https://cpw.cvlcollections.org/files/original/ede72f1fac8b7c8aa747ee331709f516.pdf 105cb865dd108bdf0ac297c61d0238d9 PDF Text Text The research in this publication was partially or fully funded by Colorado Parks and Wildlife. Dan Prenzlow, Director, Colorado Parks and Wildlife • Parks and Wildlife Commission: Marvin McDaniel, Chair • Carrie Besnette Hauser, Vice-Chair Marie Haskett, Secretary • Taishya Adams • Betsy Blecha • Charles Garcia • Dallas May • Duke Phillips, IV • Luke B. Schafer • James Jay Tutchton • Eden Vardy �Spatially Explicit Power Analyses for Occupancy-Based Monitoring of Wolverine in the U.S. Rocky Mountains Author(s): MARTHA M. ELLIS, JACOB S. IVAN and MICHAEL K. SCHWARTZ Source: Conservation Biology , February 2014, Vol. 28, No. 1 (February 2014), pp. 52-62 Published by: Wiley for Society for Conservation Biology Stable URL: https://www.jstor.org/stable/24479500 JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms Wiley and are collaborating with JSTOR to digitize, preserve and extend access to Conservation Biology This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �Contributed Paper Spatially Explicit Power Analyses for Occupancy-Based Monitoring of Wolverine in the U.S. Rocky Mountains MARTHA M. ELLIS,* JACOB S. IYAN.f AND MICHAEL K. SCHWARTZ* 'University of Montana, Wildlife Biology Program, Missoula, MT 59801, U.S.A., email martha.ellis@umontana.edu tColorado Parks and Wildlife, Wildlife Research Center, Fort Collins, CO 80526, U.S.A. 4:U.S. Department of Agriculture Forest Service, Rocky Mountain Research Station, Missoula, MT 59801, U.S.A. Abstract: Conservation scientists and resource managers often have to design monitoring programs for species that are rare or patchily distributed across large landscapes. Such programs are frequently expensive and seldom can be conducted by one entity. It is essential that a prospective power analysis be undertaken to ensure stated monitoring goals are feasible. We developed a spatially based simulation program that accounts for natural history, habitat use, and sampling scheme to investigate the power of monitoring protocols to detect trends in population abundance over time with occupancy-based methods. We analyzed monitoring schemes with different sampling efforts for wolverine (Gulo gulo) populations in 2 areas of the U.S. Rocky Mountains. The relation between occupancy and abundance was nonlinear and depended on landscape, population size, and movement parameters. With current estimates for population size and detection probability in the northern U.S. Rockies, most sampling schemes were only able to detect large declines in abundance in the simulations (i.e., 50% decline over 10 years). For small populations reestablishing in the Southern Rockies, occupancy-based methods had enough power to detect population trends only when populations were increasing dramatically (e.g., doubling or tripling in 10 years), regardless of sampling effort. In general, increasing the number of cells sampled or the per-visit detection probability had a much greater effect on power than the number of visits conducted during a survey. Although our results are specific to wolverines, this approach could easily be adapted to other territorial species. Keywords: detection probability, occupancy, population monitoring, population trends, sampling design Poder de Anâlisis Espacialmente Explicito para el Monitoreo Basado en Ocupaciôn del Glotön (Gulo gulo) en las Montanas Rocallosas de Estados Unidos Resumen: Cientificos de la conservaciôn y administradores de recursos frecuentemente tienen que disefiar programas de monitoreo para especies que son raras o estân distribuidas en fragmentos a lo largo de paisajes extensos. Taies programas frecuentemente son caros y rara vez pueden ser conducidos por una entidad. Es esencial que un anâlisis prospectivo de poder se lleve a cabo para asegurar que las metas de monitoreo enunciadas son factibles. Desarrollamos un programa de simulaciôn basado en el espacio que toma en cuenta la historia natural, el uso de hâbitaty el esquema de muestreo para investigar el poder de los protocolos de monitoreo para detectar tendencias en la abundancia de la poblaciôn a través del tiempo con un método basado en ocupaciôn. Analizamos esquemas de monitoreo con esfuerzos de muestreo diferentes para poblaciones de glotones (Gulo gulo) en 2 âreas de las Montanas Rocallosas de los Estados Unidos. La relaciôn entre la ocupaciôn y la abundancia fue no-lineal y dependia del paisaje, el tamafio de la poblaciôn y los parâmetros de movimiento. Con las estimaciones actuates del tamafio de poblaciôn y la probabilidad de detecciôn en las Rocallosas del norte de los Estados Unidos, la mayoria de los esquemas sôlo pudieron detectar disminuciones grandes en la abundancia en las simulaciones (p. ej.: 50% de disminuciôn a lo largo de 10 anos). Para poblaciones pequenas restableciéndose en las Rocallosas sureüas, los métodos basados en ocupaciôn tuvieron suficiente poder para detectar tendencias de poblaciôn solamente cuando las poblaciones Paper submitted July 17, 2012; revised manuscript accepted April 28, 201J. 5^ Conservation Biology, Volume 28, No. 1, 52-62 © 2013 Society for Conservation Biology DOI: 10.1111/cobi.l2139 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �Ellis et al. 53 estaban incre esfuerzo de m por visita tuv nuestros resu especies territ Palabras Clave cias de poblac (Field et al. 2005; MacKenzie 2005; Marsh & Trenham Introduction 2008). Before launching an occupancy study, some form of Wildlife power analysis should be conducted pop to allocate mon tions itoring in effort efficiently (Field abu et al. 2005; MacKenzie ural and 2005; Rhodes et al. 2006). Most researchers ant base power Hoffmann et al. 2010; Rands et al. 2010; Inman et analyses for occupancy estimation on detection of de al. 2011). Currently, many populations face multiple clines in occupancy over time; however, these simu threats, including habitat fragmentation and loss, climate lations rarely consider spatial dynamics. Also, monitor change, direct and indirect exploitation, disease, invasive ing trends in occupancy is often used as a surrogate species, and interactions among these threats (Primack for trends in abundance, but this link is rarely eval uated (but see Rhodes et al. 2006; Rhodes & Jonzén 2006; Laurance et al. 2008; Povilitis & Suckling 2010). In response, many countries have adopted legislation 2011). To this end, we built a species-specific model of changes in abundance over time from which we sam aimed at affording protection to species of conservation concern. Two of the more powerful pieces of legisla pled repeat detection and nondetection data to deter tion are Canada's Species at Risk Act and the United mine power to detect population trends under various scenarios. States' Endangered Species Act (ESA). These acts not only identify species at risk and aim to protect them We designed our approach to assess effort required from additional harm, but also stipulate mechanisms for for a large-scale wolverine (Gulo gulo) monitoring ef recovery. For example, in the United States approxi fort. Wolverines are a Holarctic carnivore species known mately half of the annual budget spent on threatened for their large home ranges, low densities, and occa and endangered species is designated for recovery (GAO sional long-distance movements (Lofroth & Krebs 2007; 2005; Male & Bean 2005). However, determining whenSquires a et al. 2007; Inman et al. 2012). The species is species of concern is declining or subsequently recov currently being considered for listing under the ESA (US ering requires information on trends in relevant state FWS 2010), primarily due to the large decrease in their variables. abundance and the possibility that the species was elim Most researchers who have examined trends in wildlife inated from the contiguous United States in the early have based their assessments on changes in the abun 20th century. Wolverine populations have returned to dance of individuals (Dennis et al. 1991; Bart et al. Idaho, Montana, Washington, and Wyoming, and single 2007; Foster et al. 2009; Broms et al. 2010). Although male wolverines have recently recolonized California and estimates of abundance are important, other measures Colorado (Aubry et al. 2007; Moriarty et al. 2009). Yet, such as changes in genetic or demographic param wolverines are still absent from substantial portions of eters within a population or changes in geographic their historical range. Their current abundance in the range size have been used to infer population trends contiguous United States is likely to be at most 500 individuals. (Gaston 1991; Schwartz et al. 2007; Marucco et al. 2009; Broms et al. 2010). Recently, more attention has been Aubry et al. (2007) and Copeland et al. (2011) found placed on estimating changes in occupancy of a species that the historical distribution of wolverines is consistent geographic range (Joseph et al. 2006; MacKenzie et al. with the distribution of persistent spring snow. On the 2006). Occupancy estimation usually requires multiple basis of 7 years of satellite images of snow cover from 24 visits to a set of sample units, where detection or non April-15 May, Copeland et al. (2011) found that >99% of detection of species of interest is recorded during each wolverine den sites and >89% of year-round telemetry lo visit. Repeat-visit data are used to simultaneously model cations were in areas classified as having persistent spring species occupancy and detectability so as to reduce the snow. Furthermore, Schwartz et al. (2009) demonstrated bias induced by imperfect detection (MacKenzie et al. that wolverine gene flow is facilitated in areas with per 2006). If occupancy estimation is conducted over multi sistent spring snow relative to areas that are free of ple time intervals, trends in occupancy can be estimated snow. Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �54 Power in Occupancy-Based Trend Detection though wolverines are thought to have occurred there historically (Aubry et al. 2007) and there seems to be ad equate habitat, including persistent spring snow (Aubry et al. 2007; McKelvey et al. 2011). Areas of persistent spring snow are more patchily distributed in the Southern Rockies and are separated from areas of persistent spring snow in the Northern U.S. Rockies by >200 km. Individual Utilization Distributions We randomly selected points within areas of persistent spring snow (using Copeland et al. 2010) for the center of individual home ranges for adult female, adult male, and transient male wolverines. Among these 3 groups, locations were chosen independently to allow for over lapping home ranges (Copeland 1996; Inman et al. 2011); however, within each group, selection of home range centers was constrained to reflect territoriality (Support ing Information). All home range centers were located in snow patches large enough to support at least one resident female wolverine (Krebs et al. 2007). Once home range centers were established for a given simulated landscape, we assigned a bivariate normal uti lization distribution for each individual that we based on estimated home range parameters (Supporting Informa tion). These distributions were weighted by the availabi ity of persistent spring snow. Thus, each of the individual Figure 1. Study areas (dashed lines) and distribut utilization distributions took a unique shape on the basi of persistent spring snow in the U.S. Rocky Moun of location of the home range center and availability of (shading). snow. As distance from home range center increased, probability of use decreased. Following these rules, our program, SPACE (spatially We used habitat (i.e., persistent snow), mo based power analysesspring for conservation and ecology), cre ment, and home range data to build a spatially bas ated 1000 surfaces for initial populations of N0 = 500 o model with which to assess the power of Rockies monitor N0 = 200 individuals in the Northern landscape. efforts aimed at wolverine in their current range and These values reflected high and low estimates of wolver areas they may eventually recolonize naturally or thr ine population size in the study area. We simulated 10% reintroduction. 20%, or 50% declines in population size over a decade (À = 0.989, 0.977, 0.933) by randomly removing an ap propriate number of individuals in each time step. We Methods also simulated a hypothetical reintroduced or recoloniz ing population in the Southern Rockies. These popula Study Area tions were started with N0 = 30 individuals and allowed to increase by 50%, 100%, or 200% over a decade (X = 1.041, 1.072, 1.116). We initiated all populations with a 2:1:2 ratio of females:resident males:transient males (see northwest Wyoming (Fig. 1). This area is known to be Supporting Information for details). occupied by wolverines; current population estimates range from 200 to 500 individuals (USFWS 2010). We allowed areas used by simulated wolverines to extend Sampling up to 50 km into Alberta and British Columbia, Canada, to account for continuous wolverine populations in theThe second stage of our simulation was to create en Northern Rockies, but these areas were not included in counter histories (i.e., data necessary for occupancy es timation) for each simulated landscape. We initially di the sampling. We included the mountainous region of the Southern vided the study area into 225-km2 sample units (cells), an Rocky Mountains as a secondary study area. This area area that matches home range sizes for resident females, does not currently have a population of wolverines, al which is a strategy widely used for monitoring carnivores The primary study area was the U.S. Rocky Mountains in northern and central Idaho, western Montana, and Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �Ellis et al. 55 (e.g., a random Zielin effect of year (Burnham & White 2002; Laake not & Rexstad 2012). This approach over assumes the occupancy estimates came from a normal distribution centered along resulted in region and a declining trend line, and process variance (i.e., year-to explored year differences) was treated separately from parameter ho did ning more uncertainty. As such, it may be more realistic than simply s that were 1 fitting a linear trend model to the data (with no random probability effect), which forces each of the occupancy estimates each cell (he to fall directly on a line. To account for sampling effort, simulated e we applied a finite population correction to the trend 10 years estimate that reduced the sampling variance by a(s factor of (N — n)/N, where N is the total number of cells in explored th with the sampli study area and n is the number of cells included in subsamplin the sample (Supporting Information). With a significance ing Informa value (a) of 0.05, a trend was detected if the 95% con fidence interval of the trend parameter excluded zero and was in the correct direction. Thus, we computed the Estimated Oc statistical power produced by a sampling scenario (i.e., The encoun probability a significant trend is detected given that a annual trend exists) as the percentage estim of simulations in which a trend was detected. for each sim the subject We repeated the power analysis, as described previ capable of ously, across 1000 simulated landscapes produced for visits, v each combination ofwe population change, population size, estimation simulated detection probability (psim), number of visits, t of samplin cell size, number of cells sampled, and annual or alter not change nate year sampling schemes (Table 1). For alternate-year Due to sampling, we fitted thethis linear random effect model to pancy param occupancy estimates from data in odd years only. Where in which th applicable, all sampling was cumulative to facilitate the cell is stati most meaningful contrasts between levels of a parameter. the estimat For example, a sample of 50 cells would include the same context cells as a sample of 25 cells with an wa additional 25 cells the study included. We bracketed the sampling parameters (cell a occupied, a size, detection probability, visits) on the basis of previous here efforts on ref described in the literature (Magoun et al. 2007; 2006). Gardner et al. 2010; Furt Magoun et al. 2011). bility Our simulations gene were intended to be generalizations; uct of dete we did not attempt to specifically define the sampling tion given season, sampling mechanism, or what constitutes a visit. quantity is The simulations are subject to limitations. First, the man and the pr ner in which we determined availability of animals to thus available for detection (MacKenzie et al. 2006). be detected (integrating the individual utilization distri We refer to the detection probability estimated by the butions across each cell [Supporting Information]) best model as pest and the actual detection probability spec reflects protracted sampling over time (i.e., each visit or ified for the simulations as psim, such that pest = psim x sampling occasion is composed of several weeks) with probability of presence. cameras or hair snares, which sample animals directly. We used the R package RMark (R Development Core Simulating other sampling methods such as aerial surveys, Team 2011) to input the encounter histories and fit track surveys, or scat collection, would require treating a multiple season, implicit dynamics occupancy model each visit as a snapshot in time or accounting for decay of in Program MARK (White & Burnham 1999). For each sign. With protracted sampling, the relation between oc model fit, we extracted the derived occupancy estimates cupancy and abundance may be more blurred compared (i.e., on a probability scale) and their variance-covariance to a snapshot approach due to movement of individuals matrix for each year over the 10 years of each simulation. within the sampling period. Second, we assumed visits We then used the variance components procedure in were defined through time such that the availability of RMark to fit a linear trend model to the estimates with an animal during one visit was independent of other Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �56 Power in Occupancy-Based Trend Detection Table 1. Variables and ranges of values tested in simulations of potenti Variable Values tested Initial population size Population growth rates N0 = 30, 200, 500 X = 0.933, 1.041, 1.072, 1.116 for N0 = 30 X = 0.933, 1 041 for JV0 = 200 X = 0.933, 0.977, 0.989, 1.041 for N0 = 500 none; 1, 2 SD from home range center Limit on movement Simulated detection probability Number of cells sampled 0.2, 0.8 10-90% of grid Number of visits 2-7 Cell size 100, 225, 500, 1000 km2 Sampling annual or alternating years Visits. We did not consider cases in which replicate visits occurred over a short time such that availability did not change between visits (e.g., multiple independent ob servers on a single visit or clusters of cameras in relatively close proximity). Third, we assumed the population was closed demographically over the course of each annual survey and that surveys occurred at a time of year (i.e., winter) when animals generally confined their move ments to a specific home range (e.g., other than those animals we defined as transients, adult animals did not and a declining population (X = 0.933). Even with per fect detection and intense sampling, detecting a large decline (50% over 10 years) in a large starting population (N0 — 500) required a sample of 90 of 388 cells (Fig. 2) to achieve adequate power (>80% chance of detecting the trend). As the population size decreased, the amount of sampling needed to detect a 50% decline even under this best-case scenario increased dramatically. For example, for N0 — 200, achieving 80% power required sampling approximately 120 cells (Fig. 2). Power to detect trends make exploratory movements or disperse). Finally, we was generally lower for increasing populations relative to assumed that as population size changed, animal home scenarios with decreasing populations. For example, to detect a 50% increase (X = 1.041) with > 80% confidence, ranges remained the same size. the required number of cells increased from 90 to 245 for Results No — 500 and 120 to 225 for N0 = 200. Detecting trends in small populations (N0 = 30) was difficult; a census of cells would be required to detect either a 50% increase Due to the spacing rules among individuals that we used or decrease. With current population sizes (iVo = 500) in the North to reflect wolverine territoriality, the Northern Rockies ern Rockies, the ability to detect declines decreased dra landscape became saturated with approximately 850 in matically as the strength of the decline decreased (Fig. 3). dividuals (mean [SD] across 100 simulated landscapes: For a 20% decline in population size over 10 years, a 420 [6] females, 219 [4] resident males, 219 [4] transient census of cells with perfect detection (psim = 1) would males). For TV = 800, the median probability of at least one be required to detect the population change with 80% wolverine per cell (i.e., probability of presence) was 0.74. power. For a 10% population decline, this effort would This yielded, on average, 280.4 cells in which wolver give <60% power. With either population increases or de ines were available for detection per sampling occasion clines, sampling every other year substantially increased across the 388 cells in the grid. As the population size the number of cells and visits that would need to be decreased, the probability of presence decreased to 0.54 included relative to annual sampling. (212.4 cells with wolverine available per occasion) for N0 = 500 and the probability of presence was 0.05 (18.9 cells with wolverine available per occasion) for TV0 = 30. Trade-Offs in Sampling Methods Assuming perfect detection (psim = 1), these cell-based probabilities of presence translated to an estimated occu The sampling parameter that most affected power pancy (40 of 0.97 [0.01] for populations with N0 = 500 detect change was the simulation detection probabi individuals and 0.22 [0.04] for 7V0 = 30. (psim)- In nearly all scenarios, relatively large gain power were realized when ps\m increased from 0 0.8. For instance, a monitoring scheme that require Effects of Population Size and Trend visits to each of 125 cells had approximately 10% ch of detecting a 50% decline over 10 years when psi We investigated the upper limits of power to detect pop 0.2. Power for detecting that same decline under ulation trends with occupancy estimation by examining same sampling regime increased to 80% when />si results when detection probability was perfect (psim = 1) and cells were visited numerous times (5). We focused 0.8 (Fig. 3, upper left panel). By comparison, for p = 0.2, an increase in sample size from nCeiis = 125 these analyses on the U.S. Northern Rockies landscape Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �57 N0=30 N0=30 N0 = 200 100 200 N0 = 500 300 Number of cells sampled Figure 2. Effect of initial wolverine p Rocky Mountains. Perfect detection Çk = 1.041) from initial population s a grid of225-km2 cells overlaid on th to nceiis = 300 increased cells (25,000 km2) from the power small grid versus 125 to cells app Similar gains in power relative to simulation detec (28,125 km2) for the medium-sized grid. As the size of tion probability and sample size were realized in other the grid increased, the power to detect trends decreased. scenarios. The 1000-km2 grid produced very low power to detect The number of visits to each sample unit affected population trends. In this case, the grid in the Northern power as well, although generally to a lesser degree Rockies comprised only 76 cells. Including every cell in than population change,ps\m, and sample size. Even with the population, with 7 visits and high detection proba p5im = 1, the power to detect a trend increased with the bility, we detected a 50% population declines in <5% of number of visits at each grid cell due to the number of the simulations. For some scenarios, we observed a phe opportunities for an individual to be present. When simu nomenon in which power was actually reduced when lation detection probability was high but imperfect (i.e., there were a high number of visits (Fig. 5) (500-km2 and psim = 0.8), some gain in power was realized by visiting each sampled cell 4 times versus visiting cells 2-3 times (Fig. 3). However, there was no appreciable difference in power for 4, 5, 6, or 7 visits. When simulated detection 1000-km2 scenarios). probability was low (i.e., /;sim = 0.2), potentially greater Power to Detect Increases in Small Populations The number of cells and the total area that required sampling was affected by cell size (Fig. 5). Grids of 100 For small populations (N0 = 30), power to detect pop ulation trends was limited except for situations with large population increases and high detection proba bility (Fig. 4). For the purposes of comparison, there was slightly greater power for detecting trends in the Southern Rockies landscape than in the Northern Rock ies, although the total sampling area in the Southern Rockies landscape was approximately one-third of the km2 and 225-km2 cells yielded similar power in terms of Northern Rockies. For both landscapes, a doubling of the the percentage of the grid that needed to be sampled, although the smaller cell size required sampling more cells. Assuming 5 visits and high detection, achieving 80% power for detecting a 50% decline required 250 population over 10 years (À = 1.072) could be detected with >80% power in scenarios where a large proportion of the landscape was included with relatively high cap ture probability. If simulation detection probability was gains in power were realized by making more visits, but it depended on the scenario (Figs. 3 and 4). Effect of Cell Size Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �S8 Power in OccuDancv-Based Trend Detection #*; A''''-"' , * # « * <> » . - / #/ ' y-v * ♦/ * * ' f. 4 « #/. < + ' + . 4> ,*V,'V' ,y>y.V * '* ** //vVv'^ A ^ »L *• % «1y* ,«v, »> '/ 300 0 100 Number of cells sampled Figure 3■ Results ofpower analyses population of wolverines in the No km2). Results are parsed by popula 20%, or 10% decline or 50% increase annually or every other year), dete grid cells sampled from a total of3 low, then adequate power could only be achieved via sampling a large portion of the available landscape and making a large number (>5) of visits to each sampled cell. 1000-km (Gardner et al. 2010) sampling cells to use of cameras at bait stations (Mulders et al. 2007; Magoun et al. 2011), to use of noninvasive genetic sampling (Ulizio et al. 2006; Schwartz & Monfort 2008; Magoun et al. 2011). These methods produced detection probabilities of 0.2-0.8 as bracketed in our simulations. However, Discussion matching estimates from field studies to our results re quires care. Pilot analyses of detection probability de Monitoring population trends is one of the most com rived from occupancy surveys yield pcst, which is not the mon challenges for management of endangered species. same as psim in our analyses. Occupancy models cannot Using a spatially explicit simulation for wolverine in the separate the effects of true detection probability (psim) U.S. Rocky Mountains tested the ability of occupancy and probability of presence (see Methods). Instead they based approaches to detect trends in population size estimate the product. Consequently, pest returned from under a range of monitoring scenarios. Even for large pilot studies will be smaller than the detection probabili changes in population size (e.g., 50% declines over 10 ties used in our simulations (psim). If pilot work indicates years), detecting population trends required large-scale, pl:st = 0.2, power can be assumed to be better than the intensive sampling. In many scenarios, no amount curves of shown for psim — 0.2 in our figures. The exact sampling could produce sufficient power to achieve correspondence between pesx and psim depends on the monitoring goals. Our results highlight the impor landscape, cell size, population size, territoriality, and tance of analyzing the statistical power of monitoring home range size of the species in question. Thus, no schemes. rule of thumb holds for converting between the 2 types of detection probability. However, matching pest derived from pilot work to curves for psim can still be useful; Interpreting Detection Probabilities such an exercise will result in conservative estimates of In the case of the wolverine, work has commenced to power. evaluate the effectiveness of various approaches for de Pilot work specific to occupancy monitoring for wolverine in the Northern Rockies has been conducted tecting presence. These range from using fix-winged air craft to find tracks in 100-km2 (Magoun et al. 2007) orusing camera stations (R. Inman, unpublished data) a Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �Ellis et al. 59 Northern Northern Southern * ***** * + * 4 * + + ** * * ***#* # * <> *. *.** * * t * * ****** * S" ?" *** * ** / IIh * * + + * + * s * / * / * / * + o p + * + * + * + * CD * * * . * * CO * ** ,* .* *** * ^ * ** * * **** * * <* » ** ^ CO ^#*# *%*** » * * J. .4 .4 *+* ** **.* *' ***** .** * * * +** * * * * + * * * * * , v * ** *# * #* ******** ****** >> it I! —J. * ** ** * * ^ > <» * * r i ■— ^ .si*?' ^* « * ^ 90*A ^ * "V » ^V' ****** ***** *** «►> ** ** # * *# * '+*** + **s ** / *****/* / * /// + **++ * * * + * +*■* * + * # * * * * * * li _4. * * * ,* .* * *** ** / * o ^I***** ro l-'" J" ■ WÊÊmmSm ' I. ^o-r = Y <■] <'/>.'* *'/****' '' ** ** ** * * '' ** +' y . '*' S #+# + + '* /' <» + # + // <t ' + - + *** «/ *' ** / * ' », *, * * * *# * ,y ,y ***** it il —*. o> Figure 4. Pow population tre 30 wolverines in Northern U.S. Rocky Mountains compared with a population of the same size in the Southern Rocky Mountains. Population growth rates (X = 0.933, 1.041, 1.072, 1.116) correspond to a 50% decline or 50%, 2-fold, or 3-fold increases in population size over 10 years, respectively. Sampling effort includes detection probability for sampling (pSim)> number of visits per year, and number of grid cells sampled from a total of388 cells for the Northern U.S. Rocky Mountains or 128 for the Southern Rocky Mountains. Power is based on number ' of detected trends from 100 200 300 25 50 Number 75 100 of 125 cells 1000 simulated sampled populations. hair snares (J- Waller, unpublished data) in 100-km2 Effects of Landscape and Cell Size sample units. Initial results from this work suggest pest Even for fixed population sizes, the effect of the under is approximately 0.25-0.3, which in our simulations cor lying landscape extends to the power to detect popula responded to psim «0.8 (i.e., pest = psim x probability tion changes. Power to detect trends in occupancy was of presence; mean probability of presence was 0.33, similar in terms of percentage of the total study area therefore 0.25/0.33 « 0.76). From this estimate, and included in the sample when comparing the Northern assuming 3-4 visits to each sample unit (sampling oc versus Southern Rockies but very different in terms of curred during 3-4 months over winter for each pilot the absolute area that needs to be sampled. For example, study), our results suggest that roughly 100-150 of the to detect a 3 times increase of the N0 = 30 populations 100-km2 cells would need to be sampled per year to at with a 225-km2 grid and >80% power required sampling tain an 80% probability of detecting a 50% decline in approximately 35% of either landscape, which translates the Northern Rockies population (Fig. 5). Thus, moni to sampling 30,000 km2 in the Northern Rockies versus toring will require well-coordinated surveys across mul 10,000 km2 in the Southern Rockies. Yet, changing the tiple entities and jurisdictions. Anything less than a large size of a study area would generally also change the size scale, coordinated effort will likely be of limited or no value. of the population included, which we found substantially affected power to detect trends. Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �60 rower in Occupancy-based lrend Detection 100 km* iI 0.00 o.oo - ® 0.75 0.75 '- a) a> Q a 200 300 40 Number of cells sampled Figure 5. Effect of grid size (1 = 500) in the Northern Rocky for sampling (psim) and numbe in occupancy estimates have because the loss of de To date, mostbe reflected authors individualsspecies will swamp any compensation in home range veys for mobile such t size. to or greater than the typical et al. 2010; O'Connell & Bailey 2011). Our results in dicate this type of design (i.e., cell size = 225 km2) would work well, although power to detect declines in estimated occupancy could be somewhat better when cell size was actually smaller than a typical home range (i.e., 100 km2). Efford and Dawson (2012) explore the relation between home range size, animal density, and occupancy and found that similar occupancy estimates Relation of Number of Visits to Power For some scenarios, we note a counterintuitive anomaly in which conducting more visits actually decreased power. This phenomenon was likely due to 2 characteris tics of our simulations. First, we allowed transient males to range widely over the course of the survey period such that technically each cell was used in each year and true depending on home range size. They suggest this con ^ — 1.0 for all years. Thus, if we sampled long enough founding is minimized when cell sizes are much larger (made more visits), estimates of *I> all tended toward 1.0, (i.e., 10 times larger or more) than the typical home range and power was lost because there was no trend. Second, our simulation was set up to reflect a scenario where size. However, when the sole objective is to detect trends in occupancy estimates through time, we found that very visits occurred over a protracted period (3-4 months), large cell sizes (500 or 1000 km2) resulted in poor power. and availability was independent between visits; thus, it This is likely because home ranges for many individuals was possible to sample transient animals almost every where. If all visits were made simultaneously, availability would be included in any large cell. Occupancy is less sensitive to the underlying number of animals on the would be instantaneous and fixed across visits. In that landscape, and relatively large declines in a population case occupancy should track abundance more closely could occur before cells would become unoccupied. Re and conducting more visits during this snapshot in tim gardless of cell size used for a survey, our results depend should increase power as expected. can be derived from very different underlying densities, critically on the assumption that home range size remains relatively constant, whereas abundance changes (Efford Final Considerations & Dawson 2012). If declines are related to changes in habitat quality, this assumption may be tenuous, although Using a spatially based framework to evaluate the power we argue that at some point a declining population will of monitoring efforts, we were able to quantify the effects Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �Ellis of et al. 6l Literature Cited sampling trends. Our simulations did not include cost functions, so trade-offs in sampling effort are currently missing an important real-world consideration. For instance, in a given situation, it may be easy to complete more visits Aubry, K. B., K. S. McKelvey, and J. P. Copeland. 2007. Distributio and broadscale habitat relations of the wolverine in the contigu ous United States. The Journal of Wildlife Management 71:214 2158. Bart, J., S. Brown, B. Harrington, and R. I. G. Morrison. 2007. Survey to a site, but extremely costly to improve capture proba trends of North American shorebirds: population declines or shifting bility. Therefore, managers may opt to make more visits distributions? Journal of Avian Biology 38:73-82. to improve power even though intensifying effort (visits) Broms, K., J. R. Skalski, J. J. Millspaugh, C. A. Hägen, and J. H. Schulz. by a given percentage may be inferior to improving detec 2010. Using statistical population reconstruction to estimate demo graphic trends in small game populations. The Journal of Wildlife tion probability by a similar percentage. Thus, managers should superimpose cost and logistics over these statisti cal results to make informed decisions about monitoring. Management 74:310-317. Burnham, K. P., and G. C. White. 2002. Evaluation of some random ef fects methodology applicable to bird ringing data. Journal of Applied Most studies base power analyses for occupancy esti Statistics 29:245-264. mation solely on detecting various simulated declines in Butchart, S. H. M., et al. 2010. Global biodiversity: indicators of recent declines. Science 328:1164-1168. occupancy. Here, we used a more mechanistic, spatially Copeland, J. P. 1996. Biology of wolverine in central Idaho. University based approach in which we applied simulations to force of Idaho, Moscow. declines or increases in the real parameter of interest Copeland, J. P., et al. 2010. The bioclimatic envelope of the wolverine (abundance). We then determined whether occupancy (Gulo guloy. Do climatic constraints limit its geographic distribu estimation could detect those changes. This approach tion? Canadian Journal of Zoology-Revue Canadienne De Zoologie 88:233-246. also sets the stage for direct comparisons between occu Dennis, B., P. L. Munholland, and J. M. Scott. 1991. Estimation of growth pancy and estimation of other metrics (e.g., abundance) and extinction parameters for endangered species. Ecological Mono that could potentially be used to monitor populations. graphs 61:115-143. Although our results can be used directly to guide the Efford, M. G., and D. K. Dawson. 2012. Occupancy in continuous habi monitoring of wolverine or similar species, the largest tat. Ecosphere 3:1-15. contribution is the framework, which can be used for making decisions about the design of large-scale monitor ing efforts, provided information on movement and habi tat use is available. Our goals were to establish this frame work to encourage cost-effective decisions in designing monitoring programs and to inspire well-coordinated surveys across multiple entities and jurisdictions. With out such coordination our analyses convincingly show that most efforts for species like the wolverine will be wasted. Field, S. A., A.J. Tyre, and H. P. Possingham. 2005. Optimizing allocation of monitoring effort under economic and observational constraints. The Journal of Wildlife Management 69:473-482. Foster, C. R., A. F. Amos, and L. A. Fuiman. 2009. Trends in abundance of coastal birds and human activity on a Texas barrier island over three decades. Estuaries and Coasts 32:1079-1089. GAO (U.S. Government Accountability Office). 2005. Fish and Wildlife Service generally focuses recovery funding on high priority species, but needs to periodically assess its funding decisions. Report GAO 05-21 l.GAO, Washington, D.C. Gardner, C. L., J. P. Lawler, J. M. V. Hoef, A.J. Magoun, and K. A. Kellie. 2010. Coarse-scale distribution surveys and occurrence probability modeling for wolverine in interior Alaska. The Journal of Wildlife Management 74:1894-1903 Gaston, K. J. 1991. How large is a species' geographic range? Oikos 61:434-438. Acknowledgments Hines, J., J. Nichols, J. Royle, D. MacKenzie, A. Gopalaswamy, N. S. We thank P. Lukacs, G. White, F. Allendorf, and L. BaileyKumar, and K. Karanth. 2010. Tigers on trails: occupancy modeling for cluster sampling. Ecological Applications 20:1456-1466. for providing invaluable technical advice and J. Laake for Hoffmann, M., et al. 2010. The impact of conservation on the status of implementing the "random occupancy dynamics" model the world's vertebrates. Science 330:1503-1509. into RMark so it could be used in this analysis. We thank Inman, R. M., et al. 2012. Spatial ecology of wolverines at the south ern periphery of distribution. The Journal of Wildlife Management R. Inman and J. Waller for generously sharing field data. We thank the RMRS and a PECASE award to M.K.S. for providing the initial funding for this effort. 76:778-792. Joseph, L. N., S. A. Field, C. Wilcox, and H. P. Possingham. 2006. Presence-absence versus abundance data for monitoring threatened species. Conservation Biology 20:1679-1687. Supporting Information e Krebs, J., E. C. Lofroth, and I. Parfitt. 2007. Multiscale habitat use by wolverines in British Columbia, Canada. The Journal of Wildlife Management 71:2180-2192. Laake, J. L., and E. Rexstad. 2012. RMark—an alternative approach to building linear models in MARK. In E. Cooch and G. Detailed methods for program SPACE (Appendix SI) are available online. The authors are solely responsibleWhite, for editors. Program MARK: a gentle introduction. C. Available at http ://www.phidot. org/software/mark/docs/book/pdf/app_3 .pdf. the content and functionality of these materials. Queries Laurance, W. F., S. G. Laurance, and D. W. Hilbert. 2008. Long-term mammal assemblage. Conser (other than absence of the material) should be directed dynamics of a fragmented rainforest to the corresponding author. vation Biology 22:1154-1164. Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms �62 Power in Occupancy-Based Trend Detection Lofroth, E. C., and J. Krebs. 2007. The abundance and distribution of wolverines in British Columbia, Canada. The Journal of Wildlife Primack, R. B. 2006. Essentials of conservation biology. Sinauer Asso Management 71:2159-2169. MacKenzie, D. I. 2005. What are the issues with presence-absence data R Development Core Team. 2011. R: A language and environment for wildlife managers? The Journal of Wildlife Management 69:849 860. MacKenzie, D. I., J. D. Nichols, J. A. Royle, K. H. Pollock, L. L. Bailey, and J. E. Hines. 2006. Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Elsevier, Amsterdam. Magoun, A. J., C. D. Long, M. K. Schwartz, K. L. Pilgrim, R. E. Lowell, and P. Valkenburg. 2011. Integrating motion-detection, cameras, and hair snags for wolverine identification. The Journal of Wildlife Management 75:731-739. Magoun, A. J., J. C. Ray, D. S. Johnson, P. Valkenburg, F. N. Dawson, and J. Bowman. 2007. Modeling wolverine occurrence using aerial surveys of tracks in snow. The Journal of Wildlife Management ciates, Sunderland, Massachusetts. for statistical computing. R Foundation for Statistical Computing, Vienna. Rands, M. R. W., et al. 2010. Biodiversity conservation: challenges be yond 2010. Science 329:1298-1303. Rhodes, J. R., and N. Jonzén. 2011. Monitoring temporal trends in spatially structured populations: How should sampling ef fort be allocated between space and time? Ecography 34:1040 1048. Rhodes, J. R., A. J. Tyre, N. Jonzén, C. A. McAlpine, and H. P. Poss ingham. 2006. Optimizing presence-absence surveys for detect ing population trends. The Journal of Wildlife Management 70: 8-18. Schwartz, M. K., J. P. Copeland, N. J. Anderson, J. R. Squires, R. M 71:2221-2229. Inman, K. S. McKelvey, K. L. Pilgrim, L. P. Waits, and S. A. Cushman 2009. Wolverine gene flow across a narrow climatic niche. Ecology Male, T. D., and M.J. Bean. 2005. Measuring progress in US endangered 90:3222-3232. species conservation. Ecology Letters 8:986-992. Schwartz, M. K., G. Luikart, and R. S. Waples. 2007. Genetic monitoring Marsh, D. M., and P. C. Trenham. 2008. Current trends in plant and as a promising tool for conservation and management. Trends in animal population monitoring. Conservation Biology 22:647-655. Marucco, F., D. H. Pletscher, L. Boitani, M. K. Schwartz, K. L. Pilgrim, Ecology & Evolution 22:25-33 Schwartz, M. K., and S. L. Monfort. 2008. Genetic and endocrine tools and J.-D. Lebreton. 2009. Wolf survival and population trend us for carnivore surveys. Pages 228-250 in R. A. Long, P. MacKay, J. ing non-invasive capture-recapture techniques in the Western Alps. C. Ray, and W. J. Zielinski, editors. Noninvasive survey methods for Journal of Applied Ecology 46:1003-1010. North American carnivores. Island Press, Washington, D C. McKelvey, K. S., J. P. Copeland, M. K. Schwartz, J. S. Litteil, K. B. Aubry, J. R. Squires, S. A. Parks, M. McGuire Eisner, and G. S. Mauger. 2011. Predicted effects of climate change on wolverine distribution and movement in western North America. Ecological Applications 21:2882-2897. Squires, J. R., J. Copeland, T. J. Ulizio, I. K. Schnvartz, and L. F. Ruggiero. 2007. Sources and patterns of wolverine mortality in western Montana. The Journal of Wildlife Management 71:2213 2220. Ulizio, af T. J., J. R. Squires, D. H. Pletscher, M. K. Schwartz, J. J. Claar, Moriarty, K. M., et al. 2009. Wolverine confirmation in California and L. F. Ruggiero. 2006. The efficacy of obtaining genetic-based ter nearly a century: Native or long-distance immigrant? Northwest Science 83:154-162. identifications from putative wolverine snow tracks. Wildlife Society Mulders, R., J. Boulanger, and D. Paetkau. 2007. Estimation of popula Bulletin 34:1326-1332. tion size for wolverines Gulo gulo at Daring Lake, Northwest Terri USFWS (U.S. Fish and Wildlife Service). 2010. Endangered and threat ened wildlife and plants; 12-month finding on a petition to list the tories, using DNA based mark-recapture methods. Wildlife Biology 13:38-51. North American wolverine as endangered or threatened. Federal Register 75:78030-78061 O'Connell, A. F., and L. L. Bailey. 2011. Inference for occupancy and oc White, G. C., and K. P. Burnham. 1999. Program MARK: survival es cupancy dynamics. Pages 191-205 in A. F. O'Connell, J. D. Nichols, and K. U. Karanth, editors. Camera traps in animal ecology. Springer, timation for populations of marked animals. Bird Study 46:120 New York. 138. Povilitis, A., and K. Suckling. 2010. Addressing climate change Zielinski, threats W. J., and H. B. Stauffer. 1996. Monitoring Martes populations in California: survey design and power analysis. Ecological Applica to endangered species in U.S. recovery plans. Conservation Biology tions 6:1254-1267. 24:372-376. Conservation Biology Volume 28, No. 1, 2014 This content downloaded from 174.205.238.193 on Thu, 21 Oct 2021 15:54:32 UTC All use subject to https://about.jstor.org/terms � https://cpw.cvlcollections.org/files/original/4485f8ba835a7d558b6a25b66af3d102.pdf d2ac304a706c9f6af877c0ecd367c968 PDF Text Text Appendix S1 - Detailed methods for SPACE as applied for wolverine populations in the Northern U.S. Rockies. Program summary The goal of SPACE is to create a framework for assessing the power of occupancybased methods to detect declines or increases in the real parameter of interest, population size. SPACE incorporates information on habitat, movement, and natural history for a species (e.g., territoriality, difference between sexes) into a spatiallyexplicit simulation, and outputs simulated encounter history data, which can then be analyzed using occupancy models. Below we describe the detailed methodology as applied for wolverine populations in the U.S. Northern Rockies. Methods Habitat layer For wolverine in the U.S. Northern Rockies, we based the spatial simulation in SPACE on the distribution of persistent spring snow cover (from Copeland et al. 2010) based on a 21-day composite (24 April-15 May) of images from 2000-2006 at a 0.5 km2 resolution using moderate resolution imaging spectroradiometer (MODIS) satellite images (Hall et al. 2006). Areas that were characterized as having persistent spring snow in at least one of the seven years had a weight of 1 for the probability of use whereas areas without spring snow had a weight of 1/20, based on resistance values found for models of genetic least cost paths (Schwartz et al. 2009). Distribution of individuals We considered three types of individuals in our analysis (resident females, resident males, and transient males) in a ratio of 2 females:1 resident male:2 transient males for the population. Wolverines are a territorial species; however home ranges may overlap between the different types of individuals (Copeland 1996, Inman et al. 2012). Estimated home range sizes were 225 km2 for females and 500 km2 for males (Banci 1994, Krebs et al. 2007, Schwartz et al. 2009). Parameters used in designing inidividual utilization distributions are described in Table 1 (below). The first step in SPACE is to distribute individuals on the landscape. We randomly selected points within areas of persistent spring snow for the center of individual home ranges for adult female, adult male, and transient male wolverines. Buffer distances required between home ranges centers were at least twice the radius of the home range size (i.e. 2*8.5 = 16 km between home range centers for adult females based on a 225 km2 home range, and at least 25.2 km for adult and transient males). We required that all home range centers were located in snow patches large enough to support at least one resident female wolverine (Krebs et al. 2007). Within each group (adult females, resident males, transient males), locations for home range centers were randomly selected in an iterative fashion until no additional individuals could be placed in the landscape or until the desired number of individuals was met. 1 �Table 1: Parameters used for designing indiidual utilization distributions. Types of individuals Females Resident males Transient males Approximate homerange size 225 km2 500 km2 500 km2 Buffer distance† 16 km 25.2 km 25.2 km Percent of time spent in homerange 90% 90% 90% Upper limit for movements‡ 1 S.D. 2 S.D. none †Required distance between homerange centers of like individuals (e.g. a female homerange center must be > 16 km from any other female homerange center). ‡Limit on long distance movement during the study period, implemented via truncation of tails in bivariate normal distribution. Individual utilization distributions For each individual in the simulation, we created an individual utilization distribution based on the location of the home range center, the degree of overlap allowed between home ranges, and the underlying landscape. These distributions were initially developed with a bivariate normal distribution around the home range center. The variance of these distributions was determined by the estimated overlap between individual home ranges. For resident females, we assumed that an individual spends 90% of her time within a 225 km2 home range (= 8.5 km radius). To get the variance term for the bivariate normal utilization distribution from these estimates, we first calculated the cutoff value for 90% of a standard normal distribution, then estimated the standard deviations of the bivariate normal as the home range radius (converted to degrees longitude or latitude) divided by the cutoff value. Thus, the values for standard deviation in the utilization distributions were selected such that the home range radius is the 90% cutoff for the distribution. For resident males, we assumed individuals spend 90% of their time within their 12.6 km home range radius, but we allowed for larger sizes and greater overlap among transient male home ranges by assuming individuals only spend 70% of their time in the original 500 km2 home range. Each of these distributions produces a surface with decreasing probability of use with increasing distance from the home range center. To make the utilization distributions more realistic, the bivariate normal distributions were then overlaid with the habitat layer, and the layers were multiplied together. In the persistent spring snow layer, areas of non-snow were weighted as having 1/20 the probability of use compared to snow areas, based on resistance values found for models of genetic least cost paths (Schwartz et al. 2009). The product of the two layers was standardized to sum to one, such that it is transformed back into a probability density. Thus, each individual utilization distribution takes a unique shape based on availability of snow. In this approach, it is possible for individuals to make short term, long distance movements during a given study period. The tails of the bivariate normal utilization distribution allow for a very small, but non-zero, probability of reaching any point on the landscape. For wolverine, we tested for the effect of excluding these long distance movement events by cutting off the tails of the bivariate normal, such 2 �that the probability of an individual being more than 1-2 standard deviations away from its home range center was set to 0, compared to a situation with no limit on movement. Although allowing short-term, long-distance movements did affect the estimated occupancy of the landscape, the effect on power was minor. Occasional long-distance movements are possible in wolverine ecology, especially by males and transients (Moriarty et al. 2009). For territorial males and females, we would expect these movements to be less likely over the course of the relatively short survey period. Thus we based our power analyses on a ’mixed’ scenario in which long distance movements were possible for transient males (i.e. no limit), resident males were allowed some larger movement events (limited to within 2 s.d. of home range center), and movements of females, which may have dens, were limited 1 s.d. from their home range center. Simulated encounter histories Individual utilization distributions can be created for any number of individuals on a landscape by varying the population size as a parameter in SPACE. To simulate a population trend in time, we added or removed individuals from the simulation over time by adding new home range centers and creating corresponding individual use layers or by dropping layers as individuals were removed from the population. Replicates of a simulated population were created by selecting a new distribution of home range centers across the landscape. To estimate occupancy, we sampled from the simulated landscapes during each time step or ”year” of the simulation. We divided the study area into 225 km2 sample units (cells), matching home range sizes for resident females, a strategy widely used for monitoring carnivores (e.g., Zielinski and Stauffer 1996). We excluded cells that did not overlap the persistent snow layer by ≥ 50%. This resulted in 388 cells for the main Northern Rockies study region, and 128 cells for the Southern Rockies. For each cell, the probability of at least one wolverine being present (hereafter, ’probability of presence’) was ⎞ ⎛ � � N � ⎟ ⎜ P (wolverines ≥ 1)j = 1 − P (wolverines absent)j = 1 − fi (x, y)dxdy ⎠ ⎝1 − i=1 (x,y)∈Ωj where N is the number of wolverines in the simulated study area, fi (x, y) is the probability density function (i.e., utilization distribution) describing the use surface for the ith wolverine, and Ωj represents the area included in the j th grid. We approximated integral values by summing pixel values in the raster, assuming equal pixel areas. To construct a simulated encounter history (i.e., the data necessary for occupancy estimation) for cell j in year k, we assigned a 1 (present) or 0 (absent) for each visit by comparing a random draw from Uniform(0,1) with the probability of presence for that cell (draws less than the probability of presence resulted in a ”presence”, and a 1 in the encounter history for that visit). Thus, a cell with simulated encounter history ”010” indicates that 3 visits were made to the cell in a given year, and wolverines were present in the cell only during the second visit only. After initial 3 �construction, we used progressively reduced versions of the encounter histories to explore the effect of changes in parameters associated with sampling on power to detect population changes. For example, we omitted data from even numbered years (i.e., inserted ”.” for each ”0” or ”1” of the omitted years) to examine the effect of sampling every other year; we tested the effects of smaller sample sizes by reducing the number of cells or visits included in the encounter histories; and we reduced the number of detections to simulate imperfect detection (see Table 1, main text). To create encounter histories with lower detection probability, we randomly removed an appropriate proportion of 1s from each encounter history. Thus, to go from a detection probability of 1.0 to 0.8, we retained 0.8/1.0 = 80% of the 1s; for each 1 (wolverine detected) in a given encounter history, we conducted a random draw from uniform (0,1) and compared this draw against 0.8. We retained the 1 if the draw was < 0.8, and changed it to a 0 (wolverine not detected) otherwise. Similarly, to go from encounter histories reflecting detection probability = 0.8 to detection probability = 0.2, we evaluated each 1 in a given history, retaining it if the random draw was < 0.25 (0.2/0.8), changing it to 0 otherwise. Thus, the end product of SPACE is a set of encounter history files based on the sampling parameters tested, formatted for use as input files in Program MARK. Example code applying this framework to wolverine populations in the U.S. Northern Rockies is available on request. Occupancy Model Specification We fit a ’multiple season, implicit dynamics’ occupancy model (MacKenzie et al. 2003; 2005, p.186) by specifying the ’Robust Design Occupancy’ data type in the R package, RMark (R Core Team 2012, Laake and Rexstad 2012). We coded the design matrix such that colonization (γ; the probability that a cell unoccupied in year t becomes occupied in year t + 1) could vary by year but was constrained to be the complement of extinction (�; the probability that an occupied cell in year t becomes unoccupied in year t + 1). Thus changes in occupancy were considered random rather than Markovian or static (MacKenzie et al. 2005, p. 205). Note that, in our case, estimated occupancy and changes in occupancy reflect changes in use (see main text). This model structure does not exactly match the model that generated the data. The latter assumed γ = 0 for decreasing populations or � = 0 for increasing populations. Thus, changes in occupancy were not random. Rather than making our analysis perfect for the types of changes invoked (i.e., fitting a model in which γ or � were fixed to 0), we fit a model that is misspecified, but also commonly used and likely to be implemented in reality. The result of this misspecification is that our power estimates are likely conservative. We constrained the estimated detection probability from the occupancy model (pest ) to be the same for each visit within a year, but it was allow to vary by year. This structure for pest is appropriate because ”movement” between adjacent cells forced pest to be a function of probability of presence, which changed through time depending on the simulated landscape and birth/death of individuals. Thus, pest should have varied with year. 4 �Trend detection For each model fit described above, we extracted the derived occupancy estimates (i.e., on a probability scale) and their variance-covariance matrix for the 10-year period in each simulation. We then fit a linear trend model to the estimates with a random effect for year, using the variance components procedure in RMark with restricted maximum likelihood estimation (Burnham and White 2002, Laake and Rexstad 2012). The variance components procedure assumes that the occupancy estimates came from a normal distribution with a mean that fell along the trend line, and with process variance (which is estimated by the procedure) around that line. In this context, the estimate of the slope of the trend line (and its associated sampling variance) appropriately account for the uncertainty around each individual occupancy estimate so that power is not artificially inflated by viewing each estimate without uncertainty. To account for sampling effort, we applied a finite population correction to the trend parameter, reducing the sampling variance by a factor of (N-n)/N where N is the total number of cells in the study area and n is the number of cells included in the sample. Specifically, from Burnham (2012), the standard error of the trend parameter can be written as SE(β̂) = σ̂ 2 + E[var(Ŝi |Si )] k where σ̂ 2 is the estimated process variance, E[var(Ŝi |Si )] is the estimated sampling variance, and k is the number of years. Both SE(β̂) and σ̂ 2 are returned by var.components.reml(), which allows us to solve for the sampling variance E[var(Ŝi |Si )]. We can then apply the finite population correction to this value and recalculate SE(β̂), such that SE(β̂) = σ̂ 2 + N −n N E[var(Ŝi |Si )] k where N is the total number of cells in the landscape and n is the number of cells included in the sample. We based our analysis on a standard α = 0.05 significance level. Thus, a trend was ’detected’ if the 95% confidence interval of the trend parameter based on the corrected SE excluded zero and was in the correct direction (e.g., < 0 for declining trends). References Banci, V., 1994. Wolverine. in L. F. Ruggiero, K. B. Aubry, S. W. Buskirk, L. J. Lyon, and W. J. Zielinski, editors. The scientific basis for conserving forest carnivores: American marten, fisher, lynx, and wolverine. USDA Forest Service Technical Report RM-254, Fort Collins, CO. Burnham, K., 2012. Variance components and random effects models in MARK. Pages D1–D46 in E. Cooch and G. White, editors. A Gentle Introduction to Program MARK, 11th edition (http://www.phidot.org/software/mark/docs/book/). 5 �Burnham, K., and G. White. 2002. Evaluation of some random effects methodology applicable to bird ringing data. Journal of Applied Statistics 29:245–264. Copeland, J., 1996. Biology of the wolverine in central Idaho. Ph.D. thesis, University of Idaho. Copeland, J., K. McKelvey, K. Aubry, A. Landa, J. Persson, R. Inman, J. Krebs, E. Lofroth, H. Golden, J. Squires, et al. 2010. The bioclimatic envelope of the wolverine (Gulo gulo): do climatic constraints limit its geographic distribution? Canadian Journal of Zoology 88:233–246. Hall, D. K., G. A. Riggs, and V. V. Salomonson, 2006. MODIS/Terra snow cover daily L3 global 500m grid. Version 4, 24 April - 21 May 2000-2006. National Snow and Ice Data Center, Boulder, CO. Inman, R., M. Packila, K. Inman, A. Mccue, G. White, J. Persson, B. Aber, M. Orme, K. Alt, S. Cain, et al. 2012. Spatial ecology of wolverines at the southern periphery of distribution. The Journal of Wildlife Management . Krebs, J., E. Lofroth, and I. Parfitt. 2007. Multiscale habitat use by wolverines in British Columbia, Canada. The Journal of Wildlife Management 71:2180–2192. Laake, J., and E. Rexstad, 2012. RMark - an alternative approach to building linear models in MARK. Pages C1–C115 in E. Cooch and G. White, editors. A Gentle Introduction to Program MARK, 11th edition (http://www.phidot.org/software/mark/docs/book/). MacKenzie, D., J. Nichols, J. Hines, M. Knutson, and A. Franklin. 2003. Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84:2200–2207. MacKenzie, D., J. Nichols, J. Royle, K. Pollock, L. Bailey, and J. Hines. 2005. Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Academic Press. Moriarty, K., W. Zielinski, A. Gonzales, T. Dawson, K. Boatner, C. Wilson, F. Schlexer, K. Pilgrim, J. Copeland, and M. Schwartz. 2009. Wolverine confirmation in California after nearly a century: native or long-distance immigrant? Northwest Science 83:154–162. R Core Team, 2012. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/. Schwartz, M., J. Copeland, N. Anderson, J. Squires, R. Inman, K. McKelvey, K. Pilgrim, L. Waits, and S. Cushman. 2009. Wolverine gene flow across a narrow climatic niche. Ecology 90:3222–3232. Zielinski, W., and H. Stauffer. 1996. Monitoring Martes populations in California: survey design and power analysis. Ecological Applications 6:1254–1267. 6 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Journal Articles Description An account of the resource CPW peer-reviewed journal publications Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Spatially explicit power analyses for occupancy-based monitoring of wolverine in the U.S. Rocky Mountains Description An account of the resource <span>Conservation scientists and resource managers often have to design monitoring programs for species that are rare or patchily distributed across large landscapes. Such programs are frequently expensive and seldom can be conducted by one entity. It is essential that a prospective power analysis be undertaken to ensure stated monitoring goals are feasible. We developed a spatially based simulation program that accounts for natural history, habitat use, and sampling scheme to investigate the power of monitoring protocols to detect trends in population abundance over time with occupancy-based methods. We analyzed monitoring schemes with different sampling efforts for wolverine (Gulo gulo) populations in 2 areas of the U.S. Rocky Mountains. The relation between occupancy and abundance was nonlinear and depended on landscape, population size, and movement parameters. With current estimates for population size and detection probability in the northern U.S. Rockies, most sampling schemes were only able to detect large declines in abundance in the simulations (i.e., 50% decline over 10 years). For small populations reestablishing in the Southern Rockies, occupancy-based methods had enough power to detect population trends only when populations were increasing dramatically (e.g., doubling or tripling in 10 years), regardless of sampling effort. In general, increasing the number of cells sampled or the per-visit detection probability had a much greater effect on power than the number of visits conducted during a survey. Although our results are specific to wolverines, this approach could easily be adapted to other territorial species.</span> Bibliographic Citation A bibliographic reference for the resource. Recommended practice is to include sufficient bibliographic detail to identify the resource as unambiguously as possible. Ellis, M. M., J. S. Ivan, and M. K. Schwartz. 2014. Spatially explicit power analyses for occupancy-based monitoring of wolverine in the U.S. Rocky Mountains. Conservation Biology 28:52–62. <a href="https://doi.org/10.1111/cobi.12139" target="_blank" rel="noreferrer noopener">https://doi.org/10.1111/cobi.12139</a> Creator An entity primarily responsible for making the resource Ellis, Martha M. Ivan, Jacob S. Schwartz, Michael K. Subject The topic of the resource Detection probability Occupancy Population monitoring Population trends Sampling design Extent The size or duration of the resource. 11 pages Date Created Date of creation of the resource. 2013-09-03 Rights Information about rights held in and over the resource <a href="http://rightsstatements.org/vocab/InC-NC/1.0/" target="_blank" rel="noreferrer noopener">In Copyright - Non-Commercial Use Permitted</a> Format The file format, physical medium, or dimensions of the resource application/pdf Language A language of the resource English Is Part Of A related resource in which the described resource is physically or logically included. Conservation Biology Type The nature or genre of the resource Article