Probabilities of both categories of newly encountered individuals.Parameter S bFB bSB bPFB bPSB cFB cSB cPFB Pyrvinium embonate site cPSBCategory 1 0.9085 (0.0034) 0.8935 (0.0116) 0.0196 (0.0072) 0.0803 (0.0158) 0.9999 (0.0001) 0.3236 (0.0307) 0.7349 (0.0164) 0.1734 (0.3853) 0.5029 (0.0197)Category 2 0.9463 (0.0025) 0.9221 (0.0131) 0.0684 (0.0045) 0.1717 (0.0818) 0.9934 (0.0168) 0.6548 (0.0157) 0.7250 (0.2536) 0.3721 (0.0187) 0.5362 (0.1398)P,0.001 0.102 ,0.001 0.273 0.699 ,0.001 1.000 0.606 0.Parameter estimates from a model with the same structure as Model 2 (Table 1), but with heterogeneity in breeding and success probabilities. Tests to compare parameters between both categories of individuals were performed with program Contrast [58]. doi:10.1371/journal.pone.0060353.tFigure 3. Numbers of breeding pairs of wandering albatrosses at Possession Island, from 1968 to 2008. Black dots indicate observed counts (error bars are 6 SE), grey line indicates numbers predicted by a matrix population model without heterogeneity on adult survival, and black line indicates numbers predicted by a matrix population model with heterogeneity on adult survival. doi:10.1371/journal.pone.0060353.gPLOS ONE | www.plosone.orgDifferential Susceptibility to Bycatchobservable states as: st st pt zst pt zst pt zst pt SB1 SB1 SB2 SB2 FB1 FB1 FB2 FB2 where t indicates year, 1 and 2 indicates the two categories of individuals. All other parameters were constant, except for juvenile survival, which was year-specific. Matrix population models were run with the package popbio [47] implemented in program R [48]. Initial stage abundances were set equal to the stable age distribution based on the total number of breeding females of 1968.and in success probability in failed breeders in the previous year (Table 3). The CBIC2 web deterministic matrix population model taking into account heterogeneity in survival better predicted the observed counts of breeding pairs (linear regression: r2 = 0.89, P,0.001) than the matrix population model that ignored this heterogeneity (r2 = 0.72, P,0.001, Fig. 3). Population growth rates were 0.968 for the category 1 and 1.007 and for the category 2 subpopulations, indicating respectively a 3.2 annual decrease and a 0.7 annual increase. The generation time for the category 1 subpopulation was 19 years, whereas for the category 2 subpopulation it was 25.4 years.ResultsThe approximate GOF tests indicated that our general multievent model with unobservable states, state uncertainty and heterogeneity fitted the data (total x2 = 182.9, total df = 1014, P = 1.00). This was also verified for the restricted data set (males: x2 = 173.3, df = 815, P = 1.00; females: x2 = 373.0, df = 745, P = 1.00). There was strong support for a model with a linear temporal trend in the proportion of both categories of newly encountered individuals in the population (Table 1). This model (Model 2) was 243 AIC-points lower than Model 1 (constant proportions) and eight AIC-points lower than Model 3 (quadratic trend). Model 2 clearly suggested a decrease in the initial proportion of one category of individuals (category 1) through time and an increase in the initial proportion of the other category of individuals (category 2). This pattern was particularly marked for successful breeders, which constitute the majority of the breeding population (Fig. 1). Interestingly, the decrease in the initial proportion of category 1 individuals coincided with the increase in fishing effort in the foraging areas.Probabilities of both categories of newly encountered individuals.Parameter S bFB bSB bPFB bPSB cFB cSB cPFB cPSBCategory 1 0.9085 (0.0034) 0.8935 (0.0116) 0.0196 (0.0072) 0.0803 (0.0158) 0.9999 (0.0001) 0.3236 (0.0307) 0.7349 (0.0164) 0.1734 (0.3853) 0.5029 (0.0197)Category 2 0.9463 (0.0025) 0.9221 (0.0131) 0.0684 (0.0045) 0.1717 (0.0818) 0.9934 (0.0168) 0.6548 (0.0157) 0.7250 (0.2536) 0.3721 (0.0187) 0.5362 (0.1398)P,0.001 0.102 ,0.001 0.273 0.699 ,0.001 1.000 0.606 0.Parameter estimates from a model with the same structure as Model 2 (Table 1), but with heterogeneity in breeding and success probabilities. Tests to compare parameters between both categories of individuals were performed with program Contrast [58]. doi:10.1371/journal.pone.0060353.tFigure 3. Numbers of breeding pairs of wandering albatrosses at Possession Island, from 1968 to 2008. Black dots indicate observed counts (error bars are 6 SE), grey line indicates numbers predicted by a matrix population model without heterogeneity on adult survival, and black line indicates numbers predicted by a matrix population model with heterogeneity on adult survival. doi:10.1371/journal.pone.0060353.gPLOS ONE | www.plosone.orgDifferential Susceptibility to Bycatchobservable states as: st st pt zst pt zst pt zst pt SB1 SB1 SB2 SB2 FB1 FB1 FB2 FB2 where t indicates year, 1 and 2 indicates the two categories of individuals. All other parameters were constant, except for juvenile survival, which was year-specific. Matrix population models were run with the package popbio [47] implemented in program R [48]. Initial stage abundances were set equal to the stable age distribution based on the total number of breeding females of 1968.and in success probability in failed breeders in the previous year (Table 3). The deterministic matrix population model taking into account heterogeneity in survival better predicted the observed counts of breeding pairs (linear regression: r2 = 0.89, P,0.001) than the matrix population model that ignored this heterogeneity (r2 = 0.72, P,0.001, Fig. 3). Population growth rates were 0.968 for the category 1 and 1.007 and for the category 2 subpopulations, indicating respectively a 3.2 annual decrease and a 0.7 annual increase. The generation time for the category 1 subpopulation was 19 years, whereas for the category 2 subpopulation it was 25.4 years.ResultsThe approximate GOF tests indicated that our general multievent model with unobservable states, state uncertainty and heterogeneity fitted the data (total x2 = 182.9, total df = 1014, P = 1.00). This was also verified for the restricted data set (males: x2 = 173.3, df = 815, P = 1.00; females: x2 = 373.0, df = 745, P = 1.00). There was strong support for a model with a linear temporal trend in the proportion of both categories of newly encountered individuals in the population (Table 1). This model (Model 2) was 243 AIC-points lower than Model 1 (constant proportions) and eight AIC-points lower than Model 3 (quadratic trend). Model 2 clearly suggested a decrease in the initial proportion of one category of individuals (category 1) through time and an increase in the initial proportion of the other category of individuals (category 2). This pattern was particularly marked for successful breeders, which constitute the majority of the breeding population (Fig. 1). Interestingly, the decrease in the initial proportion of category 1 individuals coincided with the increase in fishing effort in the foraging areas.