Model Evaluation

The utility of models often is limited by a number of problems. The effects of multiple interacting factors usually must be modeled as the direct effects of individual factors, in the absence of multifactorial experiments to assess interactive effects. Effects of host condition often are particularly difficult to quantify for modeling purposes because factors affecting host biochemistry remain poorly understood for most species. Moreover, models must be initialized with adequate data on current population parameters and environmental conditions. Finally, most models are constructed from data representing relatively short time periods.

Most models accurately represent the observed dynamics of the populations from which the model was developed (e.g., Varley et al. 1973), but confidence in their utility for prediction of future population trends under a broad range of environmental conditions depends on proper validation of the model. Validation requires comparison of predicted and observed population dynamics using independent data (i.e., data not used to develop the model). Such comparison using data that represent a range of environmental conditions can indicate the generality of the model and contribute to refinement of parameters subject to environmental influence, until the model predicts changes with a reasonable degree of accuracy (Hain 1980).

Departure of predicted results from observed results can indicate several possible weaknesses in the model. First, important factors may be underrepresented in the model. For example, unmeasured changes in plant biochemistry during drought periods could significantly affect insect population dynamics. Second, model structure may be flawed. Major factors affecting populations may not be appropriately integrated in the model. Finally, the quality of data necessary to initialize the model may be inadequate. Initial values for r, N0, or other variables must be provided or derived from historic data within the model. Clearly, inadequate data or departure of particular circumstances from tabular data will reduce the utility of model output.

Few studies have examined the consequences of using different types of data for model initialization. The importance of data quality for model initialization can be illustrated by evaluating the effect of several input options on predicted population dynamics of the southern pine beetle. The TAMBEETLE population dynamics model is a mechanistic model that integrates submodels for colonization, oviposition, and larval development with variable stand density and micro-climatic functions to predict population growth and tree mortality (Fargo et al. 1982, Turnbow et al. 1982). Nine variables describing tree (diameter, infested height, and stage of beetle colonization for colonized trees), insect (density of each life stage at multiple heights on colonized trees), and environmental (landform, tree size class distribution and spatial distribution, and daily temperature and precipitation) variables are required for model initialization. Several input options were developed to satisfy these requirements. Options range in complexity from correlative information based on aerial survey or inventory records to detailed information about distribution of beetle life stages and tree charac teristics that requires intensive sampling. In the absence of direct data, default values are derived from tabulated data based on intensive population monitoring studies.

Schowalter et al. (1982) compared tree mortality predicted by TAMBEETLE using four input options: all data needed for initialization (including life stage and intensity of beetles in trees), environmental data and diameter and height of each colonized tree only, environmental data and infested surface area of each colonized tree only, and environmental data and number of colonized trees only. Predicted tree mortality when all data were provided was twice the predicted mortality when only environmental and tree data were provided and most closely resembled observed beetle population trends and tree mortality.

Insect population dynamics models usually are developed to address "pest" effects on commodity values. Few population dynamics models explicitly incorporate effects of population change on ecosystem processes. In fact, for most insect populations, effects on ecosystem productivity, species composition, hydrology, nutrient cycling, soil structure and fertility, etc., have not been documented. However, a growing number of studies are addressing the effects of insect herbivore or detritivore abundance on primary productivity, hydrology, nutrient cycling, and/or diversity and abundances of other organisms (Klock and Wickman 1978, Leuschner 1980, Schowalter and Sabin 1991, Schowalter et al. 1991, Seastedt 1984,1985, Seastedt and Crossley 1984, Seastedt et al. 1988; see also Chapters 12-14). For example, Colbert and Campbell (1978) documented the structure of the integrated Douglas-fir tussock moth, Orgyia pseudotsugata, model and the effects of simulated changes in moth density (population dynamics submodel) on density, growth rate, and timber production by tree species (stand prognosis model). Leuschner (1980) described development of equations for evaluating direct effects of southern pine beetle population dynamics on timber, grazing and recreational values, hydrology, understory vegetation, wildlife, and likelihood of fire. Effects of southern pine beetle on these economic values and ecosystem attributes were modeled as functions of the extent of pine tree mortality resulting from changes in beetle abundance. However, for both the Douglas-fir tussock moth and southern pine beetle models, the effects of population dynamics on noneconomic variables are based on limited data.

Modeling of insect population dynamics requires data from continuous monitoring of population size over long time periods, especially for cyclic and irruptive species, to evaluate the effect of changing environmental conditions on population size. However, relatively few insect populations, including pest species, have been monitored for longer than a few decades, and most have been monitored only during outbreaks (e.g., Curry 1994, Turchin 1990). Historic records of outbreak frequency during the past 100-200 years exist for a few species, (e.g., Fitzgerald 1995, Greenbank 1963,Turchin 1990,T.White 1969), and, in some cases, outbreak occurrence over long time periods can be inferred from dendrochronological data in old forests (e.g., Royama 1992, Speer et al. 2001, Swetnam and Lynch 1989, Veblen et al. 1994). However, such data do not provide sufficient detail on concurrent trends in population size and environmental conditions for most modeling purposes. Data on changes in population densities cover only a few decades for most species (e.g., Berryman 1981, Mason 1996, Price 1997, Rácz and Bernath 1993, Varley et al. 1973, Waloff and Thompson 1980). For populations that irrupt infrequently, validation often must be delayed until future outbreaks occur.

Despite limitations, population dynamics models are a valuable tool for synthesizing a vast and complex body of information, for identifying critical gaps in our understanding of factors affecting populations, and for predicting or simulating responses to environmental changes. Therefore, they represent our state-of-the-art understanding of population dynamics, can be used to focus future research on key questions, and can contribute to improved efficiency of management or manipulation of important processes. Population dynamics models are the most rigorous tools available for projecting survival or recovery of endangered species and outbreaks of potential pests and their effects on ecosystem resources.

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