Sequential Decision Rules for Managing Nematodes with Crop Rotations

Abstract

A dynamic model of nematode populations under a crop rotation that includes both host and nonhost crops is developed and used to conceptualize the problem of economic control. The steady state of the dynamic system is used to devise an approximately optimal decision policy, which is then applied to cyst nematode (Heterodera schachtii) control in a rotation of sugarbeet with nonhost crops. Long-run economic returns from this approximately optimal decision rule are compared with results from solution of the exact dynamic optimization model. The simple decision rule based on the steady state provides long-run average returns that are similar to the fully optimal solution. For sugarbeet and H. schachtii, the simplified rule can be calculated by maximizing a relatively simple algebraic expression with respect to the number of years in the sequence of nonhost crops. Maximization is easy because only integers are of interest and the number of years in nonhost crops is typically small. Solution of this problem indirectly yields an approximation to the optimal dynamic economic threshold density of nematodes in the soil. The decision rule requires knowledge of annual nematode population change under host and nonhost crops, and the relationship between crop yield and nematode population density. Key words: crop rotation, cyst nematode, decision rule, dynamic control, economics, economic threshold, Heterodera schachtii, optimization, sugarbeet.