Types of Models

The term 'model' may be defined as a representation of some aspect of the real world that allows the investigation of that aspect's properties and - provided the model is reliable - prediction of future behavior. Notably, though differing models of a given aspect or system may not be compatible with one another, each model may have utility in both describing the system and predicting outcomes. For example, Newtonian physics has sufficed to land humans on the Moon and navigate robotic probes to the outer planets despite the fact that Einsteinian and quantum physics are now accepted as the better models without which we could not explain the universe at the smallest and largest scales. This parallel provides an important lesson for those developing and using models of biological control: though a large number of models are available and sometimes heated debate has surrounded the merits and problems of competing models, each constitutes a tool by which we may better understand or predict some aspect of biological control.

General Models

A useful distinction for models relevant to biological control is general and specific. General models developed from early thinking of population growth and how predator-prey interactions help account for the fact that all populations in nature appear to be constrained. Notable among early theories and models are Malthus' 'struggle for existence', Verhulst's logistic equation, the Lotka-Volterra equations, and the Nicholson Bailey model.

General models seek to provide broadly applicable rules for predator-prey, parasitoid-host, and herbivore-plant models and are strongly grounded in theory. The attendant literature is concerned with issues such as the stability of populations and magnitude of impact (suppression) of the agent or predator on the target or prey.

General models may be divided into discrete-time (difference) and continuous-time (differential) models. In the context of biological control, the first of these best describes systems in which there is strong season-ality or discrete cropping phases leading the agent or target to reproduce seasonally. Within this category of models are prey-dependent and ratio-dependent models (see below).

Continuous-time (differential) models are most applicable in biological control systems where the relevant organisms reproduce year round. Within this category are stage-structured models that include biological details such as the fact that most parasitoids are able to attack only one life stage of their host (most commonly the egg or larva).

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