Habitat choice of multiple pollinators in almond trees and its potential effect on pollen movement and productivity: A theoretical approach using the Shigesada-Kawasaki-Teramoto model

California’s almond industry which is valued at $1.9 billion per year depends on successful cross-pollination between varieties to produce nuts. Almond growers have depended primarily on the pollinator services of honey bees, although other insects, mainly solitary wild bees, are being investigated as an alternative because of recent declines in honey bees. Our objective is to model the movements of honey bees to determine if in the presence of other pollinators, honey bees will forage in less favorable areas of a tree and its surroundings. We use the Shigesada-Kawasaki-Teramoto model (1979) which describes the density of two species in a two-dimensional environment of variable favorableness with respect to intrinsic diffusions and intra- and inter-specific interactions of species. The model is applied to almond pollination by honey bees and other pollinators with environmental favorableness based on empirical data measuring the attractiveness of the canopy for honey and other pollinators. Using the spectral-Galerkin method in a rectangular domain, we numerically solved the two-dimensional nonlinear parabolic Partial Differential Equation. We found cross-diffusion effects of other pollinators on honey bees results in honey bees foraging in less favorable areas of a tree and the area surrounding a tree. We hypothesize that increased number of honey bees in unfavorable parts of the environment will increase the probability of movement to a different tree, some of which will be to ones of a different variety, thereby increasing successful pollination and fruit production. Using empirical data, we estimate the parameters using COPASI and compare with the model.