Biology subjects

Spaak, J. W.

Publications and source records attributed to Spaak, J. W..

12 recordsLinked to original sources

bioRxiv2026

From Lotka-Volterra Dynamics to Community Assembly: Theory, Topography, and Empirical Applications

AO_SCPLOWBSTRACTC_SCPLOWO_LICommunity assembly graphs (CAGs) summarize which species combinations can coexist and how single-species invasions drive transitions between them, encoding the pathways, alternative endpoints, and cycles that make up a communitys assembly history. Constructing CAGs from dynamical models requires methods that are both computationally tractable and faithful to the underlying ecological dynamics. However, existing methods rely on restrictive assumptions, such as global stability, that exclude alternative stable states and non-equilibrium dynamics known to occur in empirical systems. C_LIO_LIWe develop a computational pipeline that constructs CAGs from any generalized Lotka-Volterra model. Building on the invasion graph framework and its connection to permanence, the pipeline verifies that community dynamics are bounded, identifies which subsets of species coexist in the sense of permanence, determines which single-species invasions are dynamically realized, and assigns each community a topographic height equal to the length of the longest assembly path leading to it. We also provide a numerical algorithm to simulate the dynamics of community assembly. C_LIO_LIWe prove several general properties of the resulting graphs, including that a successful invader is never subsequently excluded and that, in the absence of assembly cycles, permanent communities can be reassembled by introducing their species one at a time in the right order. We prove that the CAG faithfully reproduces the compositional shifts seen in the numerically simulated dynamics of assembly. Applying the pipeline to three empirically based models (a New Zealand grassland, a European pasture, and a Puerto Rican ant community), we show how competition strength and mutualistic feedbacks reshape the assembly landscape and how intransitive competition generates assembly cycles. C_LIO_LIOur approach accommodates alternative stable states and non-equilibrium dynamics without requiring global stability, and it turns the long-standing landscape metaphor into a quantitative, mechanistically grounded object by resolving what "height" means. More broadly, it makes the topography of the assembly pathways measurable, providing a way to compare the historical contingency and predictability of the assembly in ecological systems. C_LI

ecology↗

bioRxiv2024

Global thermal tolerance of freshwater invertebrates and fish

Scientists have investigated the thermal tolerance of organisms for centuries, yet the field has not lost relevance as the environmental threats of thermal pollution and global change sharpen the need to understand the thermal vulnerability of organisms in landscapes increasingly subjected to multiple stressors. Freshwater fish and especially invertebrates are greatly underrepresented in recent large-scale compilations of thermal tolerance, despite the importance of freshwater habitats as a crucial resource and biodiversity havens. This inspired us to create a thermal tolerance database for these organisms that includes literature from 1900 until the present day sourced from five languages to counteract geographic bias, and 395 thermal tolerance tests conducted with additional stressors present. The database contains over 5000 records for over 800 species, including 452 invertebrates, providing a valuable resource to test hypotheses on thermal risks to freshwater organisms in present and future environments, and how these might change in multiple stressor scenarios.

ecology↗

bioRxiv2023

Multitrophic assembly: a perspective from modern coexistence theory

Ecological communities encompass rich diversity across multiple trophies. While modern coexistence theory has been useful in understanding community assembly, its traditional formalism only allows for the study of assembly within a single trophic level. Here, using an expanded definition of niche and fitness differences applicable to multi-trophic communities, we study how diversity within and across trophics affect species coexistence. Specifically, we investigate how assembly in one trophic level impacts the coexistence of three types of communities: (1) the single-trophic subcommunity with species at that level, (2) the single-trophic subcommunity with species at an adjacent level, and (3) the entire multitrophic community. We find that while coexistence mechanisms are similar for single-trophic communities, they differ for multitrophic ones. We also find that fitness differences primarily constrain diversity in lower-level tropics, while niche differences primarily constrain diversity in higher-level tropics. Empirical data corroborates our predictions about multitrophic structures. Our work provides needed theoretical expectation of multitrophic communities within modern coexistence theory.

ecology↗

bioRxiv2023

Continuous assembly required: perpetual species turnover in two trophic level ecosystems

Community assembly is often treated as deterministic, converging on one or at most a few possible stable endpoints. However, in nature we typically observe continuous change in community composition, which is often ascribed to environmental change. But continuous changes in community composition can also arise in deterministic, time-invariant community models, especially food web models. Our goal was to determine why some models produce continuous assembly and others do not. We investigated a simple two trophic-level community model to show that continuous assembly is driven by the relative niche width of the trophic levels. If predators have a larger niche width than prey, community assembly converges to a stable equilibrium. Conversely, if predators have a smaller niche width than prey, then community composition never stabilizes. Evidence that food webs need not reach a stable equilibrium has important implications, as many ecological theories of community ecology based on equilibria may be difficult to apply to such food webs.

ecology↗

bioRxiv2023

Building modern coexistence theory from the ground up: the role of community assembly

Modern coexistence theory (MCT) is one of the leading methods to understand species coexistence. It uses invasion growth rates - the average, per-capita growth rate of a rare species - to identify when and why species coexist. Despite significant advances in dissecting coexistence mechanisms when coexistence occurs, MCT relies on a "mutual invasibility" condition designed for two species communities, but poorly defined for species rich communities. Here, we review well-known issues with this component of MCT and propose a solution based on recent mathematical advances. We propose a clear framework for expanding MCT to species rich communities and for understanding invasion resistance as well as coexistence, especially for communities which could not be analyzed with MCT so far. Using two data-driven community models from the literature, we illustrate the utility of our framework and highlight the opportunities for bridging the fields of community assembly and species coexistence. Statement of authorship: Studied conceived jointly by JWS and SJS. JWS and SJS wrote the manuscript together. JWS wrote the python code and SJS wrote R code. Data accessibility: All computer code used in this manuscript will be made publicly available on figshare. Niche and fitness differences | Storage effect | Coexistence

ecology↗

bioRxiv2022

Modeling phytoplankton-zooplankton interactions: opportunities for species richness and challenges for modern coexistence theory

Many potential mechanisms can sustain biodiversity, but we know little about their relative importance. To compare multiple mechanisms, we modeled a two-trophic planktonic food-web based on mechanistic species interactions and empirically measured species traits. We simulated thousands of communities under realistic and altered trait distributions to assess the relative importance of three potential drivers of species richness: resource competition, predator-prey interactions, and trait trade-offs. Next, we computed niche and fitness differences of competing zooplankton to obtain a deeper understanding of how these mechanisms limit species richness. We found that predator-prey interactions were the most important driver of species richness and that fitness differences were a better predictor of species richness than niche differences. However, for many communities we could not apply modern coexistence theory to compute niche and fitness differences due to complications arising from trophic interactions. We therefore need to expand modern coexistence theory to investigate multi-trophic communities.

ecology↗

bioRxiv2021

Niche difference determines coexistence and similar underlying processes in four ecological groups

Understanding the drivers of species coexistence is an important objective in ecology. Yet, the multitude of methods to study coexistence hampers cross-community comparisons. Here, we standardized niche and fitness differences (i.e how species limit themselves compared to others and their competitive ability, respectively) across 1018 species pairs to investigate species coexistence across ecological groups and methodological settings (experimental setup, natural co-occurrence, population model used, and growth method). We find that, first, coexistence is driven by large niche differences, not by small fitness differences. Second, species group into clear clusters of coexisting and non-coexisting species along the niche axis. Finally, these clusters are not driven by ecological or methodological settings. This suggests differences between coexisting and non-coexisting communities transcending those measured in our empirical systems. Overall, our results show that species coexistence is mainly influenced by mechanisms acting on niche differences.

ecology↗

bioRxiv2021

Different methods for niche and fitness differences computation offer contrasting explanations of species coexistence

In modern coexistence theory, species coexistence can either arise via stabilizing mechanisms that increase niche differences or equalizing mechanisms that reduce fitness differences. Having a common currency for interpreting these mechanisms is essential for synthesizing knowledge across different studies and systems. Several methods for quantifying niche and fitness differences exist, but it remains unknown to what extent these methods agree on the reasons why species coexist. Here, we apply four common methods to quantify niche and fitness differences to one simulated and two empirical data sets. We ask if different methods result in different insights into what drives species coexistence. We find that different methods disagree on the effects of resource supply rates (simulated data), and of plant traits or phylogenetic distance (empirical data), on niche and fitness differences. More specifically, these methods often do not agree better than expected by chance. We argue for (1) a better understanding of what connects and sets apart different methods, and (2) the simultaneous application of multiple methods to enhance a more complete insight into why species coexist.

ecology↗

bioRxiv2021

The effect of non-linear competitive interactions on quantifying niche and fitness differences

The niche and fitness differences of modern coexistence theory separate mechanisms into stabilizing and equalizing components. Although this decomposition can help us predict and understand species coexistence, the extent to which mechanistic inference is sensitive to the method used to partition niche and fitness differences remains unclear. We apply two alternative methods to assess niche and fitness differences to four well known community models. We show that because standard methods based on linear approximations do not capture the full community dynamics, they can sometimes lead to incorrect predictions of coexistence and misleading interpretations of stabilizing and equalizing mechanisms. Conversely, a more recently developed method to decompose niche and fitness differences, that accounts for the full nonlinear dynamics of competition, consistently identifies the correct contribution of stabilizing and equalizing components. This approach further reveals that when the true complexity of the system is taken into account, essentially all mechanisms comprise both stabilizing and equalizing components. Amidst growing interest in the role of non-additive and higher-order interactions in regulating species coexistence, we propose that the effective decomposition of niche and fitness differences will become increasingly reliant on methods that account for the inherent non-linearity of community dynamics.

ecology↗

bioRxiv2020

Unimodal effects of pigment richness on niche and fitness differences explain species richness and ecosystem function in light-limited phytoplankton communities

Trait diversity is traditionally seen as promoting species richness and ecosystem function. Species with dissimilar traits would partition available resources, increasing niche differences, facilitating coexistence and increasing ecosystem function. Here we first show, using theory and simulations for light-limited phytoplankton, that combing photosynthetic pigments is indeed a necessary condition for coexistence and stimulates ecosystem function. However, pigment richness does mostly not permit the coexistence of more than two species, and increases productivity at most 60% compared to single-pigment communities. Surprisingly, combining all nine pigments known to date leads to a 2.5% probability that four species would coexist, illustrating that the coexistence of a high number of species along a continuous niche axis is constrained by limiting similarity. We explain these constraints by unimodal effects of pigment richness on niche and fitness differences, which jointly limit the positive effect of pigment on species richness. Empirical data and additional simulations suggest that pigment richness effects can be stronger during transient dynamics but inevitably weaken with time, i.e. pigment richness effects on species richness and function are likely short-lived. Our results highlight the need to apply coexistence theory to understand the long-term effects of trait diversity on biodiversity and ecosystem function. Statement of authorshipJ.W.S. and F.dL. developed the ideas and wrote the manuscript. J.W.S developed the mathematics and the python code to conduct the study. J.W.S conducted the literature review.

ecology↗

bioRxiv2019

Fitness differences, not niche differences, limit species richness

A key question in ecology is what limits species richness. Modern coexistence theory presents the persistence of species as a balance between niche differences and fitness differences that favor and hamper coexistence, respectively. With most applications focusing on species pairs, however, we know little about if and how this balance changes with species richness. Here, we present the first mathematical proof that the average fitness difference among species increases with richness, while the average niche difference stays constant. Extensive simulations with more complex models and analyses of empirical data confirmed these mathematical results. Taken together, our work suggests that, as species accumulate in ecosystems, ever-increasing fitness differences will at some point exceed constant niche differences, limiting species richness. Our results contribute to the expansion of modern coexistence theory towards multi-species communities.

ecology↗

bioRxiv2018

A unified definition of niche and fitness differences

Explaining natures biodiversity is a key challenge for science. To persist, populations must be able to grow faster when rare, a feature called negative frequency dependence and quantified as niche differences ([N]) in coexistence theory. Here, we first show that available definitions of [N] differ in how [N] link to species interactions, are difficult to interpret, and often apply to specific community types only. We then present a new definition of [N] that is intuitive and applicable to a broader set of (modelled and empirical) communities than is currently the case, filling a main gap in the literature. Given [N], we also re-define fitness differences ([F]) and illustrate how [N] and [F] determine coexistence. Finally, we demonstrate how to apply our definitions to theoretical models and experimental data, and provide ideas on how they can facilitate comparison and synthesis in community ecology.

ecology↗