2021 journal article

Resonance in Physiologically Structured Population Models

BULLETIN OF MATHEMATICAL BIOLOGY, 83(8).

By: K. Gross n & A. Roos *

author keywords: Benthic invertebrates; Environmental stochasticity; Intraspecific competition; Mathematical model; Population dynamics; Spectral analysis
MeSH headings : Animals; Anthozoa; Coral Reefs; Mathematical Concepts; Population Density; Population Dynamics
TL;DR: This analysis identifies a sharp multi-decade resonance driven by space competition between existing coral colonies and incoming recruits in a size-structured population model of stony corals with open recruitment, parameterized for a common Indo-Pacific coral species complex. (via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
14. Life Below Water (Web of Science; OpenAlex)
Source: Web Of Science
Added: July 6, 2021

Ecologists have long sought to understand how the dynamics of natural populations are affected by the environmental variation those populations experience. A transfer function is a useful tool for this purpose, as it uses linearization theory to show how the frequency spectrum of the fluctuations in a population's abundance relates to the frequency spectrum of environmental variation. Here, we show how to derive and to compute the transfer function for a continuous-time model of a population that is structured by a continuous individual-level state variable such as size. To illustrate, we derive, compute, and analyze the transfer function for a size-structured population model of stony corals with open recruitment, parameterized for a common Indo-Pacific coral species complex. This analysis identifies a sharp multi-decade resonance driven by space competition between existing coral colonies and incoming recruits. The resonant frequency is most strongly determined by the rate at which colonies grow, and the potential for resonant oscillations is greatest when colony growth is only weakly density-dependent. While these resonant oscillations are unlikely to be a predominant dynamical feature of degraded reefs, they suggest dynamical possibilities for marine invertebrates in more pristine waters. The size-structured model that we analyze is a leading example of a broader class of physiologically structured population models, and the methods we present should apply to a wide variety of models in this class.