[FPU2019] Non-linear animal population dynamics and perturbations

Studying population dynamics of animal species using field data is challenging. A bunch of literature has been devoted to describe a common pattern of these dynamics, and the logistic model (and its variants) has been frequently invoked. Thus, it is difficult to assess if the temporal window at which we try to analyse the behaviour of populations in space and time is proper. Also, one of the big flaws comes from the fact that most time series do not start with colonization or from very low densities, so non-linear dynamics are hard to be detected and encompassed by the models. Using data from a range of patches (Mediterranean marshes) that have been re-colonized by a large number of waterbird species in the early 80’s we pretend to explore the different patterns observed to shed some light about the properties and patterns of colonization in very mobile organisms (birds in the present case). Since some human perturbations have been monitored, these impacts, together with the rest of environmental variability, we can also assess how much variance for non-linear population dynamics is explained by these factors. Some behaviour such as boom-bust dynamics, cycles or others should be explored and why these dynamics occur, if so. The existence of thresholds, critical transitions, regime shifts and hysteresis cycles will be also explored.

Furthermore, we will explore transient dynamics since colonization, how long these dynamics are, and why there are differences between species, likely depending on their life-history traits, historical ranges and other features, some of them potentially related to some agents of global change (e.g. global warming, pollutants and habitat loss). Nonlinear density-dependent forms incorporate intrinsic drivers, such as density dependence in vital rates or Allee effects, whereas time-varying stochastic forms incorporate extrinsic drivers, such as variation in climate or resource abundance. Nonlinear, time-varying forms combine both these density dependent and stochastic approaches. Density-dependent models largely focus on analysing attractors including stable equilibria such as carrying capacity or unstable equilibria such as limit cycles. The tendency to focus on equilibria and long-term dynamics is perhaps a hangover from early theoretical paradigms that perceived ecological systems as “balanced”. A thorough understanding of transients may improve the predictive power of the simple density-independent, time-invariant models that dominate the literature and, combined with other approaches, may aid in our comprehension of how complicated population dynamics are shaped. The transient dynamics that we discuss here form a middle-ground of empirical modelling: they describe deterministic responses to (possibly stochastic) disturbances or perturbations, allowing a consideration of non-equilibrium dynamics without recourse to the computationally expensive study of fully stochastic systems.