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Modern coexistence theory is increasingly used to explain how differences between competing species lead to coexistence versus competitive exclusion. Although research testing this theory has focused on deterministic cases of competitive exclusion, in which the same species always wins, mounting evidence suggests that competitive exclusion is often historically contingent, such that whichever species happens to arrive first excludes the other. Coexistence theory predicts that historically contingent exclusion, known as priority effects, will occur when large destabilizing differences (positive frequency-dependent growth rates of competitors), combined with small fitness differences (differences in competitors’ intrinsic growth rates and sensitivity to competition), create conditions under which neither species can invade an established population of its competitor. Here we extend the empirical application of modern coexistence theory to determine the conditions that promote priority effects. We conducted pairwise invasion tests with four strains of nectar-colonizing yeasts to determine how the destabilizing and fitness differences that drive priority effects are altered by two abiotic factors characterizing the nectar environment: sugar concentration and pH. We found that higher sugar concentrations increased the likelihood of priority effects by reducing fitness differences between competing species. In contrast, higher pH did not change the likelihood of priority effects, but instead made competition more neutral by bringing both fitness differences and destabilizing differences closer to zero. This study demonstrates how the empirical partitioning of priority effects into fitness and destabilizing components can elucidate the pathways through which environmental conditions shape competitive interactions.
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Permanence via invasion graphs: incorporating community assembly into modern coexistence theory
Abstract To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subsets of species (communities) supporting an ergodic measure and directed edges correspond to potential transitions between communities due to invasions by missing species. These directed edges are determined by the signs of invasion growth rates. When the invasion graph is acyclic (i.e. there is no sequence of invasions starting and ending at the same community), we show that permanence is determined by the signs of the invasion growth rates. In this case, permanence is characterized by the invasibility of all$$-i$$ communities, i.e., communities without speciesiwhere all other missing species have negative invasion growth rates. To illustrate the applicability of the results, we show that dissipative Lotka-Volterra models generically satisfy our technical assumptions and computing their invasion graphs reduces to solving systems of linear equations. We also apply our results to models of competing species with pulsed resources or sharing a predator that exhibits switching behavior. Open problems for both deterministic and stochastic models are discussed. Our results highlight the importance of using concepts about community assembly to study coexistence.
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- Award ID(s):
- 1716803
- PAR ID:
- 10375836
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Journal of Mathematical Biology
- Volume:
- 85
- Issue:
- 5
- ISSN:
- 0303-6812
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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