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1 ESTIMATING SLOTH BEAR ABUNDANCE FR OM REPEATED PRESENCE-ABSENCE DATA IN NAGARAHOLE-BANDIPUR NATIONAL PARKS, INDIA By ARJUN MALLIPATNA GOPALASWAMY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006
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2 Copyright 2006 By Arjun Mallipatna Gopalaswamy
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3 To all who wish to save wildlife
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4 ACKNOWLEDGMENTS Without the support and encouragement of th e following people and organizations, this project would not have been possible. Generous funding and logistical support were provided by Dexter Fellowship; Jennings Scholarship; Univers ity of Florida, Depart ment of Wildlife Ecology and Conservation; Wildlife Conservation Society, India Program. I thank the Centre for Wildlife Studies (CWS), Bangalore, India, for providing fr om their database the sloth bear photographs used in this analysis. I acknowledge with greatest appreciation my advisor and committee chair, Dr. Melvin Sunquist, for leading me through my masters program and always being there to provide encouragement, wisdom and advice. I wish to ex press my gratitude to Dr. Robert Dorazio, who spent great volumes of his time in helping me analyze my data. I thank Dr. Madan Oli for giving me important comments and advice on my dr afts. I also thank Dr. Ramon Littell for his comments. I wish to specially thank Dr. Susa n Jacobson, who periodi cally encouraged my progress. I am also grateful to my academic supervisor, Dr. K. Ullas Karanth, and field supervisor, Mr. N. Samba Kumar, when I worked at CWS. Their skills and encouragement have enriched my life and this thesis. I would also like to express my gratitude to all Centre for Wildlife Studies field staff, Raghavendra Mogar oy, Narendra Patil, Anirban Da tta Roy, Vivek Ramachandran, Varun Goswami, Mathew James and Dhanapal. I wish to specially thank Kaavya Nag who meticulously compiled the sloth bear data. I than k the Centre for Wildlif e Studies administrative staff, K. V. Phaniraj and P. Mohan Kumar, who ab ly provided the logistic s upport in this project. Finally, I owe my deepest gratitude to my fa mily and friends who have encouraged me at all times.
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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ..............9 CHAPTER 1 INTRODUCTION................................................................................................................. .11 Background..................................................................................................................... ........11 Monitoring Sloth Bears......................................................................................................... ..11 2 PARAMETER ESTIMATION OF THE ROYLE AND NICHOLS (2003) MODEL USING BAYESIAN MARKOV CHAI N MONTE CARLO SIMULATION APPROACH WITH THE GIBB S SAMPLER ALGORITHM..............................................14 Introduction................................................................................................................... ..........14 Methods........................................................................................................................ ..........16 Royle and Nichols (2003) Model....................................................................................16 Parameter Estimation Using the Likelihood-Based Approach........................................17 Parameter Estimation Using the Bayesian Approach......................................................17 The Gibbs Sampler Algorithm for the Royle and Nichols (2003) Model.......................20 Simulation Design...........................................................................................................20 Results........................................................................................................................ .............21 Conclusions and Discussion...................................................................................................22 3 ESTIMATION OF SLOTH BEAR ABUN DANCE USING REPEATED PRESENCEABSENCE DATA IN NAGARAHOLE-BAND IPUR NATIONAL PARKS, INDIA.........26 Introduction................................................................................................................... ..........26 Study Design................................................................................................................... ........27 Study Area..................................................................................................................... ..27 Nagarahole...............................................................................................................27 Bandipur...................................................................................................................28 Methods........................................................................................................................ ..........29 Field Methods.................................................................................................................. 29 Application of the Royle and Nichols (2003) Model......................................................30 Definition of sites.....................................................................................................30 Selection of home range sizes for analysis...............................................................31 Constant r .................................................................................................................32 Capture histories for sloth bears...............................................................................33
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6 Selection of the mass function to model abundance................................................33 Parameters for the prior distribution of .................................................................33 Analysis of actual data.............................................................................................34 Results........................................................................................................................ .............35 Conclusions and Discussion...................................................................................................36 4 CONCLUSIONS AND DISCUSSION..................................................................................46 LIST OF REFERENCES............................................................................................................. ..47 BIOGRAPHICAL SKETCH.........................................................................................................51
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7 LIST OF TABLES Table page 2-1 Simulation results for the likelihood-b ased inference. The true values of r and were set at 0.3 and 10 during the simulation. In each case, 1000 data sets were simulated.......23 2-2 The results of the Gibbs sampler algorithm. The likelihood estimates for thesame data set were obtained using the BFGS algorithm for optimization..................................24 2-3 The results of the Gibbs sampler algorithm. The likelihood estimates for the same data set were obtained using the BFGS.............................................................................24 3-1 Sampling effort at ea ch camera trap location....................................................................39 3-3 Posterior summary statistics by ensuri ng independence between sites with prior distribution for ~Gamma(2, 4.5)......................................................................................40 3-4 Posterior summary statistics by ensuri ng independence between sites with prior distribution for ~Gamma(4.5, 2)......................................................................................40 3-5 Posterior summary statistics (relaxing site independence) with prior distribution for ~Gamma(2, 4.5)...............................................................................................................41 3-6 Posterior summary statistics (relaxing site independence) with prior distribution for ~Gamma(4.5, 2)...............................................................................................................41
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8 LIST OF FIGURES Figure page 2-1 Prior and posterior distributions for when R =50 and when T= 10. A) Prior distribution of with shape = 10 and scale = 1. B)..........................................................25 3-1 Map of the study area comprising of th e Bandipur and Nagarahole National Parks.........42 3-2 A sloth bear photograph ta ken from a camera trap............................................................42 3-3 Sloth bear detections (y ear 2004) are shown with black (dark) dots. The other dots represent camera traps that di d not detect sloth bears........................................................43 3-4 Sloth bear detections (y ear 2005) are shown with black (dark) dots. The other dots represent camera traps that di d not detect sloth bears........................................................43 3-5 A selection of 10 km2 sites using ArcView 3.2 GIS software. The dots within each site are the camera traps used for analysis.........................................................................44 3-6 An example random grid generated using ArcView 3.2 software with cell size of 10 km2. Here each cell containing camera traps.....................................................................44 3-7 Gamma(2, 4.5) prior distribution.......................................................................................45 3-8 Gamma(4.5, 2) prior distribution.......................................................................................45
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9 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ESTIMATING SLOTH BEAR ABUNDANCE FROM REPEATED PRESENCE-ABSENCE DATA IN NAGARAHOLEBANDIPUR NATIONAL PARKS, INDIA By Arjun Mallipatna Gopalaswamy December 2006 Chair: Melvin Sunquist Major Department: Wildlife Ecology and Conservation It is notoriously difficult to estimate the a bundance of bears in gene ral and most methods that are currently available are too cons umptive of time and effort. Sloth bears ( Melursus ursinus ) pose very similar challenges to field biol ogists trying to estimate their abundances. I investigated the possibility of estimati ng abundance of sloth bears using presenceabsence data from repeated samples from camera traps. The simulation results generated from the likelihood estimator for small sample sizes showed a positive bias for the mean abundance per site. To more effectively use data with small samp le sizes, a Bayesian approach to the problem was developed so that an informative prior coul d influence the parameter values to a reasonable range. A Bayesian Markov Chain Monte Carlo s imulation procedure using the Gibbs sampler algorithm was developed. Data were analyzed using two ideas of bear movement that are incorporated into the model. Data were first analyzed with the inten tion of maintaining the id ea of site independence to ensure that a bear will not occur in two sites during the samp ling period. This restricted the data set and the uncertainties in the parameter estimates were found to be very high. To
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10 incorporate the missing data, and include more sites into the problem, another assumption was introduced in the model that the immigration a nd emigration rates to and from a site was a constant. However, the abundance estimates ge nerated by this proce dure were also highly variable. The key issue that emerged from this st udy was the exceedingly low animal-specific detection probability (between 0.03 and 0.12). This suggested the need for an improved method in photographing bears both in term s of increasing spatial replicat es and the actual placement of camera traps for reliable estimates of abundan ce. With an improved study design, the suggested approach may still seem very plausibl e to estimate sloth bear abundances.
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11 CHAPTER 1 INTRODUCTION Background A variety of methods are available for estim ating animal abundances (Lancia, Nichols & Pollock, 1994), but all involve the issue of estimating detection pr obabilities for specific kinds of count statistics (Buckland, Anderson, Burnham, Laake, Borchers & Thomas, 2001; Seber, 1982; Williams, Nichols and Conroy, 2002). Depending on the species being studied, the techniques available for gathering appropriate data, and in corporating the limitations of time, money and effort, only one or just a few of these met hods may be suitable. Capture-recapture methods require repeated efforts to cap ture or observe animals (Otis, Burnham, White & Anderson, 1978; Pollock, Nichols, Brownie & Hines, 1990) and even observation-based methods such as distance sampling (Buckland et al. 2001) or multiple observers (Cook & Jacobson, 1979; Nichols, Hines, Sauer, Fallon, Fallon & Heglund, 2000) are viewed as being too time and effort consuming (Royle & Nichols, 2003). Despite the logistical co nstraints, these methods have been widely applied to estimation of large mammal abundance. Monitoring Sloth Bears Sloth bears (Melursus ursinus), like other bears, are solitary animals (Gittleman, 1989), mostly nocturnal (Joshi, Smith & Garshelis, 1999 ) and are not easily sighted. Thus, determining their abundance is a major challenge for field biol ogists. The only rigorous density estimate for any population of this species was made by Ga rshelis, Joshi and Smith (1999) using markrecapture models, based on sightings and re-si ghtings of bears accompanying radio-collared bears in Royal Chitwan National Park, Nepal. They estimated bear density at 27 bears/100 km2 (excluding dependent young). In the relatively unproductive dry tropical forests of Panna
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12 National Park, India, Yoganand (pers. comm.) used a combination of radio-collared animals and familiarity with unmarked but identifiable anim als to derive an estimate of 68 bears/100 km2. While conducting conventional distance sampli ng surveys along line transects in India, Karanth (pers. comm.) recorded few sightings of sl oth bears, despite considerable effort, and the data collected were inadequate to fit a reliab le detection function. Furthermore, photographic mark-recapture sampling (Karanth, Nichols & Ku mar, 2004) does not work for sloth bears as individuals cannot be identif ied. Mark-recapture sampling us ing noninvasive DNA extracted from hair or scat samples may be used as an alte rnative to live trapping, but it is very expensive. Additionally, all these methods ha ve technical problems that ma ke them less reliable as well (Mills, Citta, Lair, Schwartz & Tallmon, 2000). A potential approach to estimating abundance of sloth bears involve s changing the focus from numbers of animals to numbers of sample units occupied by animals (Royle & Nichols, 2003). Methods employing this general approach ar e based on presence-absence data from the sampling units. Royle & Nichols (20 03) have developed a model based on this focus to estimate abundance from repeated presence-absence data or point counts. In chapter 2 of this thesis, I investigate the performance of this model with the likelihoodbased estimator derived by the authors and also derive a Bayesi an alternative to parameter estim ation to deal with applying the model with prior distributions. In chapter 3, I use the Bayesi an approach on the Royle and Nichols (2003) model to analyze sloth bear data obtained from camera traps in BandipurNagarahole National Parks. Sloth bear diets vary seasonally and geogr aphically across their range from Nepal southward through India and Sri Lanka, depending largely on the availability of food and hardness of termite mounds (Baskaran, 1990; Baskaran, Sivaganesan & Krishnamoorthy, 1997;
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13 Gokula, Sivaganesan & Varadarajan, 1995; G opal, 1991; Joshi, Garshelis & Smith, 1997; Karanth et al. 2004; Laurie & Seidensticker, 1977). I make assumptions based on the resource distribution and abundance consequently investig ate applicability of the Royle and Nichols (2003) model under varying home range possibilities. With the absence of a rigorous estimate of sloth bear density in Nagarahole and Bandipur National Parks, the results of this study will be a useful first step in developing a monitoring program for these animals. Further, this will be the first attempt at using the sampling unit based approach towards determining densities or habitat usage rates for bears in general.
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14 CHAPTER 2 PARAMETER ESTIMATION OF THE ROYL E AND NICHOLS (2003) MODEL USING BAYESIAN MARKOV CHAIN MONTE CARL O SIMULATION APPROACH WITH THE GIBBS SAMPLER ALGORITHM Introduction Estimating the number of animals of a particular species in fo rested areas largely revolves around addressing two fundamental issues: extra polation of inferences from a study area and detection probability (Lancia et al. 1994; Skalski, 1994; Thompson, 1992; Thompson, White & Gowan, 1998; Yoccoz, Nichols & Boulinier, 2001). First, investigators often have to select representative areas within a much larger area of interest. However, this fractional area often has to be estimated and inferences must be extrapol ated to the entire area of interest. This is a standard problem in spatial sampling and sta tistical texts (Cochran, 1977; Thompson, 1992) appropriately deal with this issue by permitting such inferences. In field surveys, it is very rare that investigators detect all an imals or signs present even in the fractional area considered. Instead, data collected reflect some sort of a count statistic that only represents a portion of all the available detections present. This issue of detectability is the second fundamental issue an investigator has to deal with in estimating animal abundance. A variety of methods presented in texts (Buckland et al. 2001; Seber, 1982; Williams et al. 2002) and reviews (Lancia et al. 1994) provide different methods of estimation of detection proba bilities for specific kinds of count statistics. Depending on the species studied, the techniques available for gathering appropriate data, and incorporating the limitations of time, money and effort, often only one or just a few of these methods are likely to be suitable. For example, capture-recapture methods require repeated efforts to capture or observe animals (Otis et al. 1978; Pollock et al. 1990). Even observation based methods such as distance sampling (Buckland et al. 2001) and multiple observers (Cook
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15 & Jacobson, 1979; Nichols et al. 2000) are viewed by some as highly time and effort consuming. In many situations, presence-absence (more properly, detection-nonde tection) data on sampling units may more easily be obtained. Me thods using such data have been developed independently several times (Azuma, Baldwi n & Noon, 1990; Bailey, 1952; Bayley & Peterson, 2001; Geissler & Fuller, 1987; MacKenzie, Ni chols, Lachman, Droege, Royle & Langtimm, 2002; Nichols & Karanth, 2002) and appear to be useful for a variety of monitoring programs (e.g. patch occupancy by spotted owls in wester n North America, area occupancy of tigers in India, wetland occupancy by a nurans throughout North America). Royle and Nichols (2003) have constructed a mode l by linking the probability of detecting presence and the abundance at a sampling unit. By using repeated det ection-nondetection data gathered from occupancy surveys, they sugge st a maximum likelihood approach at estimating the parameters (that includes abundance). They al so emphasize that likelihood-based inference is not a small-sample procedure, and this should be considered in any study. In spite of the relative ease with which presence-absence data may be gathered, achieving large samples for analysis as suggested by Royle and Nichols (2003) for even practical estimates of the parameters might be difficult. Bayesian approaches at parameter estimation have found themselves to be useful in a variety of ecological applica tions (Dennis, 1996; Dixon & El lison, 1996; Ellison, 1996; Hilborn & Mangel, 1997) and have many strengths and limitations (Dennis, 1996; Ellison, 1996) Field biologists often encounter logistic difficulties that curtail them to work with very low sample sizes and yet have the need to use such info rmation. Bayesian inferential procedures under certain circumstances better makes use of su ch prior beliefs in parameter estimation.
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16 In the context of the Royle and Nichols (2003) model, a trade-off between the number of sites and the number of sampling occasions have to be made. However, biologists may also enhance the quality of data collection by better field methods and can induce changes on a parameter such as the animal-specific detecti on probability. With existing difficulties in animal abundance estimation, Bayesian inferential procedur es are likely to be more useful from a management standpoint, especially with low sample sizes. In this chapter, I construct a Bayesian Mar kov Chain Monte Carlo simulation approach using the Gibbs sampler (Gelman, Carlin, Stern & Rubin, 1995) to estimate the parameters in the Royle and Nichols (2003) model. I investigate the problems asso ciated with the likelihood-based inference procedure in this model for low sample sizes and suggest the use of a Bayesian approach with an informed prior to more appropriately deal with this problem. Methods Royle and Nichols (2003) Model Royle and Nichols (2003) use the occupa ncy based approach and assume that the detection probability of a given species at a part icular site is directly dependent on the abundance of that species in that site for a given anim al-specific detection probability and nothing else. Consequently, the heterogeneity in detection probabilities across a system of sites is caused by the heterogeneity in abundance across those sites. A nd, by modeling the variation in abundances according to some probability distribution model (e.g., Poisson), they build a model based on maximum likelihood to arrive at estimat es of abundance in these sites. The Royle and Nichols (2003) model is as follows: pi = 1-(1r )Ni (2-1) Here pi is the probability of detecting at least one animal within the site i r is the probability of an animal being detected in site i Ni is the actual animal abundance at site i
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17 Parameter Estimation Using the Likelihood-Based Approach For the construction of the final likelihood equation, Royle and Nichols (2003) recommend imposing a probability model to characterize the underlying di stribution of abundances. For animals that are distributed at random, a natu ral candidate for modeling the abundance may be the Poisson model (Royle, Nichols and Kery, 2005). The final likelihood equation by using the Pois son model for the abundance is as follows: 1 0. .] ) 1 [( ] ) 1 ( 1 [ ) | (k k w T k R k w w Te r r C r w Li i k i (2-2) R is the number of sites, T is the number of repeated samples, w is the detection vector of the total number of detections from each site i, i.e. a vector of all the individual site-specific detections, wi.. is the expected abundance at each site, also the Poisson mean. For the convenience of numerically maximizi ng the Equation 2-2, the upper limit of the variable k is set to a very large number K. So for practical estimation of the parameters, Equation 2-3 is used. 1 0. .] ) 1 [( ] ) 1 ( 1 [ ) | (k k w T k R K k w w Te r r C r w Li i k i (2-3) Parameter Estimation Using the Bayesian Approach The Royle and Nichols (2003) model that uses the Poisson distribution to characterize the abundance can be viewed as a hierarchical model of random variables as follows: ] ) 1 ( 1 [ ~ ] , | [.iN i ir T binomial N r T w (2-4) ] [ ~ ] | [ poisson N i (2-5) ] 1 0 [ ~ uni f orm r (2-6) ] [ ~ b a gamma (2-7) Here a and b are the shape and scale parameters a ssociated with the gamma distribution. Relationships 2-4 and 2-5 jointly represent th e likelihood function, while Relationships 2-6 and
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18 2-7 are the prior distributions set for r and respectively. Since the gamma prior distribution is the conjugate prior for the Poisson distribution (Gelman et al. 1995), it is a very convenient distribution that can be used, especially in a Bayesian Mar kov Chain Monte Carlo simulation. I used the Bayesian Markov Chain Monte Ca rlo simulation approach using the Gibbs sampler (Gelman et al. 1995) to determine the posterior distribution of the parameters r and Ni. The Gibbs sampler is a particular Markov chain algorithm useful in such multidimensional problems based on alternate conditional sampling. To use the Gibbs sampler, the conditional distributions of each parameter have to be de rived by treating the othe r parameters as known (full conditionals). The unnormalized jo int posterior density function is ) ( ) ( )] | ( ) , | ( [ ) | } { , (. P r P N g N r T w f w N r Pi i i i i i The objective is to sample from the joint pos terior density functi on repeatedly and the Markov chain that develops repres ents the joint poster ior distribution. However, since this is a hierarchical model and all the pr obabilities are not indepe ndent, an alternative is to sequentially sample from each full conditional derived for each parameter. This is the whole purpose of the Gibbs sampler. The full conditionals are derived as follows: Full conditional for : 1 11 ~ | R b N a gammaR i i (2-8) Full conditional for r : P( r ) = 1, 0< r <1 In a Monte-Carlo simulation, it is de sirable to move in a parameter space that is unrestricted. So to develop a full conditional on r it would be more useful to use a logit transformation on r
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19 instead of being bounded by the values between 0 and 1. So the full conditional is developed for the parameter the variable under the transformation, instead of r, for computational advantages: e e r r r 1 1 ln d dr e e P Pr. 1 ) ( 21 1 1 ) ( e e e e e P 21 ) ( e e P R i i iN T w f P P1 ., | ) ( | . .1 1 1 1 1 1 |1 2i i i i iw T N w N R i w Te e C e e P .1 21 1 1 1 |i i i iw T N R i w Ne e e e P (2-9) Full conditional for Ni : | , | |. i i i i N g N r T w f N P 1 1 1 |. .i N w T N w N w T iN e r r C N Pi i i i i i Let | , | |0 . i k i iN g k r T w f r w h | | , | |. .r w h N g N r T w f N Pi i i i i (2-10) Where Ni = 0, 1, 2,
. to K, when wi.= 0 and Ni = 1, 2,
to K, when wi. 1. The Gibbs sampler algorithm involves sampling random values sequentially from these full conditionals. Each sample is drawn from the full conditional of a parameter using the updated values of each of the othe r parameters. When this process is repeated arbitrarily a large
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20 number of times, a posterior distribution of the parameter of interest will emerge based on the time spent on each point in the parameter space. The Gibbs Sampler Algorithm for th e Royle and Nichols (2003) Model Step 1: Selecting the initial values for r and Ni. Iteration 1 r(1) : random number chosen fr om a Uniform (0,1) distribution So, (1) = logit[ r(1)] (1) : random number chosen from a Gamma ( a b ), where a and b are the shape and scale parameters initially selected. Ni (1) : random number chosen from a Poisson[ (1)], where i = 1, 2,
R sites. Step 2: Updating the values of r and Ni. Iteration j [ranging from 2 to a large number] [ Ni ( j ) | wi., ( j1), r( j -1)] : random number drawn accord ing to Equation 2-10 where i = 1, 2,
R sites [( j ) | { Ni ( j )}] : random number drawn according to e quation (8). The {} indicates the entire vector of site abundances. [( j ) | { w }, { Ni ( j )}] : random number drawn according to the proportionality relationship of Equation 2-9. Consequently ) ( ) (1) (j je e rj Step 2 is repeated a large number of times Using the Equations 2-8 and 2-10 the updates for Ni ( j ) and ( j ) can be made quite directly in the Gi bbs sampler. However, making the updates for ( j ) requires the use of the Metropolis algorithm (Gelman et al. 1995) with a Gaussian proposal distribution since Equation 29 is only a proportionality relationship. Simulation Design Royle and Nichols (2003) have already shown the performance of the model in varying large sample situations and have establishe d that the likelihood-based inference works reasonably well for inferences about estimates of for even low values of r and T when R is 200 or greater. However, in their simulation design, th ey have chosen values for the true value of
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21 ranging from 1 to 5 for which the means and medians of estimates of were within reasonable limits. In my simulations, I fixed a value of 0.3 for r and 10 for as constants and varied the number of sites (100, 50, 25, 10) and the number of sampling occasions (3, 5, 10) to evaluate the performance of the estimates. I wrote the program in R, a free statistical programming environment (Vienna University of Economics and Business Administration, 2006 ). Using direct search to numerically calculate the values of r and to maximize the likelihood Equation 2-7 is very time consuming. Instead, I used the Broyden-Fl etcher-Goldfarb-Shanno (BFGS) algorithm and also used the Nelder-Mead algorithm (Press, Teukolsky, Vetterling & Flanne ry, 1994). I used the logit transformation on r to bind the values of r between 0 and 1 during optimization. From the likelihood-based estimat es, I identified data sets that resulted in estimates quite distant from the true value used in the simula tion. I used these data se ts to obtain posterior distributions of the parameters r and by running the Gibbs sampler algorithm with two informed prior distributions. This algorithm was also programmed in R. Results The summary statistics for the estimated parameters r and by the likelihood-based inference is shown in Table 2-1. The results for al l combinations of number of sites and number of sampling occasions show a positive bias for the estimates of For sample sizes 100, 50 and 25 sites, the median value of provided a better estimate of the true value of as compared to the mean. The Nelder-Mead algorithm and BFGS algorithms provided different estimates for the mean and standard errors of For example, in the simulation with 50 sites and 5 sampling occasions, the Nelder-Mead estimate of (mean) was 26.181 24.476 while the BFGS estimate was 16.813 10.747.
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22 The summary statistics of th e posterior distributions of r and are shown in Tables 2-2 and 2-3. Further, the likelihood estimat es using the BFGS algorithm were not consistent (i.e. they failed to converge to the same estimates every tim e). The standard deviation of the estimates of r and increased with the increased variance in the prior gamma distribution set for Figure 2-1 shows the influence of the prior distributions on the posterior distribut ions with low sample sizes. Conclusions and Discussion Small sample sizes (when R is less than 100 and T is less than 10) produce flat likelihoods. This makes likelihood-based estimation difficult. Computer algorithms like BFGS or NelderMead rely on smooth likelihood surfaces (Press et al. 1994) and also rely on computers capable of high precision for parameter estimation with flat likelihoods. The la rge standard errors produced when using the Nelder-Mead algorithm is indicative of the flat likelihood surface. The inconsistency in the results from the BFGS algorithm in paramete r estimation is also indicative of such a surface. From the results in Tables 2-2 and 2-3, it may be inferred that Bayesian priors on do play an important role in the posterior distribution of the parameters when using the Gibbs sampler algorithm. Hence from a biological standpoint, given low sample sizes, the choice of an appropriate prior is critical to obtain meaningful estim ates of animal abundance. Considering that in this model is the important parameter from a wildlife management perspective and very difficult to estimate from field surveys, information obtained even from small sample sizes would be helpful from a long term monitoring perspective. Bayesian approaches do facilitate this pr ocess of updating parameter estimat es on improved prior beliefs.
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23 Table 2-1. Simulation results for the likelihood-based infere nce. The true values of r and were set at 0.3 and 10 during the simulation. In each case, 1000 data sets were simulated. R T r (mean) Standard error of r (mean) Standard error of (median) Optimization method 100 3 0.264 0.1560 16.737 10.4509 13.810 BFGS 100 5 0.268 0.1312 15.666 10.4873 10.264 BFGS 100 10 0.282 0.1013 13.024 7.7381 10.559 BFGS 50 3 0.251 0.1824 21.003 14.0927 17.780 BFGS 50 5 0.265 0.1580 16.813 10.2470 11.663 BFGS 50 10 0.278 0.1381 14.911 9.7201 10.675 BFGS 25 3 0.263 0.2081 17.799 7.5950 16.335 BFGS 25 5 0.260 0.1745 19.517 13.7354 14.972 BFGS 25 10 0.266 0.1690 17.726 11.5440 11.817 BFGS 10 3 0.405 0.3647 20.141 8.0814 17.191 BFGS 10 5 0.301 0.2775 19.039 8.3268 21.894 BFGS 10 10 0.279 0.2406 20.373 12.8811 21.350 BFGS 50 5 0.253 0.1741 26.181 24.4756 Nelder-Mead 50 10 0.276 0.1512 18.832 18.5343 Nelder-Mead 25 10 0.251 0.1826 26.950 24.9698 Nelder-Mead
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24 Table 2-2. The results of the Gibbs sampler algorithm. The likelihood estimates for thesame data set were obtained using the BFGS algorithm for optimization. Prior shape = 10 scale=1. Number of iterations in the Gi bbs sampler were 60,000 and the first 20,000 iterations were excluded in calculating the summary statistics. R T Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of Likelihood estimate of r Likelihood estimate of 50 3 0.314 0.096 10.035 2.963 0.929 25.511 50 10 0.348 0.087 11.045 2.927 0.564 27.647 25 3 0.264 0.086 9.761 2.997 0.810 14.563 25 10 0.362 0.098 10.583 2.900 0.694 13.897 Table 2-3. The results of the Gibbs sampler algorithm. The likelihood estimates for the same data set were obtained using the BFGS algorithm for optimization. Prior shape = 1 scale=10. Number of iterations in the Gibbs sampler were 60, 000 and the first 20,000 iterations were excluded in calculating the summary statistics. R T Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of Likelihood estimate of r Likelihood estimate of 50 3 0.319 0.150 11.347 5.843 0.929 25.511 50 10 0.271 0.118 16.654 8.606 0.564 27.647 25 3 0.285 0.156 11.201 7.150 0.810 14.563 25 10 0.349 0.169 12.959 6.804 0.694 13.897
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25 A B C D Figure 2-1. Prior and post erior distributions for when R =50 and when T= 10. A) Prior distribution of with shape = 10 and scale = 1. B) Posterior distribution of with priors from A. C) Prior distribution of with shape = 1 and scale = 10. D) Posterior distribution of with priors from C.
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26 CHAPTER 3 ESTIMATION OF SLOTH BEAR ABUNDA NCE USING REPEATED PRESENCEABSENCE DATA IN NAGARAHOLE-BAND IPUR NATIONAL PARKS, INDIA Introduction The estimation of bear abundance involves many difficulties. Many expensive and laborintensive mark-recapture studies, most aided by telemetry, have been conducted on populations of American black bears ( Ursus americanus ), brown bears ( Ursus arctos ) and polar bears ( Ursus maritimus ) (Garshelis et al., 1999). Such studies are lacking for the other five species of bears due to funding and logistical constr aints. Furthermore, the density of these species is perceived to be relatively low, thus making mark-recapture studies highly impractical. The only rigorous density estimate of sloth bears ( Melursus ursinus ) was derived by Garshelis et al. (1999) during their study in Royal Chitw an National Park, Nepal. They used information on bears seen in the company of ra dio-collared bears as a re-sight sample and estimated bear density using th e relatively simple, modified Peterson estimator (Bailey, 1952). During the process of obtaining 3,117 radio-teleme try locations, they sighted 47 bears in the vicinity of radio-colla red bears, 42 of which had radio-collars on them. Using the modified Peterson estimator, Garshelis et al. (1999) arrived at a density estimate ranging from 27 to 72 bears per 100 km2 depending on the season and habitat. It to ok investigators more than a year to obtain a recapture sample of 47 accompanying bears, an effort that may be feasible only when coupled with investigating other questions about sloth bear ecology that requires systematic and repeated visits to the forest. Sloth bear densities are difficult to obtain by many conventional sampling methods. It is not possible to identify sloth b ear individuals from photographs obtained in camera traps, so using a mark-recapture framework to determine densities, as done with tigers (Karanth & Nichols, 1998), is not practical Further, while conducting dist ance-sampling surveys along line
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27 transects, Karanth ( unpublished data ) recorded few sightings of sl oth bears despite considerable effort. A detection function fitted to such limited da ta is likely to be highly unreliable. Similarly, mark-recapture sampling requires large sample sizes and live trapping of sloth bears is not likely to generate the requisite numb er of recaptures. Sampling usi ng noninvasive DNA extracted from hair or scat samples may be used as an alternative to live trap ping, but it is very expensive. Additionally, all these methods presently have tec hnical problems that make them less reliable as well (Mills et al. 2000). By sampling a site repeatedly for the pres ence-absence of a species, Royle & Nichols (2003) constructed a model that may be used to determine the abundance of a species. This is a simple model that makes use of a logical assumpti on that the detectability of a species is solely dependent on the abundance at that site for a give n animal-specific detection probability. In this chapter, I investigate the applicability of this mo del for repeated presence-absence data of sloth bears obtained using camera traps in Bandipur and Nagarahole National Parks. For reasons discussed in chapter 2 of this th esis, I preferred to us e the Bayesian approach in estimating sloth bear abundance. Study Design Study Area The study area comprises two protected ar eas, Nagarahole and Bandipur, that are geographically separated by the Ka bini reservoir (Figure 3-1). Nagarahole Nagarahole was originally establishe d in 1955 as a Game Reserve of 288 km2. In 1974, it was expanded to become the Nagarahole National Park (Area: 644 km2), now officially renamed Rajiv Gandhi National Park, Na garahole but commonly referred to as Nagarahole. The reserve is located in Kodagu and Mysore districts (76 00' 76 15' E 11 15' 12 15' N) at altitudes
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28 of 700 960 m. Nagarahole is contiguous with Bandipur Reserve to the southeast and the Wayanad reserve to the southwest. The reserve receives an average annu al rainfall between 1000 1500 mm (Karanth & Nichols, 200 0). The terrain is gently undul ating and drained by several perennial streams and three large rivers: Kabini Taraka and Lakshmanateertha. An irrigation dam built in 1974 forms the Kabini reservoir that flanks the southern boundary of the reserve. Two types of tropical, mixed deciduous fore sts are found in the region. The northwestern areas of the reserve receive higher rainfall and support moist deciduous forests of the TectonaDilleniaLagerstroemia series. The dry deciduous forests of the Terminalia-Anogeissus-Tectona series occur in the southeastern areas with less than 1000 mm of ra infall. A unique feature of this site is the presence of open grassy swamps in moist areas locally called hadlus, where the soil is clayey, perennially moist and s upports the luxuriant growth of sedges and grasses year round. Nagarahole supports an impressive assemblage of herbivorous prey species: elephant ( Elephus maximus ), gaur ( Bos gaurus ), sambar ( Cervus unicolor ), chital ( Axis axis ), muntjac ( Muntiacus muntjac ), chousingha ( Tetraceros quadricornis ), wild pig ( Sus scrofa ), hanuman langur ( Presbytis entellus ) and bonnet macaque ( Macaca radiata ). The tiger ( Panthera tigris ) leopard ( Panthera pardus ), Asiatic wild dog ( Cuon alpinus ), or dhole, and sloth bear are the large carnivores. Apart from the impressive mamm alian fauna, Nagarahole is rich in avifauna, with more than 270 species of birds. The herpet ofauna includes a variety of snakes, lizards, turtles and frogs. Among the larger reptiles, the marsh crocodile ( Crocodylus palustris ), monitor lizard ( Varanus bengalensis ) and the rock python ( Python molurus ) occur in Nagarahole. Bandipur The Maharaja of Mysore orig inally established Bandipur as a hunting reserve in 1931. It was expanded after 1974 to become the Bandipu r National Park and Tiger Reserve (Area: 874 km2). It is one among the first nine tiger reserves created under Project Tiger. Bandipur is located
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29 in Mysore and Chamarajanagar Districts (76 12' 76 46' E 11 37' 11 57' N) at an altitude of 680 1454 m. Bandipur is the oldest protected area in Karnataka. It is contiguous with Nagarahole on the northwest, Wayanad reserve to the southwest and Mudumalai reserve to the south. The terrain is undulating, and the reserve is bounded by the Moyar Ri ver to the south and Kabini Reservoir to the northwest. Bandipur Reserve receives an annual rainfall of 625 1250 mm (Karanth & Nichols, 2000). The forests are mostly the mixed dry deciduous series of TerminaliaAnogeissus-Tectona type. In the northwestern parts where the rainfall is higher, moist deciduous forests of the Tectona-Dillenia-Lagerstroemia series occur. The wildlife of Bandipur is similar to that of Nagarahole; however, three additio nal large mammal species, blackbuck antelope ( Antelope cervicapra ), striped hyena ( Hyaena hyaena ), and the Indian wolf ( Canis lupus ), occur occasionally on its eastern fringes. The bird lif e and herpetofauna are similar to Nagarahole. Methods Field Methods I used commercially made TRAILM ASTER TR-1550 camera traps (Goodson and Associates, Lenexa, Kansas, US A) equipped with active infra-re d tripping devices to obtain photographs of animals. Two cameras, positioned opposite each other, were set along game trails to simultaneously photograph both flanks of an animal that broke the infrared beam. The camera traps were housed in locally ma nufactured theft-resistant metal trap shells and set about 300-350 cm from the side of a trail with the infrared beam set at a height of 45 cm. To eliminate mutual flash interference, a small delay (approx 0.1 sec) was elec tronically introduced into the splitting device connecting the two cameras. The sensitivity of the trippi ng device was set to photograph large-bodied animals. The date and time a phot ograph is taken is imprinted on the film and recorded on the receiver unit.
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30 The camera traps were placed with the primary intention of maximizing tiger captures and were set along routes where there was tiger sign (s cats, scrapes, scent deposits, tracks) and at the intersection of well-used tra ils. The spacing between camera tr aps ranged from 1-2 km. All points were marked on maps using a GPS unit. The date, time, and location of all animal captures were noted (Figure 3-2). Data were collected from the two parks from December until May in 2003-2004 and 20042005. Sampling was done at 120 camera-trap loca tions in Nagarahole and 118 camera-trap locations in Bandipur. Since it wa s logistically impractical to conduct sampling at all these camera trap locations simultaneously, the trap poin ts were divided into bl ocks of 40 trap points each. After sampling for 10-15 nights in one bloc k, the camera traps were moved to the next block and sampling would continue 10-15 nights. In total, the study area consisted of 6 blocks. Logistics, weather and budget c onstraints limited the number of consecutive nights the cameras were deployed at a tr ap site (Table 3-1) Application of the Royle and Nichols (2003) Model Definition of sites Occupancy surveys that are described in MacKenzie et al. (2002) and Royle & Nichols (2003) use sample units as sites. Implicitly, it is assumed that each site is independent and no animal will move between sites during the survey period. Unless the movement of animals is very small compared to the selected cell size, se tting up a grid system and using these models for adjacent cells will violate the assumption of i ndependence between sites. Thus, using these models for a species that ranges wi dely, like the sloth bear (Garshelis et al. 1999), will generate results that require an alternat ive interpretation. To minimize the size of sites based on different possibilities of home range size and to maintain the assumption of independence of abundance between sites, I selected site s from the study areas in Bandipur and Nagarahole National Parks
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31 that are geographically separated by more th an one expected home-range diameter for the analysis. A frequently occurring problem associated with using camera traps for converting estimated animal abundances to densities is determining the effectively sampled area. The problem is typically addressed by adding a bu ffer around the trapping grid; the width of the buffer is addressed by a number of met hods (see Wilson & Anderson, 1985). When radiotelemetry information is not available, the m ean maximum distance method (MMDM) (Karanth & Nichols, 1998; Wilson & Anderson, 1985) is wide ly used to add a buffer around the trapping grid instead of assuming geogra phic closure within the trapping grid to reduce bias. However, Soisalo & Cavalcanti (2006), in their work on jaguars ( Panthera onca ), point out the limitations of using MMDM, and suggest that density estima tes based on MMDM are likely to be biased and inflated. With the lack of information on individual bears being tr apped in the study, the MMDM method cannot be used in this study. The analys is in this study relies on the assumption of different home range sizes of sloth bears in the absence of real data. Hence, I assume these different assumed home range sizes as the effectively sampled areas for each scenario, without actually defining a buffer around the camera trap grid in each site. Selection of home range sizes for analysis Sloth bears have not been radi o-collared in either Nagarahol e or Bandipur National Parks. So information on home range sizes has to be inferred from other studies in the country. In Chitwan, male sloth bears occupied larger home ranges than females (Joshi, Garshelis & Smith, 1995), which was primarily due to larger wet season ranges. Mean home ranges were 9.4 and 14.4 km2 for females and males, respectively. Yoga nand (unpublished data) observed that sloth bears in Panna had much larger annual home ranges (ranging from 25 100 km2 95% kernel estimate) and varying sizes of seasonal ranges.
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32 The diet of the sloth bears consists mostly of social insects and fruits. These are predominantly ground-living ants and termites that are common a nd found in large colonies, and sugar-rich fruits of commonly occurring plan ts that produce large fruit crops (Laurie & Seidensticker, 1977; Yoganand, unpublished data). In sects dominated the diet of sloth bears in Chitwan, both during fruiting a nd non-fruiting seasons (Joshi et al. 1997). In Panna, however, fruits dominated the diet, excep t during monsoons when they fed on more insects. From the two studies (Garshelis et al. 1999), sloth bears appear to persist in much highe r densities in Chitwan than in Panna. The hard so il conditions in Panna may ma ke feeding on termites nearly impossible during the dry season and may explai n why insectivory is curtailed during this season. Since sloth bears in Panna show a prefer ence for insects over fruits in the wet season, I presume that the protein-rich in sect dominated diet is preferred over a fruit-dominated diet, which probably explains why slot h bears have smaller home ranges in Chitwan than in Panna. In relation to habitat type and rainfall char acteristics, Nagarahole a nd Bandipur appear to be more similar to Chitwan than to Panna. Acco rdingly, with the lack of information on sloth bear home range sizes in Nagarahole and Bandipur National Parks, for this study, I considered 4 home range sizes, 10 km2, 18 km2, 25 km2 and 50 km2 as options for the analysis. The fourth home range size, namely, 50 km2, was primarily used to study the behavior of the model and is a home range size that may not be realistically expected to oc cur in Nagarahole or Bandipur National Parks, at least not a home range size expected for a brief period of 15 continuous sampling nights. Constant r Territoriality has not been obs erved with sloth bears (Joshi et al. 1999; Laurie & Seidensticker, 1977), hence each camera trap is likely to be within more than one sloth bears
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33 home range. Further, no measurable covariate information to model r were available, hence an assumption of constant r is made in this analysis. Capture histories for sloth bears Royle & Nichols (2003) suggest building up cap ture histories by sites based on captures and recaptures of the species in concern on repeat ed visits. Since sloth bears move widely (Joshi et al. 1999), it is not likely that a bear captured at a given camera tr ap location will be caught at that same location with the same probability over subsequent camera tr ap nights. Instead, I substitute the temporal replicates as suggested in Royle & Nichol s (2003) with spatial replicates. By doing this, I assume that all bears have an eq ual animal-specific detect ion probability. In this arrangement, a camera-trap location is said to have detected bear presence if a bear appears in that location on any single trap night over all the sampling nights. A capture matrix incorporating such an arrangement is shown in Table 3-2. The total number of detections at a site i is wi .. If a bear appeared once at a camera trap over the period of the entire sampling period, that cam era trap is said to have detected a bear and marked as 1, as in the matrix (Table 3-2). Selection of the mass function to model abundance The selected study areas are prot ected areas and are fa irly homogenous in habitat structure. I also know from sloth bear de tections observed in 2004 and 2005 (Figures 3-3 and 3-4), that with the exception of one hol e in 2005, no other holes or clus ters are obvious. With a random spatial occurrence of detections of this na ture, based on the recommendation of Royle and Nichols (2003) I assume a Poisson model to describe abundance. Parameters for the prior distribution of From Equation 2-7 in Chapter 2 ] [ ~ b a gamma where a and b are the shape and scale parameters.
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34 By the properties of a gamma distribution, Mean = ab Variance = ab2 From the home range information of adjacent sloth bears (Joshi et al. 1999), a maximum density of 6 male bears and 3 female bears we re observed using a common area and each bear shared 50% or more of its home range area within the area of other bears. I assume that the degree of overlap is independent of home range size, based on th e logic that sloth bear home ranges overlap due to the energe tic costs that are involved in sustaining territoriality and the home range size is a function of resource distribution and abunda nce. Consequently, I assume that bear abundance per home range is invariant of home range si ze. I use this idea in deciding the shape and scale parameters for the prior gamma distribution. Using the information from (Joshi et al. 1999), I set the mean as 9 for the gamma distribution. However, there is no prior informat ion on the degree of vari ation in abundance per home range. While I tried various priors to evaluate the performance of the model, I include results from only two prior distributions, one being more informative than the other. Analysis of actual data Sloth bear home range size in the NagaraholeBandipur region was expe cted to lie within the range of 10-25 km2. To ensure independence between sites and incorpor ating these home range classes of this order, the analysis had to be performed with rela tively low sample sizes (number of sites). By the simulation results from chapter 2 with low sample sizes, I chose to use the Bayesian approach to derive the posterior distributions of and r. Four home range classes were selected for the analysis (10 km2, 18 km2, 25 km2 and 50 km2). Although I tried various combinations of shape and scale parameters for the prior gamma distribution, I present the results from two prior distributions:
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35 Shape = 2, scale = 4.5 (relat ively uninformative) Shape = 4.5, scale = 2 (relatively informative) I conducted the analysis under two model settings: By ensuring independence between sites. This resulted in R values of 32, 15, 13 and 8 for home range sizes 10 km2, 18 km2, 25 km2 and 50 km2 respectively. An example of such an arrangement is shown in Figure 3-5 for the 10 km2 sites. By relaxing the assumption of independence between sites. Here, I assumed that the average abundance in each cell remains constant. This resulted in R values of 116, 79, 58 and 35 for home range sizes 10 km2, 18 km2, 25 km2 and 50 km2 respectively. An example of such an arrangement is shown in Figure 3-6 for the 10 km2 sites. The Gibbs sampler was run 100,000 times and the first 30,000 iterations were left out in the calculations of the statistics, called the b urn-in period. I checked for auto-correlation and thinned the results from the remaining 70,000 draws to ensure that indepe ndent and identically distributed ( iid ) draws are made for the calculations of the statistics. The analysis has been run on one subjective selection of sites based on assume d home range sizes. This selection is based on the criterion that two sites are separated by at least one home-range diameter and does spatially cover the area systematically. Hence, I did not consider it worthy of an effort to derive estimates of the two parameters with other sim ilar selections with the expectation of similar results. Results Assuming independence between sites. The posterior summary statistics for the results by ensuring independence between sites are tabulated (Tables 33 and 3-4). For the two prior distributions (Figures 3-7 and 3-8) considere d, gamma(2, 4.5) has a mean of 9 and a standard deviation of 6.364 while gamma(4.5, 2) has a m ean of 9 and a standard deviation of 4.243. The mean estimates of animal-specific de tection probabilities ar e considerably low (between 0.0377 to 0.1055). The posterior standard deviations for the estimates of either r or in an analysis for a given year did not vary by much There is a reduction in the variability of the
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36 estimates in the posterior standard deviation in comparing it with the pr ior standard deviation. The estimates of posterior means of did not differ by much for the different home range assumptions. Relaxing site independence and instead assu ming that the average abundance at each site remains a constant. The posterior summary statistics for the results by ensuring independence between sites are ta bulated (Tables 3-5 and 3-6). Th e mean estimates of animalspecific detection probabilities were still low (between 0.038 to 0.122). The posterior means of in 2005 for the home range sizes of 25 km2 and 50 km2 were lower than the posterior means of in 2004. However, the mean values of were influenced by th e prior distributions. Conclusions and Discussion From these results it is clear that the increase in the number of sites has little effect on the variability of the parameter estimates. By increasing the home range sizes, more spatial replicates were added to each site for analys is and there was a reduction in the number of available sites for analysis. This trade-off is pe rhaps the largest cause fo r the less variability in the parameter estimates. After relaxing the assumption that animals detected in one site will not be detected in another site, a nd instead making the assumption that the abundance at each site at any given point remains a constant irrespective of immigration or emigration to or from the site, the estimate of the animal-specific detection probabil ity is still very low. Placing more traps per site and placing them in higher probability loca tions (e.g., near termite mounds or even placing baits to attract bears) may change r to values to provide better estimates of As an alternative, other data gathering tools such as sign encounter surveys in some conditions may serve as better techniques to improve r. The results from Tables 3-3 to 3-6 may not be indicative enough to derive abundance estimates. However, in the year 200 4, with an assumption of an 18 km2 home range size, the
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37 highest animal-specific detecti on probability (0.122 0.061) was derived and the estimate of as 4.16 2.74. The mean value of estimate of was quite distant from the prior mean. This result was derived after using th e relatively uninformed prior dist ribution indicating a more data driven posterior distribu tion for this result. My data show that on only few cases (<10%) did a camera trap that detected a bear on one sampling night detect a bear subsequently in the remaining nights. So, using temporal replicates, as suggested in Royle and Nichols (2003) for sloth bear s, is not likely to change the results by much. Further, in using temporal replicates in stead of spatial replic ates the number of traps per cell either has to be maintained as a constant (which has not be en the case as per this study design) or an additional parameter to model r must be introduced to deal with the problem of having unequal number of traps placed in different cells. Prior to determining abundances of animals, especially animals that move fairly widely relative to the size of the site defined, basic information regarding the home range size of the animal, daily movement pattern and other behavi oral aspects such as feeding behavior and habitat utilization in a particular region of in terest will provide invaluable information in designing a study to monitor their abundance. For a widely distribut ed species such as the sloth bear, it is expected that the above mentioned variables are likely to be quite differe nt in different habitats, as already seen in Panna and Chitwan. Both, from the perspective of identifying high probability sites for sloth bear captures on the field and by having to deal with the model assumptions, information on the above parameters are vital. The Bayesian approach will be particular ly useful from a long term monitoring perspective. If sampling is repeated over mu ltiple years during the same season, the posterior
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38 distribution of one year may serve as the prior distribution for the subs equent year making the estimates of abundance more accurate progressively. Since, sloth bears are not likely to exist in numbers greater than 20 animals per home range area, incorporating Royle and Ni chols (2003) model into estimating occupancy rate (MacKenzie et al., 2002) of sloth bears may be necessary. For a reasonable animal-specific detection probability r between 0.2 and 0.8, a great variation in th e site-specific detection probability is reflected for a range of abundances between 0 and 30. When the values of abundance are very high (>30), the site-specific detection probability is less sensitive to the changes in abundance. I recommend the use of the Royle a nd Nichols (2003) model to addr ess any issue with respect to occupancy of sloth bears as compared to the MacKenzie et al. (2002) model which implicitly assumes that sites have a constant or nearly constant abundance.
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39 Table 3-1. Sampling effort at each camera trap location. Number of sampling occasions per trap site Sites Year 2004 Year 2005 Nagarahole 10 15 Bandipur 13 15 Table 3-2. An example capture matr ix for sloth bear detections Camera traps in a site Total number of detections Sites 1 2 3 4 5 6 wi. Site 1 0 1 0 0 1 0 2 Site 2 1 1 0 0 0 1 3
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40Table 3-3. Posterior summary statistics by ensuring independ ence between sites with prior distribution for ~Gamma(2, 4.5) Year 2004 Year 2005 Home range sizes (in km2) Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of 10 0.1055 0.0681 6.0967 4.2567 0.0748 0.0545 6.1131 4.6529 18 0.0854 0.0582 5.7517 4.4398 0.0487 0.0356 7.2965 5.0511 25 0.0830 0.0557 6.2497 4.4459 0.0771 0.0548 5.8449 4.2864 50 0.0710 0.0461 8.6492 5.2951 0.0476 0.0330 6.8824 4.6002 Table 3-4. Posterior summary statistics by ensuring independ ence between sites with prior distribution for ~Gamma(4.5, 2) Year 2004 Year 2005 Home range sizes (in km2) Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of 10 0.0806 0.0463 7.0333 3.5023 0.0538 0.0330 6.9798 3.6714 18 0.0603 0.0382 6.9837 3.7051 0.0408 0.0237 7.3616 3.6405 25 0.0652 0.0381 6.9894 3.7199 0.0537 0.0345 7.1341 3.5928 50 0.0631 0.0340 8.6509 3.7132 0.0377 0.0222 7.5661 3.6745
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41 41Table 3-5 Posterior summary statistics (relaxing site independence) with prior distribution for ~Gamma(2, 4.5) Year 2004 Year 2005 Home range sizes (in km2) Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of 10 0.10134 0.06130 5.18893 3.65330 0.06243 0.04432 5.92929 4.75334 18 0.12290 0.06185 4.16892 2.74911 0.04822 0.03282 6.74578 4.23767 25 0.06889 0.03957 7.37141 4.57556 0.10504 0.04627 2.77987 1.64058 50 0.05298 0.03016 9.10935 5.33008 0.10094 0.05411 3.27652 2.69101 Table 3-6. Posterior summary statistics (relaxing s ite independence) with prior distribution for ~Gamma(4.5, 2) Year 2004 Year 2005 Home range sizes (in km2) Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of Posterior mean of r Posterior standard deviation of r Posterior mean of Posterior standard deviation of 10 0.07188 0.04074 6.48642 3.32368 0.04810 0.03153 6.40936 3.43146 18 0.08380 0.04603 5.92916 3.15890 0.03891 0.02290 7.57562 3.96615 25 0.05990 0.02927 7.54454 3.41925 0.07087 0.03607 4.29506 2.35607 50 0.05120 0.02340 8.42673 3.61803 0.06201 0.03840 5.16315 3.09212
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42 Figure 3-1. Map of the study area comprising of the Bandipur and Nagarahole National Parks. Figure 3-2. A sloth bear photogra ph taken from a camera trap.
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43 Figure 3-3. Sloth bear detections (year 2004) are shown with black (dark) dots. The other dots represent camera traps that did not detect sloth bears. Figure 3-4. Sloth bear detections (year 2005) are shown with black (dark) dots. The other dots represent camera traps that did not detect sloth bears.
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44 Figure 3-5. A selection of 10 km2 sites using ArcView 3.2 GIS software. The dots within each site are the camera traps used for analys is. Similar selections were made for 18 km2, 25 km2 and 50 km2 sites. Figure 3-6. An example random grid generated us ing ArcView 3.2 software with cell size of 10 km2. Here each cell containing camera traps we re used in the analysis. Similar grids for 18 km2, 25 km2 and 50 km2 cell sizes were generated.
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45 010203040 0.000.020.040.060.08 AbundanceDensity Figure 3-7. Gamma(2, 4.5) prior distribution 010203040 0.000.020.040.060.080.10 AbundanceDensity Figure 3-8. Gamma(4 .5, 2) prior distribution
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46 CHAPTER 4 CONCLUSIONS AND DISCUSSION Animal abundance is a very important paramete r from a wildlife management perspective. However, most estimation methods require very large sample sizes to obtain reliable estimates of abundance and seldom does such information help for a wildlife manager. The progressively subjective nature of Bayesian approaches at a bundance estimation can to some extent be more informative to the wildlife mana ger (Stow, Carpenter & Cottingham, 1995). Such approaches do facilitate this process of updating parameter es timates on improved prior beliefs and will help wildlife managers use such a pproaches more effectively in monitoring animal populations (Hilborn and Mangel, 1997). The simulation results from my study show that the Royle and Nichols (2003) can still be a valuable tool for determining abundance, specially since it is relatively inexpensive to obtain presence-absence data from sites. The data gathered from my st udy on sloth bears were insufficient for good estimates of animal abundan ce. However, improving the quality of field data in terms of improving r will go a long way in making this model more useful for determining sloth bear abundance.
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47 LIST OF REFERENCES Azuma, D.L., Baldwin, J.A., & Noon, B.R. ( 1990). Estimating the occupancy of Spotted Owl habitat areas by sampling and adjust ing bias. USDA Forest Service General Technical Report PSW124 Bailey, N.T.J. (1952) Improvements in th e interpretation of recapture data. Journal of Animal Ecology 21 120127. Baskaran, N. (1990) An ecological investig ation on the dietary composition and habitat utilization of sloth bear (Melursus ursinus) at Mudumalai wildlife sanctuary, Tamil Nadu (South India). Thesis, A. V. C. College, Mannambandal, Tamil Nadu, India. Baskaran, N., Sivaganesan, N., & Krishnamoort hy, J. (1997) Food habits of sloth bear in Mudumalai Wildlife Sanctuary, Tamil Nadu, Southern India. Bombay Natural History Society 94 19 Bayley, P.B. & Peterson, J.T. (2001) An appr oach to estimate probability of presence and richness of fish species. Transactions of the American Fisheries Society 130 620633. Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., & Thomas, L. (2001) Introduction to distance sampling Oxford University Press, Oxford, UK. Cochran, W.G. (1977) Sampling techniques. Third edn. John Wiley, New York, NY. Cook, R.D. & Jacobson, J.O. (1979) A design for es timating visibility bias in aerial surveys. Biometrics 35 735742. Dennis, B. (1996) Discussion: Shoul d ecologists become Bayesians? Ecological Applications 6 10951103. Dixon, P. & Ellison, A. (1996) Bayesian inference. Ecological Applications 6 10341035. Ellison, A.M. (1996) An introduction to Bayesian inference for ecological research and environmental decision-making. Ecological Applications 6 10361046. Garshelis, D.L., Joshi, A.R., & Smith, J.L.D. (1999) Estimating density and relative abundance of sloth bears. Ursus 11 8798. Geissler, P.H. & Fuller, M.R. (1987) Estimation of the proportion of area occupied by an animal species. Proceedings of the Section on Survey Research Methods of the American Statistical Association 1986 533538. Gelman, A., Carlin, J.B., Ster n, H.S., & Rubin, D.B. (1995) Bayesian Data Analysis Chapman & Hall, London, UK.
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51 BIOGRAPHICAL SKETCH Arjun Mallipatna Gopalaswamy was born on 10 June 1976 in Bangalore, India. He grew up in a city with his parents and a sister. Wh ile pursuing his undergradu ate education, he was actively involved with a mountaineering club in his college which exposed him to myriad landscapes and forests of India. This made him think more seriously about wildlife and nature conservation issues and a future along those lines. He comple ted his undergraduate education with a bachelors degree in i ndustrial engineering in May 1999. He then started his own software business company and was part of it for two ye ars before deciding to dedicate all his time doing ecology related field work. He worked as a field research assistant in a tiger project of the Wildlife Conservation Society India Program, where he was fortunate to know and benefit from outstanding field biologists and conservationists with whom he worked. In August 2004, he began his graduate study at the University of Florida in the Department of Wildlife Ecology and Conservation. He received his Ma ster of Science in December 2006.