Population dynamics in variable environments. IV. Weak ergodicity in the Lotka equation

Environmental variability is ubiquitous, but its effects on populations are not fully understood or predictable. Recent attention has focused on how rapid evolution can impact ecological dynamics via adaptive trait change. However, the impact of trait change arising from plastic responses has received less attention, and is often assumed to optimize performance and unfold on a separate, faster timescale than ecological dynamics. Challenging these assumptions, we propose that gradual plasticity is important for ecological dynamics, and present a study of the plastic responses of the freshwater green algae Chlamydomonas reinhardtii as it acclimates to temperature changes. First, we show that C. reinhardtii 's gradual acclimation responses can both enhance and suppress its performance after a perturbation, depending on its prior thermal history. Second, we demonstrate that where conventional approaches fail to predict the population dynamics of C. reinhardtii exposed to temperature fluctuations, a new model of gradual acclimation succeeds. Finally, using high-resolution data, we show that phytoplankton in lake ecosystems can experience thermal variation sufficient to make acclimation relevant. These results challenge prevailing assumptions about plasticity's interactions with ecological dynamics. Amidst the current emphasis on rapid evolution, it is critical that we also develop predictive methods accounting for plasticity.

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Population Dynamics for Conservation

10.1093/oso/9780198758365.001.0001 ◽

2019 ◽

Cited By ~ 5

Author(s):

Louis W. Botsford ◽

J. Wilson White ◽

Alan Hastings

Keyword(s):

Population Dynamics ◽

Mathematical Models ◽

Life Stage ◽

Mathematical Concepts ◽

Philosophical Approach ◽

Animal Populations ◽

Variable Environments ◽

In The Wild ◽

Basic Calculus ◽

High Yields

This book is a quantitative exposition of our current understanding of the dynamics of plant and animal populations, with the goal that readers will be able to understand, and participate in the management of populations in the wild. The book uses mathematical models to establish the basic principles of population behaviour. It begins with a philosophical approach to mathematical models of populations. It then progresses from a description of models with a single variable, abundance, to models that describe changes in the abundance of individuals at each age, then similar models that describe populations in terms of the abundance over size, life stage, and space. The book assumes a knowledge of basic calculus, but explains more advanced mathematical concepts such as partial derivatives, matrices, and random signals, as it makes use of them. The book explains the basis of the principles underlying important population processes, such as the mechanism that allow populations to persist, rather than go extinct, the way in which populations respond to variable environments, and the origin of population cycles.The next two chapters focus on application of the principles of population dynamics to manage for the prevention of extinction, as well as the management of fisheries for sustainable, high yields. The final chapter recapitulates how different population behaviors arise in situations with different levels of density dependence and replacement (the potential lifetime reproduction per individual), and how variability arises at different time scales set by a species’ life history.

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