How do grazers achieve their distribution? A continuum of models from random diffusion to the ideal free distribution using biased random walks

A conceptual model is described for generating distributions of grazing ani mals, according to their searching behavior, to investigate the mechanisms animals may use to achieve their distributions. The model simulates behavio rs ranging from random diffusion, through taxis and cognitively aided navig ation (i.e., using memory), to the optimization extreme of the Ideal Free D istribution. These behaviors are generated from simulation of biased diffus ion that operates at multiple scales simultaneously, formalizing ideas of m ultiple-scale foraging behavior. It uses probabilistic bias to represent de cisions, allowing multiple search goals to be combined (e.g., foraging and social goals) and the representation of suboptimal behavior. By allowing bi as to arise at multiple scales within the environment, each weighted relati ve to the others, the model can represent different scales of simultaneous decision-making and scale-dependent behavior. The model also allows differe nt constraints to be applied to the animal's ability (e.g., applying food-p atch accessibility and information limits). Simulations show that foraging- decision randomness and spatial scale of decision bias have potentially pro found effects on both animal intake rate and the distribution of resources in the environment. Spatial variograms show that foraging strategies can di fferentially change the spatial pattern of resource abundance in the enviro nment to one characteristic of the foraging strategy.