Drivers of demography: past challenges and a promise for a changed future

There is an urgent need to understand how populations and metapopulations respond to shifts in the environment to mitigate the consequences of human actions and global change. Identifying environmental variables/factors affecting population dynamics and the nature of their impacts is fundamental to improve projections and predictions. This chapter examines how environmental drivers, both continuous (stress) and episodic (disturbance), are incorporated in demographic modelling across many types of organisms and environments, using both observational and experimental approaches to characterise drivers. It critically summarises examples of the main approaches and identifies major accomplishments, challenges, and limitations. The chapter points to promising approaches and possible future developments. In the initial sections, models in closed systems without migration among populations are considered. The chapter then focuses on metapopulation models, emphasising the importance of understanding drivers affecting migration and differential extinction among populations. Finally, it concludes with a discussion of some important and general problems associated with assessing how population dynamics may be affected by environmental drivers that are dynamic, nonlinear, and with indirect and/or interacting effects with other drivers..

Final size and convergence rate for an epidemic in heterogeneous populations

We formulate a general SEIR epidemic model in a heterogeneous population characterized by some trait in a discrete or continuous subset of a space [Formula: see text]. The incubation and recovery rates governing the evolution of each homogeneous subpopulation depend upon this trait, and no restriction is assumed on the contact matrix that defines the probability for an individual of a given trait to be infected by an individual with another trait. Our goal is to derive and study the final size equation fulfilled by the limit distribution of the population. We show that this limit exists and satisfies the final size equation. The main contribution of this work is to prove the uniqueness of this solution among the distributions smaller than the initial condition. We also establish that the dominant eigenvalue of the next-generation operator (whose initial value is equal to the basic reproduction number) decreases along every trajectory until a limit smaller than 1. The results are shown to remain valid in the presence of a diffusion term. They generalize previous works corresponding to finite number of traits (including metapopulation models) or to rank 1 contact matrices (modeling e.g. susceptibility or infectivity presenting heterogeneity independently of one another).

Dispersers’ habitat detection and settling abilities modulate the effect of habitat amount on metapopulation resilience

Context Metapopulation theory makes useful predictions for conservation in fragmented landscapes. For randomly distributed habitat patches, it predicts that the ability of a metapopulation to recover from low occupancy level (the “metapopulation capacity”) linearly increases with habitat amount. This prediction derives from describing the dispersal between two patches as a function of their features and the distance separating them only, without interaction with the rest of the landscape. However, if individuals can stop dispersal when hitting a patch (“habitat detection and settling” ability), the rest of habitat may modulate the dispersal between two patches by intercepting dispersers (which constitutes a “shadow” effect). Objectives We aim at evaluating how habitat detection and settling ability, and the subsequent shadow effect, can modulate the relationship between the metapopulation capacity and the habitat amount in the metapopulation. Methods Considering two simple metapopulation models with contrasted animal movement types, we used analytical predictions and simulations to study the relationship between habitat amount and metapopulation capacity under various levels of dispersers’ habitat detection and settling ability. Results Increasing habitat detection and settling ability led to: (i) larger metapopulation capacity values than expected from classic metapopulation theory and (ii) concave habitat amount–metapopulation capacity relationship. Conclusions Overlooking dispersers’ habitat detection and settling ability may lead to underestimating the metapopulation capacity and misevaluating the conservation benefit of increasing habitat amount. Therefore, a further integration of our mechanistic understanding of animals’ displacement into metapopulation theory is urgently needed.

Spatial population dynamics

This chapter considers populations structured in a different dimension: space. This begins by representing population dynamics with a spatial continuity equation (analogous to the M’Kendrick/von Foerster model for continuity in age or size). If organisms move at random, this motion can be approximated as diffusion. This proves useful for modeling spreading populations, such as the expansion of sea otter populations along the California coast. Adding directional advection represents a population in a flowing stream. Metapopulation models are then introduced using a simple model of the fraction of occupied patches; these are made more realistic by accounting for inter-patch distance using incidence function models. The next level of complexity is models with population dynamics in each patch. These are used to examine how metapopulations can persist as a network even if no patch would persist by itself. Finally, the consequences of synchrony (or lack thereof) among spatially separated populations is described.

Optimised prophylactic vaccination in metapopulations

A highly effective method for controlling the spread of an infectious disease is vaccination. However, there are many situations where vaccines are in limited supply. The ability to determine, under this constraint, a vaccination strategy which minimises the number of people that become infected over the course of a potential epidemic is essential. Two questions naturally arise: when is it best to allocate vaccines, and to whom should they be allocated? We address these questions in the context of metapopulation models of disease spread. We discover that it is optimal to distribute all vaccines prophylactically, rather than withholding until infection is introduced. For small metapopulations, we provide a method for determining the optimal allocation. As the optimal strategy becomes computationally intensive to obtain when the population size increases, we detail an approximation method to determine an approximately optimal vaccination scheme. Through comparisons with other strategies in the literature, we find that our approximate strategy is superior.