Overview
This concept of using body mass ratios to determine potential feeding links between species was primarily developed by Rohr et al. (2010) and has become quite popular in paleo settings (Yeakel et al. 2014; Pires et al. 2015)
Methods
Core idea relates to the ratio between consumer and resource body sizes - which supposedly stems from niche theory (still trying to reconcile that myself). The probability of a link existing between a consumer and resource (in its most basic form) is defined as follows:
\[ P_{ij} = \frac{p}{1+p} \]
where
\[ p = exp[\alpha + \beta log(\frac{M_{i}}{M_{j}}) + \gamma log^{2}(\frac{M_{i}}{M_{j}})] \tag{1}\]
The original latent-trait model developed by Rohr et al. (2010) also included an additional latent trait term \(v_{i} \delta f_{j}\) however for simplicity we will use Equation 1 as per Yeakel et al. (2014). Based on Rohr et al. (2010) it is possible to estimate the parameters \(\alpha\), \(\delta\), and \(\gamma\) using a GLM but we will use the parameters from Yeakel et al. (2014), which was ‘trained’ on the Serengeti food web data and are as follows: \(\alpha = 1.41\), \(\delta = 3.75\), and \(\gamma = 1.87\).