Mathematics and Mallard Management

Abstract

Waterfowl managers can effectively use simple population models to aid in making management decisions. We present a basic model of the change in population size as related to survival and recruitment. A management technique designed to increase survival of mallards (Anas platyrhynchos) by limiting harvest on the Chippewa National Forest, Minnesota, is used to illustrate the application of models in decision making. The analysis suggests that the management technique would be of limited effectiveness. In a 2nd example, the change in mallard population in central North Dakota is related to implementing programs to create dense nesting cover with or without supplementary predator control. The analysis suggests that large tracts of land would be required to achieve a hypothetical management objective of increasing harvest by 50% while maintaining a stable population. Less land would be required if predator reduction were used in combination with cover management, but questions about effectiveness and ecological implications of large scale predator reduction remain unresolved. The use of models as a guide to planning research responsive to the needs of management is illustrated. J. WILDL. MANAGE. 43(1):18-35 Management of a wildlife population is a complicated task that often requires decisions based on limited data. To make logical decisions we need (1) a management policy or objective defined in terms of some goal, (2) a relationship between that goal and parameters of the population to be managed, and (3) estimates of these parameters. Such a relationship is often termed a model, and can be either quite rudimentary and qualitative or complicated and quantitative. Inadequate information often forces us to use models that grossly oversimplify the behavior of the real population and to employ estimates that are frequently little better than informed guesses. The manager cannot postpone a decision until the dynamics of the population are fully understood and precise estimates of all parameters are available. Inaction is in fact a decision by default. The development of simple models, imperfect though they may be, and the graphic representation of these models can facilitate logical and orderly development of management strategy. Because of the large quantity of pertinent banding and survey data available, the mallard has been the subject of several published models (Walters et al. 1974, Anderson 1975a,b, Brown et al. 1976). These models use estimates of production based on survey data for the continental population. In contrast, our model relates recruitment to various components that are frequently measured in local studies and that are subject to manipulation by the waterfowl manager. The exercise of presenting a model has a number of benefits: (1) inspection of the model may focus attention on critical parameters; (2) the model provides a frame of reference for evaluating policy and assessing the feasibility of objectives; (3) insight into possible alternatives for reaching an objective is gained; and (4) we are forced to face the reality of the management problem and to answer important questions such as cost effectiveness and political feasibility. The purpose of this paper is to demonstrate a simple model that can facilitate decisions concerning management of mallards in the north central