Encounter theory for conservation and management: An application for risk of collision between wildlife and motor vehicles
The theory of encounter rates was first developed in the context of antisubmarine warfare operations, it was later extended to model the community structure of zooplankton. More recently it has been considered to evaluate risk of collision with wildlife. Here we present an analytical description of the solution for encounter rates in two dimensions, which is relevant to many ecological applications. We define encounter rates as the expected number of encounters in an interval of time. We use the theory of encounter rates to examine the process of wildlife collisions. More specifically we consider the example of watercraft collisions with the endangered Florida manatee Trichechus manatus latirostris. Watercraft mortality has been identified as one of the primary threats for this species. We explore key parameters of the model such as boating activities, boat speed, manatee shape and size (e.g., young versus adults), movement patterns and manatee speed on encounter rates with boats. We derived an estimate of expected mortality based on encounter rates. We used a Monte Carlo method to account for uncertainty associated with manatee mortality.
The shape and size of boats and manatees were important in predicting encounter rates. We developed a correction factor to account for the shape of animals. For the set of parameters that we considered we found a 30% reduction in encounter rates (with the estimate based on the correction factor) when compared to a method in which boats and manatees were treated as circles with a radius of encounter based on their width. We also explored the effect of three functional forms for the relationship between boat speed and probability of death given strike speed on expected mortality. The functional form of this relationship influenced expected mortality nonlinearly. Although we did not find that accounting for uncertainty associated with manatee speed had a significant effect on risk of mortality, other sources of uncertainty had an effect on the overall estimate of mortality. For instance, in the scenarios that we explored, ignoring uncertainty led to a difference of 8% in the estimate of reduction in mortality (associated with a decrease in boat speed from 9 m/s to 1 m/s). In addition to providing new insights about wildlife collisions and the management of wildlife protection areas, our analyses should also be useful to understanding other ecological processes involving encounters between moving agents (e.g., foraging, mate encounters).