R

dt Y

The maximum reproduction rate under nonlimiting resources in this equation is Mo. The concentration of resources in the environment is given by R, and the change in R over time is dR/dt. The half-saturation constant, or resource concentration at which the reproduction rate is at half its maximum, is Ks. Maintenance utilization of resources, m, is the amount of resources used by organisms to stay alive (not reproduce). The growth yield, Y, is the amount of biomass produced per unit of resource consumed and accounts for extra utilization of resources during reproduction that are not retained in biomass. Intraspecific competition is explicitly modeled through the impacts of population size and growth rate on R, which then influences future population growth. The number of variables required for this model is double that of the logistic equation, but the simultaneous modeling of population growth and environmental resources extends the utility of the model. Additional terms added to the third equation can describe inputs of resources such as through diffusion, physical movement, or primary production, as well as losses such as leaching.

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