A general tritrophic model of intermediate complexity representing the dynamics of trophic level biomass and numbers is presented. The rudiments of the behavior and physiology of resource acquisition and conversion are incorporated as functional and numerical response models. The tritrophic model is used to examine the effects of trophic position on bottom—up—top—down regulation of populations in theory and in practice. The zero growth isoclines of the interacting populations are used to examine the dynamics of the tritrophic system. The herbivore (M2) and predator (M3) but not the plant (M1) isoclines can be solved explicitly. The plant and herbivore isoclines have two forms that depend on whether the proportion of the trophic level available to its consumer (i.e., its apparency) is greater than or less than its potential per unit biomass population growth rate. Rough estimates of the parameters of these inequalities may be deduced from our knowledge of the search biology of the species and known size to growth rate relationships. The model shows clearly that bottom—up regulation sets the upper limit for trophic—level growth and top—down regulation determines the level of realized growth. The model explains the paradoxes of enrichment and of biological control that arise from the standard Lotka—Volterra models, and its qualitative predictions compare well to the general conclusions of intensive studies on biological control of the cassava mealybug on cassava by an exotic parasitoid. However, discrepancies that were found caution against unconsidered extrapolation of theoretical predictions to specific situations. The model qualitatively defines the dynamics required of a successful weed biological control agent, of a stable fresh water algal—arthropod herbivore—vertebrate predator system, and of a marine phytoplankton—krill—whale system. The utility of the model is its generality and its basis in quantifiable biology.

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Summary Vine mealybugPlanococcus ficus is an invasive pest of vineyards in many areas of the world. In California, USA, it infests all plant subunits and has a spatial refuge from natural enemies under the bark and on roots. A temporal refuge is created when ants tending the mealybug reduce the efficacy of natural enemies. 2. Biological control of vine mealybug is only partially successful and varies among California grape-growing regions. To improve control and help determine appropriate natural enemies for importation, the effects of weather on mealybug regulation by two parasitoids, Anagyrus pseudococci and Leptomastidea abnormis , and a coccinellid predator, Cryptolaemus montrouzieri , were examined across the ecological regions of California. 3. Weather-driven, physiologically based age-mass structured demographic models of the mealybug and its natural enemies were parameterized using laboratory data and field observations. Temperature was used to define the thermal limits and development rates of each species, and resource supply/demand ratios were used to scale daily per capita growth, fecundity and survivorship rates from maximal values at optimal conditions. 4. The population dynamics of the mealybug and its natural enemies were simulated at 108 locations in California over a 10-year period using observed weather. The simulation data were mapped using a geographical information system (GIS) and analysed using linear multiple regression and marginal analysis. 5. The models predictions indicated that: (i) the parasitoid A. pseudococci has a larger impact on vine mealybug than either L. abnormis or C. montrouzieri ; (ii) mealybug densities will be lowest in the hot desert regions of southern California and highest in the cooler areas of northern California; (iii) mealybug density increases with season length and the size of the combined spatial-temporal refuge; (iv) biological control of mealybug could be achieved by reducing the size of the spatial-temporal refuge. 6. Synthesis and applications. Models, no matter how detailed, will always be incomplete; despite this, the complexity of tri-trophic systems can be modelled and the effects of biotic factors and of weather separated. The predictions of our model coincided well with field observations on vine mealybug, and clearly showed why the biological control will require additional species of natural enemies and/or why the size of the spatial and temporal refuges must be reduced.

An age-mass structured multi-year tritrophic simulation model of the coffee (Coffea arabica var. mundo novo) - coffee berry borer [Hypothenemus hampei (Ferrari)], borer - three parasitoid system was developed. Three years of extensive plant drymatter data and one year of field data on borer dynamics were collected at Londrina, PR, Brazil. The allometric relationships and parameter for plant drymatter allocation were estimated from the field data, but the parameters for borer and its three parasitoids were summarized from the literature. Initial levels of soil factors (e.g., nitrogen and water) and observed weather data were used to drive the model. The model is largely independent of the field data, yet it simulated the dynamics of plant branching, fruiting and drymatter growth of plant subunits. Simulation results suggest that of the three parasitoids commonly introduced to control the borer, only the eulophid adult endo-parasitoid (Phymastichus coffea La Salle) has the demographic characteristics to potentially regulate borer populations. The effects of harvesting, cleanup of abscised berries, inundative releases of parasitoids and pesticides with various toxicity and persistence characteristics on borer dynamics were evaluated. The model is very flexible, and may provide a sound foundation for incorporating new findings, new varieties, and the biology of new natural enemies worldwide

Species of plants and animals have characteristic climatic requirements for growth, survival and reproduction that limit their geographic distribution, abundance and interactions with other species. To analyze this complexity requires the development of models that include not only the effects of biotic factors on species dynamics and interactions, but also the effects of abiotic factors including weather. The need for such capacity has appreciably increased as we face the threat of global climate change. In this paper, bi-and tri-trophic physiologically based demographic models of alfalfa, cotton, grape, olive and the noxious weed yellow starthistle systems are used to explore some of the potential effects of climate change. A general model that applies to all species in all trophic levels (including the economic one) is used to simulate the effects of observed and projected weather on system dynamics. Observed daily weather and that of climate model scenarios were used as forcing variables in our studies. Geographic information system (GRASS GIS) is used to map the predicted effects on species across the varied ecological zones of California. The predictions of the geographic distribution and abundance of the various species examined accords well with field observations. Furthermore, the models predict how the geographic range and abundance of the some species would be affected by climate change. Among the findings are: (1) The geographic range of tree species such as olive that require chilling to break dormancy (i.e. vernalization) may be limited in some areas due to climate warming, but their range may expand in others. For example, olive phenology and yield will be affected in the southern part of California due to high temperature, but may expand in northern areas until limited by low winter temperatures.Pest distribution and abundance will also be affected. For example, climate warming would allow the cold intolerant pink bollworm in cotton to expand its range into formerly inhospitable heavy frost areas of the San Joaquin Valley, and damage rates will increase throughout its current range. The distribution and abundance of other cold intolerant pests such as olive fly, the Mediterranean fruit fly and others could be similarly affected. In addition, species dominance and existence in food webs could change (e.g. in alfalfa), and the biological control of invasive species might be adversely affected (e.g. vine mealybug in grape). The distribution and abundance of invasive weeds such as yellow starthistle will be altered, and its control by extant and new biological control agents will be difficult to predict because climate change will differentially affects each. (2) Marginal analysis of multiple regression models of the simulation data provides a useful way of analyzing the efficacy of biological control agents. Models could be useful as guides in future biological control efforts on extant and new exotic pest species. (3) Major deficiencies in our capacity to predict the effects of climate change on bio...