Effects of disturbance on the probability of permanence and colonization
After the parameters of permanence and basal colonization of the functional groups were estimated, we used the results of the artificial substrates under different disturbances to assess the effect of water flow changes on genus occurrence. We added a new parameter to the model, which modifies the probability of genera permanence of during the experiment. The model used was:
\begin{equation} {O_{i,k,t}\sim Bern\left(P_{i,k,t}\right)\backslash n}{P_{i,k,t}=\theta_{g}+O_{i,k,t-1}\bullet\psi_{g}\bullet\delta_{k,g}\backslash n}{\delta_{k,g}\sim N\left(0,0.001\right)}\nonumber \\ \end{equation}
(model 3)
where Oi,k,t is the occurrence of genus iin treatment k at time t . In model 3 \(\delta_{k,g}\) was the deviation of the probability of permanence of group g from treatment k , when compared to the baseline permanence of the group observed in the control (\(\psi_{g}\)). We assumed the six factorial interactions by treatment (I1.F1, I1.F2, I1.F3, I2.F1, I2.F2 and I2.F3).
We highlight that the parameters of interest in the study were the hyperparameters estimated in model for \(\psi\) and \(\theta\). These hyperparameters are calculated using the values for \(\alpha\) and\(\beta\). Thus, each genus has its estimated probability value; however, all are linked to the baseline values of the functional groups in which they were categorized.