* Slightly modified to give a Type III functional response.

** Data from figure in (Skalski & Gilliam 2001)

Each of the equations in Table 2 was calibrated using Bayesian inference (Hamiltonian Monte Carlo No U-Turn Sampler algorithm (Hoffman & Gelman 2014)) with each of the datasets, using weakly informative priors.

In the case of experiments where prey densities were held constant (theoretically infinite predation opportunities), the data was modelled with a Poisson distribution as follows:

\begin{equation} y\sim Poisson(\mu*n)\nonumber \\ \end{equation}

Where y is the total number of predation events observed (across all replicates), n is the number of replicates, and µ is calculated according to each equation’s specification.

When (as was most often the case) prey were not replaced to maintain constant density throughout the experiment, the data was modelled with a Binomial distribution:

\begin{equation} y\sim Binomial(n=\mu*n,\ p=\max\left(\frac{\mu}{N},\ 0.999\right))\nonumber \\ \end{equation}

With the same parameter definitions as above, and N being the initial number of prey. Note that p had to be bounded to avoid overflows with several equation types.

Following calibration, each equation’s performance within a dataset was ranked according to the Widely-applicable Information Criterion (WAIC) (Watanabe 2013; Vehtari et al. 2017), which takes the number of parameters into account (and penalises equations with more parameters in order to avoid overfitting); lower scores indicate better model fit.