One important limitation of traditional capture-recapture methods isthat density cannot be explicitly estimated. SCR explicitly estimates thesurveyed area whilst traditional CR derived estimates of density by ad hoc estimationof the effective surveyed area. Multiple methods can be used to estimate thisincluding buffering by the mean maximum distance move (MMDM), or half MMDM orby an estimated female home range radius if such data is available. All ofwhich would return three potentially vastly different estimates of density forthe same N. Additionally, it isassumed that no animals are able to move across the buffer established by this method.
Spatially-explicit capture-recapture (SECR, Borchers and Efford, 2008) or spatialcapture-recapture (SCR, Royle et al., 2013b) models areincreasingly used for monitoring animal populations worldwide and have beenshown to produce more precise estimates than conventional mark-recapturemethods (Sollmann et al., 2011). Bias in N also arises from unmodelledheterogeneity in capture probability, p.In non-spatial CR p remains constant,i.e.
all individuals are assumed to be equally detectable. Detectability ofindividuals is clearly related to their location relative to traps and, evenbetween two individuals in the same location the rate at which they move aroundthe environment and thus encounter traps. Models of heterogeneity (Mh) in SCR account forheterogeneity through considering the processes which generated the data ratherthan the resulting data itself (Royle et al., 2013b)RG1 .
Royle et al. (2013b) identify fourkey limitations of traditional CR methods:1. Densityestimation is conducted ad hoc2. Heterogeneityin detection probability cannot be explicitly estimated3. Trap-levelcovariates are not considered4. The spatialprocesses underlying the data are not considered5.
Individuals mustbe uniquely identifiableSuch limitations were not unrecognised by the scientific community;however, methods with which to approach these problems are a relatively recentdevelopment. What is SCR?Efford (2004) developed amethod for using the spatial information inherent in capture-recapture studies andthese methods were subsequently formalised to explicitly model density eitherthrough maximum likelihood estimation (MLE, Borchers and Efford, 2008) or in aBayesian framework (Royle and Young, 2008). SCR modelsexploit the spatial information, such as the juxtaposition between thelocations of individuals and traps, inherent to capture-recapture surveys. Thedistribution (or location) of individuals in space is described by a pointprocess model. The points represent the activity centres of individuals (si ; i = 1,2,…N) which are latent, or unobserved, variables in themodel. We gather information about them by observing animals with detectors(traps, cameras, area searches, acoustic detectors, DNA sampling…). Theserealised locations, ui,represent a thinned point process model where the thinning is determined by howthe locations are observed, such as the location of detectors. All possiblelocations of si, i.
e. allanimals that could be captured, are represented by the state-space, . Therefore, N is the number of siin and density can be expressed as (Royleet al.
, 2013b).So, as SCR models link individuals withspace, so too do they define N interms of the surveyed area. Consequently, density is explicitly modelled andpopulation size, as a function of density, can be estimated for a specificstate-space, or survey area. The main limitation of traditionalcapture-recapture was the inability to define the survey area, or state-space.By formally associating with , SCR allows us to gain meaningful ecological inference fromcapture-recapture surveys by explicitly modelling density.RG2 The model which concernsus in spatially explicit density estimation is that which relates the thinned pointprocess we observe, to the actual distribution of animals in space, N. Recall that our variables are theunobserved activity centres, s, therealised locations of individuals, u,in addition to our response variable, y,which is what we record upon capture.
Relating our encounter model, movementmodel and point process model we have (Royleet al., 2013b, p.42) .Where s is the distribution of activitycentres in the state space, , which may or may not be homogenousdepending on whether density varies across space, u|s models thelocations of animals given their activity centre and y|u describes how theobserved data arise given the locations of animals. Additionally, note that u is the realisation of a movementmodel which most SCR models do not quantify, there y|s is modelled. Infixed detector location designs the observation model is therefore (Royleet al., 2013b, p.45) .
This is theencounter model, that is the probability of detecting an individual given thedistance between s and the detectorand can also be written as (Royleet al., 2013b, p. 43).It hasparameters p0 (Borchersand Efford (2008) use g0), which is the capture probability when si is at the tap location xj, and is a spatial scale parameter determining howrapidly capture probability declines with distance.
Often is a spatial scaleparameter determining how rapidly capture probability declines with distance.Often the encounter model is yij|si = Bernoulli (pij). Where yij is the observed data whenindividual recognition is possible.
For count or detection data, densityestimation of unmarked individuals is possible through specifying observed dataas n(y) giving us the model n(y)|y.Looking moreclosely at s and recalling that itis the distribution of animals across space, recalling that this point processdescribes N, we can characterise itas s|, where is the intensity of this process or population density. Therefore, N ~ Poisson , where is the area of the state-space or in the caseof implementing Bayesian analysis N ~ Binomial , where ,and M is a large integer used for data augmentation (Royleet al.
, 2013b, p. 42). Bringing thistogether our simple SCR model has a population size which is Possiondistributed, where activity centres are uniformly distributed and captureprobability is a function of the distance between the location of theseactivity centres and that of our detectors. Or can be described by (Royleet al.
, 2013b, p. 43),,.This simplemodel can then be modified as our situation requires, examples of which will befound in my thesis.Whilst the workdiscussed above shows the many advancements in capture-recapture modelling bythe spatial framework, SCR models, like all models are not without limitationsand assumptions. Key assumptions of (but not unique to) spatially-explicitdensity estimation include (Royleet al., 2013b):1. Demographicclosure: no recruitment, migration or mortality2. Geographicclosure3.
Randomdistribution of activity centres, si4. Detectiondeclines as a function of distance: of an activity centre from a detector5. Encountersare independent between and within individuals6.
Marksare not lost or misidentifiedOtherlimitations which may be confronted in conducting SCR include trap saturationlimiting recaptures, dealing with partially marked or unmarked populations,low-density populations, appropriate spacing of detectors relative to animalmovements, and a lack of stationarity and symmetry of animal home ranges.Nonetheless spatially explicit methods offer the scope to address these issues,particularly through Bayesian inference, and solutions can be used to gainfurther insight into animal populations. An increasing body of literatureinvestigates the robustness of SCR to departures from these assumptions, someof which are pertinent to my research and are discussed below in addition toother advances in modelling techniques such as continuous time models.
Additional research is required in some areas, such as the independence ofencounters between individuals (i.e. for social species), which I will explorein the fourth chapter of my thesis.
By explicitly including spatial elements in ourpopulation models we can thereby explicitly model factors central to manyecological questions using one framework. For example, resource selection (Royle et al., 2013c), sex-specific movement and detectability (Sollmann et al., 2011), landscape connectivity (Fuller et al., 2016;Royle et al., 2013a)and population dynamics (Chandler and Clark,2014; Ergon and Gardner, 2014; Gardner et al., 2010; Schaub and Royle, 2014;Whittington and Sawaya, 2015)