Ecosystem model

Ecosystem models, or ecological models, are mathematical representations of ecosystems. Typically they simplify complex food webs down to their major components or trophic levels, and quantify these as either numbers of organisms, biomass or the inventory/concentration of some pertinent chemical element (for instance, carbon or a nutrient species such as nitrogen or phosphorus).

History

One of the earliest, and most well-known, ecological models is the predator-prey model of Alfred J. Lotka (1925) and Vito Volterra (1926). This model takes the form of a pair of ordinary differential equations, one representing a prey species, the other its predator.

${\frac {dX}{dt}}=(\alpha .X)-(\beta .X.Y)$

${\frac {dY}{dt}}=(\gamma .\beta .X.Y)-(\delta .Y)$

where,

• $X$ is the number/concentration of the prey species;
• $Y$ is the number/concentration of the predator species;
• $\alpha$ is the prey species' growth rate;
• $\beta$ is the predation rate of $Y$ upon $X$;
• $\gamma$ is the assimilation efficiency of $Y$;
• $\delta$ is the mortality rate of the predator species

Volterra originally devised the model to explain fluctuations in fish and shark populations observed in the Adriatic Sea after the First World War (when fishing was curtailed). However, the equations have subsequently been applied more generally. Although simple, illustrate some of the salient features of ecological models: modelled biological populations experience growth, interact with other populations (as either predators, prey or competitors) and suffer mortality.

See also

• Compartmental models in epidemiology
• Mathematical biology
• Population dynamics
• Population ecology
• System dynamics