Functional response models were fit separately to uninfected and infected crabs, allowing us to examine the effects of parasite infection on the functional response. First, to determine the type of functional response (i.e. type I, II or III), we used polynomial logistic regression on the proportion of prey consumed as a function of prey density (Juliano 2001). For both uninfected and infected crabs, the first order term in this regression was significantly negative (i.e. declining proportion consumed at very low prey densities), indicative of a type II functional response (Juliano 2001). Because prey were depleted over the 24 h that crabs foraged and not replaced, a Rogers type II functional response model that accounts for prey depletion was fit separately to uninfected and infected crabs (Rogers 1972):
Ne = No(1 - exp (α(NeTh - PT))) (1)
where Ne is the number of prey eaten, No is the initial prey density, a is attack rate, Th is handling time, P is the number of predator individuals (set to 1), and T is the experimental duration (set to 13 h). Equation 1 is a recursive function of Ne, and so we used the Lambert W function to implement the model (see Bolker 2008 for details):
Ne = No(W(αThNo exp−α (PT−ThNo))/αTh) (2)
where W is the Lambert W function and all other parameters are the same as in Eq. 1. This functional response model was fit to prey consumption data using maximum likelihood estimation with binomial errors in the statistical software R (package "bblme").
BCO-DMO Processing:
- added conventional header with dataset name, PI name, version date, reference information
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