American Society of Naturalists

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“Effect of stressors on the carrying capacity of spatially distributed metapopulations”

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Bo Zhang, Donald DeAngelis, Wei-Ming Ni, Yuanshi Wang, Lu Zhai, Alex Kula, Shuang Xu, and David Van Dyken (Aug 2020)

We prove mathematically and test empirically that a homogeneous distributed stressor leads to the lowest metapopulation

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Scaling the effect of stressors from populations to metapopulations. We first question, at individual level, what is the effect of stressors, including microbistatic (green lines) and microbicidal (orange lines), on cell division rate, resource use efficiency and mortality probability? Then scaling up to population level, we ask what is the effect of stressors on population growth rate, yield and mortality rate? Ultimately, at metapopulation level, when there is dispersal between neighbor patches, and certain does of stressor can be distributed heterogeneously or homogeneously across patches, we address the following question: How do the physiological consequence and spatial distribution of a stressor interact with dispersal to determine the impact of stress on metapopulation size (TRAPA: total realized asymptotic population abundance)?<br/><br />(Credit: Zhang et al.)
Scaling the effect of stressors from populations to metapopulations. We first question, at individual level, what is the effect of stressors, including microbistatic (green lines) and microbicidal (orange lines), on cell division rate, resource use efficiency and mortality probability? Then scaling up to population level, we ask what is the effect of stressors on population growth rate, yield and mortality rate? Ultimately, at metapopulation level, when there is dispersal between neighbor patches, and certain does of stressor can be distributed heterogeneously or homogeneously across patches, we address the following question: How do the physiological consequence and spatial distribution of a stressor interact with dispersal to determine the impact of stress on metapopulation size (TRAPA: total realized asymptotic population abundance)?
(Credit: Zhang et al.)

Abstract

Stressors such as antibiotics, herbicides and pollutants are becoming increasingly common in the environment. The effects of stressors on populations are typically studied in homogeneous, non-spatial settings. However, most populations in nature are spatially distributed over environmentally heterogeneous landscapes with spatially-restricted dispersal. Little is known about the effects of stressors in these more realistic settings. Here, we combine laboratory experiments with novel mathematical theory to rigorously investigate how a stressor’s physiological effect and spatial distribution interact with dispersal to influence population dynamics. We prove mathematically that if a stressor increases death rate and/or simultaneously decreases population growth rate and yield, a homogeneous distribution of stressor leads to a lower total population size than if the same amount of stressor was heterogeneously distributed. We experimentally test this prediction on spatially-distributed populations of budding yeast, Saccharomyces cerevisiae. We find that the antibiotic, cycloheximide, increases yeast death rate but reduces growth rate and yield. Consistent with our mathematical predictions, we observe that a homogeneous spatial distribution of cycloheximide minimizes the total equilibrium size of experimental metapopulations, with the magnitude of the effect depending predictably on dispersal rate and geographic pattern of antibiotic heterogeneity. Our study has implications for assessing population risk posed by pollutants, antibiotics, and global change, and in the rational design of strategies for employing toxins to control pathogens and pests.