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© 2004 Museu de Ciències NaturalsMacKenzie, D. I. & Nichols, J. D., 2004. Occupancy as a surrogate for abundance estimation. 461–467.Occupancy as a surrogate for abundance estimationexpensive to estimate the actual abundance of a bird species in a defined area, particularly at large spatial scales,by the species as an alternative state variable. However, as with abundance estimation, issues of detectability mustbe taken into account in order to make accurate inferences: the non–detection of the species does not imply thespecies is genuinely absent. Here we review some recent modelling developments that permit unbiased estimationof the proportion of area occupied, colonization and local extinction probabilities. These methods allow for unequalsampling effort and enable covariate information on sampling locations to be incorporated. We also describe howquestions of population dynamics (such as turnover rate of nest sites by specific breeding pairs) to be addressed.We believe these models may be applicable to a wide range of bird species and may be useful for investigatingvarious questions of ecological interest. For example, with respect to habitat quality, we might predict that apairs, in poor quality habitats.Occupancy, Species distribution, Abundance, Metapopulation, Monitoring.La ocupación como sustituto de la estimación de la abundancia.— En muchos programas de monitorizaciónpuede resultar extremadamente caro estimar la abundancia real de una especie de ave en un área definida,especialmente a grandes escalas espaciales, o donde las aves se dan a densidades muy bajas. A menudo, esposible que resulte conveniente considerar la proporción del área ocupada por la especie como una variable deestado alternativa. Sin embargo, al igual que sucede con la estimación de la abundancia, para poder realizardeducciones exactas es preciso tener en cuenta ciertas cuestiones de detectabilidad: el hecho de que una especieno pueda detectarse no significa que realmente esté ausente. En este estudio analizamos algunos modelos dereciente desarrollo que permiten una estimación no sesgada de la proporción del área ocupada, de la colonizaciónla posibilidad de incorporar información sobre covariantes en los emplazamientos de muestreo. También describimosel procedimiento para ampliarlos a fin de incorporar información acerca de individuos marcados, lo que permitiríaabordar con mayor detalle cuestiones acerca de la dinámica poblacional (como el índice de rotación de losemplazamientos de los nidos por parte de parejas de reproducción específicas). Consideramos que estos modelospodrían aplicarse a una amplia gama de especies de aves, pudiendo resultar útiles para investigar diversascuestiones de interés ecológico. Por ejemplo, respecto a la calidad del hábitat, podríamos predecir que unaespecie presenta más probabilidades de extinción local, o índices de rotación más elevados de determinadasparejas de reproducción, en hábitats de baja calidad.Ocupación, Distribución de especies, Abundancia, Metapoblación, Control.Darryl I. MacKenzie, Proteus Wildlife ants, P.O. Box Nichols, USGS Patuxent Wildlife Research Center, 11510 American Holly Drive, Laurel, MD 20708–4017, U.S.A. darryl@proteus.co.nz Occupancy as a surrogate forabundance estimation 462Mackenzie & Nichols that they will always be detected at a sampling unitnaïve count of the number of sites where the spe-cies is detected will underestimate the true level ofoccupancy. Furthermore, inferences about changesin occupancy based upon an observed differencebetween two (or more) naïve counts should bemade with caution, as the difference may be theresult of a change in our ability to detect thespecies rather than a change in occupancy. Thearguments against using a naïve count for occu-pancy are very similar to those given for not usingYoccoz et al., 2001, MacKenzie & Kendall, 2002;Williams et al., 2002; Schmidt, 2003).logical advances for modelling occupancy data whilego undetected at a site when present. These can be2002; Tyre et al., 2003); a single season model withstatistically robust framework for modelling occu-pancy data, enabling occupancy to be seriouslytoring programs. There are strong similarities be-subtle differences in their application.In this paper we briefly review the multipleseason model of MacKenzie et al. (2003). This isThe differences between the approaches ofare in some ways analogous to the differencesmark–recapture models (e.g., Seber, 1982;Williams et al., 2002). We also outline how infor-pancy dynamics may be very useful for identifyingthe underlying processes that generate patterns inoccupancy (e.g., metapopulations). In particular,draw inferences about such processes by obser-vations of occupancy pattern over space at a1997). Indeed, there are often many different bio-Introductionprogram should be to track the status of populationsso that substantial changes can be identified andappropriate management actions taken. Abundancemeasure that can be used to characterise the stateabundance reflecting changes in the population’sstatus. However, in order to make accurate conclu-sions about changes in abundance, it is importantincorporated into our inferential process (e.g., Yoccozal., 2002; Schmidt, 2003). This often requires thatpatternings such as colour patterns, or by applyingsome bird species, especially those that are difficultto capture, this may require a level of effort that isinfeasible to sustain as part of a long–term monitor-ing program, particularly at a reasonably large spa-as occupancy). Determining whether a target speciesthe past for a number of bird species including themurrelet (e.g., see Stauffer et al., 2002) and gos-hawks (P. Kennedy, pers. comm.). The reasoningbehind using occupancy rather than abundance isthat at an appropriate scale the two state variablesshould be positively correlated (i.e., occupancy maybe noted that the two state variables are addressingdistinctly different aspects of the population dynam-ics. While intuitively the questions "What fraction ofthe landscape does the species occupy?" and "Howscape?" are similar, it must be recognised that someidentified using an occupancy approach to monitoringchanges in range and occupancy may not be re-flected by changes in abundance. However, for cer-tain species the discrepancies between the two stateis chosen appropriately. For example, the number ofbreeding pairs of a territorial bird species (such asmany raptors) may be closely related to occupancy ifsame size as a nesting territory. There may also besituations where occupancy is actually the state vari-changes in species range and metapopulation inci- the same pattern of occupancy (e.g., Tyre et al.,2001). This should not be surprising. As an anal-ogy, suppose that you are given a randomly se-taken throughout a football game. You are thenasked to comment on the current state of thestate of play such as which team has the ball andprogressed. Not until you are able to go throughthe entire stack of photographs (in order) wouldstudies where processes of population dynamicscan only be fully understood by observing thepopulation at systematic points in time, notinghow the patterns change and modelling thesechanges in terms of relevant rate parameters.Basic sampling schemepancy for a target species in some arbitrarily de-fined "area". The term "area" is used ambiguouslyas a forest or national park, or it may be a collec-tion of discrete habitat patches such as ponds orfragmented forest stands. The area can be consid-ered as a collection of subunits that we shall ge-situation and target species, a site may constitute asuitably sized quadrat, potential nesting territory oran individual habitat patch. At chosen sites, mul-target species over a relatively short timeframe: achanges in occupancy so that sites are either al-random, although it alters the interpretation of theparameters, e.g. proportion of area occupied be- sites from the areaof interest. One of the fundamental rules for statis-tical inference states that in order to be able togeneralize the results from the study sites to thescheme (e.g., random sampling). This is some-of the population. We do not give further considera-advice is often situation specific, but we wish tohighlight that it is an important issue that is often can berecorded as a sequence of 1’s and 0’s (respec- = {10 00 11} would denote that the be the probability a site is occupied by the =1) and be the within season . Further, let and+1 (colonization), and let denote the probabilitya site that was occupied by the species in seasondynamic parameters enable the modelling ofFor any given detection history, these param- = {01 00} indicatingprobability of observing the first season’s datathere are two options. Either the species did notsurvey, with probability). The probability of observing the = {00 11}. Now there aretwo options for the occupancy state of the site insite being occupied immediately before the start of colonized the site between seasons. The probabilityGenerally, however, there could be a large numberof possible pathways that would result in the samedetection history. It is therefore useful to define atransition probability matrix that details how sitespied state between seasons and + 1 (1). A rowpancy state the site is in the first season (2)., conditional upon each state.be zero as clearly the site cannot be in theunoccupied state (for example see equation (3).Conversely, when the species is not detectedwithin a season, then there is some probabilityassociated with the occupied state, and if the site) is a diagonal matrix with the elements along the main diagonal (top left to bottom is the number ofseasons of data collection. The model likelihood is sites are inde- L ability of occupancy in any given year (5) and therate of change in occupancy between successive = (1 – (5)The model may even be reparameterized so thatrectly. However, experience to date suggests that itcan be difficult to obtain convergence on the esti-mates for reparameterized models. stances it might not be possible to collect therequired data: weather conditions may prevent ac-sample all sites within a suitably small time frame.show that missing observations can easily be incor-porated into the models described above. In effect,a site is set to zero, which fairly reflects the fact thattially, this removes the detection probability param-eter from the model likelihood (with respect to thesite and time in question). The ability of the modelto handle missing observations has important rami-fications for study designs, as it enables differentsites to have different sampling intensities. Incorporating covariatesOften researchers may be interested in potentialrelationships between the model parameters (oc-cupancy, colonization, local extinction and detec-years). Further, the surveyor’s ability to detect thespecies during any given survey may also beaffected by localized conditions at the samplingtraffic noise). Using the logistic model (7),information can be incorporated. The logistic model (which for the covariate(s). Analyses of this type could betainty in the binary observation of occupancy state(due to imperfect detectability). An important question that often arises in variousat some sites (the "rescue effect" of Brown & Kodric–reliably differentiate between the two possibilitiesfrom detection/nondetection data, and auxiliary in-obtained from having uniquely marked individualsinference. We imagine that such an approach wouldsmall groups effectively exist as a single unit (e.g.,breeding pairs).We could now consider that a site may be in oneof three possible mutually exclusive states; i) occu-(state S); ii) occupied by a different individual fromwere not previously being monitored. Therefore, inthe first season there are only two states that canbe considered; occupied and unoccupied. The tran- 1 can then beredefined as (see table 1 for parameter definitions); S DN for 2. denote the occupancy state of sites in, and columns denote the state in season+ 1. Between any two seasons, then all possiblefrom an unoccupied state to being occupied by thevidual was there previously), hence the bottom–leftshould sum to 1.0, hence not all of the parameterswe have presented the concepts here in terms of avery general model. In practice not all of the param-research. However, various constraints could be im-posed upon the parameters to express (and com-pare competing) plausible biological hypotheses. Foroccurs at a site different for sites that had an estab-comparing sets of models where the constraint is imposed against models without such aIn any given season, however, there are fourtypes of observations that could be made. The sameor a different individual may be detected at the site,the three states because of imperfect detectability),and fourthly, because not all of the individuals mayis unknown whether it is the same or a differentprobability vectors. In the case where the site’s stateis known with certainty, there is only one non–zeroelement in the vector, i.e., that indicates the site is occupied by adifferent individual, and is the probability of ob-detected, all three elements will be non–zero indicat-ing that the site may have been in any state, i.e.,be occupied, but it unknown whether it is a new orprevious occupant, then the first two elements will 466Mackenzie & Nichols ing estimation to deal with occupancy dynamicsof rate of change in occupancy, as well as local ratespancy dynamics. In addition, these rate parameterscovariates including site–specific habitat, site isola-tion or proximity to source locations, etc. We thusbelieve that this framework permits investigation of aReferencesBarbraud, C., Nichols, J. D., Hines, J. E. & Hafner,the metapopulation and community levels. 101: 113–126.Bradford, D. F., Neale, A. C., Nash, M. S., Sada,D. W. & Jaeger, J. R., 2003. Habitat patchoccupancy by toads (Bufo punctatusEcology,Table 1. Definition of parameters (P) used to describe the transitions between states for occupancyTabla 1. Definición de los parámetros (P) utilizados en los estudios de ocupación para describir transiciones entre estados, con información proporcionada por individuos marcados.P Definition of parameters is occupied in 1Probability that an occupied site becomes unoccupied between seasons 1 and 2 Probability that a site occupied by an established individual in season , is unoccupied in tDProbability that a site occupied by a new individual in season t, is unoccupied in t 1Probability that the same individual occupies the site in season 2 as in season 1 Probability that a site occupied by an established individual in season is occupied by the is occupied by the same Probability that a different individual occupies the site in season 2 than in season 1 Probability that a site occupied by an established individual in season is occupied by adifferent individual in is occupied by a different tional state variable used in animal population stud-the use of an alternative state variable, occupancyrange size, and metapopulation dynamics, this isthe state variable of primary interest. In other situ-ations, the reduced effort required to estimate oc-cupancy, relative to that required to estimate abun-dance, may warrant consideration of occupancy asOur initial work on occupancy estimation focusedMacKenzie & Bailey, in press). We have recently ex-species with possible dependencies in both occupancyof detection probabilities among different sites or sam-pling units beyond that associated with identified counts. Royle, J. A. & Nichols, J. D., 2003. Estimatingabundance from repeated presence–absence dataor point counts. Schmidt, B. R., 2003. Count data, detection prob-abilities, and the demography, dynamics, distri- 326: S119–S124Stauffer, H. B., Ralph, C. J. & Miller, S. L., 2002.Incorporating detection uncertainty into presence–P. J. Heglund, M. L. Morrison, J. B. Haufler, M.G. Raphael, W. A. Wall & F. B. Samson, Eds.).Island Press, Washington, District of Columbia,Tyre, A. J., Possingham, H. P. & Lindenmayer, D.B., 2001. 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