When a prey species is potentially at risk due to the overabundance of a predator species, the decision of whether to intervene or not can be informed by knowledge of the critical density of the predator species that would yield extinction of the prey species. However, different assumptions about the functional form of the predator-prey relationship (e.g. Holling’s type I, II or III) can be made when estimating these critical densities. In the present study, we used a combination of data from a field experiment, deterministic mathematical modelling and Bayesian inference to estimate the critical density of urchins that would, through excessive herbivory, lead to extinction of the local seagrasses. We found that models of varying complexity fit the data well; however, these models’ predictions of the critical urchin density depend strongly on the functional form of the predator-prey relationship assumed in each model. Surprisingly, a key outcome of our study is that the most complex model tested is recommended to inform risk-averse decisions to manage herbivory pressure, as this model provided the lowest (and therefore most conservative) estimates of critical predator density. This conclusion may hold in many other ecosystems where a prey species is threatened by predator overabundance.