3.2 Comparison of factors influencing relative specialization
Based on AIC values, \(r^{2}\ \text{results}\), and model likelihood, the best fit GLMM was Month*Sex + (1|Sample Size) + (1|Location) + (1|Year) (Table 2). The \(r^{2}\) value and residual plots indicate that this model fit the data well (Table 2, Figure S3). The random factors of Sample Size, Location, and Year explained 0.39, 0.36, and 0.002 of the variance (SD = 0.62, 0.597, 0.05), respectively. The \(r^{2}\) value calculated with fixed and random effects was over four times that of the \(r^{2}\) value calculated using just fixed effects. Removing Month from the model caused a larger decrease in goodness-of-fit measurements than removing Sex (Table 2). Removal of the interaction term also caused a decrease in goodness-of-fit measurements (Table 2). Further, the interaction terms for Sex and the Months of August and October were significant (t = 2.86, 2.68, p = 0.004, 0.007 respectively). However, correlation analysis between the percent female scat collected for each paired group (which acted as a proxy for the effect of sex ratio in the population) and the average \(\text{PS}_{i}\) for that pairing revealed no significant trend (rho = -0.071, p = 0.655).
To further examine the interaction between Sex and Month, the factor of Month was grouped into three levels: spring (April and May), summer (June, July, August), and fall (September, October, and November). The specialization metric showed a distinct shift throughout the year in males but not females (Figure 2). In summer and fall, males had relatively lower levels of specialization than females (Figure 2). To address the potential bias introduced by sample size for this mode of data analysis, we plotted the sample size for each group by season. The pattern observed in \(\text{PS}_{i}\) values was not reflected in sample size (Figure 3).
Visual inspection of the data by month suggested males had a decrease in relative specialization in July through October (Figure 4). Based on 95% confidence intervals of logit transformed \(\text{PS}_{i}\) values,\(\text{PS}_{i}\) during these months only overlapped with April (Figure 4). The same pattern was not apparent in females because the 95% confidence interval for logit transformed \(\text{PS}_{i}\) of female groups overlapped for all months (Figure 4). This trend varied in intensity by location (Figure 5). The described pattern was reflected most strongly in Belle Chain, Comox, and Fraser River (Figure 5). However, because scat were not collected at Baby Island after July, no comparison could be made at that location (Figure 5, Table S1).