ACTIVACION DE LAS CASPASAS A TRAVES DE LA

Capture-recapture studies with fixed trap locations have a spatial component: animals close to traps are more likely to be caught than animals further away. This is not addressed in standard capture-recapture analyses and without this spatial component, rigorous estimates of density cannot be obtained (Conn et al., 2006; Borchers and Efford, 2008; Borchers, 2011). The incorporation of spatial information into capture-recapture analyses was first proposed by Efford (2004) and Efford et al. (2004). This approach avoids estimation of the effective trap- ping area, instead using the known location of the traps and the pattern of

recapture events to estimate the density of home range centers and a capture function. The capture function is conceptually consistent with distance sampling approaches (c.f. section 2.2), in that the probability of detecting an individual is assumed to be a radially decreasing function of the distance between the cen- ter of the animal’s home range and the distance to the trap. More formally, the capture probability model is the probability that an animal located at X (a vector specifying the coordinates of the home range center) is detected by trapkon occasions. Three forms of the capture probability model are available (Table 2.1), that typically require two parameters: g0, the probability of being trapped if the animal’s home range is centered at a trap (i.e.,d(X) = 0); andσ, the spatial scale (the hazard-rate function also has an additional parameter, b, Table 2.1).

Table 2.1: Three forms of the capture probability model used in spatially-explicit capture-recapture. d is the distance between an animals home range centre and a detector. The parameterg0is common to all functions and represents the prob- ability of detection at a single detector placed in the centre of the home range; values of the spatial scale parameter σ are not comparable between functions (Efford et al., 2009b).

Detection function Equation Parameters in vector θ

Halfnormal g0 exp(−d

2

2.σ2) g0, σ

Exponential g0 exp(−_σd) g0, σ

Hazard rate g0 [1−exp{−(−_σd)−b}] g0, σ, b

In early implementations of this approach, simulation and inverse prediction were used to jointly estimate density, ˆD, and the parameters of the capture function (Pledger and Efford, 1998). For example, Efford et al. (2005) found density estimates of brushtail possums to be similar to those based on removal methods, and Efford (2004) conclude density estimates were virtually unbiased and relatively precise when applied to simulated data. Despite some success, using inverse prediction was limited with respect to model selection and the

inclusion of covariates (Borchers and Efford, 2008). Recent developments now enable spatially-explicit capture-recapture models to be fitted within both max- imum likelihood (Borchers and Efford, 2008; Efford et al., 2009b) and Bayesian frameworks (Royle and Young, 2008; Royle et al., 2009).

Requisite data for a SECR analysis are individual capture histories, similar to standard capture-recapture analyses but instead of recording a string of 1s and 0s if the individual was detected or not, respectively, when the individual is captured, the location of capture is recorded. That is, a capture history of “0,10,14,0” represents an individual not captured during the first or last sampling occassion, and was captured at trap location 10 and 14 on the second and third sampling occasions, respectively. Since the survey design and therefore trap locations are known, the distance between recapture events (i.e., between trap locations 10 and 14) are known. Given the capture historyωiof individualiand

an estimate of the capture function, the probability density of the location of the home range center of this individual can be estimated (Borchers and Efford, 2008).

The maximum-likelihood estimation method of this approach is readily im- plementable using the ‘secr’ package in program R (Efford, 2010), which allows model selection methods to be based on Akaike’s Information Criterion, AIC (Burnham and Anderson, 2003). The inclusion of covariates in the capture- probability function, such as trapping occasion, whether an individual has been trapped before and additional heterogeneity not attributable to distance of trap (e.g., individual covariates such as sex, and unobservable covariates accounted for using a two-point mixture model of Pledger (2000)), is straight-forward.

The maximum-likelihood based SECR approach assumes the population is closed (i.e., no births, deaths, immigration or emigration), although recent de- velopments within the Bayesian framework can permit open-population models

(Gardner et al., 2010). As per standard capture-recapture, SECR assumes that tags are not lost and the identity and location of capture of each individual is recorded accurately. Other assumptions of the method are:

• Animals occupy circular home ranges,

• Home range centers are distributed in space according to a Poisson point- process,

• Detectors are operated at known locations for a fixed period of time,

• Animals are detected independently of each other, and

• Detector placement is random with respect to location of animal home range centers.

The method is remarkably robust to violation of the first two of these as- sumptions (non-circular home ranges and a clumped distribution of individuals), causing increased estimates of variation, rather than significant bias in density estimates (Efford, 2004; Efford et al., 2005). The other assumptions can be assured by good survey design (e.g., by placing traps randomly in the survey area). One particular strength in this approach is its flexibility in terms of ac- commodating any spatial arrangement (regular or irregular spatial arrangement of lines, webs and random placement, or otherwise) of traps (Efford, 2004), and traps can include physical capture of an individual, or a proximity detector such as a camera trap, or passive detector array (e.g., microphones, Efford et al., 2009a or hydrophones, Marques et al., 2011).