Predation increases species turnover and structural stability in ecological communities

Logan Jones, Jonas Wickman, Nasser Rabi, Christopher A. Klausmeier

Contact Abstract Proposal References KBS REU Program

Background

A mechanistic understanding of species coexistence is a central pursuit in ecology. Prior eco-evolutionary models show that seasonal temperature fluctuation can facilitate coexistence through the storage effect – species with differing traits can coexist if their gains in good times exceed their losses in bad times. However, the role of predation in shaping coexistence and diversity is less well understood. We compare two models, with and without predation, to explore its effects on emergent community structure and stability.

Methods

The model

We compare nested consumer–resource models with and without a predator. Outer equations include predation; the inner box is the predator-absent subset. Fixed parameters are held constant; T_amp is the continuation parameter.

Nested predator-present and predator-absent model equations with state variables, fixed parameters, and explored seasonal amplitude — **The model.** Predator present (outer) nests the predator-absent equations (inner); −aP and −P complete the predator-present forms. Keys list state variables, fixed parameters, and the explored amplitude T_amp.

Seasonal temperature forcing over one period for several temperature amplitudes — **Fig. 1.** How temperature is modeled over one season (τ), for several amplitudes (T_amp).

How temp. changes

Our model uses seasonal temperature fluctuation (T_amp) to study the evolution of thermal optima and its impact on species coexistence.

Species densities settling into a repeating seasonal limit cycle — **Fig. 2.** Species densities once the community settles into a repeating seasonal pattern (a limit cycle), shown over one full season (τ).

Finding a stable seasonal cycle

First we simulate the density of our community over time. After a long simulation we find a periodic solution to the ecological dynamics, which repeats with the seasonal temperature.

Survival of the fittest

Next we allow thermal optima to evolve. These seed communities eventually reach an equilibrium where no other species can invade. We call these Evolutionarily Stable Communities (ESCs).

Thermal optima evolving on a fitness landscape toward an evolutionarily stable community — **Fig. 3.** Thermal optima (x) evolving from a scattered start; each climbs the fitness landscape (λ) to a peak, where no new species can invade (an ESC).

Results

Community bifurcation diagrams comparing predator-absent (top) and predator-present (bottom) models across seasonal amplitude — **Fig. 4.** Community bifurcation diagrams: evolutionarily stable community (ESC) trait values across seasonal amplitude T_amp. Top: predator absent. Bottom: predator present. Shading highlights structural stability: lighter represents a relatively wider range of environments over which the community persists. Vertical dashed lines mark qualitative transitions (by eye) in species densities; the small intervals between these dashed lines represent regions where species densities are quickly changing.

How to explore

Interactive version of Fig. 4 — toggle predator absent vs present, then inspect branches, densities, and fitness landscapes.

Predator switches the whole bifurcation between predator absent and predator present (Fig. 4 top ↔ bottom).
Hover a curve to read T_amp, trait x, and stability class.
Zoom by dragging a box on the bif plot (or scroll); use the mode-bar home icon to reset.
Branch picks which community continuation to follow; Point slides along that branch.
Right-hand panels update with the selected point: seasonal densities (log & linear) and the fitness landscape λ(x).
Background shading is structural stability; the dark outer funnel is the empty-niche (uninhabitable) region.
Other toggles add dynamically unstable / invasion-unstable segments, trait guides, or density-transition dashes.

Predator absent

Predator Stable Dyn. unstable Invasion unstable Trait guides Density transitions

Branch Point loading…

Diversity

Discussion

Predation increases structural stability, widening the range of environments under which communities can stably coexist.
Introducing a predator increases species turnover, β.
Predation supports more species richness at lower temperature amplitudes ecologically, but these communities fail to persist once thermal optima are allowed to evolve.

Our study implies that predation can foster communities that are more robust to varying amplitudes of temperature fluctuations, raising an exciting empirical question: does predation allow communities to remain qualitatively unchanged as temperature fluctuations intensify?

Acknowledgments

Funding: Douglas and Maria Bayer Scholarship Fund.

Thanks: Thank you to the KBS community, the Klausmeier-Litchman lab, and all who lent support. I couldn't have done it without you!

Abstract

Top-down predation increases species turnover and structural stability in ecological communities

A mechanistic understanding of species coexistence is a central pursuit in ecology. One factor known to enable coexistence is temporal variation of an environmental variable. Prior eco-evolutionary models show that seasonal temperature fluctuation can facilitate coexistence through the storage effect – species with differing traits can coexist if their gains in good times exceed their losses in bad times. However, the role of predation in shaping coexistence and diversity is less well understood. We compare two models, with and without predation, to assess its effects on emergent community structure and stability. Our analysis shows that introducing a predator increases species turnover (β-diversity). This effect is mediated by a decrease in average instantaneous species diversity (α-diversity) alongside a relatively smaller decrease in time-integrated species diversity (γ-diversity); the resulting shift in their ratio drives higher average turnover. We also find that predation provides communities with increased structural stability – widening the range of environments under which communities can stably coexist. Interestingly, this increase in turnover does not translate into more species-rich evolutionarily stable communities. Predation supports more species richness at lower temperature amplitudes in our ecological model, but these communities fail to persist once thermal optima are allowed to evolve. Our study implies that predation can foster communities that are more robust to varying amplitudes of temperature fluctuations, raising an exciting empirical question: does predation allow communities to remain qualitatively unchanged as temperature fluctuations intensify?

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Proposal

Eco-Evolutionary Dynamics: Surveying how predation and cyclical temperature forcing influence emergent community structure

Empirical data and theory agree that the introduction of predation can facilitate a greater number of species coexisting within a guild (Paine, 1966; Holt, 1977; Holt et al., 1994; Chesson, 2000; Leibold et al., 2017). However, a thorough mechanistic grasp of the fundamental physical constraints, the intermediate causal relationships – such as the ways in which predation may promote guild diversity – and the overall system behavior, remains crucial for understanding biological systems. Ecological theory is increasingly being translated into real world application (Anderson et al., 2021; Mouquet et al., 2015). Navigating such applications under a warming climate, and other intensifying anthropogenic pressures necessitates more accurate forecasting and a detailed understanding of individual mechanisms. This study examines one such system by looking at the role, if any, that predation plays in guild diversity. Our approach models the number of species which can stably coexist with and without predation.

Our line of inquiry follows an approach which showed that cyclical temperature forcing in species coexistence models allows for greater species trait diversity (Kremer and Klausmeier, 2017). Without temperature forcing, trait evolution is optimized for whichever species has the trait which is equal to the constant temperature value. Our periodic setup prevents any one species from being optimal at all times, allowing seasonal specialists to coexist. Prior models include regional migration – preventing true extinction – or do not introduce predation. We explore whether this increase in species packing – “the study of the co-occurrence of different species of organisms in a particular sampling area (Slobodkin, 2001)” – holds under more stringent modeling conditions. Hence, we have no regional migration and introduce predator-prey dynamics. We ask the question: Does top-down predation increase species packing in closed systems? We believe that predation may compress realized niche widths, reducing absolute niche overlap – limiting similarity – which could create space for increased guild diversity.

This project focuses on coupling ecological and evolutionary model dynamics under periodic environmental forcing, a computationally demanding, yet technically feasible extension of existing population density models (Kremer and Klausmeier, 2017). We use a system of differential equations, including one equation for each prey species coupled with a predator equation. The trait we focus on is thermal optimum, such that populations have a set temperature which facilitates their fastest growth. The temperature is periodically forced using sine waves; this emulates real world temperature fluctuations in varying climate regimes, smaller amplitude being analogous to the tropics, larger to more temperate regions.

We begin our analysis by solving for ecological dynamics with empirically motivated parameter values. This requires finding a stable attractor, in our model taking the form of a limit cycle which begins and ends on the same value. After obtaining our limit cycle we introduce trait based evolution, tracking thermal optimum at the ecological attractor. We use game theoretic framing to find evolutionarily stable strategies (ESS) and evolutionarily stable communities (ESC), then sweep parameter space with numerical continuation to generate bifurcation diagrams of community structure as temperature amplitude grows.

Comparing the maximum number of and the general trend in species diversity which emerges from our model, against a baseline without predation will shed light on whether predation facilitates species packing, decreases diversity, or has no effect on the number of species which can coexist on a shared resource.

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Bibliography

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loganjones.org Original proposal (PDF)