Heavy-tailed abundance distributions from stochastic Lotka-Volterra models

Descheemaeker, Lana; Grilli, Jacopo; Buyl, Sophie de

doi:10.1103/physreve.104.034404

Cited by 7 publications

(6 citation statements)

References 15 publications

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“…Unrestrained growth in a mutualistic scenario can be circumvented by replacing linear species interaction terms with non-linear saturating functions. The net sign of species interactions can be allowed to vary through time by, for example, adding a joint carrying capacity [ 24 , 29 , 70 , 79 ]. Higher-order interactions can also be included [ 74 , 80 ].…”

Section: Ecological Modelsmentioning

confidence: 99%

“…Environmental heterogeneity has been modelled as fluctuations in mortality rates [ 82 ], and by using time-varying interactions [ 64 ]. Another means to incorporate stochasticity is through adding a noise term to the equations [ 79 , 83 ], or by randomly drawing interaction coefficients and/or intrinsic growth rates from predefined distributions [ 30 , 56 , 66 , 84 ]. Indirect, metabolite-mediated, interactions can also be explicitly modelled as a quadratic species-metabolite interaction model [ 84 ].…”

Section: Ecological Modelsmentioning

confidence: 99%

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Ecological modelling approaches for predicting emergent properties in microbial communities

et al. 2022

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Recent studies have brought forward the critical role of emergent properties in shaping microbial communities and the ecosystems they are part of. Emergent properties - patterns or functions that cannot be deduced linearly from the properties of the constituent parts - underlie important ecological characteristics such as resilience, niche expansion, and spatial self-organisation. While it is clear that emergent properties are a consequence of interactions within the community, their non-linear nature makes mathematical modelling imperative for establishing the quantitative link between community structure and function. As the need for conservation and rational modulation of microbial ecosystems is increasingly apparent, so is the consideration of the benefits and limitations of the approaches to model emergent properties. Here we review ecosystem modelling approaches from the viewpoint of emergent properties. We consider the scope, advantages, and limitations of Lotka-Volterra, consumer-resource, trait-based, individual-based, and genome-scale metabolic models. Future efforts in this research area would benefit from capitalising on the complementarity between these approaches towards enabling rational modulation of complex microbial ecosystems.

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Section: Ecological Modelsmentioning

confidence: 99%

Section: Ecological Modelsmentioning

confidence: 99%

Ecological modelling approaches for predicting emergent properties in microbial communities

et al. 2022

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“…converging to a delta distribution as the number of sites increases), whereas empirical data tends to follow a broad lognormal distribution ( Grilli, 2020 ). Contrastingly, recent efforts have determined that the predictions of a model of self-limiting growth with environmental noise, the SLM, is capable of quantitatively capturing multiple empirical macroecological patterns in observational and experimental microbial communities ( Grilli, 2020 ; Zaoli and Grilli, 2021 ; Zaoli et al, 2022 ; Descheemaeker et al, 2021 ; Descheemaeker and de Buyl, 2020 ; Shoemaker et al, 2023c ; Lim et al, 2023 ). The stationary solution of this model predicts that the abundance of a given community member across sites follows a gamma distribution ( Grilli, 2020 ), a result that provides the foundation necessary to predict macroecological patterns among and between different taxonomic and phylogenetic scales.…”

Section: Introductionmentioning

confidence: 98%

Investigating macroecological patterns in coarse-grained microbial communities using the stochastic logistic model of growth

Shoemaker,

Grilli

2024

eLife

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The structure and diversity of microbial communities is intrinsically hierarchical due to the shared evolutionary history of community members. This history is typically captured through taxonomic assignment and phylogenetic reconstruction, sources of information that are frequently used to group microbes into higher levels of organization in experimental and natural communities. Connecting community diversity to the joint ecological dynamics of the abundances of these groups is a central problem of community ecology. However, how diversity and dynamics depend on the scale of observation at which groups are defined has never been systematically examined. Here, we used a macroecological approach to quantitatively characterize the structure and diversity of microbial communities among disparate environments across taxonomic and phylogenetic scales. We found that measures of biodiversity at a given scale can be consistently predicted using predictions derived from a minimal model of ecology, the Stochastic Logistic Model of growth (SLM). Extending these within-scale results, we examined the relationship between measures of biodiversity calculated at different scales (e.g., genus vs. family), an empirical pattern predicted by the Diversity Begets Diversity (DBD) hypothesis. We found that the relationship between richness estimates at different scales can be quantitatively predicted assuming independence among community members. Contrastingly, only by including correlations between species abundances (e.g., as consequence of interactions) can we predict the relationship between estimates of diversity at different scales. The results of this study characterize novel microbial patterns across scales of organization and establish a sharp demarcation between recently proposed macroecological patterns that are not and are affected by ecological interactions.

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“…One relevant example is that the UNTB predicts that the distribution of mean abundances of community members across sites is extremely narrow (i.e., converging to a delta distribution as the number of sites increases), whereas empirical data tends to follow a broad lognormal distribution [40]. Contrastingly, recent efforts have determined that the predictions of a model of self-limiting growth with environmental noise, the Stochastic Logistic Model (SLM), is capable of quantitatively capturing multiple empirical macroecological patterns in observational and experimental microbial communities [40][41][42][43][44][45][46]. The stationary solution of this model predicts that the abundance of a given community member across sites follows a gamma distribution [40], a result that provides the foundation necessary to predict macroecological patterns among and between different taxonomic and phylogenetic scales.…”

Section: Introductionmentioning

confidence: 99%

Investigating macroecological patterns in coarse-grained microbial communities using the stochastic logistic model of growth

Shoemaker

Grilli

2023

Preprint

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Microbial communities are intrinsically hierarchical due to the shared evolutionary history of community members. This history is primarily captured through taxonomic assignment and phylogenetic reconstruction, sources of information that are frequently used to group microbes into higher levels of organization in experimental and natural communities. However, our understanding of how community diversity depends on one’s scale of observation has yet to be systematically examined. This omission is not simply a methodological detail, as the shared history of community members captured by taxonomic and phylogenetic information provides an opportunity to investigate how patterns of diversity and abundance (i.e., macroecology) are altered across scales of organization. Here, we evaluate the extent that macroecological laws endure across taxonomic and phylogenetic scales among disparate environments using data from the Earth Microbiome Project. We found that measures of biodiversity at a given scale can be consistently predicted using predictions derived from a minimal model containing zero free parameters, the Stochastic Logistic Model of growth (SLM). Extending these within-scale results, we examine the relationship between measures of biodiversity calculated at different scales (e.g., genus vs. family), an empirical prediction known as the Diversity Begets Diversity (DBD) hypothesis. We found that the relationship between richness estimates at different scales can be quantitatively predicted assuming Independence among community members. Contrastingly, only by including correlations between species (i.e., interactions) can we predict the relationship between estimates of diversity at different scales. The results of this study characterize novel microbial patterns across scales of organization and establish a sharp demarcation between recently proposed macroecological patterns that can and cannot be captured by a minimal model of biodiversity.

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Heavy-tailed abundance distributions from stochastic Lotka-Volterra models

Cited by 7 publications

References 15 publications

Ecological modelling approaches for predicting emergent properties in microbial communities

Ecological modelling approaches for predicting emergent properties in microbial communities

Investigating macroecological patterns in coarse-grained microbial communities using the stochastic logistic model of growth

Investigating macroecological patterns in coarse-grained microbial communities using the stochastic logistic model of growth

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