A comprehensive review of descriptive insect models and their construction is beyond the scope of this article; however, an overview of model efficacy in pest management is presented here. Insect models, like other ecological models, are commonly classified as deterministic or stochastic, discrete or continuous, and static or dynamic. A model may be regarded as deterministic or stochastic depending on the causal relationship between input and output. The output of a deterministic system can be predicted if the inputs and the initial state of the system are known, that is, probability and uncertainty play no role in determining the model output. Such models are justified whenever we are fairly confident of our understanding of cause and effect in the real world. However, a stochastic system in a given state may respond to a given input with an output which is included among a range or distribution of outputs, that is, an output generated through one or more probabilistic statements.

Insect models can also be thought of as simulations of discrete or continuous systems depending upon how the model changes state. Discrete time models describe the state of the system at given time intervals. An example of a discrete system is an insect population which consists of integer numbers of individual insects in various life stages from egg to adults. On the other hand, continuous systems have variables which can take on any real value at any given instant oftime, that is, a continuous model produces results for every instance in a time step. For continuous insect models, a set of differential equations is often used if there is no distinction of age or maturity of the individuals in the population (and no consideration of spatial distribution). A well-known simple continuous model is the Verhulst-Pearl logistic equation:

where N is the population size at time t, r is the growth or the intrinsic rate of natural increase, and Kis the carrying capacity (the maximum attainable population size).

Finally, there is the distinction between a static and a dynamic model with respect to time. In a static model, the variables have no memory and are only dependent on the most recent value of the independent variables. Conversely, dynamic models have a memory for their state and are capable of describing the change in independent variables as a function of time; hence insect models that describe how populations change in time are called dynamic models. In general, most IPM work is done with either deterministic-discrete-dynamic or deterministic-continuous-dynamic models. Whether a discrete or continuous form is chosen depends primarily on how the model will be used and the personal preferences of the model developers.

Beyond the above characteristics, model form can vary considerably. For example, changes in population size may be modeled as a function of time alone; or as a function of birth, death, and developmental rates (all time varying); or even as a function of these rates when the rates themselves are functions of other external variables (e.g., climate, type of crop, parasitoid population, etc.). In addition, population models may simultaneously consider spatial and temporal effects. These types of models became common in the 1990s and are sometimes designated as spatially explicit population models (SEPMs). SEPMs require knowledge of insect population spatial structure, dispersal, and movement rates, and commonly combine a population dynamics simulator with a GIS-based map describing the spatial distribution of landscape features. They are employed mainly for ecological research aimed at illuminating spatiotemporal phenomena, and, through simulation, for the exploration of strategies (e.g., the main factors driving the population temporal and spatial trends of the insect pest) of area-wide pest control. The utilization of SEPMs in IPM should continue to increase because: (1) spatial heterogeneity is a critical factor in population dynamics, that is, averaging population density over space often leads to unrealistic results; and (2) transition of pest management practices from the local level to the landscape level requires spatial population models.

A final approach to developing insect models is to incorporate object-oriented programming (OOP) technologies. The philosophy behind OOP is to increase modeling efficiency through the construction of modular code that can specify a particular 'object', including its structure, function, and interaction with other objects. For example, individual insects may be modeled as objects - each insect object would have attributes (age, sex, location, activity, etc.) and procedures or methods allowing it to respond to its surroundings and stimuli. Objects and object classes can be created using various techniques; a popular object-oriented language is C++. By representing individuals as discrete instances of an object class, behavioral models can be built with relative ease. OOP also provides several other advantages including: (1) inheritance of attributes between objects which allows for program modification without rewriting the code; and (2) components of the program can be developed independently - thus, complex models may evolve gradually from simple ones. Examples of this include OOP models of host/parasite population dynamics in cotton and corn.

Many insect models accurately represent observed pest dynamics for the conditions and circumstances from which the model was developed, but confidence in applying them over an applicable range of environmental conditions depends to a certain extent on proper model evaluation. Evaluation involves comparison of predicted and observed population dynamics using independent data representing ecological conditions over which the model can be reasonably applied. Departure of predicted results from observed results can indicate several possible weaknesses in the model. For example, the model structure may be flawed or the quality/ quantity of data needed to parametrize or calibrate the model may be inadequate. Models are evaluated (not validated) by subjecting them to experimental data designed to falsify them, and they should be accepted in practice only to the extent that they are not falsified. After model evaluation, a typical next step is to use the model to make predictions about the physical system under study. New computer and hardware and software technology have made insect modeling technology more accessible and usable than ever before, especially for solving complex spatiotemporal problems that are routinely encountered.

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