A PDE formulation and numerical solution for a boll weevil-cotton crop model with soil water and light penetration

Abstract

A mathematical model that describes the population dynamics of a cotton crop and the boll weevil is discussed. A system of partial differential equations forms the model's core. A finite-difference solution procedure is presented. Various predictions of the model are compared with field data. The four major divisions of the model are (1) an insect model, (2) a plant model, (3) a soil water model, and (4) a light penetration model. The insect model estimates the expected population and age structure of immature and adult boll weevils. It affects the plant model through adult feeding and oviposition in cotton fruiting forms. The plant model estimates the expected population and age structure of cotton fruiting forms and the expected dry matter of fruiting forms, leaves, stems, and roots. Expected plant canopy height and width are also estimated. The plant model affects the insect model by providing adult food and oviposition sites. It also provides crop architecture information necessary for the light penetration model. The soil water model estimates the amount of soil water available to the plant roots. It determines any crop water stress. The light penetration model estimates light utilization by the crop and shading of the soil surface. It also provides microclimate information to the insect model. The model appears to predict adequately: (1) light penetration, (2) evapotranspiration, (3) soil water status, (4) crop water stress, (5) development and dry matter of fruiting forms, leaves, and stems, (6) plant canopy height and width, and (7) developmental timing of immature weevil stages.