University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln
Dissertations & Theses in Natural Resources Natural Resources, School of
7-2019 Relative Density and Resource Selection of Urban Red Foxes in Lincoln, Nebraska Kyle Dougherty University of Nebraska-Lincoln, [email protected]
Follow this and additional works at: https://digitalcommons.unl.edu/natresdiss Part of the Natural Resources and Conservation Commons
Dougherty, Kyle, "Relative Density and Resource Selection of Urban Red Foxes in Lincoln, Nebraska" (2019). Dissertations & Theses in Natural Resources. 289. https://digitalcommons.unl.edu/natresdiss/289
This Article is brought to you for free and open access by the Natural Resources, School of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Dissertations & Theses in Natural Resources by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln.
Relative Density and Resource Selection of Urban Red Foxes in Lincoln, Nebraska
By
Kyle Dougherty
A THESIS
Presented to the Faculty of
The Graduate College at the University of Nebraska
In Partial Fulfillment of Requirements
For the Degree of Master of Science
Major: Natural Resource Sciences
Under the Supervision of Professor Elizabeth VanWormer
Lincoln, Nebraska
July 2019
Relative Density and Resource Selection of Urban Red Foxes in Lincoln, Nebraska
Kyle Dougherty, M.S.
University of Nebraska, 2019
Advisor: Elizabeth VanWormer
Since early reports of urban red fox (Vulpes vulpes) populations in Great Britain, red fox populations have been studied in many large cities throughout Europe, North America, and
Australia. However, there has been relatively little research conducted in moderately sized North
American cities. To further the ecological understanding of red foxes in moderately sized cities, we investigated relative density and resource selection of the urban fox population in Lincoln,
Nebraska. We used presence-only data collected from a citizen science project and inhomogeneous point process models to investigate relative density of urban foxes and deployed
GPS collars on ten red foxes to investigate home range size, resource selection, and activity patterns. Our results indicate fox density is highly dependent upon developed open spaces, such as parks, golf course, and low-density residential areas. Further, we observed red foxes selecting developed open spaces and herbaceous areas, with activity being high through the majority of the night and peaking in the early morning. Together, our results indicate that developed open spaces and herbaceous areas are important habitat types for urban foxes. In these areas, red foxes are likely able to benefit from anthropogenic food subsidies and avoid predation by coyotes while minimizing the costs of living within urban areas, such as disturbance from human activity and mortality risk associated with roads. Our results and conclusions are consistent with much of the existing literature on urban foxes in other cities throughout the world, suggesting that red fox ecology in moderately sized North American cities is similar to that of foxes in other urban areas around the world.
iii
TABLE OF CONTENTS
TABLE OF CONTENTS ...... iii
LIST OF FIGURES ...... v
LIST OF TABLES ...... vii
INTRODUCTION ...... 9
References: ...... 12
CHAPTER I ESTIMATING DENSITY OF RED FOXES IN LINCOLN, NEBRASKA
USING PRESENCE-ONLY DATA OBTAINED FROM CITIZEN SCIENTISTS ...... 15
Introduction: ...... 15
Methods: ...... 19
Study Area: ...... 19
Presence-only Data: ...... 20
Point Process Models: ...... 21
Covariates: ...... 25
Model Selection: ...... 26
Prediction: ...... 27
Results: ...... 27
Discussion: ...... 30
References: ...... 34
iv
CHAPTER II HOME RANGE SIZE AND RESOURCE SELECTION OF RED FOXES
IN LINCOLN, NEBRASKA ...... 39
Introduction: ...... 39
Methods: ...... 43
Trapping and Animal Handling: ...... 43
Home Range Estimation: ...... 44
Resource Selection Functions: ...... 44
Activity Patterns: ...... 46
Results: ...... 47
Home Range Estimation: ...... 47
Resource Selection Functions: ...... 49
Activity Patterns: ...... 51
Discussion: ...... 51
References: ...... 56
CONCLUSIONS ...... 63
SUPPLEMENTARY MATERIAL ...... 67
v
LIST OF FIGURES
CHAPTER I
Figure 1. A) State of Nebraska with Lancaster County highlighted in red. B) Observations of red foxes in Lincoln, Nebraska, submitted by iNaturalist users from January 2018 – March 2019 after the 10% most extreme outliers as well as repeat observations by the same user within 1 km of that user’s previous observation were removed...... 21
Figure 2. Observed K-function and theoretical K-function under complete spatial randomness with 5% acceptance intervals...... 22
Figure 3. Observed inhomogeneous K-function after border correction and theoretical inhomogeneous K-function with 5% acceptance intervals...... 23
Figure 4. Log-pseudolikelihood at different resolutions of quadrature points in a rectangular grid in the observation window. This shows that there is little benefit to analyzing data with more than 67,500 quadrature points...... 25
Figure 5. Predicted relative density of red foxes within Lincoln, Nebraska obtained from the averaging the predictions of all models with DAIC* < 2 with iNaturalist Observation Intensity =
1...... 29
vi
CHAPTER II
Figure 1. 2016 National Land Cover Database (NLCD) raster with 95% a-LoCoH home range estimates for nine red foxes tracked during the study period...... 48
Figure 2. b coefficients and 95% confidence intervals from the top resource selection model with all land use variables and sex interaction. Negative coefficients indicate selection while positive coefficients indicate avoidance...... 50
Figure 3. Overall kernel density for red fox activity in Lincoln, Nebraska over a 24 hour period.
...... 50
SUPPLEMENTARY MATERIALS
Supplementary Figure 1. Q-Q plot of the top model selected with pointwise 95% critical envelope (grey) obtained by simulation...... 67
vii
LIST OF TABLES
CHAPTER I
Table 1 Composite AIC and differences between the top model and competing models (DAIC).
A table of all models with DAIC* < 2 is available in supplementary table X...... 27
Table 2. Beta coefficients, standard errors, and 95% confidence intervals for the top model of relative fox density...... 30
CHAPTER II
Table 1. Mean home range sizes (km2) and SD of red foxes trapped and collared in Lincoln,
Nebraska, 2018Table ...... 47
Table 2. Top resource selection models compared to the null model. Land Use refers to the following six land cover categories: Developed Open + Developed Low Intensity + Developed
Medium Intensity + Developed High Intensity + Herbaceous + Wetland...... 49
SUPPLEMENTARY MATERIAL
Supplementary Table 1. Descriptions of each land cover class appearing in the National Land
Cover Database raster. Adapted from Yang et al. (2018)...... 68
Supplementary Table 2. Composite AIC and differences between the top model and all competing models with DAIC* < 2...... 70
viii
Supplementary Table 3. Unadjusted b coefficients, standard errors, and 95% confidence intervals from the top resource selection model with interactions between sex and all resources.
Negative coefficients indicate selection while positive coefficients indicate avoidance………..72
9
INTRODUCTION
In the early 1930s, reports of large red fox (Vulpes vulpes) populations within several
British cities began to surface (Bateman and Fleming 2012). Since those early records, reports of high-density red fox populations have become increasingly common in cities throughout Europe,
North America, and Australia (Bateman and Fleming 2012; Šálek et al. 2015; Lombardi et al.
2017). Due to the frequency with which foxes are reported in urban areas, there has been considerable research investigating the ecology of urban foxes. In most cities, the presence of anthropogenic food subsidies in the form of synanthropic prey species, refuse, and food intentionally fed to foxes is a major factor facilitating the ability of red foxes to live in urban areas (Bateman and Fleming 2012; Šálek et al. 2015). Additionally, red foxes in North America are able to utilize urban areas to avoid predation from coyotes, which tend to favor undeveloped areas when available (Randa and Yunger 2006; Gehrt et al. 2010; Nagy 2012). However, existing literature largely neglects small to moderately sized cities within North America, as the majority of research comes from either Europe or large metropolitan areas within North America
(Lombardi et al. 2017). The response of red foxes to urbanization may depend upon the landscape characteristics, development histories, and management practices of the area they are present in, which highlights the importance of continuing to investigate urban fox ecology in settings where their response to urbanization has not yet been documented (Fischer et al. 2015).
In addition to the fundamental reasons for studying urban red fox ecology, many researchers have sought to answer practical questions, such as how to best manage urban fox populations to minimize human-wildlife conflict. In a survey of metropolitan residents of the
United States, 61% of respondents reported problems caused by wildlife and 42% of respondents stated that they attempted to prevent or solve wildlife related problems within one year of the
10 survey, with the majority of those efforts being unsuccessful (Conover 1997). Foxes have been observed frequently denning under building (Harris 1981; Marks and Bloomfield 2006), which is one of the most common ways that carnivores cause property damage (Bateman and Fleming
2012). In addition to property damage, foxes may also make noise which can disturb residents, prey upon small pets, and in very rare cases, attack humans (Bateman and Fleming 2012;
Cassidy and Mills 2012; Soulsbury and White 2016). As a result, there has been interest in controlling populations of red foxes in some cities, though these efforts often prove to be expensive and ineffective (Harris 1985; White et al. 2003). Because of the cost associated with control of red fox populations, educating the public on how to best handle human-wildlife interactions may be a more effective method of reducing the impact of these events.
Researchers have also investigated disease prevalence in red fox populations and found that in some cases red foxes may be useful in the surveillance of various zoonotic diseases as a sentinel species (Slavica et al. 2011; Otto et al. 2013; Meredith et al. 2015). Because of the complex nature of zoonotic diseases in urban areas, surveillance is necessary to provide critical information to assess and manage the health of both human and wildlife populations. The use of a sentinel species can provide this information before significant numbers of humans are infected
(McCluskey 2003; Rabinowitz et al. 2006; Childs and Gordon 2009). While there are several zoonotic diseases known to be present in the state of Nebraska (Leptospirosis, Tularemia, and
Echinococcosis), we currently know very little about their prevalence in urban areas (Bischof and Rogers 2005; Raghavan 2011; White et al. 2017).
Our primary motivation in conducting this research is to investigate red fox density and resource selection as they relate to zoonotic disease prevalence. The first chapter of this thesis describes our efforts to estimate relative density of red foxes in Lincoln, Nebraska using
11 presence-only data obtained by citizen scientists. The second chapter details our use of GPS collars to collect telemetry data, which we used to investigate home range size, activity patterns, and resource selection of red foxes. At the time of writing, we are beginning to investigate the prevalence of various zoonotic diseases using samples we collected during our field work. We plan to synthesize these results to investigate relationships between red fox density, resource selection, and patterns of disease prevalence. In addition to increasing ecological understanding of red foxes in urban areas, we believe our results will be useful to both wildlife managers and professionals working in the fields of wildlife and human health.
12
References:
BATEMAN, P. W., AND P. A. FLEMING. 2012. Big city life: carnivores in urban environments.
Journal of Zoology 287:1–23.
BISCHOF, R., AND D. G. ROGERS. 2005. Serologic survey of select infectious diseases in coyotes
and raccoons in Nebraska. Journal of wildlife diseases 41:787–791.
CASSIDY, A., AND B. MILLS. 2012. “Fox Tots Attack Shock”: Urban Foxes, Mass Media and
Boundary-Breaching. Environmental Communication 6:494–511.
CHILDS, J. E., AND E. R. GORDON. 2009. Surveillance and control of zoonotic agents prior to
disease detection in humans. The Mount Sinai Journal of Medicine, New York 76:421–
428.
CONOVER, M. 1997. Wildlife management by metropolitan residents in the United States:
Practices, perceptions, costs, and values. Wildlife Society Bulletin 25:306–311.
FISCHER, J. D., S. C. SCHNEIDER, A. A. AHLERS, AND J. R. MILLER. 2015. Categorizing wildlife
responses to urbanization and conservation implications of terminology. Conservation
Biology 29:1246–1248.
GEHRT, S. D., S. P. RILEY, AND B. L. CYPHER. 2010. Urban carnivores: ecology, conflict, and
conservation. JHU Press.
HARRIS, S. 1981. An Estimation of the Number of Foxes (Vulpes vulpes) in the City of Bristol,
and Some Possible Factors Affecting Their Distribution. Journal of Applied Ecology
18:455–465.
13
HARRIS, S. 1985. Humane control of foxes. Humane control of land mammals and birds:
proceedings of a symposium held at the University of Surrey... England, 17th to 19th
September, 1984/(edited for UFAW by David P. Britt). Potters Bar: Universities
Federation for Animal Welfare, c1985.
LOMBARDI, J. V., C. E. COMER, D. G. SCOGNAMILLO, AND W. C. CONWAY. 2017. Coyote, fox,
and bobcat response to anthropogenic and natural landscape features in a small urban
area. Urban Ecosystems 20:1239–1248.
MARKS, C., AND T. E. BLOOMFIELD. 2006. Home-range size and selection of natal den and
diurnal shelter sites by urban red foxes (Vulpes vulpes) in Melbourne. CSIRO Wildlife
Research 33:339–347.
MCCLUSKEY, B. J. 2003. Use of sentinel herds in monitoring and surveillance systems. Animal
Disease Surveillance and Survey Systems: Methods and Applications:119–133.
MEREDITH, A. L., S. C. CLEAVELAND, M. J. DENWOOD, J. K. BROWN, AND D. J. SHAW. 2015.
Coxiella burnetii (Q-Fever) Seroprevalence in Prey and Predators in the United
Kingdom: Evaluation of Infection in Wild Rodents, Foxes and Domestic Cats Using a
Modified ELISA. Transboundary and Emerging Diseases 62:639–649.
NAGY, C. 2012. Validation of a citizen science-based model of coyote occupancy with camera
traps in suburban and urban New York, USA. Wildlife Biology in Practice 8:23–35.
OTTO, P. ET AL. 2013. Serological Investigation of Wild Boars (Sus scrofa) and Red Foxes
(Vulpes vulpes) As Indicator Animals for Circulation of Francisella tularensis in
Germany. Vector-Borne and Zoonotic Diseases 14:46–51.
14
RABINOWITZ, P. ET AL. 2006. Animals as Sentinels of Bioterrorism Agents. Emerging Infectious
Diseases 12:647–652.
RAGHAVAN, R. 2011. Geospatial analysis of canine leptospirosis risk factors in the central Great
Plains region. PhD Thesis, Kansas State University.
RANDA, L. A., AND J. A. YUNGER. 2006. Carnivore occurrence along an urban-rural gradient: a
landscape-level analysis. Journal of Mammalogy 87:1154–1164.
ŠÁLEK, M., L. DRAHNÍKOVÁ, AND E. TKADLEC. 2015. Changes in home range sizes and
population densities of carnivore species along the natural to urban habitat gradient.
Mammal Review 45:1–14.
SLAVICA, A. ET AL. 2011. Prevalence of leptospiral antibodies in the red fox (Vulpes vulpes)
population of Croatia. Veterinarni Medicina 56:209–213.
SOULSBURY, C. D., AND P. C. L. WHITE. 2016. Human–wildlife interactions in urban areas: a
review of conflicts, benefits and opportunities. Wildlife Research 42:541–553.
WHITE, A. M. ET AL. 2017. Hotspots of canine leptospirosis in the United States of America. The
Veterinary Journal 222:29–35.
WHITE, P. C. L., P. J. BAKER, J. C. R. SMART, S. HARRIS, AND G. SAUNDERS. 2003. Control of
foxes in urban areas: modelling the benefits and costs. Symposium on Urban Wildlife,
Third International Wildlife Management Congress’, Christchurch, New Zealand.
15
CHAPTER I
ESTIMATING RELATIVE DENSITY OF RED FOXES IN LINCOLN, NEBRASKA USING
PRESENCE-ONLY DATA OBTAINED FROM CITIZEN SCIENTISTS
Introduction:
Estimating the number of animals present in an area and understanding the manner in which distributed in that space are fundamental questions in ecology. Ecologists frequently aim to determine how a species responds to environmental changes that may range in scale from local to global (Guisan and Thuiller 2005; Ehrlén and Morris 2015). Throughout the world, the increasing rate of urbanization is a major source of environmental change; by 2025, sixty-five percent of humans are projected to live in cities, and the footprint of those cities is expected to double (Bradley and Altizer 2007). In response to the growing importance of urban wildlife management, research on urban mammals has increased, leading to an improved understanding of how many species respond to human-dominated landscapes (Magle et al. 2012).
Depending upon their response to urbanization, species can generally be placed into one of three categories: urban avoiders, adapters, or exploiters (McKinney 2002). Species classified as urban avoiders tend to be sensitive to habitat fragmentation (McKinney 2002; Ripple et al.
2014). Urban adapters generally require less space and are better adapted to edge habitats and open spaces, while urban exploiters are almost entirely reliant upon anthropogenic subsidies
(McKinney 2002). Large-bodied predators are often unable to sustain viable populations in urban areas due to persecution from humans and a lack of suitable habitat, which creates an opportunity for mesopredators to flourish in urban areas (Crooks and Soulé 1999; Ripple et al. 2014). In addition to being released from predation, many mesopredators are able to utilize a variety of
16 anthropogenic subsidies, including synanthropic prey species, food from intentional feeding, and refuse, which contributes to their ability to sustain large population sizes in urban areas
(Bateman and Fleming 2012; Šálek et al. 2015). While the classification of a species as an urban avoider, adapter, or exploiter is useful, a species’ response to human-dominated landscapes is often context-specific and depends largely upon the landscape characteristics, development histories, and management practices of any given area (Fischer et al. 2015). Therefore, it can be difficult to predict how a species responds to urbanization in a region where they have not yet been well studied (Magle et al. 2016).
Red foxes have the largest geographical range of any terrestrial carnivore and are perhaps one of the most successfully adapted urban carnivores (Bateman and Fleming 2012). Since the
1930s, when the first reports of urban red foxes in British cities surfaced, reports of large urban fox populations in cities throughout Europe, North America, and Australia have become increasingly common, with population densities reaching up to 37 individuals per km2 (Bateman and Fleming 2012). The majority of urban fox research has been conducted in Europe, with only a small proportion coming from North America. While the majority of North American urban canid research focuses on large urban areas such as New York City, Los Angeles, and Chicago, the general trend of red foxes utilizing urban areas appears to be consistent in smaller cities throughout the Midwest (Gosselink et al. 2003; Cove et al. 2012; Lombardi et al. 2017).
However, the density of red foxes in a particular urban area and their distribution in that space varies considerably and requires thorough investigation, particularly when that information is needed to investigate a related biological phenomenon, such as disease prevalence.
Gese (2004) outlined several direct and indirect methods frequently used to survey and census populations of wild canids, including: scat deposition transects, remote camera trapping,
17 and capture-mark-recapture studies. We evaluated scat deposition transects as a method for estimating relative abundance in this study, but surveys along recreational trails in Lancaster
County yielded inconsistent results, likely due to differences in the levels of traffic and maintenance of urban and rural trails leading to inconsistency in scat persistence along the trails.
While we were able to utilize remote cameras to identify potential trapping locations, large scale deployment of remote cameras in urban areas can be difficult. When using remote cameras to estimate density of wildlife populations, researchers frequently distribute cameras at a predetermined density either randomly or systematically (Kolowski and Forrester 2017). In urban areas, access to large areas of public and private land is often limited, which makes both random and systematic deployment of cameras difficult. Kolowski & Forrester (2017) also determined that camera placement can dramatically alter the rate that animals are detected, which can be problematic when attempting to model density of a species. Because the majority of the locations available to us were public parks, density estimates would have likely suffered from substantial bias. Lastly, camera theft in urban areas can make deployment of large numbers of cameras more expensive. Though capture-mark-recapture is a well-established method of estimating population size of wild canids, our overall capture rates were low and only one fox was recaptured during our trapping period (> 1 year), which rendered capture-mark-recapture ineffective.
The use of presence-only data to model density and distribution of many species has been of growing interest to ecologists, particularly in situations where there is no reliable method of collecting presence-absence data, funds available are limited, or there is already an accessible source of information regarding where the species of interest has been observed (Pearce and
Boyce 2006). Presence-only data is often more widely available and easier to collect than
18 presence-absence data (Gomes et al. 2018). A common source of presence-only data is opportunistic sightings from citizen science projects, which allow volunteers to collect large amounts of data at little or no cost to the researchers. This type of project is particularly useful in urban areas where large amounts of volunteers are available (McCaffrey 2005). Additionally, citizen science projects also offer a natural method for keeping the public engaged in science and establishing networks for disseminating results to a broad audience (Silvertown 2009). However, these projects often face problems involving observer error and bias which need to be accounted for during data analysis (Dickinson et al. 2010). Despite these challenges, several studies have successfully implemented citizen science projects to monitor trends in wild canid populations.
Scott et al. (2014) used a nationwide survey to collect presence-only data and documented changes in the distribution of red foxes in urban areas across Great Britain. Soysal (2017) also used recorded sightings of red foxes on social media to monitor the fox population of Baton
Rouge, Louisiana. Shumba et al. (2018) used citizen science data to evaluate habitat used and selection of a wild canid species and obtained results that were generally consistent with a companion telemetry study. Weckel et al. (2010) were also able to model occupancy of coyotes using sightings from citizen scientists, the model they created was later successfully validated using camera surveys, which suggests that similar citizen science projects can be used to successfully evaluate distribution of wild canids in urban areas (Nagy 2012). Though the use of presence-only data from citizen scientists in wild canid research has become more commonplace, particularly in efforts to educate the public, it is still an underutilized tool for management and conservation.
In this chapter, we model relative density and distribution of red foxes in Lincoln using presence-only data obtained from citizen scientists. We hypothesized that red fox density varies
19 along an urban to rural gradient, with the highest density being reached at low to intermediate levels of development. Specifically, we predicted that fox density would be highest in areas close to developed open space and low-intensity development and lower at areas close to medium- and high-intensity development. Developed open spaces and areas of low-intensity development are composed primarily of parks, golf courses, other urban green spaces, and large lot single-family housing units (Yang et al. 2018). These areas should support larger numbers of red foxes by providing anthropogenic food subsidies and reduced mortality from anthropogenic sources, such as roadkill, which may be more prevalent at higher levels of development, and predation, which we expect to be more prevalent in undeveloped areas. Currently, there is limited information regarding urban fox density in moderately sized urban areas of the United States. Apart from filling that gap, we will use results from this study to accomplish two main objectives. First, we will use the predictions of relative density to investigate connections between red fox density and disease prevalence. Second, this information can be used to provide targeted outreach to the public to provide resources about how to coexist with urban wildlife in areas where red fox density is expected to be high and human wildlife conflicts are most likely, which will be useful to professionals in Lincoln who are involved in managing human-wildlife conflict.
Methods:
Study Area:
Lancaster County was located in the southeastern portion of Nebraska and covered approximately 1 percent of the state. Lincoln covered approximately 11 percent of the county and was home to over 250,000 residents, making it the second largest city in the state (U.S.
Census Bureau 2010). The city was composed of varying degrees of development, ranging from open areas consisting mostly of vegetation in the form of lawn grasses to dense commercial and
20 residential areas where impervious surfaces accounted for 80-100 percent of total land cover
(Supplemental Table 1) (Yang et al. 2018). Rural areas were dominated by agricultural lands and grassland, which accounted for nearly 80 percent of the county’s land (Homer et al. 2015).
Lincoln was expected to expand service limits and develop approximately 52 square miles of land before 2040 and could expand an additional 165 square miles after 2040 (City of Lincoln
Nebraska Planning Department 2016)
Presence-only Data:
Using iNaturalist, citizen scientists recorded the location of red fox sightings within
Lancaster County. We recruited participants at outreach events, on social media, and through news stories about the project. 235 participants recorded a total of 400 red fox sightings between
January 2018 and March 2019. Due to a lack of submitted observations from rural areas of the county, we restricted the window of observation to the extent of Lincoln City Limits.
Additionally, we used a local distance-based outlier factor to remove points with the 10% most extreme outlier scores (Zhang et al. 2009). Additionally, we removed observations that were within 960 meters of another observation by the same user, 960 meters is the approximate radius of a circle with an area of 2.7 km2, which is the average home range size of GPS collared red foxes in Lincoln (Chapter 2; Figure 1).
21
Figure 1. A) State of Nebraska with Lancaster County highlighted in red. B) Observations of red foxes in Lincoln, Nebraska, submitted by iNaturalist users from January 2018 – March 2019 after the 10% most extreme outliers as well as repeat observations by the same user within 1 km of that user’s previous observation were removed. Point Process Models:
Point process models model the intensity of a point pattern as a log-linear function of environmental covariates, expressed as the formula:
��l(�) = �(�)′� (Equation 1) where l(s) is the expected number of points per unit area and b corresponds to the environmental covariates x(s) (Baddeley et al. 2015; Renner et al. 2015). Assuming sightings of red foxes are proportional to density, intensity can be interpreted as a measure of relative density (Fithian and
Hastie 2013; Renner et al. 2015). While this is a critical assumption, there is evidence that sightings of wild canids can be used to successfully evaluate canid distribution, site occupancy,
22 and habitat use (Weckel et al. 2010; Nagy 2012; Shumba et al. 2018; Mueller et al. 2019). We believe that the utility of citizen science sightings of wild canids may be extended to estimates of relative density if we are able to properly account for observer bias and other sources of error in our model.
The simplest model, a Poisson point process model, assumes that intensity is homogeneous and that points in the point pattern exhibit no interpoint dependence (Baddeley et al. 2015). To assess if observations of red foxes collected from iNaturalist exhibit interpoint dependence, we used the K-function and inhomogeneous K-function (Ripley 1977; Baddeley et al. 2015). The K-function is the cumulative average number of points within a distance r of a typical data point, corrected for edge effects, and standardized by dividing by intensity (Ripley
1977). Baddeley et al. (2015) suggested that the choice of edge correction method itself is not critical as long as some edge correction method is performed.
Figure 2. Observed K-function and theoretical K-function under complete spatial randomness with 5% acceptance intervals.
23
We first tested that the point pattern created from observations of red foxes is inhomogeneous by using 5% acceptance envelopes centered around the K-function of a point pattern exhibiting complete spatial randomness (Figure 2) (Baddeley et al. 2015). After confirming that the red fox point pattern is inhomogeneous, we used the inhomogeneous K- function to determine if there is evidence of interpoint interaction after allowing for spatial variation in intensity. The inhomogeneous K-function requires an accurate estimate of the intensity function, which we obtained through kernel estimation using a bandwidth automatically selected via likelihood cross validation (Loader 2006). The result of this test suggested that there was clustering of red fox observations in Lincoln (Figure 3). Because of the apparent clustering, we used a model capable of accounting for interpoint interaction should be used in place of the simpler point process model described above.
Figure 3. Observed inhomogeneous K-function after border correction and theoretical inhomogeneous K-function with 5% acceptance intervals.
24
Area-interaction point process models are able to model both clustering and inhibition of point patterns by adding a new term to the intensity function so that intensity is conditional upon other points in the pattern as well as the environmental covariates (Renner et al. 2015). The area- interaction model’s intensity function can be written as