 64% moved away from the helicopter and 36% moved towards it (n=448). In addition, as demonstrated in chapter 4, goats moved greater distances when the helicopter was 150 m distant or less (Figure 4-2), which is close to the outer boundary for transects sampled in this study (Figure 2-1).
5.3.3.2 Probability that animals are available for recounting
Of groups of goats that occurred within sampled transects, the probability of moving, pm,
0.483 [−(0.017d p ) ] decreased with perpendicular distance travelled, dp (Figure 5-5, pm = e ). Over 60% of groups moved, but only 30% moved further than 100 m and 8% further than 400 m. As the probability of goats moving is not 1 when the perpendicular distance equals 0, the Weibull function was adjusted using the observed proportion of goats moving when the helicopter was directly overhead (i.e. 0.61). The maximum recorded perpendicular distance moved was 1200m (mean 104 m, median 12 m). The probabilities of goats moving (pm) perpendicular to the helicopter was estimated using the proportion of groups of goats observed, hence these calculations assume distance moved is not a function of group size. Further testing of this assumption is recommended, but was beyond the scope of this study.
80 Chapter 5: Testing assumptions in aerial survey using ground observations
0.7
0.6
0.5
Probability a 0.4 group of goats will move 0.3
0.2
0.1
0 0 200 400 600 800 1000 1200 Perpendicular distance moved (m)
Figure 5-5: The probability that a group of goats (y) will move x distance perpendicular to the Transect direction.
The Weibull function was used to estimate the probability that a group moves into another transect with relevance to the transect spacing of the current study (Figure 2-1), i.e.: • east-west transects were placed 300 m apart, • 100 m was sampled on either side of the helicopter, • 60 m (30 m each side) was unavailable directly underneath the helicopter, and • 40 m was unsampled between transects.
As goats moved unevenly in southern and northern directions relative to the helicopter (Section 5.3.4.1), probabilities were estimated separately for each side and were weighted for direction moved according to the observed proportions (i.e. 0.64 ‘away’ and 0.36 ‘towards’). The probability of a group moving into another transect was estimated by averaging probabilities predicted for perpendicular distance moved (Figure 5-5). These predicted probabilities were calculated separately for the range of distances to each adjacent transect (Table 5-1).
81 Chapter 5: Testing assumptions in aerial survey using ground observations
Table 5-1: Predicted probabilities (pm) of groups of goats, once available for sampling, moving to additional transects. Final values are weighted for direction moved
(m). Calculations assume goats that are available for sampling are those that: (a) move in one direction or (b) move in both directions.
(a) Move in one direction 1 transect 2 transects 3 transects 4 transects mx 0.32 0.18 0.32 0.18 0.32 0.18 0.32 0.18 weighting
Range 200- 340- 500- 640- 800- 940- 1100- 40-140 (m) 300 440 600 740 900 1040 1200 Average 0.307 0.135 0.082 0.051 0.036 0.025 0.019 0.014 pmx
Av p x mx 0.09824 0.0243 0.02624 0.00918 0.01152 0.0045 0.00608 0.00252 wt.
Weighted 0.12254 0.03542 0.01602 0.0086 pmx pm = ∑ pmx = 0.18
(b) Move in both directions 1 transect 2 transects 3 transects 4 transects mx 0.64 0.36 0.64 0.36 0.64 0.36 0.64 0.36 weighting Range 200- 340- 500- 640- 800- 940- 1100- 40-140 (m) 300 440 600 740 900 1040 1200 Average 0.307 0.135 0.082 0.051 0.036 0.025 0.019 0.014 pmx
Av p x mx 0.19648 0.0486 0.05248 0.01836 0.02304 0.009 0.01216 0.00504 wt.
Weighted 0.24508 0.07084 0.03204 0.0172 pmx pm = ∑ pmx = 0.37
82 Chapter 5: Testing assumptions in aerial survey using ground observations
Assuming transects are flown consecutively from one edge of the study site to the other, as is usually the case, the probability of animals moving into an adjacent transect occurs in only one direction. For example, if transects are flown from north to south goats that move north will not be available in another transect. Hence the probability of animals moving south is 0.18 for goats on the northern side (½ of 0.36) and 0.32 for goats on the southern side (½ of 0.64).
When testing estimators against known numbers (Chapter 7) all available transects were sampled. Hence for these studies the probability of sampling an adjacent transect (ps) was 1. Despite sampling all transects, 100 m for every 200 m sampled was unavailable (60 m underneath plus 40 m between transects, Figure 2-1), which translates to a sampling rate of
67%. Using pa (Section 5.2.4), and pm values (Table 5-1), and assuming transects were sampled consecutively the probability that a group of goats was available for recounting
(pa) would be 0.18. When estimating seasonal abundance for the whole site, 18 of 28 transects were sampled. Hence the probability of sampling a transect (ps) was 0.64 (=18/28), which translates to a sampling rate of 43% when considering the area unavailable. In this case the probability goats were available for recounting (pa) was estimated as 0.12 (=0.64 x 0.18).
However, as consecutive transects were omitted on the first pass and sampled on a second pass, probabilities were calculated separately.
pa (First Pass) = 0 + 0.03542 (0.5)+ 0.01602 (0.5)+ 0.0086(0.5) = 0.03;
where pm is calculated using Table 5-1 (a), ps=1, ps (First Pass)=0.5
pa (Second Pass) = 0.24508 (0.5) + 0.07084 (0.5) + 0.03204 (0.5) + 0.0172 (0.5) = 0.183;
where pm is calculated using Table 5-1 (b). ps=1, ps (Second Pass)=0.5
pa = pa (First Pass)+ pa (Second Pass) = 0.21
83 Chapter 5: Testing assumptions in aerial survey using ground observations
5.4 Discussion
5.4.1 Assumption 1: All animals are counted within the designated strip
5.4.1.1 Activity, vegetation and colour
During aerial surveys animals are commonly perceived to be more difficult to observe when stationary than when moving (Gasaway et al.1985; Barnes et al. 1986; Samuel et al. 1987; Jachmann 2002). Jachmann (2002) classified 22 large herbivore species in Zambia into four classes according to their reaction to aircraft and found species that move were more likely to be observed. Gasaway et al.(1985) found standing moose (Alces alces) had a higher detection probability than moose that were lying down. Samuel et al. (1987) found differences in the detection probability of lying (0.29), standing (0.56) and moving (0.72) elk using univariate correlation analysis but these effects disappeared after group size and vegetation were considered. Similarly in chapter 3, activity was non-significant (P>0.05) using multiple regression, despite a higher detection probability being evident for moving goats (pc=0.56; n=1681) than those standing (pc =0.49; n=43), hiding or lying down (pc= 0.49, n=35). However, the effects of activity and vegetation may be interrelated, as animals may be more likely to move when in the open, and conversely more likely to stand or hide when in cover.
A comparison of aerial observations with ground observations in this chapter also indicated stationary goats were less likely to be observed from the air. However, these effects were analysed separately from other factors. Of potential importance are the relative differences in detection probability estimated using the double count technique (moving pc=0.56; standing pc =0.49) and those reported here (standing 0.18). This difference suggests that the double count technique may be over-estimating detectability of standing goats.
84 Chapter 5: Testing assumptions in aerial survey using ground observations
Failure to appropriately correct for stationary animals is likely to result in negatively biased estimates of density. This may also have implications for aerial shooting campaigns, with potentially five times (=1/0.18) the number of stationary animals being present than are observed. By removing animals that move, managers may be selecting for those that have a greater tendency to stand or hide, which is likely to reduce the effectiveness of future control efforts.
Results of this study also suggest fewer animals were detected in denser (forest) and more structured (shrubby woodland) vegetation, which has been frequently observed elsewhere (Chapter 3, 6; Caughley et al. 1976; Steinhorst and Samuel 1989; Choquenot 1995a,b; Southwell 1996).
Comparison of colour ratios from mustered goats with aerial observations indicated that coloured and dark goats were more difficult to see than light coloured goats. Mahood (1985) suggested this was also the case during helicopter surveys of goats in western New South Wales and hence counted only white goats, correcting for other colours using known proportions from mustering. Jachmann’s (2002) study however, suggests the opposite, with darker coloured African herbivores easier to see against a lighter background. Jachmann (2002) used a 14 point scale to classify species from ‘sandy pale’ to black.
Goats in the Coolah Tops were predominantly white and were mainly observed against a darker background. Black basalt soil, shrub foliage, and green or brown pasture all provided a dark contrast to white and light coloured goats. Fallen timber, black burnt tree stumps, grey lichen-covered rocks, and crevices that accentuated dark shadows were also common and likely to affect the detection of coloured and dark individuals (Figure 5-6).
85 Chapter 5: Testing assumptions in aerial survey using ground observations
Figure 5-6: Contrast of white (4) and dark (1) goats in the Coolah Tops. This photo was taken with a zoom lens (75-300 mm) from a helicopter, and provides greater resolution than would be available to observers during aerial surveys.
Detection probabilities estimated from ground observations show similar differences between classes of activity, vegetation and colour to those estimated using th e double count technique (Chapter 3). However, the estimated probabilities were generally lower when using ground observations (Chapter 3), which may highlight the problem of correlated search images between observers (Caughley and Grice 1982). If substantiated this would result in overestimation of detection probability and underestimation of density.
5.4.1.2 Comparison against known locations
Of the 45 goat groups known to occur within transects at the time of sampling, 39 goat groups were observed from the air, indicating a detection probability (pg) of 0.87, only marginally higher than the average detection probability estimated using the double-count technique (pd = 0.8; Chapter 3). The small difference between detection probability estimates that were calculated from multiple aerial observers and those calculated from goats known to occur within the transect suggests that the issues associated with non-
86 Chapter 5: Testing assumptions in aerial survey using ground observations independence of sighting and re-sighting (Caughley and Grice 1982) may not have been important in this study which is contrary to previous discussion.
5.4.2 Assumption 2: Transect boundaries are accurately delineated
Groups of animals were rarely (0.16%; 9 in 5686) identified as occurring inside the transect by one observer and outside by the other. Although this suggests observers scanned the same transect widths, which is important for the assumptions of the double-count technique, it doesn’t necessarily confirm that the transect width of 100 m was constant. Observing out to 100 m in steep country involved projecting the transect boundary further than indicated by the calibration pole when viewing uphill and closer than indicated when viewing downhill (e.g. Figure 3-1). This was seen as a major impediment to the use of line transect methods in this study. Further research is required to appropriately test the ability of observers to mentally adjust strip width in variable terrain. This could be achieved simply by placing fixed markers at different distances from the transect line in steep terrain and recording the number of occasions markers were correctly identified at different distances. Alternatively if calibration poles were always adhered to, actual distances or distance classes could be estimated afterwards if locations of animals and slope of the terrain were known (e.g. formula Section 3.2.2).
The area unavailable to observers directly beneath the helicopter (Figure 2-1) is also an important consideration when designing aerial transects. For example, if a random sampling design is used, transect spacing must take account of this distance to ensure sections of the transect area are not scanned twice. This may also prevent high rates of sample coverage (e.g. Fleming et al. 2000) and if not taken into consideration would increase the probability of recounting animals.
87 Chapter 5: Testing assumptions in aerial survey using ground observations
5.4.3 Assumption 3: Animals are not counted more than once
Examination of assumption violations in aerial survey have focussed on the problem of the failure to count all animals within a defined sample area (Assumption 1) (e.g. Caughley et al. 1976; Short and Bayliss 1985; Cairns 1999; Walter and Hone 2003). However, the potential for recounting animals, while discussed by researchers (e.g. Seber 1982; Krebs 1999; Walter and Hone 2003) is rarely examined (Beasom et al. 1986; Linklater and Cameron 2002) and often assumed to be negligible (e.g. Choquenot 1995a,b). The results of the current study suggest that under intensive sampling, movement between transects may be substantial and result in serious overestimates of density.
The distance ungulates travel in response to aerial disturbance, and hence the potential for recounting is difficult to compare across studies, as elevation, distance to the aircraft and type of aerial activity are widely varied and in some cases not reported. During low flying (10-15m AGL) helicopter surveys, Beasom et al. (1986) reported re-sightings of marked white-tailed deer between 0 and 13% of total deer seen. Beasom et al. (1986) determined that intensive sampling resulted in multiple sightings of individual deer, but concluded that this rendered total counts less conservative. However, the proportion of marked deer in the population was not reported, and only 26% to 40% of deer were observed. Hence, the reported figure of 13% for a 100% sampling intensity would indicate a higher proportion was actually available for recounting (i.e. between 33 and 50%). The low altitude flown (10-15m AGL) and the recorded flushing behaviour of ungulates in other studies (e.g. Calef et al. 1976; Krausman et al. 1986; Harrington and Veitch 1991, 1992; Cote 1996) would also suggest greater movement between transects than reported.
Linklater and Cameron (2002) found recounting of feral horses resulted in overestimates of 15 to 32% in the Kaimanawa Ranges of New Zealand. Their Hughes 500 helicopter was flown at 60 m AGL and horses were reported moving 0.1 to 2.75 km in response to the helicopter. However, the objective in this study was a census rather than an estimate, hence sampling intensity was maximised (Linklater and Cameron 2002). Walter and Hone (2003) used a Bell Jet Ranger in the Australian Alps and suggested recounting of feral horses was
88 Chapter 5: Testing assumptions in aerial survey using ground observations unlikely due to a higher altitude (100 m AGL), increased vegetation cover and greater transect spacing (2 km).
The results of this project suggest the probability of recounting is negatively correlated with sampling rate and positively correlated with the distance animals move between transects. This is likely to hold true for any wildlife transect survey. Studies which sample intensively, e.g. for higher accuracy, and apply correction factors for an inability to detect all animals are likely to produce positively biased estimates of density. Recounting is of increased important for ungulates that are known to flush large distances (e.g. caribou: Calef et al. 1976; Harrington and Veitch 1991, 1992; mule deer: Krausman et al. 1986; and mountain goat: Cote 1996) and further study of flushing behaviour in other species requires investigation.
As discussed in Chapter 4, 150 m appeared to be the threshold distance to the helicopter that goats would tolerate before moving away from the transect over large distances (>150 m and up to 2500 m) (Figure 4-2). The distance goats travelled steeply increased if the helicopter was within this distance, which had implications for the probability that animals were available for recounting. Hence this study suggests goats do not have an equal chance of moving into or out of an adjacent transect, as those that occur within sampled transects move significantly further than those outside it.
Most studies which compare aerial survey estimates with actual numbers report underestimation (Caughley 1974 for review), which suggests recounting animals is uncommon, or causes less conservative estimates of density (e.g. Beasom et al.1986). However, as knowledge of detection probability and estimation procedures improve, recounting may be of increasing importance in ensuring that estimates are not positively biased, which is especially relevant under high sampling regimes.
89
CHAPTER 6
AERIAL SURVEYS AS INDICES
6.1 Introduction
Aerial surveys are widely used to monitor wildlife populations for comparison of abundance over time (e.g. Serengeti ungulates, Sinclair 1972; Broten and Said 1995) and between sites (e.g. bighorn sheep in canyon habitats, Bodie et al. 1995, feral pigs and macropods in semi-arid north-western New South Wales, Choquenot 1995a,b). Despite the development of line transect (e.g. Hensbergen et al. 1996; Southwell 1996) and capture- recapture (Caughley and Grice 1982; Eberhardt and Simmons 1987; Pollock and Kendall 1987; Graham and Bell 1989; Choquenot 1995a,b) techniques to correct for visibility bias and estimate absolute density, underlying counts and indices are often used in research and management because of their simplicity and practicality (e.g. Bayliss and Giles 1985). Caughley’s (1980) definition of a density index is adopted in the present study, being any measurable correlative to absolute density. Implicit in this definition is that density indices are rates, for example, catch per unit effort (e.g. Lancia et al.1996a), and counts per unit distance (e.g. Caley and Morley 2002). The use of indices assumes sampling is representative and detection probability is constant between compared populations, but this is not always applied or tested (Anderson 2001). These assumptions can equally apply to absolute measures of abundance (Engeman 2003).
Variable probability of detection has been considered a major impediment to the use of indices (Anderson 2001). Of particular importance is the constancy of detection between sites and over time, and their effects on monitoring wildlife populations. As previously reported detection probability of feral goats is known to vary considerably with factors such as group size, vegetation cover, observer, coat colour and helicopter type (Chapter 3). These factors may be of varying importance for other species, in different locations and on different sampling occasions. In this chapter, the major determinants of detection probability were investigated for a range of medium–sized mammals (feral goats, feral pigs, eastern grey kangaroos, common wallaroos, swamp and red-necked wallabies) for the
90 Chapter 6: Aerial surveys as indices specific interest of evaluating the validity of aerial surveys to compare abundance between species, between sites and over time.
6.2 Methods
The indices used for comparing species abundance were the number of each species observed per kilometre of aerial transect flown. The effects of species, observer pair, site, sampling period, group size and vegetation on detection probability were tested using a binomial linear model (Knoke and Burke 1980) using a conditional probability. Groups were recorded as seen by only one or both observers, hence the response variable was conditional on one observer seeing a group and was: 0 (seen by only one observer) or 1 (seen by both). A combined model was used initially for all species, then the six species were analysed separately to test the individual effects of each variable.
The procedure used was typical of generalised linear modelling (e.g. Crawley 1993) and examined the significance (P<0.05) of all factors and 1st order interactions using analysis of variance. Computation of analyses were undertaken using S-PLUS (Venables and Ripley 2002). Predicted conditional detection probabilities for comparisons between species were made using Spatial Analysis of Mixed Models (SAMM), an S-PLUS module for mixed models that uses restricted (or residual) maximum likelihood (REML) (Gilmour et al. 1999). Predictions were made across all significant factors to remove the effects of unequal samples between variables. Average detection probabilities were estimated using a modified Petersen mark-recapture model (Seber 1982) applied to simultaneous observers in aerial surveys (e.g. Caughley and Grice 1982).
As the three sites were not sampled on every sampling occasion, and to remove potential confounding effects, separate individual species models were fitted for (i) sampling period as a factor for data within one site; and (ii) site as a factor for data from all sites (without sampling period). Group size was taken as the larger of the two observer counts, as this was more likely to reflect the true group size because units were counted not estimated. A square root transformation was used for group size to stabilise the estimates. Since multiple observers are necessary for deriving conditional probabilities they could not be included
91 Chapter 6: Aerial surveys as indices separately, hence observer pair was used in the analyses.
6.3 Results
In the overall model detection probability varied significantly between species, group size, vegetation, observer pair and the interaction between site and sampling period (Table 6-1). Detection probabilities for feral goats were significantly (P<0.05) greater than other species after removing the effects of other factors (Figure 6-1). Eastern grey kangaroos also had significantly higher probability of detection than other macropodoids (P<0.05; Figure 6-1).
Table 6-1: Variables affecting conditional detection probability of six sympatric medium sized mammals in helicopter surveys using binomial linear modelling.
Overall model (all species) Variable Wald Statistic P-value Species 47 <0.001 Group Size 507 <0.001 Vegetation 21 <0.001 Observer Pair 16 0.007 Site:Sampling Period 22 0.002
Feral goats Variable Wald Statistic P-value Group Size 80 <0.001 Vegetation 19 0.002 Observer Pair 3 Ns Sampling Period 6 Ns Site 4 Ns
Eastern grey kangaroos Variable Wald Statistic P-value Group Size 188 <0.001 Vegetation 4 Ns Observer Pair 14 0.007 Sampling Period 9 0.04 Site 6 Ns
Common wallaroos Variable Wald Statistic P-value Group Size 18 <0.001 Vegetation 5 Ns Observer Pair 3 Ns Sampling Period 12 0.006 Site 0 Ns
92 Chapter 6: Aerial surveys as indices
1 0.8 Detection Probability 0.6 (pc) 0.4 0.2 0 eastern feral feral wallaroos red-necked swamp grey goats pigs wallabies wallabies kangaroos
Figure 6-1: Detection probabilities for six sympatric medium-sized mammals using double- count helicopter surveys. Detection probability was estimated using average values using a modified Petersen mark recapture estimate following Caughley and Grice (1982).
Analysis for each species separately revealed group size and vegetation were significant for feral goats; group size, observer pair and sampling period for eastern grey kangaroos; and group size and sampling period for wallaroos (Table 6-1). Site was not significant for any species. No variables were found to be significant for swamp wallabies, red-necked wallabies or feral pigs (P>0.05). Using Chi-squared analysis differences in the frequency of group sizes between sampling periods were significant for eastern grey kangaroos (P=0.03) but not other species (P>0.05).
To demonstrate the effects of variable detection probability between sampling periods, corrected and uncorrected indices of eastern grey kangaroos and wallaroos were plotted over time (Figure 6-2). These same counts were normalised and plotted separately for eastern grey kangaroos and wallaroos to compare relative differences (Figure 6-3). Despite significant differences in detection probability between sampling periods for both eastern greys (P=0.04) and wallaroos (P=0.006), corrected and uncorrected indices were highly correlated (eastern grey kangaroos: r=0.95, P=0.003, df=4; wallaroos: r=0.93, P=0.008, df=1; Figure 6-2).
93 Chapter 6: Aerial surveys as indices
4 3.5 Abundance 3 index -1 2.5 Corrected egk (count km ) 2 Uncorrected egk 1.5 Corrected wro 1 Uncorrected wro 0.5 0 0 1 2 3 4 5 6 Sampling Period
Figure 6-2: Corrected (---) and uncorrected (—) indices of eastern grey kangaroos (egk, ¢) and common wallaroos (wro, ) observed during helicopter surveys. For each species, corrected indices (counts km-1) were adjusted for separate detection
probabilities (pc) in each sampling period.
94 Chapter 6: Aerial surveys as indices a.
1 0.8 Abundance 0.6 Corrected Index 0.4 Uncorrected 0.2 0 0 1 2 3 4 5 6 Sampling Period
b.
1 0.8 Abundance Index 0.6 Corrected 0.4 Uncorrected 0.2 0 0 1 2 3 4 5 6 Sampling Period
Figure 6-3: Relative changes in corrected (---) and uncorrected (—) indices of eastern grey kangaroos (a) and common wallaroos (b) between sampling periods. Abundance indices (counts km-1) were normalised (between 0 and 1) to compare relative changes.
95 Chapter 6: Aerial surveys as indices
6.4 Discussion
For indices to be useful in comparing wildlife populations they must be applicable across sites and between sampling periods (Caughley 1980). Apart from animal density, factors such as seasonal behavioural changes including group size and habitat use, and vegetation cover may change between and within species, between sites and across time. These factors will affect detection probability and hence the utility of indices and estimates of abundance.
The differences between species evident in the overall model suggest that indices from aerial surveys should not be used to compare densities of medium-sized mammals without adjustment for detection probability. This is particularly so when comparing the abundance of feral goats and other species, and eastern grey kangaroos from other macropodoids (Figure 6-1). These differences could be because feral goats in this study were predominantly lightly coloured (Chapter 5 for discussion, 98.9% of groups contained at least one lightly coloured goat) and highly visible in open habitat (average detection probability= 0.8) compared to other species. Red-necked and swamp wallabies are more cryptic in their behaviour than the other macropodoids in this study and tend to form small disjoint groups or forage individually (Jarman and Coulson 1989). Wallaroos form smaller groups than eastern grey kangaroos (Taylor 1982). Detection probability may be affected by between-species differences in behaviour, including use of refugia and foraging behaviour, and within group spacing (Jarman and Coulson 1989), and preferences for vegetation types (Southwell et al. 1999).
No differences were evident for site when species were analysed separately. This suggests abundance indices were comparable across sites for all species. However, both sites were located in the Coolah Tops within similar habitats, landscapes, terrain and species composition. These results cannot be generalised to other studies in different environments; for example, indices from this study site are unlikely to be comparable to arid areas without adjustment for detection probability.
As Choquenot (1995b) found in semi-arid environments, vegetation affected detection probability for macropod species. Macropodoids preferences for vegetation types may
96 Chapter 6: Aerial surveys as indices change with season and forage availability (Taylor 1984), which will affect detection probability (Southwell et al. 1999) and comparisons of indices between species across time. Changes in vegetation structure can occur between seasons and in response to changes in climatic conditions. For example, eucalypts drop their leaves during extended dry periods resulting in a reduction of foliage projective cover (e.g. Myers et al. 1997; Pook et al. 1997) and a likely increase in detection probability. The prevalence and height of cane grass (Eragrotis australasica, Leptochloa digitata) in floodplains of the semi-arid rangelands can also vary substantially with rainfall, fluctuating from bare soil where animals are easily observed to thick mono-specific stands where detection probability is likely to be much lower. Changes in grazing and fire management regimes may also influence shrub layers and canopy structure (Hodgkinson et al. 1984) and movements of animals (Caughley et al. 1985), and hence may influence the probability of detection. Differences in detection probability between vegetation types are also important when investigating habitat preferences within and between species. For example, if uncorrected, greater detection probability in open vegetation will result in positively biased estimates of species preferences in these habitats.
Group size is a significant factor (<0.001) influencing detection probability, which is a consequence of larger groups being more easily observed than smaller isolated groups or individuals (Cook and Jacobson 1979). Fluctuations in group size over time or between sites can occur for several reasons and may compromise the use of uncorrected indices. Mean group size for eastern grey kangaroos and common wallaroos is affected by density (Taylor 1982) and this may apply to other macropodoids and feral goats and pigs. Species differences might also be affected by groups of mixed species where a larger group of one species may conceal a small group of another, for example a single wallaroo occurring with a large group of eastern grey kangaroos. Such occurrences can increase problems with identification, or may increase detectability of both species.
Observers are a common source of variation in wildlife studies (e.g. Pople et al. 1998b; Beard 1999), as they have distinct search images and detect species differently. This can be an inherent difference in ability or can occur as a result of previous experience; for example pest animal controllers regularly involved in aerial culling are likely to have a search image
97 Chapter 6: Aerial surveys as indices for vertebrate pests but not macropodoids. Observers could also unconsciously show bias towards the prime species of interest. To lessen the effects of learning and previous experience, training periods should also be adopted as standard practice (Beard 1999).
6.4.1 Feral goats
Consistent with the previous more detailed analysis (Chapter 3), vegetation and group size had significant effects on the detection probability of feral goats. Vegetation preferences of feral goats may vary between seasons with groups favouring high plateaus of open grassland during winter (Fleming and Tracey, unpublished data) where they are more visible. Hence, where vegetation is significantly different over time or between sites uncorrected indices may be inappropriate. The effects of these differences may be reduced by applying habitat-specific correction factors (e.g. Choquenot 1995a) or stratifying according to vegetation type.
Group size for feral goats ranged considerably in this study (1-154) but was not significantly different between seasons (P>0.05). Hence differences evident between groups should not compromise the use of indices for feral goats over time. Further, neither sampling periods nor sites were significant factors, which suggests feral goat abundance can be compared across space and time. Observer was not significant with goats having the highest probability of detection of any species (Figure 6-1).
6.4.2 Macropodoids
The detection of eastern grey kangaroos and wallaroos was mainly dependent on group size and sampling period. However, observer pair was also significant (P=0.007) for eastern grey kangaroos but not other species, implying that observers have different search images for different species. Hence separate corrections are necessary for different species and observers. Alternatively, observers could be standardised across sampling periods and between sites, either by using the same observers or conducting prior testing and using comparable observers.
98 Chapter 6: Aerial surveys as indices
Vegetation was not significant for eastern grey kangaroos or wallaroos, which would indicate habitat preferences could be viewed across time or between sites for these species. However, these results should not be generalised across environments or biomes. Group sizes of the larger macropodoids may be influenced by a range of factors, including density (Taylor 1982), time of day (Clarke et al. 1995) and seasonal forage conditions (Jarman and Coulson 1989). Clarke et al. (1995) found significant time of day differences in group size with larger groups coinciding with increased movement at dusk. In this study, the frequency of group sizes for eastern grey kangaroos, but not wallaroos, was significantly different (P=0.03) between seasons. For monitoring eastern grey kangaroo populations, this may accentuate the differences evident between sampling periods and emphasises the need to investigate detection probability between groups.
The significant difference in detection probability between sampling periods for eastern grey kangaroos and wallaroos demonstrates violation of an underlying assumption for using indices. Hence these results suggest uncorrected indices should not be used to monitor abundance of these species over time. Comparisons of normalised indices for both species suggest large changes are still detected without correcting for detection probability, but corrected indices should be used for tracking minor changes.
Individual models for swamp wallabies, red-necked wallabies and feral pigs revealed that no variables were significant. This may be partly due to smaller sample sizes and, for smaller macropodoids, to the occurrence of single animals or small aggregations resulting in lower detection probabilities.
6.4.3 Conclusion
Wildlife managers require measures of abundance for monitoring populations in space and time. These can assist in measuring responses to control programs for vertebrate pests (e.g. Saunders and Bryant 1988; Grey et al. 1997), detecting changes in endangered species (e.g. Humphrey 1988), or setting quotas for wildlife harvesting (Gilroy 1999; Lundie-Jenkins et al. 1999). Indices are attractive to managers due to their simplicity and practicality, but have been regarded as inappropriate (Anderson 2001, 2003; Ellingson and Lukacs 2003)
99 Chapter 6: Aerial surveys as indices due to unrepresentative sampling and variable detection probability.
This study suggests detection probability can vary significantly between species, group size, vegetation, observers and sampling period. Hence separate corrections for these variables should be made when applying indices. Equally, absolute abundance estimates that do not take into account these differences are likely to be negatively biased. For example, applying general corrections using capture-recapture or distance sampling without considering separate detection probabilities between species, observers, group sizes, vegetation and between sampling periods may result in estimation bias.
Despite significant variation between sampling periods, uncorrected indices were highly correlated with those corrected for detection probability. These results suggest adjustments for detection probability were useful for monitoring subtle changes in populations but an uncorrected index may still prove useful for detecting large differences. Standardising for observer, and investigating group size and vegetation differences will also reduce the effects of variable detection probability between sites and over time. This study suggests that indices from aerial surveys can be useful for monitoring of medium-sized mammals across space and time if these factors are considered.
100
CHAPTER 7
DENSITY ESTIMATION AND KNOWN NUMBERS
7.1 Introduction
Despite the increasing complexity of density estimators (Schwarz and Seber 1999; Buckland et al. 2000), there remain few studies that have evaluated these techniques against known densities. Hence true bias for many estimators remains unknown. Due to the difficulties in obtaining actual density in wildlife, many studies have compared techniques (e.g. Walter and Hone 2003), used simulation (e.g. Hone 1986) or attempted to determine actual density in sub-sections of the study area (Short and Bayliss 1985). Studies that have assessed the true or approximated bias of various density estimates, or applied estimators to feral goats are reviewed in this section.
Caughley et al. (1976) and Hone (1986) tested a technique proposed by Caughley (1974) to estimate bias in fixed-wing aerial surveys using multiple regression with speed, strip width and altitude. Detection probability is known to decline with increasing speed, strip width and altitude (Caughley 1974). This technique is based on a regression for these independent variables, where observed density should estimate true density at the y-intercept, i.e. where they approach zero (Caughley 1974). Some more recent techniques include predicting the effects of a range of other variables (such as vegetation, observers, group size - Chapter 3) on detection probability using other methods (e.g. Alho 1990; Marques and Buckland 2003). Known densities of sheep and simulated numbers of beans (Hone 1986) and dots projected onto a screen (Caughley et al. 1976) were compared with estimated density. Caughley et al. (1976) found the estimates were generally consistent with actual numbers, and demonstrated an application to kangaroos. However, Hone (1986) reported large underestimation of true sheep density using this technique and attributed this, in part, to inaccuracy of the technique at higher density.
The correction factors developed by Caughley et al. (1976) were adopted for broad-scale fixed-wing kangaroo surveys in Australia. The accuracy of these surveys was assessed directly by Short and Hone (1988), who compared uncorrected counts of kangaroos with 101 Chapter 7: Density estimation and known numbers drive counts. Approximately 43% of red kangaroos (Macropus rufus), 17% of western grey kangaroos (M. fuliginosus) and 9% of euros (wallaroos) were visible from the air in open country. These compared favourably with the estimates of detection using regression analysis (Caughley et al.1976) for red kangaroos, but Short and Hone (1998) suggested western greys and particularly euros could be severely underestimated using these techniques. Similarly, further studies suggested that initial correction factors (Caughley et al. 1976) also underestimated densities of western and eastern grey kangaroos (Hill et al. 1985; Barnes et al. 1986; Southwell et al. 1986; Clancy et al. 1997; Pople et al. 1998a). Short and Bayliss (1985) had previously found greater visibility for red kangaroos (56%) than Short and Hone (1988) but similar visibility for western grey kangaroos (21%) when comparing against strip transect, driven at night and searched by spotlight. The continuing application of Caughley et al.’s (1976) correction factors has been attributed to the uncertainty of the other correction methods in estimating true population size (Cairns 1999).
Line transect estimators are commonly applied for aerial and ground surveys (Buckland et al. 2001; Thomas et al. 2002) and the accuracy of these has been assessed in a number of studies. Burnham et al. (1985) examined the efficiency and bias of strip and line transects survey methods using an estimate of percent relative bias (100[E(Dˆ ) − D]/ D) , and calculating the expected value of density ( E(Dˆ ) ) from a function of detection probability. Line transect sampling generally had smaller mean square error (sampling variance + (bias)2 ) than strip transects and Burnham et al. (1985) concluded that line transects have three main advantages: they avoid the assumption that p =1 across all distances; bias does not increase as transect width increases; and data on all observations can be used.
The use of line transects in aerial surveys was first evaluated against a known number by Hone (1988), who tested the accuracy and precision of strip counts and eight line transect models using helicopter surveys of feral pig carcases. Accuracy declined with increasing strip width (Hone 1988), which is a requirement for most line transect estimators (Buckland et al. 2001), and this decline is commonly observed in aerial surveys (Caughley 1974; Hone 1986; Walter and Hone 2003). All the models that were tested provided accurate estimates of density, with the Fourier series model being the most accurate (Hone 1988).
102 Chapter 7: Density estimation and known numbers
However, by applying the same models to helicopter surveys of known mule deer (Odocoileus hemionus hemionus) density, White et al. (1989) found the exponential polynomial and negative exponential models performed better, and that most estimators were negatively biased. White et al. (1989) attributed this underestimation to the failure of counting all deer on the line, and that deer were not observed in their original position because of flushing.
Walked line transects have been evaluated for kangaroos using populations of known size (Southwell and Weaver 1993; Southwell 1994). Estimates were slightly negatively biased for tame populations, with greater bias associated with populations of higher actual density (Southwell 1994). Bias was greater in wild populations and this was associated with reactive movement (flushing) from the transect line (Southwell 1994). Density estimates were generally more accurate when observations were ungrouped rather than grouped for the analyses (Southwell and Weaver 1993), but analyst expertise did not have a significant influence on accuracy (Anderson and Southwell 1995).
Accuracy of capture-recapture methods have been examined by comparing against known densities of cottontail (Sylvilagus floridanus, Edwards and Eberhardt 1967), taxicabs (Carothers 1973), deer (Bartmann et al. 1987; McCullough and Hirth 1988; Vincent et al. 1996) and mice (Druhan 1993; Davis et al. 2003). As discussed (Chapter 1), an important assumption of capture-recapture studies, which is commonly violated, is that all animals are equally likely to be captured in each sample (Otis et al. 1978). Studies of known populations confirm that this assumption can be violated for many capture-recapture estimators, which can lead to serious underestimates of density.
Edwards and Eberhardt (1967) found initial estimators of Schnabel (1938), who allowed for heterogeneity of capture over time, and Schumacher and Eschmeyer (1943) grossly underestimated the actual density of cottontails, and that maximum likelihood estimates for the Poisson distribution also underestimated true density. Improved estimates were obtained using estimators with a geometric distribution (Eberhardt et al. 1963), which was attributed to individuals having a different or changing probability of capture (Eberhardt et al. 1963; Edwards and Eberhardt 1967). Carothers (1973) examined various methods of
103 Chapter 7: Density estimation and known numbers estimating the number of taxicabs in Edinburgh with or without consideration of equal catchability (Leslie et al. 1953), and found they all underestimated the actual number by 15 to 30%.
The inaccuracy of some capture-recapture estimates has been attributed to low proportions of marked individuals (Strandgaard 1967; Bartmann et al. 1987) and low recapture rates (Krebs et al. 1994). However, McCullough and Hirth (1988) found an increasing percentage of marked white-tailed deer up to 68%, did not improve accuracy. In that study Lincoln-Petersen (Bailey 1951) estimates were more often positively biased, and inaccuracy was associated with unrepresented sex and age classes, spatial location of home ranges and habitat (McCullough and Hirth 1988). Differences in the observability of sex and age classes were also reported in estimates of fallow deer, but estimates were relatively unbiased (Vincent et al. 1996).
Davis et al. (2003) showed that estimators that are designed to correct for unequal catchability and low capture probability (Chao 1987, 1988) improved estimates of known wild house mouse (Mus musculus) density. Chao’s (1987) modified moment estimator was the only one of nine to show no obvious bias (Davis et al. 2003). However, this estimator was unreliable when the population was trapped on fewer than 5 occasions (Davis et al. 2003), a result also emphasised by Chao (1987). However, Druhan (1993) found frequency- of-capture methods (binomial, Poisson, geometric, negative-binomial) performed better under simulation and with real populations of mice and turtles (Emydura krefftii) than the non-parametric techniques (Chao 1987; Chao et al. 1992; Wilson and Collins 1992), except where individuals had a high and heterogenous probability of capture. The individual mice in Druhan’s (1993) study tended to exhibit a trap-happy response most likely caused by bait addiction (G. Saunders, pers. comm. 2004), which has been observed in mouse populations elsewhere (Tanton 1965; Roff 1973).
No studies have evaluated the double-count aerial survey method with known numbers. The effects of sampling design in aerial surveys have been investigated (Caughley 1977). Kraft et al. (1995) investigated the effects of a range of sampling intensities (16, 33 and 50%), sample selection (simple random without replacement, systematic and probability
104 Chapter 7: Density estimation and known numbers proportional to size) and stratification on the accuracy of estimating actual pronghorn (Antilocapra americana) density. All estimators were nearly unbiased but precision was low (CV=29%), which was attributed to the clumped distribution of pronghorn. Stratification increased precision (Kraft et al. 1995), which is generally accepted to occur whenever it is applied (Krebs 1999).
There have been no studies identified that compared density estimators of feral goats with actual numbers but several applications of techniques have been applied. Southwell (1996) evaluated bias in fixed-wing aerial surveys of feral goats in the rangelands of Western Australia using line transect methods. Group size was not found to be important, and in open country, there was no decline in sighting frequency within the 200 m strip width. However, in medium and high vegetation cover, only slightly more than half the groups of goats were estimated to have been observed using line transect methods (p=0.56 and 0.51 respectively), which lead to underestimation of population size by 30-40%. Southwell (1996) suggested that bias may have been even larger because of the violation of the assumption that all animals were counted on the line (i.e. g(0)≠1).
In the semi–arid rangelands of New South Wales, Maas (1997) compared index- manipulation-index (Section 1.3.3), the cumulative catch method (Section 1.3.3) and the double-count technique (Chapter 2) for estimating feral goat density. A double-count correction factor was estimated using a Bell Jet Ranger, which was then used to calibrate groups of goats observed from a Kawasaki Bell 47 helicopter. Detection probability (pc) was found to be significantly different for group size and habitat (closed woodland from all other habitats), when analysed separately (Maas 1997). Density estimates using the double- count technique were similar to other techniques, with estimates only slightly larger for one of two sites (Maas 1997).
Pople et al. (1998b) found group size but not habitat influenced detection probability (pc) of feral goats using the double-count technique, log-linear modelling and analysis of variance. The index-manipulation-index method (Section 1.3.3) provided similar estimates of density before removal via helicopter shooting (Pople et al. 1998b).
105 Chapter 7: Density estimation and known numbers
Dung counts for feral goats in the same environment (Landsberg et al. 1994; Landsberg and Stol 1996), using average numbers of pellets per goat (Putman 1984) compared favourably with uncorrected ground surveys (Landsberg et al. 1994) and helicopter surveys, which were corrected with habitat-specific correction factors using the double-count technique (Choquenot, D. pers. comm. 1997). However, Downing et al. (1965) reported estimates from dung counts of only 20-25% of actual white-tailed deer density and attributed the underestimate to dung beetles destroying faecal pellets.
Henzell and McCloud (1984) estimated the density of feral goats in arid South Australia by tagging and releasing animals at watering points. They applied the Petersen estimate and corrected for sub-populations that were more likely to be recaptured using an estimated ‘drinking rate’, which increased estimates from 4.4 goats km-1 to 5.0 goats km-1 (Henzell and McCloud 1984).
Ground-based area counts or quadrat sampling has been identified as a method for surveying wildlife populations (Caughley 1980; Krebs 1999) but there is no evidence of adoption of this technique. The technique has potential for estimating density effectively in smaller areas where animals are easily identified and conspicuous. Area counting in this case refers to randomly selecting a sample of unequally sized units and counting all animals visible within them. The ratio method (Jolly 1969) or Probability-Proportional-to-Size (PPS) sampling, an example of sampling with replacement (Caughley 1980; Krebs 1999), could be applied to this technique. Although unequal sized quadrat sampling is commonly included in reviews of sampling design in ecology (Caughley 1980; Krebs 1999; McCallum 2000) there are no known applications of the method for estimating wildlife from the ground or air.
In this chapter the accuracy of a range of density estimators is evaluated by comparing directly against populations of known feral goat density (Section 2.3). These include five aerial survey estimators using strip counts and the double-count technique; two capture- recapture estimators based on a novel ground-based area count technique; two capture-
106 Chapter 7: Density estimation and known numbers recapture estimates using tagged animals and re-sightings from ground observations; and six index-manipulation-index estimators.
7.2 Methods
7.2.1 Aerial survey
Helicopter surveys (Section 2.3) were conducted in eight study sites where known numbers of feral goats were later obtained (Section 2.2). Estimated density (goats km-2) from uncorrected strip counts was compared with four capture–recapture estimators: a Petersen estimator (Seber 1982); a stratified Petersen estimator using separate detection probabilities estimated for group size, vegetation and observer (after Choquenot 1995a,b; Pople et al. 1998b); Chao’s (1987, 1988) moment estimator; and an approach using unconditional detection probability and logistic regression of co-variates (Huggins 1989; Alho 1990).
Groups of goats but not individuals were identified as having been seen by one or both observers using a multi-track tape recorder (Section 2.3.1). Hence corrections could be made for groups and converted to individuals within the sample area using the average group size (e.g. Choquenot 1995a,b; Walter and Hone 2003). The variance estimate should then include a component for estimating the mean group size (i.e. variance of a product s2 = h2s2 (a) + a 2s2 (h) − s2 (a)s2 (h) , where h = mean herd size, a = mean herd density, s2 (a) = estimated variance of mean herd density and s2 (h) = estimated variance of mean size, Goodman 1960; Leatherwood et al. 1978). However, estimation of group size is likely to be very inaccurate particularly where its variable (e.g. group size ranged from 1 to 200 for feral goats in the current study). This may lead to abnormally high estimates of variance and potentially result in errors when correcting for visibility bias with some of the estimators. For example, a group of 200 animals is likely to have a detection probability of 1 and therefore will not contribute to the correction of the number groups observed, but will still contribute significantly to the calculation of mean group size.
An alternative approach was applied in the present study using modified Horvitz- Thompson equations (Oh and Scheuren 1983; Steinhorst and Samuel 1989; Borchers et al.
107 Chapter 7: Density estimation and known numbers
1998b), which allows correction of observations without grouping and overcomes potential errors associated with estimating mean group size. These equations consider survey design and detection probability in density and variance estimates. This approach also allows inclusion of the observations from the side of the helicopter with only one observer, which doubled the available data. Detection probability for the rear seat of the single side was predicted for a range of variables by assuming detection was equivalent for the same observer from the rear seat of the double-count side. On the double-count side, maximum group sizes were used because these were more likely to reflect actual sizes. This approach was applied to all five estimators (Strip counts, Petersen, stratified Petersen, Chao and Alho).
Multiple transects in repeated surveys were used as replicates to calculate variance using the equations below, rather than the variance estimates associated with the different estimators. Hence the differences evident between the estimators were a result of estimating detection probability and not sampling error, which was consistent for all estimators used for aerial surveys. The variance provided below reduces to the classical Horvitz-Thompson variance when all animals are observed (p=1), which is assumed when using strip counts. The ‘design probability’ (which is the probability of selecting a sample with equal sized units) for the abundance and variance estimate of Steinhorst and Samuel (1989) could not be determined accurately in this study as transects were of unequal length in sites where known numbers were obtained and study sites could not be saturated with transects due to the area un-sampled directly beneath the helicopter (Figure 2-1). A variance estimate was also not provided by Borchers et al. (1998b) who also described an application of the Horvitz-Thompson estimator using line transects when animals are detected in groups. Instead an approach to estimate abundance, X and a two-stage model-based variance, V(X) was adopted following Melville and Welsh (unpublished data) using the notation in Table 7-1. This approach allows an estimation of the number of animals ( Xˆ ) in the study area (A)
l using the number of animals estimated to occur within sampled transects ( X ) and the ƒi=1 i total area sampled (a).
108 Chapter 7: Density estimation and known numbers
Table 7-1: Notation for parameters and statistics used for the Horvitz-Thompson estimator (after Melville and Welsh, unpublished data).
Symbol Description
X the actual number of goats in the study area
Xi the actual number of goats in the ith transect
mji the number of animals in the jth group in the ith transect
pji the detection probability for the jth group in the ith transect
ni the number of groups (secondary sampling units) observed in the ith transect L the number of transects sampled (primary sampling units)
A the area of the study site
a the total area sampled of l transects D the population density T time periods
The Horvitz-Thompson estimate of goat numbers is:
ni m ni 1− p ˆ A ji ˆ ˆ ij 2 X i = ƒ , with variance V (X i ) = ƒ m ij a j=1 p ji j=1 pij ˆ Since the Horvitz-Thompson estimate is unbiased we have E(X i ) = X i .Therefore
A l E(Xˆ ) = ƒ X , which is unbiased for Xi assuming a uniform density of goats across the a i=1 i region. By conditioning on the sample and assuming a Poisson model for the spatial distribution of goats, it is possible to derive the following model-based variance estimate for Xˆ (Melville and Welsh, unpublished data)
2 l ni A ≈ a ’ A 1− p ji 2 ˆ ˆ ∆ ÷ ˆ ji V (X ) = 1− X + 2 ƒƒ m a « A ◊ a i=1 j=1 p ji
Now let Xk be an estimate of X from period k. An estimate for the average count over t periods is given by
t ˆ 1 ˆ X = ƒ X k , t k =1
109 Chapter 7: Density estimation and known numbers
t ˆ ˆ 1 ˆ ˆ with variance V (X ) = 2 ƒV (X k ) , assuming the t periods are independently sampled, and t k =1
Dˆ = Xˆ / A , for average density with variance Vˆ(Dˆ ) = Vˆ(Xˆ ) / A2 .
7.2.1.1 Strip Counts
Density (D =X/A; V(D) = V(X)/A2) from strip counts was estimated using the sum of the number of goats counted by the single side observer and the maximum number observed on the double-count side within a 100 m strip on each side of the helicopter (Section 2.3). The area sampled (a) was included in the abundance (X) and variance (V(X) ) estimate and the detection probability was assumed to be 1. Transects within repeated surveys of the study areas were used as replicates, with an additional variance component included for between- survey variation as described above.
7.2.1.2 Petersen estimate
The Petersen estimate (Seber 1982) was first applied to aerial surveys with multiple observers by Caughley and Grice (1982). Goat groups were recorded as seen by one or both observers, and detection probability estimated using the equations in Section 2.3.1.
7.2.1.3 Stratified Petersen estimate
The log linear model used in Chapter 3 investigated the factors influencing S1, S2 and B following the approach of Pople et al. (1998b). Group size, observer and vegetation were significant using a step-wise multiple regression and an analysis of deviance (Section 3.3). Hence detection probabilities were calculated for all possible combinations of these three factors using the Petersen capture-recapture model (Section 2.3.1). These detection probabilities were then used to correct individual observations on the basis that a group of goats occurred in one of four group size classes (1-4; 5-9; 10-18; >=19), one of five vegetation classes (Section 2.3), and was observed by one of six observers. To allow adequate sample sizes for estimating detection probability for each combination, data were pooled across all surveys throughout the 5 year study, which provided a large number of
110 Chapter 7: Density estimation and known numbers observations of feral goat groups (n=5687).
7.2.1.4 Chao moment estimator
Chao (1984, 1987, 1988) derived a moment estimator of abundance intended for capture- recapture data with low capture frequencies and addressed the problem of heterogeneity (Seber 1982) by allowing individuals to have a different but constant probability of detection. To enable use of the Horvitz-Thompson approach, Chao’s estimate of abundance ˆ 2 ( N = S + f1 (2 f 2 ) ) was modified to provide an estimate of detection probability using:
t
ƒ nk k pˆ = , where nk is the number of animals captured or in this application the number of tNˆ groups seen by an observer, in the kth sample, and t is the number of trapping samples or observers.
7.2.1.5 Alho estimator
Huggins (1989) introduced an estimator for double-counting that allows heterogeneous capture probabilities (Seber 1982) by modelling a range of co-variates. A similar approach was independently developed by Alho (1990) using logistic regression and is the approach used here. Using the final model presented in Chapter 3 (Table 3-3), a unique unconditional detection probability was estimated for every observation based on group size, vegetation, and their interaction, observer pair, goat colour, helicopter, site and rear observer experience in hours. Predictions were made separately for front and rear observers on the logit scale using conditional maximum likelihood equations averaged and then transformed to an overall unconditional detection probability value.
7.2.2 Area count technique
Parts of the study sites were divided into unequal-sized sub-sections using panoramic photos taken from fixed observation points. Independent counts with binoculars were made by two observers from these locations, which also allowed capture-recapture estimates. Each animal was recorded as seen by one or both observers by individual identification
111 Chapter 7: Density estimation and known numbers after independently but simultaneously observing each sub-section. The steep terrain was conducive to this type of counting as sections could be systematically observed from vantage points without disturbing animals. However this application is unlikely to be useful in flat country.
To determine accurate measures of the area visible from the vantage points, each section was digitised in a GIS (Arcview 3.2, ESRI 2000) and a viewshed (Johnston 1998) was used to eliminate areas not visible to observers. A viewshed is a line-of-sight calculation and uses input layers including elevation (digital elevation model), height and location of the observation point, and a defined study area or maximum observable distance (Johnston 1998). Viewshed analyses were conducted in Arcview 3.2 using Spatial Analyst, which produces an area surface. Air photos were rectified using ground control points, cadastre, drainage and multi-spectral and landsat imagery. Individual air photos were joined and colour balanced using Imagine software (ERDAS). The proportion of each vegetation type was calculated for each section by overlaying vegetation maps. A vegetation score was then calculated for each section based on a weighted percent of foliage projective cover from the classification previously described (Section 2.1). A weighted mean distance to every sub- section was also estimated to allow inclusion of distance in the analyses. Density was estimated using the mean number of goats observed in all sections divided by the sample area using the ratio method for unequal sized units (Jolly 1969). Repeated counts of the same area over consecutive days were used to calculate variance. The Petersen and Chao estimators (Section 7.2.1) were also used to estimate a corrected number of individuals observed.
7.2.3 Ground-based capture-recapture
Two capture-recapture estimators were applied to four populations of feral goats with known density. The methods used here are those described by Fleming and Tracey (unpublished data). Briefly, the Petersen estimator (Section 1.3) was used to estimate the density of goats from mustering, tagging, releasing and re-capturing a discrete feral goat sub-population within a period of two days. A survival-modified population estimator using the robust design and ancillary data proposed by Fleming and Tracey (unpublished data)
112 Chapter 7: Density estimation and known numbers was also applied to populations from intensive ground observations of individually ear- tagged goats.
7.2.4 Index-manipulation-index
Index-manipulation-index is a method used to estimate population abundance when standardised indices are collected before and after the removal or addition of a known number of animals (Eberhardt 1982). Six indices of abundance based on the numbers of goats and groups observed during behavioural studies and standardised counts from fixed locations were used to estimate absolute abundance using the formula and associated variance given in Section 1.3.3 (Eberhardt 1982; Caughley and Sinclair 1994).
Indices included standardised counts from fixed locations (tower counts), individuals seen per hour, groups seen per hour, individuals seen per workday, groups seen per workday, individuals seen per area surveyed, groups per area surveyed and an estimate of abundance based on a survival-modified capture-resight estimator (Fleming and Tracey, unpublished data). In spring 2000, known numbers of goats (C) were removed from Pyramids and Sid Eagle sites after initially estimating indices.
7.2.5 Comparison of estimates
The accuracy of all techniques was compared using a measure of bias, calculated using the following equation: Estimate - Known Bias = Known
113 Chapter 7: Density estimation and known numbers
7.3 Results
7.3.1 Aerial survey
Without adjusting for goats that were available for recounting (Chapter 5) all estimates with corrections were positively biased with some overestimating by up to 60% (Figure 7-1). Un-corrected strip counts were unbiased (-0.007).
Chao Petersen Alho Stratified Petersen 1 Strip Counts 0.8 0.6 0.4 0.2 Bias 0 -0.2 -0.4 -0.6 -0.8 -1 Average Calamity Snakey Little Devils Sid Pyramids No 23 Ration Bias Devils Hole Eagle Hole
Figure 7-1: Bias associated with five estimators of feral goat density for eight sites where known numbers were obtained and average bias.
After correction for the goats available for recounting (pa = 0.21) the Alho estimator performed the best (Bias= 0.02), followed by the Stratified Petersen, which was negatively biased (-0.146), the Petersen, which was positively biased (0.154), strip counts, which were negatively biased by over 20% (0.22) and the Chao estimator, which was positively biased by over 25% (0.28) (Figure 7-2)
114 Chapter 7: Density estimation and known numbers
Chao Petersen Alho 1 Stratified Petersen 0.8 Strip Counts 0.6 0.4 0.2 Bias 0 -0.2 -0.4 -0.6 -0.8 -1 Average Calamity Snakey Little Devils Sid Pyramids No 23 Ration Bias Devils Hole Eagle Hole
Figure 7-2: Bias associated with five estimators of feral goat density for eight sites where
known numbers were obtained after correcting for recounting (pa = 0.21).
7.3.2 Area count technique
7.3.2.1 Detection probability in area counts
Step-wise linear regression was used to examine the main determinants of conditional detection probability (pc) calculated separately for 557 areas observed. A mixed-effects model was fitted by REML in S-PLUS. The initial model included 11 variables and 3 interaction terms (pc ~ Observer + Group size + Tree Cover + Distance + Year + Season + Site + Colour + Slope + Aspect + Section + Group:Tree Cover + Observer:Tree Cover + Tree Cover: Distance). Non-significant terms were progressively removed using an analysis of variance (P>0.05). In the final model, year and season were included as random effects and observer, group size and colour were significant fixed effects (Table 7-2).
115 Chapter 7: Density estimation and known numbers
Table 7-2: The final fixed effects model of the main determinants of detection probability
(pc) from area counts. AIC = 214.6356, BIC = 309.6925, logLik = -85.31781.
Fixed effects: pc ~ Observer + Group size + Colour.
Variable Value Standard Error t-value P-value
(Intercept) 0.553 0.055 10.059 <0.0001
Observer 1 -0.008 0.014 -0.546 0.585
Observer 2 -0.013 0.023 -0.566 0.571
Observer 3 -0.064 0.010 -6.230 <0.0001
Observer 4 0.006 0.007 0.790 0.430
Observer 5 0.001 0.011 0.073 0.942
Observer 6 -0.028 0.009 -3.055 0.002
Group size 0.001 0.001 2.436 0.015
Colour- White -0.347 0.106 -3.268 0.001
Colour- Col 0.076 0.036 4.624 <0.0001
Colour- Dark 0.166 0.036 4.624 <0.0001
7.3.2.2 Density estimates from area counts
Overall the area count technique was slightly negatively biased (-0.11) but particular sites showed severe bias, both significantly overestimating (1.27, Gap Road) and underestimating density (-0.83, Devils Hole). Detection probabilities (pc), estimated using Petersen and Chao estimators, were high, 0.93, and 0.92 respectively, and did little to improve accuracy (Figure 7-3).
116 Chapter 7: Density estimation and known numbers
Area Count Petersen 1.5 Chao
1
0.5
Bias 0
-0.5
-1
-1.5 Average Sid Eagle1 Snakey Devils Hole No 23 Little Sid Eagle2 Pyramids1 Pyramids2 Gap Road Bias Devils Hole Figure 7-3: Bias associated with ground-based area counts using estimators uncorrected (Area count) and corrected (Petersen and Chao) for detection probability.
7.3.3 Ground-based capture-recapture
The Petersen estimate based on mustering, tagging, releasing and recapturing goats was negatively biased by around 8%. The survival-modified estimate based on re-sightings of tagged goats overestimated density by about 13% (Figure 7-4).
117 Chapter 7: Density estimation and known numbers
1.00 Survival-modified 0.80 Petersen 0.60 0.40 0.20 Bias 0.00 -0.20 -0.40 -0.60 -0.80 -1.00 Average Bias Pyramids 1 Pyramids2 Sid Eagle1 Sid Eagle2
Figure 7-4: Bias associated with a Petersen capture-recapture technique using mustering and a survival-modified estimator using re-sightings from ground observations to estimate the density of feral goats on four sites.
7.3.4 Index-manipulation-index
Six indices of abundance were applied before and after a removal of 86% and 55% of feral goats from Pyramids and Sid Eagle respectively (Figure 7-5). Of these indices the survival- modified robust estimator was the least biased index for both sites.
118 Chapter 7: Density estimation and known numbers
2 1.5 Sid Eagle Pyramids 1 0.5 Bias 0 -0.5 -1 -1.5 Goats/ Goats/ Groups/ Groups/ Survival- Tower area surveyed workday area surveyed workday modified Count
Index-Manipulation-Index
Figure 7-5: Bias for index-manipulation-index estimates using six indices on two sites with known numbers. No data was available for tower counts in Pyramids.
7.4 Discussion
Investigations of aerial surveys using actual numbers (Caughley 1974; Caughley et al. 1976; Hone 1986, 1988; Short and Hone 1986); line transect (Hone 1988; White et al. 1989; Southwell 1996); and capture-recapture theory (Walter and Hone 2003) have shown they underestimate density in most cases (cf. Linklater and Cameron 2002). However, all estimators based on helicopter counts in this study were positively biased, except for strip counts (Figure 7-1). By using multiple observers, it was evident that all animals were not observed within the sampled area. That uncorrected strip counts were unbiased most likely indicates that recounting (Chapter 5) caused positive bias, which was co-incidentally almost equal to the negative bias associated with the failure of counting all animals within the designated strip. Estimators that were adjusted for recounting (Chapter 5), are therefore used for further discussion (Figure 7-2).
The Petersen and Chao estimators were both positively biased, which may have been a result of applying an average detection probability across all variables. Correction of large
119 Chapter 7: Density estimation and known numbers sized groups (up to 200) in particular is likely to lead to overestimation and poorer precision. This is consistent with the findings of Kraft et al. (1995) who suggested a clumped distribution of pronghorn resulted in low precision during fixed-wing aerial surveys. The greater bias evident in the Chao estimator may be a result of attempting to account for unequal detection probability not accounted for with the Petersen model. However, Chao’s estimator is not recommended for less than five capture occasions (Chao 1988; Davis et al. 2003), hence appears to be unsuitable for double-count technique.
Estimators that used predicted detection probabilities specific for a range of variables (Alho and Stratified Petersen) were least biased. The Alho estimator was most accurate, which is probably due to the way in which unconditional detection probabilities were estimated. The Alho estimator, however, like all double-count techniques using multiple observers, cannot provide a correction for transects or surveys where no animals were observed. For example, when animals are unavailable in the sample, such as those completely hidden inside caves, or totally obscured by vegetation (Marsh and Sinclair 1989a). If a proportion of animals are unavailable for observation this may result in negative bias which was not evident in the current study, but may be more important when detection probability (Caughley and Grice 1982) and density are lower. Similar estimates of detection probability were also evident using independent ground observations (pg), which also suggests the double-count technique was unbiased.
Although the area count technique was unbiased when averaged across sites, it was the most unreliable of all estimates. On one site (Gap Road) density was overestimated by over 120% and underestimated on another by more than 80%. The double-count estimates of Petersen and Chao similarly underestimated density with detection probability predicted at over 0.9, hence the high correlation with underlying counts. It is clear that the use of multiple observers in this situation failed to produce reliable estimates of detection probability or density. This may have been partly caused by unequal catchability evident between individual goats, which were not sufficiently accounted for using the Petersen or Chao moment estimator. The difference between availability and visibility bias as proposed by Bayliss (1986) and Marsh and Sinclair (1989a,b) is relevant here, where only a proportion of animals appears to be available to observers at the time of surveying. The
120 Chapter 7: Density estimation and known numbers behaviour of goats when applying the area count technique was quite different from the flushing behaviour apparent in aerial surveys (Chapter 4). Animals were unaffected by observers and were rarely observed moving, which is known to increase the probability of detection (Chapter 5). Although considerable efforts were undertaken to ensure the area searched was accurate (Section 7.2.2), and distance and tree cover were not found to affect detection probability (P>0.05), vegetation and terrain are likely to have caused some animals to have been unavailable for counting. This would explain the underestimation of the area count technique evident in some sites, but does not explain the overestimates.
Overestimating density using the area count technique may be caused by counting animals more than once (Chapter 5), or sampling areas that are more likely to contain the animals of interest. Recounting was unlikely to have occurred when surveying from the ground as animals were not disturbed by observers. However, sampling may not have been representative of the study area as only those sections visible to observers were able to be searched. For example, open areas and ridge-tops (which may represent preferred habitat) are more likely to have been included in the sample, than smaller concealed gullies, creek- lines and dense vegetation, which may have been avoided. The behaviour of animals may have also contributed to this bias. Highest densities were apparent in the Gap Road study site, where goats behaved as several large groups and were often observed on open ridges at the time of sampling. Further refinement of this technique such as stratification (Caughley 1980; Krebs 1999) is required.
The Petersen method, applied to two consecutive mustering campaigns for feral goats was slightly negatively biased (0.08), possibly a result of unequal catchability of individuals, which is commonly observed in other capture-recapture studies (Tanton 1965; Druhan
1993; Davis et al. 2003). If marked goats were more likely to be recaptured then m2 would be inflated and density would be underestimated. This is described as a ‘trap happy’ response (Pollock et al. 1990). The converse, ‘trap shy’ response, occurs when marked animals are less likely to be recaptured. Although impossible to examine with two capture events, there are several tests of equal catchability that can be applied where there are >3 captures (Krebs 1999). Repeated mustering over four years revealed that differences in the capture history between individuals did occur. Some individuals, although frequently
121 Chapter 7: Density estimation and known numbers observed in the study site by identifiable marks were never captured, others were captured once but were frequently observed to be available for capture and others were often captured.
The survival–modified estimator incorporated temporal variations in detection probability and survival rate (Fleming and Tracey, unpublished data), but the potential differences in detection probability between individuals (Burnham 1972) were not examined (Pledger et al. 2003). Pledger et al. (2003) suggested that this can lead to incorrect model selection and biased parameter estimates including population size (Otis et al. 1978). In some populations, detection probability is known to vary more between individuals than between sampling occasions or locations (e.g. hares [Lepus americanus] and bird species, Dorazio and Royle 2003). The ‘trap response’ model (Pollock 1974; Otis et al. 1978) is not relevant in this study as only re-sightings, not musters were used in Fleming and Tracey’s (unpublished data) analysis. However, individual heterogeneity of detection may have occurred, where particular goats were observed more often than others. For example, goats with individual markings, or with radio-telemetry collars were often more readily identifiable, and goats that were located in areas more frequently accessed by ground observers were more likely to have occurred in the sample. In another study of feral goats, where observations were highly concentrated, unequal probabilities of re-sighting between sub-populations were apparent (Henzell and McCloud 1984). However, field observations in the current study were distributed more evenly across the study area. Moreover, increased sightings of particular individuals would be expected to produce negatively biased estimates of density (i.e. inflated m2 values). However, comparison with known numbers implies the survival-modified estimator was positively biased (13%), suggesting that individual heterogeneity had a minimal affect on density estimation. The positive bias of this estimator may have been a result of errors associated with observers failing to differentiate kids from sub-adults, or in underestimating the area actually sampled, which was not standardised across all observers and sub-populations throughout the study. This technique is also labour intensive and therefore expensive, hence is likely only to be practical where mustering, individual ear-tagging and monitoring is necessary for other reasons.
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Index-manipulation-index (IMI) is a technique which relies on indices that are precise and consistent with actual density (Eberhardt 1982). Hence the accuracy of an IMI technique is mainly determined by the validity of the index used, and precision is determined by the percentage of the population seen and the percentage of the population removed. This method is imprecise if the percentage of the population seen is below 40% and the percentage removed below 20% (Eberhardt 1982; Krebs 1999). The two indices of the number of goats observed (goats/ area surveyed; goats/ work day) provided accurate IMI estimates for Pyramids, but the IMI’s overestimated density for Sid Eagle when using area surveyed and underestimated when using work-day. Conversely indices using the number of goat groups observed (goats/ area surveyed; goats/ work day) provided IMI’s that were overestimates for Pyramids, but more accurate for Sid Eagle. The inconsistency of these findings may be caused by the index not displaying linearity with density, inadequate sample size, or by altered behaviour of remaining animals following removals. For example, after mustering, animals may be more aggregated in specific locations, analogous to the response of gregarious ungulates to a predator (Chapter 4). Hence larger numbers of goats may have been observed in fewer workdays and less area searched resulting in overestimates of I2, and therefore positively biased estimates of density. Changes in grouping behaviour as a result of mustering will also have implications for the numbers of goats versus groups observed before and after removals. Applying the survival-modified estimator before and after removals achieved the least biased IMI estimate, which may reflect the consistency of this technique in estimating density in isolation.
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CHAPTER 8
GENERAL DISCUSSION
There have been significant developments in the methods used for estimating the density of wildlife populations in the last two decades (Schwarz and Seber 1999; Buckland et al. 2000). The literature on statistical sampling theory, including improved stratification procedures (Iachan 1985; Krebs 1999), two-stage sampling (Thompson 1992; McCallum 2000), adaptive or cluster sampling (Thompson 1991a,b; Thompson and Seber 1996), model selection (Burnham and Anderson 2002) and model-based estimation (Lohr 1999) is extensive. Considerable efforts have been directed in correcting for capture or detection bias particularly through advances in capture-recapture theory (Pollock et al. 1990; Chao 1988) and distance sampling (Buckland et al. 2004). In this thesis a variety of density estimators have been applied; the validity of their assumptions examined; and their accuracy tested using known populations of feral goats.
A major assumption of capture-recapture experiments is that all animals are equally likely to be captured or detected in each sample (Pollock et al. 1990). This assumption has been the focus of much investigation (Pollock 1974; Otis et al. 1978) and must be considered when applying capture-recapture techniques for estimating population parameters. The probability of capturing or detecting feral goats and the conditions where this was variable for a range of applications was examined, and this was used as a basis for assessing the accuracy of capture-recapture methods to estimate density. A variety of capture-recapture techniques was applied to aerial surveys, standardised ground counts, mustering and marking, and re-sightings from ground observations.
In the aerial surveys studied, the main factors influencing the probability of observing a group of feral goats were group size, vegetation and observer. However, different approaches to analysing these data influenced the significance of the variables, the predicted probabilities and subsequently the estimates of density. Goat colour, type of helicopter, site and rear observer experience in hours were also found to be important determinants of detection using the approach of Alho (1990). Different detection
124 Chapter 8: General discussion probabilities between groups of goats may be particularly relevant when using double- counting, where multiple observers are ‘capturing’ and ‘recapturing’ animals in the same instant. Many analyses test and adjust for this ‘unequal catchability’ assumption in different ways (Eberhardt 1969; Chao 1987; Pollock et al. 1984; Huggins 1989; Alho 1990). The approaches of Huggins (1989) and Alho (1990) attempt to address this problem by providing estimates of unconditional detection probabilities (pd) using maximum likelihood equations, allowing prediction of unique pd values for a range of co-variates. The methods of Chao (1987) and Alho (1990) and an additional technique (Stratified Petersen) were examined in this study, as were strip counts and a Petersen estimator (Section 7.2.1). A Horvitz- Thompson approach (Oh and Scheuren 1983) provides a useful basis for estimating abundance (or density) when detection probability can be estimated and is known to vary between observations according to a range of independent variables. This approach overcomes the errors with estimating mean group size and allows correction of observations on recorded on both sides of the helicopter.
Indices of abundance are commonly used in wildlife management for their simplicity and practicality (e.g. Cairns 1999). However, variable probability of detection has been considered a major impediment to their application in wildlife studies (Anderson 2001). Of particular importance is the constancy of detection between sites and over time, and how this affects the monitoring of population size. As discussed in chapter 3 and above, the detection probability of feral goats in aerial surveys was known to vary considerably with group size, vegetation and observer. In chapter 6, the major determinants of detection probability in helicopter surveys were examined for a range of other species (feral pigs, eastern grey kangaroos, common wallaroos, swamp and red-necked wallabies). Detection probability was found to vary significantly between species (P<0.001). Group size, vegetation, observer and sampling period were also of importance for different species. Even where detection probability was significantly different over time, underlying counts were highly correlated with corrected counts. Results suggest aerial survey indices may be effective for monitoring large changes in population size, but the factors affecting detection probability need to be considered when attempting to detect small fluctuations, or when comparing density between species.
125 Chapter 8: General discussion
Another assumption of most sampling regimes that is fundamental but rarely examined (Linklater and Cameron 2002) is that animals do not occur in the sample more than once. Survey techniques that influence behaviour can cause bias from movement of animals between sampling units. Few studies (e.g. Calef et al. 1976; Cote 1996) have explored the reasons animals respond to a disturbance and the factors that influence the extent of alert response. This thesis examines the behavioural responses of feral goats to helicopters during aerial surveying and uses this information to estimate the probability that individual goats occurred in one or more adjacent transects and were thereby available for recounting. Alert behaviour and distance travelled in response to helicopters were influenced by the distance goats were from the helicopter, their activity, site, cumulative survey hours, helicopter type and density. These results suggest that under intensive sampling regimes, movement between transects may be substantial and result in serious overestimates of density. For the current study, 21% of animals were estimated to be available for re- sampling.
Rugged terrain introduces other considerations for abundance estimators. Delineating strip widths from aerial surveys is difficult in variable terrain as observers have to visually project the transect boundary further than indicated by the calibration pole when viewing up hill and closer when viewing downhill (Chapter 5). Results also indicate that slope and its effects on the distance from observers (Chapter 3) could be important when surveying at higher elevation and in steeper terrain, which could be particularly relevant when using distance to predict detection functions (Buckland et al. 1993). When using ground counts, calculating the area observed from fixed vantage points becomes more involved when terrain is hilly, i.e. introducing the requirement for a viewshed analysis and a digital elevation model (Chapter 7).
After correcting for recounting in aerial surveys, the Alho (1990) estimator was found to be the most accurate estimator of known numbers. The Stratified Petersen estimator produced detection probabilities specific for group size, vegetation and observer and was the next most accurate, but negatively biased (-0.146). The improved estimates of these two techniques over the Chao, Petersen and strip counts methods may be attributed to correction of individual observations according to their characteristics. The improved accuracy of the
126 Chapter 8: General discussion
Alho estimator can be explained by the calculations of the detection probabilities that attempt to consider all animals in the population and not just those in the sample (i.e. they are unconditional). The Chao and Petersen estimators were positively biased possibly because of averaging detection probabilities across all observations. This may be of less importance where independent variables have less affect on the probability of detection (e.g. group size is less variable).
The inconsistency and inaccuracy of the ground-based area count technique emphasises the importance of other assumptions in density estimation. Estimating and correcting for detection probability from multiple observers in this case did not improve density estimates. Ensuring that sampling is representative, and stratifying by habitat are likely to improve accuracy and precision. Future research is needed before the area count technique can be applied.
The accuracy and reliability of index-manipulation-index techniques were dependent on the index used. Of particular importance would be the relationship of the index to actual density. Ground capture-recapture techniques using mustering and re-sightings may have been influenced by unequal catchability; however, the survival-modified robust estimator was positively biased, which suggests underestimation of the area sampled and overestimation of the number of unmarked individuals may have occurred. This technique is labour intensive and requires many observations and animals that are individually distinguishable.
The relative importance of assumptions in density estimation, and the ability of more complex analysis to correct for these where they are violated can only be examined effectively by comparing against known populations. Future study using known populations to assess the true accuracy of density estimators for other species is recommended.
In conclusion, helicopter surveys using double-counting is the preferred technique for surveying feral goats in rugged terrain, and is likely to be accurate in other areas. However, consideration must be given to recounting when sampling is intensive and to improving
127 Chapter 8: General discussion predictions of detection probability. Recommended improvements include using equations that are not conditional on animals occurring in the sample (Huggins 1989, 1991 or Alho 1990), avoiding the use of average group sizes, and adjusting for the variability in detection according to a range of factors, particularly group size, vegetation and observer.
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