2.3 Statistical analyses
All statistics and graphics were carried out using R, version 3.2.5 (http://r-project.org).
(i) The effect of L. intestinalis infection on host fecundity was tested using a generalized linear mixed-effects model (glmmPQL) fitted with fecundity as a response variable (assuming Quasi-Poisson distribution), and maturity stage and infection status as predictor variables. Because the data were collected over a 10-year period, year of sampling was included as a random effect factor in the model.
(ii) To test whether reproductive investment at maturity has increased over time, we used a generalized linear model (glm) fitted with a binomial distribution. The binomial response variable combined gonadal weight of uninfected E. sardella and somatic weight. We chose to use relative gonad weight at stage IV because this is the stage whereE. sardella reach reproductive maturity. Year was included as a numerical predictor variable.
(iii) To test whether size of E. sardella at maturity has decreased over time, we first fitted for each year a logistic regression model with maturity status as a binomial response variable (0: immature; 1: mature), and body length as a continuous predictor variable (Supplementary Figure S2). From the parameters of these logistic regression equations, and following Diaz Pauli and Heino (2013), we estimated for each year the length at which the probability of maturing is 50% (i.e., LM50):
LM50\(=\frac{\text{Log}e(\frac{p}{1-p})-(a)}{b}\)
Where, p is the probability of maturity (0.5), a is the intercept and b is the slope.
To test whether LM50 decreased over time, we fitted a linear model (lm) with LM50 as a response variable and year as a numerical predictor (linear and quadratic terms).