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by claude@2026-07, 2026-07-04
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The paper develops simple, one-parameter ecological abundance/count models by deriving a discrete probability mass function from a transform of a uniform random variable, producing three proposed variants parameterized by fitted constants. It shows that the resulting distributions are consistent with basic non-competitive equilibrium population dynamics in which species-specific recruitment (and sometimes death) rates vary randomly across species, with recruitment counts Poisson-distributed and death modeled as per-capita, and it notes the caveat that coexistence is assumed in the absence of competition. Using large-scale and local biodiversity inventory datasets across multiple taxa, the authors report that the models fit observed high-unevenness count distributions and predict other inventories, outperforming eight alternative models based on decisive likelihood differences. This paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.
Abstract
1. Counts of species in ecological samples are of interest when they tell us about community assembly processes. Older process-based models of count distributions are either complex, widely rejected, or not able to predict high unevenness. 2. I leverage a general strategy for deriving simple one-parameter models. A distribution of abundances x on a continuous scale is predicted from a transform of a uniform distribution U; U is solved for to yield one minus a cumulative distribution function (CDF) for x; and the result is differenced and rounded to down to yield a probability mass function. The same workflow has long been used to derive the geometric series from the exponential distribution. Three variants are proposed, respectively based on the transforms /U – = ( – U)/U where is a constant (a scaled odds ratio); (1/U – 1)1/p where p is a constant; and [–ln(U)/]2 where –ln U is just an exponential random variate and is a constant. 3. The distributions are all consistent with simple population dynamical models in which recruitment rates, and sometimes death rates, vary randomly amongst species and are fixed for each species. The number of recruited offspring produced during each interval by each species is Poisson-distributed, and death rates are per-capita. Population counts are equilibrial, allowing co-existence in the absence of competition. 4. Large-scale surveys of corals, fishes, butterflies, and trees are consistent with the distributions, as are local-scale inventories of trees and assorted vertebrate and insect groups. Each inventory is used to predict the counts of another one that is matched based on group representation, biogeography, and richness. Based on examining decisive differences between the resulting likelihoods, the new models routinely outperform eight different rivals. 5. Thanks to their simplicity, grounding in non-competitive equilibrial population dynamics, and predictive power, the new approaches have considerable relevance throughout ecology.
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2. I leverage a general strategy for deriving simple one-parameter models. A distribution of abundances x on a continuous scale is predicted from a transform of a uniform distribution U; U is solved for to yield one minus a cumulative distribution function (CDF) for x; and the result is differenced and rounded to down to yield a probability mass function. The same workflow has long been used to derive the geometric series from the exponential distribution. Three variants are proposed, respectively based on the transforms μ/U – μ = (μ – U)/U where μ is a fitted constant (a scaled odds); [–ln(U)/λ]2 where –ln U is just an exponential random variate and λ is the constant; and [–ln(2/U – 1)/γ]4 where γ is the constant. They collectively cover the range of functions that lead from some U to a non-negative real number.
3. The distributions are all consistent with simple population dynamical models in which recruitment rates, and sometimes death rates, vary randomly amongst species and are fixed for each species. The number of recruited offspring produced during each interval by each species is Poisson-distributed, and death rates are per-capita. Population counts are equilibrial, allowing co-existence in the absence of competition.
4. Large-scale surveys of corals, fishes, butterflies, and trees are consistent with the distributions, as are local-scale inventories of trees and assorted vertebrate and insect groups. Each inventory is used to predict the counts of another one that is matched based on group representation, biogeography, and richness. Based on examining decisive differences between the resulting likelihoods, the new models routinely outperform eight different rivals.
5. Thanks to their simplicity, grounding in non-competitive equilibrial population dynamics, and predictive power, the new approaches have considerable relevance throughout ecology.
">This is a Preprint and has not been peer reviewed. This is version 2 of this Preprint.
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- Data from: three models of ecological community assembly: terrestrial species inventories
- R code for: Simple and robust models of ecological abundance
1. Counts of species in ecological samples are of interest when they tell us about community assembly processes. Older process-based models of count distributions are either complex, widely rejected, or not able to predict high unevenness.
2. I leverage a general strategy for deriving simple one-parameter models. A distribution of abundances x on a continuous scale is predicted from a transform of a uniform distribution U; U is solved for to yield one minus a cumulative distribution function (CDF) for x; and the result is differenced and rounded to down to yield a probability mass function. The same workflow has long been used to derive the geometric series from the exponential distribution. Three variants are proposed, respectively based on the transforms μ/U – μ = (μ – U)/U where μ is a fitted constant (a scaled odds); [–ln(U)/λ]2 where –ln U is just an exponential random variate and λ is the constant; and [–ln(2/U – 1)/γ]4 where γ is the constant. They collectively cover the range of functions that lead from some U to a non-negative real number.
3. The distributions are all consistent with simple population dynamical models in which recruitment rates, and sometimes death rates, vary randomly amongst species and are fixed for each species. The number of recruited offspring produced during each interval by each species is Poisson-distributed, and death rates are per-capita. Population counts are equilibrial, allowing co-existence in the absence of competition.
4. Large-scale surveys of corals, fishes, butterflies, and trees are consistent with the distributions, as are local-scale inventories of trees and assorted vertebrate and insect groups. Each inventory is used to predict the counts of another one that is matched based on group representation, biogeography, and richness. Based on examining decisive differences between the resulting likelihoods, the new models routinely outperform eight different rivals.
5. Thanks to their simplicity, grounding in non-competitive equilibrial population dynamics, and predictive power, the new approaches have considerable relevance throughout ecology.
https://doi.org/10.32942/X2VW3G
Ecology and Evolutionary Biology
half-power exponential distribution, inverse power distribution, log series, negative binomial distribution, Poisson log normal distribution, scaled odds distribution, Weibull distribution
Published: 2024-05-13 22:20
Last Updated: 2024-05-21 00:12
CC BY Attribution 4.0 International
Conflict of interest statement:
None
Data and Code Availability Statement:
The data are available on Dryad (doi:10.5061/dryad.brv15dvdc). The analytical code is available on Zenodo (doi:10.5281/zenodo.11180841).
Language:
English
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