A time for every purpose: using time-dependent sensitivity analysis to help understand and manage dynamic ecological systems

Sensitivity analysis is often used to help understand and manage ecological systems, by assessing how a constant change in vital rates or other model parameters might affect the management outcome. This allows the manager to identify the most favorable course of action. However, realistic changes are often localized in time--for example, a short period of culling leads to a temporary increase in the mortality rate over the period. Hence, knowing when to act may be just as important as knowing what to act upon. In this article, we introduce the method of time-dependent sensitivity analysis (TDSA) that simultaneously addresses both questions. We illustrate TDSA using three case studies: transient dynamics in static disease transmission networks, disease dynamics in a reservoir species with seasonal life-history events, and endogenously-driven population cycles in herbivorous invertebrate forest pests. We demonstrate how TDSA often provides useful biological insights, which are understandable on hindsight but would not have been easily discovered without the help of TDSA. However, as a caution, we also show how TDSA can produce results that mainly reflect uncertain modeling choices and are therefore potentially misleading. We provide guidelines to help users maximize the utility of TDSA while avoiding pitfalls.