Effects of fertility control on populations of ungulates: General, stage-structured models

Regulating the abundance of ungulate populations using hunting can prevent populations from reaching levels that cause harm to natural and human dominated systems. However, there are an increasing number of cases where hunting is infeasible, and in such cases, fertility control has been widely advocated as an alternative means for controlling populations. Here, we develop simple analytical models offering general insight into the feasibility of using fertility control to regulate the abundance of ungulates. The models are structured in stages to represent variation in the duration of effect of fertility control agents. Analysis of these models offers several predictions, amenable to testing in field studies. (1) More than 50% of fertile females will need to be maintained infertile to achieve meaningful reductions in ungulate numbers even when fertility rates are low (2) The relationship between the proportion of females maintained infertile and the steady state density is highly nonlinear. This means that small errors in estimating levels of infertility can lead to large errors in achieved density. It also means that managers should expect to see little change in steady-state density across a broad range of delivery rates. (3) The efficacy of fertility control as a management technique depends strongly on the persistence of the effect of the fertility control agent and the ability of managers to recognize previously treated animals. (4) Fertility control using long-lived agents can be more efficient than culling in regulating ungulate numbers. (5) Treating small populations with irreversible agents magnifies the likelihood of population extinction relative to treatment by culling. As with all techniques, managing population fertility must extend from a sound understanding of the influence of management actions on the state and dynamics of the population.