Geology topics

Wei-Ming Ni

Publications and source records attributed to Wei-Ming Ni.

5 recordsLinked to original sources

USGS2021

Carrying capacity of spatially distributed metapopulations

Carrying capacity is a key concept in ecology. A body of theory, based on the logistic equation, has extended predictions of carrying capacity to spatially distributed, dispersing populations. However, this theory has only recently been tested empirically. The experimental results disagree with some theoretical predictions of when they are extended to a population dispersing randomly in a two-patch system. However, they are consistent with a mechanistic model of consumption on an exploitable resource (consumer–resource model). We argue that carrying capacity, defined as the total equilibrium population, is not a fundamental property of ecological systems, at least in the context of spatial heterogeneity. Instead, it is an emergent property that depends on the population’s intrinsic growth and dispersal rates.

Trends in Ecology and Evolution↗

USGS2020

Carrying capacity of a population diffusing in a heterogeneous environment

The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reaction-diffusion equations describing populations in space. Analysis of reaction-diffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space, conditions exist for which the total population size at equilibrium (i) exceeds the total population that which would occur in the absence of diffusion and (ii) exceeds that which would occur if the system were homogeneous and the total carrying capacity, computed as the integral over the local carrying capacities, was the same in the heterogeneous and homogeneous cases. We review here work over the past few years that has explained these apparently counter-intuitive results in terms of the way input of energy or another limiting resource (e.g., a nutrient) varies across the system. We report on both mathematical analysis and laboratory experiments confirming that total population size in a heterogeneous system with diffusion can exceed that in the system without diffusion. We further report, however, that when the resource of the population in question is explicitly modeled as a coupled variable, as in a reaction-diffusion chemostat model rather than a model with logistic growth, the total population in the heterogeneous system with diffusion cannot exceed the total population size in the corresponding homogeneous system in which the total carrying capacities are the same.

Mathematics and Computers in Modern Science - Acou↗

USGS2020

Effect of stressors on the carrying capacity of spatially distributed metapopulations

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, nonspatial 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 the death rate and/or simultaneously decreases the population growth rate and yield, a homogeneous distribution of the stressor leads to a lower total population size than if the same amount of the 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 the yeast death rate but reduces the 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 the dispersal rate and the geographic pattern of antibiotic heterogeneity. Our study has implications for assessing the population risk posed by pollutants, antibiotics, and global change and for the rational design of strategies for employing toxins to control pathogens and pests.

The American Naturalist↗

USGS2017

Carrying capacity in a heterogeneous environment with habitat connectivity

A large body of theory predicts that populations diffusing in heterogeneous environments reach higher total size than if non-diffusing, and, paradoxically, higher size than in a corresponding homogeneous environment. However, this theory and its assumptions have not been rigorously tested. Here, we extended previous theory to include exploitable resources, proving qualitatively novel results, which we tested experimentally using spatially diffusing laboratory populations of yeast. Consistent with previous theory, we predicted and experimentally observed that spatial diffusion increased total equilibrium population abundance in heterogeneous environments, with the effect size depending on the relationship between r and K . Refuting previous theory, however, we discovered that homogeneously distributed resources support higher total carrying capacity than heterogeneously distributed resources, even with species diffusion. Our results provide rigorous experimental tests of new and old theory, demonstrating how the traditional notion of carrying capacity is ambiguous for populations diffusing in spatially heterogeneous environments.

Ecology Letters↗

USGS2015

Effects of dispersal on total biomass in a patchy, heterogeneous system: Analysis and experiment

An intriguing recent result from mathematics is that a population diffusing at an intermediate rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. We extended the current mathematical theory to apply to logistic growth and also showed that the result applies to patchy systems with dispersal among patches, both for continuous and discrete time. This allowed us to make specific predictions, through simulations, concerning the biomass dynamics, which were verified by a laboratory experiment. The experiment was a study of biomass growth of duckweed ( Lemna minor Linn.), where the resources (nutrients added to water) were distributed homogeneously among a discrete series of water-filled containers in one treatment, and distributed heterogeneously in another treatment. The experimental results showed that total biomass peaked at an intermediate, relatively low, diffusion rate, higher than the total carrying capacity of the system and agreeing with the simulation model. The implications of the experiment to dynamics of source, sink, and pseudo-sink dynamics are discussed.

Mathematical Biosciences↗