Model selection

Data were analysed using program MARK (v.5.2, White and Burnham, 1999). Huggins’ full heterogeneity model with a robust design was specified that used an open population, Jolly-Seber model between primary sessions (Kendall, 2008). Within each primary session, a model that combines Huggins’ closed popula- tion model (Huggins, 1989, 1991) with the mixture models for heterogeneity of Pledger and Efford (1998); Pledger (2000) and Norris and Pollock (1995) was specified. This closed population model is conditioned on each animal that is caught at least once in each primary trapping period (i.e., population size, N, is not included in the likelihood). This allows capture probability, p, and recap- ture probability, c, to be modelled as functions of individual covariates (here, sex; White, 2008). Since the data were naturally sparse (i.e., few captures across the 32 grids, despite a large survey effort), grid could not be used as a covari- ate in the model, and consequently the probability of capture (and recapture, where appropriate) is assumed equal across all grids. As population size is not

included in the likelihood, it is derived using a Horvitz-Thompson estimator (i.e., ˆN =Pn

i=11/pi, where pi is the probability of first capture for individual i= 1, ..., n; calculated for each primary session).

Given there are three primary sessions and four secondary sessions, the full, time dependent model has 50 parameters (Table 3.1), and cannot be fitted due to parameter identifiability issues (White, 2005). Staying in the realms of biological plausibility, a set of 31 models were chosena priori. Twenty of these models did not include individual heterogeneity (i.e., π1 = 1) and investigated the effect of session (sess) and sex on capture (p) and recapture (c) probability, and whether temporary emigration was not present (γ00 =γ0 = 0), or was random (γ00 =γ0, Table 3.2). A Markovian emigration model could not be fitted as with only three primary sessions,γ0 is confounded with survival. A further eleven models were fitted that investigated heterogeneity not already modelled (i.e., due to individual, excluding a behavioral response due to capture or affect of sex), using a two-part mixture (i.e., each variable was estimated using the mixture of two distributions, where g was the group in the mixture model). Due to parameter identifiability issues, all heterogeneity models assumed there was no migration, except one (model {p(g+sex).c(g+sex)}, where random migration was also investigated, Table 3.3). Akaike’s Information Criterion (AIC) was used to select models (Burnham and Anderson, 2003).

Table 3.1: Definition of terms used in model formulae presented in Tables 3.2 and 3.3. There were 50 parameters in the full, time dependent model relating to sur- vival (S), migration (γ00 and γ0), the two-part mixture process for heterogeneity (π), and probability of capture (p) and recapture (c).

Symbol No. of Definition

parameters

S 2 Survival between primary session 1 and 2, and survival be- tween session 2 and 3.

γ00 2 Probability of emigrating away from the study area in either session 1 or session 2.

γ0 1 Probability of remaining away from the study area between sessions 2 and 3, given animal has emigrated in the previous time step (session 1).

π 3 Probability of mixture distribution, one for each primary session.

p 24 Apparent encounter probability, which is conditional on the probability that the animal is alive and available for recap- ture (2 mixture distributions x 4 secondary sessions x 3 pri- mary sessions).

c 18 Probability of recapture (2 mixture distributions x 3 sec- ondary sessions x 3 primary sessions).

54 γ00=γ0 = 0) (i.e., 20 models were run in total, but for brevity I report only 10). Survival between sessions was always assumed

constant.

Model notation Definition

{p(.) =c(.), γ00=γ0} Null model, capture probability is constant for duration of study. {p(sess) =c(sess), γ00=γ0} Probability of capture changes between the three primary trapping ses-

sions.

{p(sex) =c(sex), γ00_=γ0_{} Probability of capture is different for male and female woodrats.}

{p(sess+sex) =c(sess+sex), γ00_=γ0_{} Probability of capture is different across sessions, and affect of sex is}

additive.

{p(sess∗sex) =c(sess∗sex), γ00=γ0} Probability of capture is different for male and female woodrats across sessions.

{p(sess∗hab) =c(sess∗hab), γ00=γ0} Probability of capture is different for habitat stratum across sessions. {p(.).c(.), γ00=γ0} Capture probability is constant for duration of study. Once an individual

has been captured, its probability of recapture changes (i.e., a behavioral response, such as trap happiness or trap shyness).

{p(sess).c(sess), γ00=γ0} Probability of capture changes between the three primary trapping ses- sions. Once an individual has been captured, its probability of recapture changes (i.e., a behavioral response), depending on session.

{p(sex).c(sex), γ00=γ0} Probability of capture and recapture is different for male and female woodrats.

{p(sess+sex).c(sess+sex), γ00=γ0} Probability of capture and recapture is different across sessions, but affect of sex is additive.

55 (g) based on a 2-point mixture process. Survival and the 2-point mixture process was always assumed constant across each

session.

Model notation Definition

{p(g) =c(g), γ00=γ0= 0} Probability of capture is constant for duration of study, but is separated into two groups (i.e., a high capture probability group and a low capture probability group). No tempo- rary emigration between sessions.

{p(g+sex) =c(g+sex), γ00=γ0= 0} Probability of capture is separated into two groups with an additive sex effect. No temporary emigration between sessions.

{p(sess+g) =c(sess+g), γ00=γ0= 0} Probability of capture differs across session, and group. No temporary emigration be- tween sessions.

{p(g∗sex) =c(g∗sex), γ00=γ0= 0} Probability of capture is separated into two groups with an interactive sex effect. No temporary emigration between sessions.

{p(sess+g+sex) =c(sess+g+sex), γ00=γ0= 0} Probability of capture differs across session, with an additive effect of sex and group. No temporary emigration between sessions.

{p(sess+g∗sex) =c(sess+g∗sex), γ00=γ0= 0} Probability of capture differs across session, with an interactive effect of sex and group. No temporary emigration between sessions.

{p(sess∗sex+g) =c(sess∗sex+g), γ00=γ0= 0} Probability of capture differs across session and sex, with an additive effective of group. No temporary emigration between sessions.

{p(g).c(g), γ00=γ0= 0} Probability of capture is constant for duration of study, but depends on group. Proba- bility of recapture differs (i.e., behavioural effect) and depends on group. No temporary emigration between sessions.

{p(g+sex).c(g+sex), γ00=γ0} Probability of capture with an additive sex effect. Once an individual has been caught, its probability of recapture changes (i.e., a behavioral response). Random temporary emigration between sessions.

{p(g+sex).c(g+sex), γ00=γ0= 0} As per previous model, with no temporary emigration.

{p(sess∗g).c(sess∗g), γ00=γ0= 0} Probability of capture and recapture differs across session and group. No temporary emigration between sessions.