Making the most of your matrix model: Novel analytical techniques for effective population management

Background/Question/Methods

Population projection matrix (PPM) models are extensively used to inform management and policy for conservation, pest control and harvesting.  Perturbation analyses of PPM models are integral to population management.  They describe how changes in a population’s vital rates translate to changes in population dynamics, thus identifying ecologically and economically effective management strategies.  Asymptotic sensitivity analyses are popular, providing a linear approximation of the effect of management strategy on long-term (asymptotic) population growth.  However, these ignore important short-term (transient) dynamics, and the potential for nonlinearity in the dynamical response of the population to management.  We explore how these oversights may impact management conclusions, using novel methods for assessing nonlinear perturbation curves of transient population dynamics.  These methods require no more data than traditional asymptotic sensitivity analyses, and so are a viable alternative for studies that cannot provide the rich data required by density-dependent and stochastic alternatives.

Results/Conclusions

We show that management strategies based on asymptotic sensitivity analyses often fail to exploit desirable transient dynamics, and may cause undesirable transient dynamics antagonistic to management goals.  Perturbation curves of transient dynamics are often markedly nonlinear, and linear approximations of transient sensitivity analyses frequently prove a poor descriptor of actual dynamical response to perturbation.  We therefore advocate use of nonlinear perturbation analyses of transient dynamics, alongside more traditional perturbation analyses.  We present an R package that enables free, easy application of our methods to empirical PPM models.