Estimating Observational Home Ranges for Female Grizzly Bears with Cubs Using Citizen Science Data

ESTIMATING OBSERVATIONAL HOME RANGES (OHR) FOR FEMALE GRIZZLY BEARS WITH CUBS USING CITIZEN SCIENCE DATA PREPARED BY:

TYLER BRASINGTON

Brasington, T.J. (2020). Estimating Observational Home Ranges (OHR) for female grizzly bears with cubs using citizen science data. Unpublished data. College of Natural Resources, University of Wisconsin – Stevens Point. Wisconsin, USA.

Estimating observational home ranges (OHR) for female grizzly bears with cubs in Yellowstone National Park using citizen science data

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Presented to

Dr. Michael Demchik of the College of Natural Resources University of Wisconsin - Stevens Point

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In Partial Fulfillment of the Requirements for the Degree of Master of Natural Resources

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by Tyler Brasington

May, 2020

The Greater Yellowstone Grizzly Project www.yellowstonegrizzlyproject.org Š 2019 Tyler Brasington All rights reserved. No portion of this manuscript may be reproduced in any form without permission from the publisher, or appropriate authors, except as permitted by U.S. copyright law.

For permissions contact: yellowstonegrizzlyproject@gmail.com

Author Tyler Brasington is a native born and raised Pennsylvanian, yet proud current Wisconsin resident. He graduated from the University of Wisconsin-Whitewater with a B.S. in Environmental Science. Currently, Tyler is pursuing his masters in Natural Resources with the University of Wisconsin-Stevens Point. He has worked in Yellowstone National Park under the guidance and supervision of Dr. George Clokey and Dr. Jim Halfpenny.

Tyler is a current member of the International Association for Bear Research and Management, The Wildlife Society, and Polar Bears International.

Research and academic work has focused on different aspects of grizzly bear ecology and behavior. Ongoing research: spatial ecology and identification of females with cubs, and integrated approaches to monitoring grizzlies in Yellowstone and Grand Teton National Parks. Side projects include: selected life histories of park bears, bear viewing etiquette and responses.

Currently Tyler is employed as a Park Ranger with the Bear Management Office in Grand Teton National Park (GTNP). He previously worked as a Biological Science Technician with the US Geological Survey, National Wildlife Health Center and as a Biological Science Technician (Fisheries/AIS) in GTNP, and served as a volunteer, assisting the Bear Management Office in Yellowstone National Park.

Disclaimer: The information and views expressed in this manuscript do not necessarily represent the views of the Department of Interior, US Geological Survey, National Park Service or the United States Government.

5 May 2020 Tyler J. Brasington 5156 Brindisi Ct, Apt 2 Middleton, WI. 53562 Tbras709@uwsp.edu Running Head: Observational Home Ranges (OHR) for female grizzly bears with cubs using citizen science Title: Estimating observational home ranges (OHR) for female grizzly bears with cubs in Yellowstone National Park using citizen science data Authors: Tyler J. Brasington1,2 James C. Halfpenny3 Affiliations: 1 College of Natural Resources, Trainer Natural Resources Building, University of Wisconsin – Stevens Point, Stevens Point, WI. 54481-3897 2 The Yellowstone Grizzly Project, Jackson, WY. 83001 3 A Naturalist's World - Gardiner, MT. 59030

Introduction: Since Yellowstone National Park was established in 1872, it continues to serve as a premier opportunity for the public to observe wildlife, with grizzly bears (Ursus arctos) and the American black bears (Ursus americanus) being the highlight for a vast majority of park visitors (Skinner 1925, Schullery 1992, Wondrak-Biel 2006, Haroldson & Gunther 2013). Grizzly bears were first listed under the Endangered Species Act (ESA) in 1975. In the following decades postlisting, the estimated population grew from 200-350 bears in the 1980s (Eberhardt & Knight 1996) to roughly 600 bears in 2012 (Haroldson et al. 2013). Since the 1980s, the grizzly bear population within Yellowstone National Park (YNP) and the Greater Yellowstone Ecosystem (GYE) has had a positive trajectory (Eberhardt et al. 1994; Boyce et al. 2001; Harris et al. 2006, 2007). Grizzlies have also simultaneously increased their spatial occupancy and extent throughout the ecosystem (Schwartz et al. 2002, 2006a).

In recent years, growth rates have observably slowed (IGBST, 2012), and further research has shed light and provided evidence surrounding density-dependent effects on various aspects of bear ecology and biology (i.e., reproduction, survival) (Schwartz et al. 2006; Boyce et al. 2001).

Grizzly population density and decreasing or diminishing food availability could potentially have negative impacts on survival and reproduction; there is potential that either or the combination of these two factors have contributed to the slowing of population growth in the GYE grizzly population (Bjornlie et al. 2014). Additional research findings in combination with constant trends of unduplicated females with cubs of the year (FCOY) have suggested that the grizzly bear population may be at, or close to approaching carrying capacity (Schwartz et al. 2006c).

The overall recovery of the grizzly bear in the GYE can be hailed as one of the greatest conservation successes of our current time. The continuation of protections and research from the 1970s and forward has shed significant new developments in our understanding of bear biology, ecology, and physiology. During 1973, when open-pit garbage dumps first closed in YNP, the

Interagency Grizzly Bear Study Team (IGBST) was formed as a direct result of controversy surrounding the management and welfare of the species for the future. The research methodology and objectives of the team have remained constant over time which includes: 1) monitor the status and trend of the grizzly bear population and (2) determine patterns of habitat use by bears; relations of land management activities to the overall short and long term welfare of the grizzly bear population. Additionally, the three current objectives which help the team attain their goals: (1) unique females with cubs-of-the-year (COY) (2) radio-collaring and monitoring and (3) whitebark pine monitoring.

The IGBST records unduplicated counts of females with cubs of the year (FCOY) to gather quasi-quantitative data on the GYE grizzly population. FCOY are typically easier to count as opposed to other demographics because of their visibility, combined with their timing surrounding maternal care (Blanchard and Knight 1991; Knight et al. 1995). The IGBST uses the “Knight et al. 1995” rule to differentiate unique FCOY. This approach is very conservative, with no way to quantify the level of uncertainty, producing estimates known to be bias-low. The magnitude of this bias is directly influenced as the population continues to increase (Schwartz et al. 2008).

Monitoring and surveillance are superb applications for citizen science, requiring little if any technical or specialized equipment (Dickinson et al. 2010). Yellowstone National Park provides a unique opportunity for the utilization of citizen science, given its dedicated local community, wildlife-watching community, and continual accessibility (In prep. Brasington 2020). Citizen scientists contributed observations from 2016-present, of grizzly bears observed within Yellowstone National Park (n = 3174) (Appendix 9). During this period, citizen scientists also contributed to the identification of family groups and annual counts of unduplicated females with cubs of the year (FCOY). Integrating citizen science with agency data allows for better spatial and temporal continuity of information (In prep. Brasington 2020). The compilation of citizen science data with agency observations and information, will extend data collection capabilities and assist budget-strapped federal agencies with limited plasticity concerning finances and staff resources (In prep. Brasington 2020).

In our study, we analyzed observations of females with cubs obtained via citizen scientists between 2016-2018. We created ‘Observational Home Ranges’ (OHR) for ten females with cubs using three home range estimators: minimum convex polygons (MCP), local convex hull polygons (LoCoH.k), fixed kernel density estimation (FKDE; hLSCV & hREF).

Due to the nature of the data gathered (visual observation) as opposed to telemetry or GPS technology, we elected to differentiate our terminology from the home range to ‘observational range.’

Traditional home range sizes have been documented to reflect species response to population density or resource variability (Kjellender et al. 2004; McLoughlin & Ferguson 2000; van Beest et al. 2011). Several ursids have been observed to broaden their home range size in direct response to less desirable conditions, or changes in food availability (Garshelis & Pelton 1981; Dobey et al. 2005; Moyer et al. 2007; Brodeur et al. 2008; Koike et al. 2012). Brown bears, in comparison to other populations, exhibit a negative relationship between their home-range size and habitat productivity (Dahle & Swenson 2003; Nilsen et al. 2005).

This study intends to provide supplementary data and analysis to federal agencies to aid bear management decisions within Yellowstone National Park while providing insight to the effectiveness of home range estimators on visual observation data for grizzly bears in Yellowstone National Park.

Methods: Data in the form of observations and sightings were collected and reported via park employees, agency personnel, and citizen scientists between January 1, 2016, and December 31, 2018. Most observations and sightings of grizzly bears inside of Yellowstone National Park were acquired via ground; however, some agency sightings were documented from the air (aerial observations).

Information gathered from sightings includes sex, species, activity, location, date, time, boundary affiliation, and if cubs are present (ages of cubs) and other relevant info (if the bear was ear-tagged, radio marked, or displayed unique scarring). Citizen scientists used several platforms to document and log grizzly bear locations including but not limited to: Yellowstone SPOTR (app), Google Maps, Google Earth, Garmin 64 GPS, SpyGlass. The use of various optics, including Swarovski, Vortex, and Nikon spotting scopes (binoculars), made observing bears at a great distance possible. For this project, we did not combine agency reported data, and instead on used citizen science, or directly contributed data. To identify unduplicated females with cubs (FCOY), we followed procedures outlined by Knight et al. (1995) with slight modifications, which included physically identifiable features (Craighead et al. 1995) and photographic identification.

The Yellowstone Bear Management Office (BMO) and Yellowstone National Park GIS & Spatial Analysis Office provided necessary shapefiles including but not limited to vegetation type, bear management areas, roads, trails, and boundaries for analysis.

Home Ranges: We used visual observations obtained from citizen science contributed data for females with cubs between 2016-2018. We included females bears which recorded >1 location June or earlier, >1 location between June-September and an average of 10 locations per year (x=69.8, range = 35-185), totaling >30 locations in the three years to estimate observational home ranges.

We estimated observational home ranges (OHR) on cumulative observations within the three years (2016-2018) using 95% minimum convex polygons (MCP; Lohman-Jacoby, Duke University, in adehabitatHR for R v. 2.14.1, R Development Core Team, www.R-project.org) 95% k-local convex hull (LoCoH.k in adehabitatHR for R v. 2.14.1, R Development Core Team, www.R-project.org) and 95% fixed kernel density estimation (FKDE in adehabitatHR for R v.

2.14.1, R Development Core Team, www.R-project.org) with selected bandwidths (hREF & hLSCV) (Appendix 5, 8, 10).

For FKDE, we altered bandwidth selection using reference bandwidth (hREF) and least-squares cross-validation (hLSCV). For large datasets, only default or reference bandwidth (hREF) has been successful when generating KDE home range estimates using adehabitat and adehabitatHR (Calenge 2007, 2011). Traditionally, multimodal datasets do not produce reliable KDE home

ranges due to ‘over-smoothing’ of home ranges; multimodal distribution of documented locations is typical for many species (Worton 1995; Seaman et al. 1999). Since data collected in our study is not traditional, and strictly observational (not aided by the use of radio telemetry or GPS), we elected to make an effort to evaluate FKDE using hREF for OHR and report our results (Appendix 1, 2, 8, 10).

FKDE using hLSCV has been suggested by previous researchers in attempts to prevent oversmoothing of home ranges that result from using hREF as a bandwidth selection (Rodgers & Kie 2010). FKDE using hLSCV has historically been used on VHF datasets with great success; however, its use to evaluate GPS datasets has been minimally explored. FKDE using hLSCV also performs better on data, identifying distributions with tight clumps; the chance of failure drastically increases when datasets are increasingly large and when distributions have very tight clusters of locations (Gitzen et al. 2006, Pellerin et al. 2008, Walter et al. 2011). However, regardless of modifications and changes we made to hlim or the extent, hLSCV would not converge for any of our grizzly family groups. We jittered all locations for each family group 500m for better presentation in our data and to allow convergence. Because FKDE using hLSCV has been so successful on VHF datasets, we used this method to evaluate OHR as the sample size is comparable (Appendix 3, 4 , 8).

LoCoH is a non-parametric kernel method, which generalizes the minimum convex polygon method, and produces bounded home ranges (Getz et al. 2007, Getz and Wilmers 2004). LoCoH has three modifications, which include: fixed k (k-NNCH), fixed radius (r-NNCH), and adaptive (a-NNCH). For our purposes, we chose to use LoCoH.k (fixed k). We graphed area versus ‘k’ to choose the optimal value for each family group, similar to what has been previously used in grizzly bear home range creation (Bjornlie et al. 2014). Previous methods have utilized LoCoH.a, using the maximum distance between any two locations in each bear’s data as the initial ‘a’ value. We recognize the importance of evaluating LoCoH as an OHR estimator, as this method reduces Type I error by excluding areas not utilized (Lichti & Swihart 2011); other methods such as MCP and FKDE tend to overestimate home range size (Burgman & Fox 2003) (Appendix 7, 8, 10).

Habitat & Vegetation Preference: In our study, we evaluated habitat and vegetation preference using LoCoH.k OHR to clip vegetation and habitat available to each family group (ArcGIS v.

10.0, Environmental Systems Research Institute, Inc., Redlands, CA). We recognize that because our data is strictly observational and does not include traditional methods of VHF or GPS use, that this particular dataset may not be the best method available to evaluate preference, avoidance, or selection of habitat and vegetation for grizzly bears. However, direct observation has been widely used as a technique for estimating food habits of large herbivores, watched through binoculars, or spotting scopes (Litvaitis, Titus & Anderson 1996).

For our study purpose, we approached evaluating habitat preference using procedures outlined

by Neu et al. (1974) and Byers et al. (1984). This method is extremely straightforward, combining an initial chi-square comparison with confidence intervals on practical use. We generated the expected habitat type and locations by using the portion of each family group LoCoH.k OHR. Observed use was documented by the presence in given vegetation or habitat type. By comparing the confidence interval on practical use to the proportion of the LoCoH.k OHR, we hope to evaluate the selection and avoidance of specific habitat and vegetation types (Appendix 11).

Results: We monitored ten female grizzly bear families between 2016-2018, which met our criteria for observational home-range (OHR) evaluation. These family groups recorded a cumulative average (three-year total) 69.8 observations demonstrating a range of 35-185 observations (Table 1.1). The ten family groups also averaged 5.3 months observed, accounting for 66% of the known active period (8-months; April-November). The largest home ranges attained by a grizzly bear family groups recorded using home range methods: MCP = 333 km2; LoCoH.k = 65 km2; FKDE(hLSCV) = 119 km2; FKDE(hREF) = 911 km2 (Table 1.1). Four home range methods we used to calculate OHR for individual grizzly family groups averaged: MCP method at 83 km2 with a standard deviation of 108 km2; LoCoH.k method at 25 km2 with a standard deviation of 19 km2; FKDE(hLSCV) at 42 km2 with a standard deviation of 30 km2; FKDE(hREF) at 252 km2 with a standard deviation of 295 km2 (Table 1.2). The two home range estimators with the lowest variance were (1) LoCoH.k and (2) FKDE (hLSCV); the home range estimator, which exhibited the greatest variance, was FKDE (hREF) (Figure 1.1).

Of the ten grizzly family groups monitored during our study, four groups demonstrated no significance based on our chi-square test. Based on these results, we could conclude that these four bears (F23, GB 980, F32, and F13) were using their habitat types in proportion to their availability within their LoCoH.k OHR (Tables 1.3-1.13). Six groups (F05, F20, F5A, F3A, GB 815, GB 663) demonstrated high significance with their chi-square results, concluding that they were not using their habitat types (Appendix 11) in proportion to their availability within their LoCoH.k OHR. We examine the selection and avoidance of each habitat type by constructing confidence intervals (a = 0.05) for the proportion of use in each type using the following formula:

Where z is the z-score, p is the population proportion, and n is the sample size. Since our a = 0.05 our z-score value was 1.96. By comparing established confidence intervals on the practical use to the proportion of the LoCoH.k OHR in each habitat type, we could designate selected habitat types and avoided habitat types for each of the six groups (Tables 1.3-1.13).

Discussion: Citizen science can help play a critical role in the monitoring initiatives of grizzly bears within the Greater Yellowstone Ecosystem (GYE). Here we demonstrate reliable and quality data gathered to evaluate the ability to use home range estimators to create observational home ranges (OHR) for females with cubs. Additionally, citizen scientist observations of unduplicated females with cubs-of-the-year could supplement agency data and provide less conservative data for use in population estimates. While agencies have strict protocol and methodology for recording counts of unduplicated FCOY, supplementary data from citizen scientists could help build stronger relationships with the general public, while contributing to scientific processes.

In our study, we documented smaller home range sizes for female groups in the northern range of Yellowstone National Park than in other areas. Based on overall sightings between 20162018, it is visibly apparent that density in the Lamar Valley region and northern range may be higher than other areas of the park. With this in mind, the highest number of unduplicated sightings in a single day in the Lamar Valley yielded 31 different grizzly bears. Conservative estimates place the grizzly population in Yellowstone at roughly 130-150 bears with home ranges partially or entirely inside of the park.

Previous literature has reflected that female grizzly bears in the GYE, home-range size are more strongly impacted with population density as opposed to availability of whitebark pine and other food sources (Bjornlie et al. 2014). The relationship between population density and home-range size is not something new or surprising, especially considered dispersal and matrilineal home ranges (Dahle & Swenson 2003; Schwartz et al. 2003). Male grizzly bears are less affected by changes in population density because their home ranges are relatively large, allowing them to maximize their breeding ability across the landscape while simultaneously accessing high-quality food resources (Bjornlie et al. 2014). Female home-range sizes decrease as population density increases, potentially through means of competition for available space, avoidance behavior, and foraging ability while other bears saturate high-quality habitats (Wolff 1985; Ambramsky & Tracy 1980; Oli, Jacobson & Leopold 2002).

We also documented that FKDE using hREF as a bandwidth, does not produce quality observational home ranges (OHR) for visual observations, and grossly exaggerates OHR. Oversmoothing, which has been reported by other research for the utilization of FKDE, was apparent in our constructed ranges. However, FKDE using hLSCV bandwidth produced consistent observational ranges for all bears and exhibited one of the lowest variances, second to the LoCoH.k method. The LoCoH and MCP methods have been used by researchers previously in the GYE to estimate home ranges for grizzly bears, demonstrating reliable success. We have found for observational home ranges that most sightings (>45%) take place within .75 miles of given roadways in Yellowstone National Park. We acknowledge that by not being able to observe far distances in other sections of the park, could hamper or skew data for ranges constructed in the south or central regions; large open spaces, such as Hayden Valley and Lamar Valley, or Swan Lake Flats, where observers may see miles from the roadway, maybe better areas for using our observational home range techniques.

Supporting Information: Appendix 1: Fixed Kernel Density Estimate Raster (FKDE) using hREF for Grizzly bear observations via adehabitatHR in R Appendix 2: Fixed Kernel Density Estimates (FKDE) using href for home range estimation via adehabitatHR in R Appendix 3: Fixed Kernel Density Estimate Raster (FKDE) using hLSCV for Grizzly bear observations via adehabitatHR in R Appendix 4: Fixed Kernel Density Estimate (FKDE) using hLSCV for home range estimation via adehabitatHR in R

Appendix 5: Minimum Convex Polygons (MCP) for home range estimation via adebhabitatHR in R **Appendix 6: Convex Hull Polygon Estimate (CHP) for home range estimation via adehabitat in R (not in text; additional resource) Appendix 7: Local Convex Hull Polygon Estimates (LoCoH.k) using k for home range estimation via adehabitatHR in R Appendix 8: Home range estimation methods combined (LoCoH, FKDE (hREF & hLSCV), MCP) Ex: Grizzly F5A Appendix 9: Compiled Grizzly bear Observations during 2016-2018 Appendix 10: Home range estimation methods by individual female (LoCoH, FKDE (hREF), MCP) Appendix 11: Habitat & Vegetation Type Breakdown by Home range estimation method (LoCoH, FKDE (hREF), MCP) Appendix 12: Scripts for observation home ranges (MCP, FKDE: hREF & hLSCV, LoCoH.k) Appendix 13: Chi-square (x2) distribution table Figure 1.1: Observational home range (OHR) size comparisons based on home-range estimation methods and number of observations Table 1.1: Observational home ranges (OHR) measured for ten female grizzly bears with cubs monitored between 2016-2018. All observations and locations were reported by citizen scientists. Four different home range methods were used including 95% minimum convex polygon (MCP) method, 95% local convex hull polygon (LoCoH.k) method, 95% fixed kernel density estimation (FKDE) using two different bandwidth calculations: least squares cross validation (hLSCV) and reference bandwidth (hREF). *Using FKDE, hLSCV we jittered locations 500m from their original placement to allow hLSCV to converge.

Table 1.2: Four averaged home range methods to estimate observational home ranges (OHR) for ten female grizzly bears with cubs between 2016-2018: 95% minimum convex polygon (MCP) method, 95% local convex hull polygon (LoCoH.k) method, 95% fixed kernel density estimation (FKDE) using two different bandwidth calculations: least squares cross validation (hLSCV) and reference bandwidth (hREF). *Using FKDE, hLSCV we jittered locations 500m from their original placement to allow hLSCV to converge.

Table(s) 1.3-1.13: LoCoH.k OHR clipped region breakdown by habitat type for individual family groups & Analyses of LoCoH.k OHR clipped regions evaluating selection and avoidance of habitat and vegetation type for individual family groups

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42. Schullery, P. (1992) The bears of Yellowstone. High Plains, Worland, Wyoming, USA. 43. Schwartz, C. C., Haroldson, M. A., Cherry, S., & Keating, K. A. (2008). Evaluation of rules to distinguish unique female grizzly bears with cubs in Yellowstone. The Journal of Wildlife Management, 72(2), 543-554.

44. Schwartz, C. C., Haroldson, M. A., Gunther, K. A., Moody, D. (2002) Distribution of grizzly bears in the Greater Yellowstone Ecosystem, 1990-2000. Ursus 13:203-212.

45. Schwartz, C. C., Haroldson, M. A., Gunther, K. A., Moody, D. (2006a) Distribution of grizzly bears in the Greater Yellowstone Ecosystem in 2004. Ursus 17:63-66.

46. Schwartz, C. C., Haroldson, M. A., White, G. C. (2006c) Survival of cub and yearling grizzly bears in the Greater Yellowstone Ecosystem, 1983–2001. Pages 33–43 in C.C. Schwartz, M.A. Haroldson, G.C. White, R. B. Harris, S. Cherry, K. A. Keating, D. Moody and C. Servheen, authors. Temporal, spatial, and environmental influences on the

demographics of grizzly bears in the Greater Yellowstone Ecosystem. Wildlife Monographs 161.

47. Schwartz, C. C., Haroldson, M. A., White, G. C., Harris, R. B., Cherry, S., et al. (2006) Temporal, spatial, and environmental influences on the demographics of grizzly bears in the Greater Yellowstone Ecosystem. Wildlife Monographs 161: 1–68. doi:10.2193/00840173(2006)161[1:TSAEIO]2.0.CO;2.

48. Schwartz, C. C., Miller, S. D., & Haroldson, M. A. (2003). Grizzly bear. Wild mammals of North America: biology, management, and conservation, 556-586.

49. Seaman, D. E., Millspaugh, J. J., Kernohan, B. J., Brundige, G. C., Raedeke, K. J., & Gitzen, R. A. (1999). Effects of sample size on kernel home range estimates. The journal of wildlife management, 739-747.

50. Skinner, M. P. (1925) Bear in the Yellowstone. A. C. McClurg & Co., Chicago, Illinois, USA. 51. van Beest, F. M., Rivrud, I. M., Loe, L. E, Milner, J. M., Mysterud, A. (2011) What determines variation in home-range size across spatiotemporal scales in a large browsing herbivore? Journal of Animal Ecology 80: 771–785. doi:10.1111/j.1365.2656.2011.01829.x.

52. Walter, W. D., Fischer, J. W., Baruch-Mordo, S., & VerCauteren, K. C. (2011). What is the proper method to delineate home range of an animal using today’s advanced GPS telemetry systems: the initial step. Modern telemetry, 68.

53. Wolff, J. O. (1985). The effects of density, food, and interspecific interference on home range size in Peromyscus leucopus and Peromyscus maniculatus. Canadian Journal of Zoology, 63(11), 2657-2662.

54. Wondrak-Biel, A. (2006) Do not feed the bears, the fitful history of wildlife and tourists in Yellowstone. University Press of Kansas, Lawrence, Kansas, USA. 55. Worton, B. J. (1995). Using Monte Carlo simulation to evaluate kernel-based home range estimators. The Journal of wildlife management, 794-800.

Appendix 12: (1) FKDE using hREF: library(sp) library(rgdal) library(raster)

panther<-read.csv("pantherjitter.csv", header=T) str(panther) panther$CatID <- as.factor(panther$CatID) #Note below the code uses the original adehabitat package to run home range library(adehabitat) loc <- panther[, c("X", "Y")] ## Estimation of UD for each animal separately id <- panther[, "CatID"] udbis <- kernelUD(loc, id, h = "href") ud <- kernelUD(loc, id = id, h = "href", grid = 40, same4all = FALSE, hlim = c(0.1, 1.5), kern = c("bivnorm"), extent = 0.5) image(ud) ## Note that the contours are under the locations

## Calculation of the 95 percent home range ver <- getverticeshr(ud, 95) plot(ver)

## Look at the estimates of home range by contour cuicui1 <- kernel.area(loc, id) plot(cuicui1) cuicui1 # write output #write.table(cuicui1,"output.csv", row.names=TRUE, sep=" ", col.names=TRUE, quote=TRUE, na = "NA") ######################################################### # OVERRIDE the default kver2spol function so that we can #include the projection info ######################################################## kver2spol <- function(kv,projstr) { x <- kv if (!inherits(x, "kver")) stop("x should be of class \"kver\"") if (!require(sp)) stop("sp package needed") lipols <- lapply(1:length(x), function(i) { y <- x[[i]] class(y) <- c("data.frame", "list") res <- split(y[, 2:3], y[, 1])

lipol <- lapply(res, function(z) { if (sum(abs(z[1, ] - z[nrow(z), ])) > 1e-16) z <- rbind(z, z[1, ]) Polygon(as.matrix(z)) }) pols <- Polygons(lipol, ID = names(x)[i]) return(pols) }) return(SpatialPolygons(lipols, proj4string=CRS(as.character(projstr)))) }

#################################################### # Function to export specific levels of isopleths of # a "kv" object ####################################################

#Code creates contours for each animal at each level kv<-list() class(kv) <- "kver"

kvtmp <- getverticeshr(udbis, lev = 99) kv$KHR99<- kvtmp[[1]] kvtmp <- getverticeshr(udbis, lev = 95) kv$KHR95<- kvtmp[[1]] kvtmp <- getverticeshr(udbis, lev = 90) kv$KHR90<- kvtmp[[1]] kvtmp <- getverticeshr(udbis, lev = 75) kv$KHR75<- kvtmp[[1]] kvtmp <- getverticeshr(udbis, lev = 50) kv$KHR50<- kvtmp[[1]] kvtmp <- getverticeshr(udbis, lev = 25) kv$KHR25<- kvtmp[[1]]

spolTmp <- kver2spol(kv,"+proj=utm +zone=17 +ellps=WGS84") dfTmp <- data.frame(Isopleth=c("99","95","90","75","50","25"),row.names=c("KHR99","KHR95","KHR90","KHR75","KHR50","KHR25")) spdfTmp <- SpatialPolygonsDataFrame(spolTmp, dfTmp, match.ID = TRUE) writeOGR(spdfTmp,"HREF","FP048HREF", "ESRI Shapefile")

kvtmp <- getverticeshr(udbis, lev = 99) str(kvtmp) plot(kvtmp[[2]]) kv$KHR99<- kvtmp[[2]] kvtmp <- getverticeshr(udbis, lev = 95) kv$KHR95<- kvtmp[[2]]

kvtmp <- getverticeshr(udbis, lev = 90) kv$KHR90<- kvtmp[[2]] kvtmp <- getverticeshr(udbis, lev = 75) kv$KHR75<- kvtmp[[2]] kvtmp <- getverticeshr(udbis, lev = 50) kv$KHR50<- kvtmp[[2]] kvtmp <- getverticeshr(udbis, lev = 25) kv$KHR25<- kvtmp[[2]]

spolTmp <- kver2spol(kv,"+proj=utm +zone=17N +ellps=WGS84") dfTmp <- data.frame(Isopleth=c("99","95","90","75","50","25"),row.names=c("KHR99","KHR95","KHR90","KHR75","KHR50","KHR25")) spdfTmp <- SpatialPolygonsDataFrame(spolTmp, dfTmp, match.ID = TRUE) writeOGR(spdfTmp,"HREF","FP094HREF", "ESRI Shapefile")

#OR

#Using the "adehabitatHR package library(adehabitatHR) #Let's select only one animal panther <- subset(panther, panther$CatID == "143") panther$CatID <- factor(panther$CatID) loc <- data.frame("x"=panther$X,"y"=panther$Y) proj4string <- CRS("+proj=utm +zone=17N +ellps=WGS84") cats <- SpatialPointsDataFrame(loc,panther, proj4string = proj4string) udbis <- kernelUD(cats[,1], h = "href") image(udbis)

ver <- getverticeshr(udbis, standardize = FALSE) ver50 <- getverticeshr(udbis, percent=50) ver80 <- getverticeshr(udbis, percent=80) ver90 <- getverticeshr(udbis, percent=90) ver95 <- getverticeshr(udbis, percent=95) ver99 <- getverticeshr(udbis, percent=99) ver plot(ver99, col="grey",axes=T);plot(ver95, add=T);plot(ver90, add=T);plot(ver80, add=T);plot(ver50, add=T) points(cats)

(2) FKDE using hLSCV: library(adehabitatHR) library(sp)

panther <-read.csv("pantherjitter.csv", header=T) str(panther)

loc <- data.frame("x"=panther$X,"y"=panther$Y) proj4string <- CRS("+proj=utm +zone=17N +ellps=WGS84")

pantherspdf <- SpatialPointsDataFrame(loc,panther, proj4string = proj4string) plot(pantherspdf, col=pantherspdf$CatID)

## Example of estimation using LSCV udbis2 <- kernelUD(pantherspdf[,2], h = "href", hlim = c(10,50),extent=1) image(udbis2)

#Now change h to href for comparison to LSCV later

## Compare the estimation with ad hoc and LSCV method ## for the smoothing parameter cuicui2 <- kernel.area(udbis2) cuicui2

#Note that regardless of change hlim or extent, LSCV will not converge for these animals so let's try #a trick here. I believe LSCV is a poor estimator with GPS locations being too numerous #and very close together compared to traditional VHF datasets which LSCV were originally evaluated. #So lets jitter locations 50 meters from their original location and try again.

## Example of estimation using LSCV panther$jitterX <- jitter(panther$X, factor=500) panther$jitterY <- jitter(panther$Y, factor=500) locjitter <- data.frame("x"=panther$jitterX,"y"=panther$jitterY) proj4string <- CRS("+proj=utm +zone=17N +ellps=WGS84") jitterspdf <- SpatialPointsDataFrame(locjitter,panther, proj4string = proj4string) plot(jitterspdf, col=pantherspdf$id) points(pantherspdf, col="blue") udbis3 <- kernelUD(jitterspdf[,2], h = "LSCV")#, hlim = c(1, 5),extent=1) image(udbis3)

#Now rerun with jitter factor = 100 then 500 instead of 50 and see what happens?

cuicui3 <- kernel.area(udbis3) ## LSCV cuicui3

#Now rerun with jitter factor = 500 instead of 100 and see what happens?

iso <- cbind(cuicui2,cuicui3) colnames(iso) <- c("FP121_lscv","FP143_lscv","FP121_Jitter","FP143_Jitter") iso

(3) LoCoH using k: library(adehabitatHR) library(shapefiles) library(rgeos) library(rgdal)

library(maptools)

#Get input file panther <- read.csv("pantherjitter2.csv") str(panther) panther$CatID <- as.factor(panther$CatID)

#Or explore with one panther with 381 relocations cat159 <- subset(panther, CatID=="159") str(cat159) cat159$CatID <- factor(cat159$CatID)

#Get the relocation data from the source file data.xy = cat159[c("x","y")]

xysp <- SpatialPoints(data.xy)

#Creates a Spatial Data Frame from sppt<-data.frame(xysp) #Creates a spatial data frame of ID idsp<-data.frame(cat159[1]) #Adds ID and Date data frame with locations data frame coordinates(idsp)<-sppt proj4string(idsp) <- CRS("+proj=utm +zone=17 +ellps=WGS84") locsdf <-as.data.frame(idsp) head(locsdf) ## Shows the relocations plot(data.xy, col="red") locsdf[1:5,] table(panther$CatID)

## Examinates the changes in home-range size for various values of k ## Be patient! the algorithm can be very long ar <- LoCoH.k.area(idsp, k=c(15:25)) ## 24 points seems to be a good choice (rough asymptote for all animals) ## the k-LoCoH method: nn <- LoCoH.k(idsp[,1], k=19) ## Graphical display of the results plot(nn, border=NA) ## the object nn is a list of objects of class ## SpatialPolygonsDataFrame length(nn) names(nn) class(nn[[1]]) ## shows the content of the object for the first animal as.data.frame(nn[[1]])

## The 95% home range is the smallest area for which the ## proportion of relocations included is larger or equal ## to 95% In this case, it is the 339th row of the ## SpatialPolygonsDataFrame. plot(nn[[1]][339,],lwd=2)

#The 50% home range code is on line 146 plot(nn[[1]][146,],add=TRUE)

#The 99% home range code is on line 359 plot(nn[[1]][359,],lwd=3, add=TRUE)

#Save shapefiles of resulting home range ver <- getverticeshr(nn) ver plot(ver) writeOGR(ver,dsn="FixedK",layer="FixedK24", driver = "ESRI Shapefile", overwrite=TRUE) ##Overwrite will not work so must edit path so "FixedK" folder is created with code below. ver50 <-getverticeshr(nn, percent=50) writeOGR(ver50,dsn="FixedK",layer="50FixedK24", driver = "ESRI Shapefile",overwrite=TRUE) ver95 <-getverticeshr(nn, percent=95) writeOGR(ver95,dsn="FixedK",layer="95FixedK24", driver = "ESRI Shapefile",overwrite=TRUE) ver99 <-getverticeshr(nn, percent=99) writeOGR(ver99,dsn="FixedK",layer="99FixedK24", driver = "ESRI Shapefile",overwrite=TRUE)

Appendix 1: Fixed Kernel Density Estimate Raster (FKDE) using hREF for Grizzly bear observations via adehabitatHR in R

adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

GB 815

Latitude

Latitude

Latitude

Longitude

F05

Latitude

Latitude

Latitude

F13

Longitude

Longitude

Longitude

GB 663

F20

Latitude

Latitude

F3A

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Longitude

Longitude

GB 980

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F23

F32

Longitude

Longitude

GB 815

Longitude

F3A

F05

Latitude

Latitude

F20

Longitude

Latitude

Latitude

Longitude

Latitude

F32

Latitude

F23

Longitude

Longitude

Longitude

GB 663

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GB 980

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F13

Longitude

Longitude

Longitude

Appendix 2: Fixed Kernel Density Estimates (FKDE) using href for home range estimation via adehabitatHR in R

adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

Longitude

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GB 815- 95% FKDE h = href

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F23- 95% FKDE h = href

GB 663- 95% FKDE h = href

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F13- 95% FKDE h = href

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F3A- 95% FKDE h = href

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GB 980- 95% FKDE h = href

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F20- 95% FKDE h = href

F32- 95% FKDE h = href

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F05 - 95% FKDE h = href

Longitude

Longitude

Appendix 3: Fixed Kernel Density Estimate Raster (FKDE) using hLSCV for Grizzly bear observations via adehabitatHR in R

adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

F05 - 95% FKDE h = hLSCV

F32- 95% FKDE h = hLSCV

F20- 95% FKDE h = hLSCV

GB 980- 95% FKDE h = hLSCV

F3A- 95% FKDE h = hLSCV

GB 815- 95% FKDE h = hLSCV

F23- 95% FKDE h = hLSCV

F13- 95% FKDE h = hLSCV

GB 663- 95% FKDE h = hLSCV

Appendix 4: Fixed Kernel Density Estimate (FKDE) using hLSCV for home range estimation via adehabitatHR in R

adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

F05 - 95% FKDE h = hLSCV - 500m jitter

F32- 95% FKDE h = hLSCV - 500m jitter

F20- 95% FKDE h = hLSCV - 500m jitter

GB 980- 95% FKDE h = hLSCV - 500m jitter

F3A- 95% FKDE h = hLSCV – 500m jitter

GB 815- 95% FKDE h = hLSCV – 500m jitter

F23- 95% FKDE h = hLSCV – 500m jitter

F13- 95% FKDE h = hLSCV – 500m jitter

GB 663- 95% FKDE h = hLSCV – 500m jitter

Appendix 5: Minimum Convex Polygons (MCP) for home range estimation via adehabitatHR in R

adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

Longitude

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Latitude

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F05 – 95% MCP

F13 – 95% MCP

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GB 663 – 95% MCP

F20 – 95% MCP

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F3A – 95% MCP

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GB 980 – 95% MCP

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F23 – 95% MCP

F32 – 95% MCP

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GB 815 – 95% MCP

Longitude

Longitude

Appendix 6: Convex Hull Polygon Estimates (CHP) for home range estimation via adehabitat in R

adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

F05 – CHP (20-100%)

F32 – CHP (20-100%)

F20 – CHP (20-100%)

GB 980 – CHP (20-100%)

F3A – CHP (20-100%)

GB 815 – CHP (20-100%)

F23 – CHP (20-100%)

F13 – CHP (20-100%)

GB 663 – CHP (20-100%)

F32 – 95% CHP

Longitude

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F23 – 95% CHP

GB 663 – 95% CHP

F13 – 95% CHP

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F3A – 95% CHP

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Appendix 7: Local Convex Hull Polygon Estimates (LoCoH.k) using k for home range estimation via adehabitatHR in R adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

F05 – LoCoH.k (20-100%)

F32 – LoCoH.k (20-100%

GB 980 – LoCoH.k (20-100%)

F3A – LoCoH.k (20-100%)

F23 – LoCoH.k (20-100%)

F13 – LoCoH.k (20-100%)

F20 – LoCoH.k (20-100%)

GB 815 – LoCoH.k (20-100%)

GB 663 – LoCoH.k (20-100%)

F3A – 95% LoCoH.k k = 24

Latitude

Latitude

GB 980 – 95% LoCoH.k k = 21

Longitude

GB 815 – 95% LoCoH.k k = 24

Longitude

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F13 – 95% LoCoH.k k = 16

GB 663 – 95% LoCoH.k k = 24

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F23 – 95% LoCoH.k k = 21

Longitude

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Longitude

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F20 – 95% LoCoH.k k = 21

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F32 – 95% LoCoH.k k = 19

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F05 – 95% LoCoH.k k = 22

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Appendix 8: Home range estimation methods combined (LoCoH, FKDE (hREF & hLSCV), MCP) EX: Grizzly F5A

adehabitatHR for R v. 2.14.1 R-Development Core Team www.R-project.org

Latitude

Longitude

Longitude

F5A – 95% FKDE h = href

F5A – KDE Raster (3)

Latitude

F5A – KDE Raster (2)

Latitude

F5A – KDE Raster (1)

F5A – 20-100% LoCoH k = 18

Latitude

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F5A – 95% LoCoH k = 18

Longitude

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F5A – 95% MCP

Longitude

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F5A – 95% FKDE (hLSCV)

F5A – 95% FKDE (hLSCV)

Appendix 9: Compiled Grizzly bear Observations during 2016-2018

ArcGIS v. 10.0, Environmental Systems Research Institute , Inc., Redlands, CA., USA.

Appendix 10: Home range estimation methods by individual female (LoCoH, FKDE (href), MCP)

ArcGIS v. 10.0, Environmental Systems Research Institute , Inc., Redlands, CA., USA.

Observations of Grizzly F23 (2016-2018) in Yellowstone National Park

Observational Home Range (OHR) Grizzly F23 Yellowstone National Park

Observational Home Range (OHR) Grizzly F23 Yellowstone National Park

Observational Home Range (OHR) Grizzly F23 Yellowstone National Park

Appendix 11: Habitat & Vegetation Type Breakdown

by Home range estimation method (LoCoH, FKDE (href), MCP) Note: Habitat types instead of being listed directly on the map in a legend are instead consolidated into general vegetation and habitat categories.

Please refer to Tables 1.3-1.13 for more information.

ArcGIS v. 10.0, Environmental Systems Research Institute , Inc., Redlands, CA., USA.

Figure 1.1: Observational home range (OHR) size comparisons based on home-range estimation methods and number of observations

Appendix 13: Chi-square (x2) distribution table (Degrees of freedom (df)