We did not estimate calf:cow ratios with sample sizes <20 groups, as optimization was problematic when there were few groups and observers typically classify >20 groups. Calf:cow ratios in all simulations

were estimated with function dbetabinom within package bbmle in Program R using the Nelder-Mead algorithm for optimization. Selecting an appropriate level of precision is difficult, as the desired level of precision will depend upon how the data are used. Clearly, we would like to be able to identify years in which reproduction fails and a relative precision of 20% should be sufficient to delineate years of high vs. low calf production. For example, attaining 20% relative precision for a calf:cow ratios would allow differentiation of ratios that differ by more than 1 calf per 100 cows for small ratios, such as 0.05

buy PLX3397 (i.e., 0.05 × 0.2 = 0.01), or 3 calves per 100 cows for larger BYL719 ratios, such as 0.15 (i.e., 0.15 × 0.2 = 0.03). However, if calf:cow ratios are used as measures of fecundity in population models, more precision may be necessary. We chose to present relative precisions as functions of sample size, so users can decide what sample sizes are necessary. Nine surveys classified walrus groups along the ice edge between 1982 and 1999 (Fig. 3; Table 2). Two surveys occurred in 1981 and 1982, single surveys occurred in 1983, 1984, and 1998, and two surveys occurred in 1999. Walruses would sometimes enter the water before all individuals were counted and classified to

sex and age. A total of 1,200 groups of walruses were encountered; of these, 1,107 (92%) were completely PAK5 counted and 886 were completely classified to sex and age. A total of 773 groups were completely classified and contained at least one cow. Pooling within sample years, the number of groups with cows that were classified ranged from 59 in 1983 and 1998 to 218 in 1982 (Table 2). The average size of groups with cows was 7.03 (SD = 10.35) and ranged from 5.52 (SD = 4.92) in 1982 to 9.48 (SD = 16.47) in 1981. The maximum observed sizes of groups with cows were 133 in 1981, 109 in 1982, 22 in 1983, 62 in 1984, 32 in 1998, and 30 in 1999. The entire sea ice front, from Alaska to Russia, was surveyed in 1982, 1998, and 1999 (Fig. 3). In 1981, during the Polar Star survey, time of day was not recorded for 30 cow groups (115 individual cows) and these data were not used for covariate modeling. The data were more appropriately modeled with a beta-binomial distribution (Δ AIC = 0; 2 parameters) than a zero-inflated beta-binomial distribution (Δ AIC = 2.1; 3 parameters), a zero-inflated binomial distribution (Δ AIC = 78.6; 2 parameters), or a binomial distribution (Δ AIC = 127.1; 2 parameters). Hence, a beta-binomial distribution was assumed for subsequent analyses.