We first ran a GLM with maturity status (i.e., mature or immature) as a binomial response variable and the following as explanatory variables: standard length, year, and the interaction between SL and year.
To test for differences in L50, we ran a nested generalized linear model (GLM) with maturity status (i.e., mature or immature) as a binomial response variable and the following as explanatory variables: perturbation level, lake nested within perturbation level, and standard length.
Generalized linear models were conducted with the "glm" function in the "stats" package for models with binary responses and with the "glm.nb" function in the "MASS" package for models with negative binomial responses (Venables and Ripley 2002) using the programming language and software environment, R, version 3.1.0 (R Core Team 2014).
The clustered binomial responses are generated using a beta-binomial distribution [ 22].
D) It is not possible in the classical GLM to generate near-binomial responses and still capture the overall ISI distribution.
Table 1 shows the results of the best adjusted generalized models, the GLM models using negative binomial distribution: glm.nb1 and glm.nb2, and GAM gam1.
Similarly, a negative binomial GLM better fit the hybrids adult returns data than did a Poisson GLM (LRT = 65.0, df = 2, P < 0.001).
A negative binomial GLM better fit the adult returns data for pure families than a Poisson GLM (LRT = 115.5, df = 2, P < 0.001).
However, sexual cannibalism did not affect female mortality (binomial GLM, P = 0.92), which likely was caused by heavy rainfall.
Using a binomial GLM with canonical logit-link, we modeled the protection index as a function of covariates.
The majority (80%; 28/35) of the cannibalistic females did so, whereas only 39% (13/33) of non-cannibalistic females sealed their burrows (binomial GLM, χ21 = 12.1; P = 0.0006).
