Fig 1.
The left panel is a schematic of the models in Eqs 1 and 2. Resources flow into the system at fixed rate ρi, while consumers die at rates ηi Ni. The arrows connecting resources to consumers represent non-zero consumption coefficients Cij. In this example, all consumers are capable of consuming resource 2, so there is community-wide competition for it. At the same time, consumer 1 is the only consumer that can utilize resource 1 and, similarly, consumer 3 is the only consumer that can deplete resource 3. The right panels are examples of the C matrices resulting from our two different parametrizations. In the generalist case, each entry is an independent sample from the same probability distribution with positive support. In the specialist case, consumer i can consumer resource i more quickly than any other resource. Other than this special resource, consumers consume every other resource at the same rate.
Fig 2.
Species abundance distribution (SAD) results for the generalists scenarios (A-C) and specialist scenarios (D-F). A: In the generalist scenario, the log-series distribution (black curve) fits the SAD when the coefficient of variation (CV) in the consumption matrix is sufficiently low (red points; Cramér-von Mises goodness-of-fit test p-value 0.78), but is rejected when the CV is sufficiently high (blue points; CvM test p-value 0.02). B: Probability that the logs-series distribution fits the SAD decreases with the CV of the consumption matrix. Points and error bars show the mean and standard error of the count of successful fits, out of an ensemble of 106 communities. Blue curve shows logistic regression. The threshold CV, defined as the point where the probability falls below 50%, is CVthreshold = 0.23. C: log(CVthreshold) has a linear relationship with log(n), with slope −0.61 ± 0.09. This indicates a power law between CVthreshold and n, with an exponent close to our analytic prediction of −0.5. Error bars show uncertainty propagated from the standard errors of the fitted parameters in the respective logistic regressions. Bands show the 95% CI of the linear regression. D: In the specialists scenario, communities with low Cd/Co ratio (red points; CvM test p-value 0.267) conform to the log-series distribution, while communities with sufficiently high Cd/Co (blue points; CvM test p-value <0.001) reject the LS distribution. E: The probability of the LS distribution fitting the SAD decreases as Cd/Co increases, with the threshold at (we set Co = 1). Each data point summarizes an ensemble of 143 communities. F:
increases linearly with the number of species in the community, in qualitative agreement with Eq 4. Parameters: A-B: K = S = 50, n = 500, r = 100. C: K = S = 50, r = 100. D-F: K = S = 50, n = r = 100.
Fig 3.
SAD results: Generalists vs specialists.
Probability of log-series SAD plotted against a non-neutrality index defined as NNI = 1 − cos, where cos is the cosine between vectors representing species resource preferences, averaged across all species pairs in the community. Complete neutrality would correspond to NNI = 0 (i.e. cos = 1), reflecting full overlap in resource preferences. For the same NNI value, communities in the generalist scenario are typically more likely to conform to the log-series distribution than communities in the specialist scenario. Parameters: S = K = 50, n = r = 100.
Fig 4.
Extinction time results for the generalist (A-C) and specialist (D-F) scenarios. A: Points and error bars show average and standard errors of extinction times for species in logarithmically binned abundance categories. Curves show neutral predictions. In the generalist scenario, species extinction times match predictions from the neutral model in communities with low CV, but consistently exceed neutral predictions in communities with high CV, especially for high-abundance species. B: Plotting observed versus predicted extinction times in communities with different CV (colors) reveals that those with low CV conform closely to the neutral predictions (black line illustrates a perfect match), while higher CVs lead to increasingly poor matches to neutrality, especially for high-abundance species. Note that extinction times seem linearly related to predictions regardless of the CV. C: The slope of this relationship increases with the CV, being close to 1 (perfect match to neutral predictions) at low CV and > 1 at higher CV. D-F: Results in the specialist scenarios are analogous to the generalist scenarios, except that extinction times of high-abundance species saturate. Parameters: A-C: K = S = 50, n = 500, r = 100. D-F: K = S = 50, n = r = 100. Summary statistics were obtained from ca. 5,000 to 20,000 data points for each abundance bin in the generalists scenario, and 1,000 to 7,000 data points in the specialists scenario.
Fig 5.
Variance in species abundances over time, for different parametrizations of the specialist scenario. Vertical axis plots the variance across histories of the stochastic process of , which is then averaged across species with different initial abundances n0 (bands show standard error of the mean). Colors show parametrizations with increasing non-neutrality index (NNI), with lines showing the loess regression with smoothing parameter set to 1. Black line shows neutral prediction. Inset highlights similarity of all curves except NNI = 1 at timescales up to 10 generations.