Methodology and Analysis

Ecological basis of the CASAS Physiologically-based demographic modeling (PBDM) approach

Commonly used Ecological Niche Modeling (ENM) approaches attempts to characterize and climatically model the ecological niche (ENM) of a species using observed weather and knowledge of its current distribution. These models may be either statistical or physiologically based, or both. Another term used for this is the climate envelope approach. Physiologically-based demographic models (PBDM) approach reverses the process. The physiological and demographic responses (processes) of the organism (species) to abiotic and biotic factors are modeled on a per capita basis, and the model(s) at the population level is embedded in GIS and used to explore the distribution and abundance of a species.

Diagrams depicting the GIS PBDM levels and methodology
Physiologically Based Demographic Models (PBDM) – a. Levels of simulation include an individual, population, across ecological zones, and across large geographic regions; b. A weather driven PBDM/GIS ecosystem analysis including marginal analysis (see ecological basis of the approach).

The model driven by appropriate weather data and in a tritrophic context is expected to reproduce qualitatively the observed geographic distribution and abundance of the species.  The physiologically-based approach assumes that the per capita maximum rate of growth is reduced by conditions the organism experiences and by its interactions with other species. PBDMs can be used to model the development at all trophic levels – at the individual, population, food webs and meta-population and the regional levels. Tritrophic systems are composed of interacting populations in different trophic levels including the economic one with the input and output functions in all trophic levels being analogous and having similar shaped function, albeit with different units (see Gutierrez 1996). 

Diagram depicting trophic levels
Analogies between trophic levels including the economic one. (from John Wiley & Sons, New York)

All species are consumers, but many are also resource species for higher trophic levels. Resource and consumer populations are characterized by resource-limited growth captured as the interplay between the acquisition supply and potential assimilation demands that change during the species development.  For example, the plant first grows vegetative, but then as the fruit mature, the photosynthate is allocated to fruit growth causing the demand to be greater than the supply (see figure below). A similar model can be constructed for insects in anay trophic level, or as indicated in the figure for say the farmer where the crop dry matter is multiplied by price. The allocation rates will differ among species altering supply-demand relationships.

Cotton fruit growth charts
Growth of individual cotton fruit and the interplay between plant photosynthate supply and demand (see Gutierrez 1996).

Plant populations integrate the bottom-up effects of weather and edaphic factors (moisture, nutrients and others) and are in turn regulated by the top-down effect of consumers that may also be influenced by lower and higher trophic levels.  The models for attack and consumption in all populations are analogous and the same functional response model is used. Nutritional quality and phenology of the resource population also affect the demography and phenology of consumer populations.

The models are driven by observed weather and are used to predict site-specific dynamics or the dynamics across a landscape.  When imbedded in a GIS (e.g., GRASs), the model can be used to estimate the range and relative abundance of the species (sub fig. b). Marginal analyses of multi-variate models of the simulation data can be used to quantify the trends in the data and may prove more useful than the insights gained from the maps of range shifts alone. Considerable realism can be added in PBDM and they may be used to explore how weather and climate change may affect trophic interactions that may determine the geographic range of species.

Food webs in systems as diverse as alfalfa, cassava, cotton, coffee, bean, olive, rice, wheat, yellow starthistle, and aquatic systems have been modeled using this approach, and many of the models have been tested with field data, and used to develop IPM strategies and to explore theory (see Regev, U., A. P. Gutierrez, S. J. Schreiber, and D. Zilberman. 1998. Biological and Economic Foundations of Renewable Resource Exploitation. Ecological Economics, 26: 227-242.).

Below we examine the bioeconomics of the cotton agroecosystem.

Cotton agro-ecosystem diagram
Cotton agro-ecosystem: Cotton and cotton pest with the effect of pest attack indicated as reducing the supply (e.g., photosynthesis) or the demand (reduce sink strength) side. Pink bollworm attacks the standing crop.

Supply-side pests reduce the photosynthetic rate by attacking root, leaves and stem in a manner that reduces the photosynthetic rate. Important supply-side pests are defoliators, sapsuckers, spidermites, nematodes, diseases, and others. Defoliation attacks leaves and may cause wound healing losses, but the effects on yield depend on the age of leaves attacked, the loss rate, and compensation due to increased light penetration. In contrast, spidermites kill leaf cells, reducing photosynthesis in damaged leaves that are not shed, reducing light penetration to lower leaves. Stem borers and vascular plant diseases may slow the photosynthetic rate by reducing the translocation of water and nutrients, and some may kill whole plants. Thrips and armyworms may damage the terminal, inducing developmental delays and reducing yield.

Plant demand-side pests may attack fruit (e.g., sinks) causing premature abscission altering present and future demands for photosynthate. High abscission rates may cause rank growth as the excess photosynthate is allocated to vegetative growth. Most plant species have a reproductive surplus that allows for varying degrees of compensation. Of crucial importance in compensation is the time and energy lost in abscised fruits. Little time and energy is lost in abscised buds and small fruit, and replacement buds may be produced in many species at rates sufficient for compensation. Attacks on older fruits may involve considerable losses in time and energy often precluding compensation. The ratio of the cumulative buds initiated to the cumulative numbers abscised may provide the basis for determining whether compensation is possible. Such data yield a convex function that estimates the compensation point and may provide a rule of thumb for estimating the economic threshold. For example, loss of 30% of fruit bud in many cotton varieties does not affect yield.

Some pests attack the standing crop (e.g., pink bollworm) and may not affect either the supply or the demand side of the acquisition or allocation biology.