When does spatial structure matter in models of wildlife harvesting?
The most broadly applied generalizations of bioeconomics were derived from simple, non-spatial models. We develop a simple continuous spatial model in which harvesting costs are consisted of travel and capture costs. This is used to determine the conditions under which the spatial behaviour of harvesters is important and its implications, particularly for the assessment of maximum achievable sustainable yield and the optimal management of exploited animal populations. The model suggests that, as a rule of thumb for harvested systems where density dependence is essentially a local process and harvesters act as independent agents, spatial structure causes a significant impact on the dynamics and reduction in productivity of the system where the ratio of maximum travel cost to minimum capture cost is approximately 5 or more, and a very large impact within the ratio of approximately 10 or more. Also, in a spatial harvesting system, secure ownership rights will not result in socially efficient harvesting if the owner only exercises control over overall off-take levels. Efficient management requires control of the spatial pattern of harvesting as well. These findings are expected to be helpful in cases where the spatial scale over which density dependence acts on the exploited population is limited in relation to the extent of the potential harvesting area, and where harvesters act as independent agents, choosing individually where to harvest. In most systems these conditions cannot be used perfectly, and in many cases they may be seriously violated, but the rule of thumb above may be used to establish whether spatial structure should warrant further investigation. In managed systems where harvesting decisions are regulated, the model may still be used to understand the gains produced by management.