A Spatially Explicit Individual-Based Model of the Population Dynamics of the greenhouse whitefly (Trialeurodes vaporariorum), Encarsia formosa and tomato powdery mildew (Oidium neolycopersici) in Tomato Crops.

The greenhouse whitefly Trialeurodes vaporariorum – Westwood is one of the most important insect pests in crops. The spatial dynamics and population grow of the insects are affected by different biotic and abiotic factors like the host plant quality, the control by natural enemies or the presence of another kind of pest such as mildew fungus. Patterns of the population behavior in tomato crops were used to develop an age-structured, spatially explicit, individual-based model with a description of the developmental biology of the whitefly individuals. The model comprises three types of entities: 1) plant leaves, 2) pest insects, 3) parasitoid insects and the presence of the fungus Oidium neolycopersici (powdery mildew). The plants are modeled only as space units with a dynamic size to store insects. The insects’ populations are modeled in an age-structured design to mimic their growth and development as in real systems. For the pest insects, the key process is the dispersal, in which the individuals decide where to move, for this purpose four different basic rules under density dependent and density independent context were tested with respect to their ability to create patterns similar to the patterns observed in nature. The parasitoid insect Encarsia formosa is also modeled in an age-structured population and its effect on the pest insect is implemented to affect the second stage of nymphs, mimicking host-feeding, and the third and fourth stage of nymphs, representing the parasitization. The mildew fungus, that affects the behavior of E. formosa is modeled as present or absent in the leaves and its effect on the behavior of the insects was tested. The results show that whitefly dispersal follows rules probably related with chemical or visual cues to orient their flights and this rules can be used to represent population growth patterns and spatial distribution. The effect of biocontrol by E.formosa is important and vary with the three dispersal rules tested, where the exponential function gives the more realistic representation of the parasitoid foraging behavior. Furthermore, the presence of mildew in the leaves affecting the parasitoid foraging activity result in an increase of dispersion of the whitefly population. As the interaction between the fungi and whiteflies is not explicitly modeled in this study the results suggest that the presence of mildew have a negative direct effect on the parasitoids foraging behavior and a positive indirect effect on the whiteflies increasing its dispersion probably because the presence of mildew makes the infected leaf a protected refuge for the whitefly. This interaction deserves more research in the field and in real experiments in order to get more details to be included later in the simulations to study a more realistic scenario. The severity or incidence of mildew in the crop related with the dynamics of whiteflies and parasitoids in real-like experiments could help to improve the knowledge about this multitrophic interactions. The main conclusion is that this research tool can be used to orient the future research on this system. Some gaps in knowledge were found that can be important to better understand the function of the systems