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How Much Habitat Management is Needed to Meet Mallard Production Objectives?

Lewis M. Cowardin, Terry L. Shaffer, and Kathy M. Kraft


We used results from simulation models to demonstrate the benefit-cost ratios of habitat management to increase the number of mallard (Anas platyrhynchos) recruits produced. The models were applied to hypothetical 2-habitat landscapes comprised of managed and unmanaged habitat. Managed habitats were predator barrier fencing and CRP cover; unmanaged habitat was grassland. As the amount of managed cover increased, the production curve rose rapidly and leveled off. If 2 managed habitats are added to a landscape, the cover can compete for available nesting hens, thus negating the benefits of 1 of the covers. After converting benefits and costs to dollars, we determined the point at which maximum net benefit occurs. We present an equation that can be used to determine the maximum net benefit of a management treatment given the size of the breeding population and the values of costs and benefits. Our examples demonstrate that, on local areas, it is inefficient to spend money for habitat management once maximum net benefit has been attained. If desired production can not be attained efficiently on an area, the manager can invest effort on alternative areas with greater management potential. If recruitment is inadequate to maintain a stable population, managers should manage to increase recruitment before attempting to attract additional breeding pairs. If recruitment more than maintains the breeding population, managers should attempt to attract additional breeding pairs to the area.

Key Words: Anas platyrhynchos, ducks, economics, habitat management, mallard, model.





Our purpose is to explore how much habitat management is necessary to accomplish production objectives for mallards (Anas platyrhynchos). Although our examples are from mallard production, the principles generally apply to upland nesting ducks.

Managers sometimes manage until funds are exhausted rather than manage by costs and benefits. Some researchers have used economic benefit-cost analyses Pearse and Bowden 1968, Hammack and Brown 1974, Lokemoen 1984) to compare potential benefits from various management techniques. Others have investigated optimization methods (Anderson 1975, Williams 1989). However, these studies have not directly addressed the question of how much of a single management technique is useful.

Lack of data may prevent an objective assessment of how much effort to devote to a management technique. Much of the data needed to understand the relation between effort expended and results obtained require experimentation in a controlled environment. Unfortunately, such experiments are both difficult and costly, and few have been conducted (Clark and Nudds 1991). We stress the need for conducting these experiments despite the cost. A need also exists for studying basic waterfowl biology. Such studies would improve existing population models and lead to new and improved models. However, crucial management decisions must be made prior to further model development. We contend that current knowledge of ducks and existing models can be used to guide management decisions. Models are being used increasingly as tools for management planning (Williams and Nichols 1990).

We used a stochastic model of the productivity of mallards (Johnson et al. 1987). This model was designed to simulate production from a mallard population given composition of available habitats during the nesting season and nest success rates in various habitats.

We first execute the stochastic model on habitat data derived from real landscapes to illustrate the problem. Next, we reduce the problem to a simple 2-habitat situation and, with the aid of a deterministic model that approximates results obtained from the stochastic model, we demonstrate an objective method of determining the point of diminishing returns. Finally, we illustrate how the methodology could be used if cost of treatment and value of product were available.


Data sources

The stochastic model required input data on habitat availability and nest success for each habitat. Two plots (51.8 km2 each) in central North Dakota were mapped in detail (Fig. 1) and digitized. The maps were prepared from 1:63,360 (1 inch = 1 mile) color infrared photographs. Maps were verified during extensive field visits and Conservation Reserve Program (CRP) lands, which were not present at the time of the original mapping, were added. Locations of CRP lands were obtained from county offices of the Agricultural Stabilization and Conservation Service. These plots provided habitat data for simulation. Plot 601 represented stagnation moraine with a mixture of tilled land and native grassland pastures. Plot 701 represented till plain with extensive tilled land. Both plots contained a fenced predator-free exclosure (Lokemoen et al. 1982) in the center, 22.9 ha in Plot 601 and 27.2 ha in Plot 701.

For our simulations, we treated the existing fenced areas on the plots as unfenced habitat and the existing CRP cover as cropland. This illustrated starting management in a landscape with no managed cover. In the analysis of adding CRP cover to Plot 701, we used the existing fenced cover to illustrate a competing cover. Nest success estimates for the habitats were the same as those currently used by the Habitat and Population Evaluation Team of the U.S. Fish and Wildlife Service in Bismarck, North Dakota (Table 1).

Two treatments illustrated the principles discussed here. Predator barrier fencing represented a highly intensive management technique in which nest success is much higher than in unmanaged habitats (Table 1). Establishing CRP cover involved conversion of vast areas from cropland to grass-legume cover, an extensive management treatment. Although local managers have no direct control over where or how much cropland is converted to CRP, they must consider this treatment in their management planning. Thus, we used 2 simple 2-habitat landscapes, each with a managed (fenced or CRP) and an unmanaged (grassland) habitat. Nest success for the fenced cover and CRP cover were the same as those given for Plots 601 and 701 (Table 1).

The model also required data on visual obstruction by vegetation as an index of attractiveness to nesting hens. We used the method developed by Robel et al. (1970) and modified by Kirsch et al. (1978). Visual obstruction values were modified from those used by Cowardin et al. (1988) according to unpublished data and are on file at Northern Prairie Wildlife Research Center.


The stochastic model has been used to simulate results from various management scenarios (Johnson et al. 1986, Cowardin et al. 1988). It has never been completely validated because of difficulty obtaining actual counts of young produced by a local breeding population. Extensive studies to validate model predictions for specific treatments are currently in progress in prairie Canada (M. G. Anderson, Inst. for Wetland and Waterfowl Research, Stonewall, Manit., Can., pers. commun., 1994). Despite the need for verification, we believe that the basic biology underlying the stochastic model and results obtained in ongoing applications of the stochastic model (R. E. Reynolds, U.S. Fish and Wildl. Serv., Bismarck, N.D., pers. commun., 1993) are sufficiently realistic to warrant the model's use in illustrating management principles.

Executing the stochastic model for multiple scenarios is laborious and the results contain stochastic variation. For our economic analysis we wanted smooth curves. Therefore, we developed a deterministic model that combined models presented by Cowardin and Johnson (1979:equations 5 and A2) and Klett et al. (1988:equation 3). Deterministic models suited our purpose because they are easily expanded upon in the series of equations which follow. Results obtained from the deterministic and stochastic models are similar (Table 2). In addition, a manager can experiment with the models without relying on complex computer software. In a 2-habitat situation, let Pt denote nest success in the treatment habitat and Pu nest success in the untreated habitat. Without a treated habitat, nest success for the entire plot is simply Pu, and the number of recruits produced from the area is

Equation 1 (1)

where N is the number of breeding pairs. Brood survival rate (Z) and number of recruits/fledged brood (B) are constants. We used 0.74 for brood survival rate and 4.9 for recruits fledged/brood from Cowardin and Johnson (1979). That article described the success of a hen in 1 or more nesting attempts as a lengthy summation of probabilities of initiating 1 or more nests and the probability of their success. The summation was expanded by a power series resulting in the exponential component of equation (1). With treatment, nest success for the entire plot (P) is the weighted average of Pu and Pt, with weights proportional to the number of nests initiated in each habitat. We approximated those weights by the product of habitat attractiveness, indexed by visual obstruction. and availability. and obtained

Equation 2 (2)

where (θt), is the preference for the treated habitat and At represents the proportion of the area that is treated. The number of recruits from the plot after treatment is

Equation 3 (3)

We call the additional recruits resulting from treatment incremental recruits (Rinc), a quantity that is easily obtained by subtraction:

Equation 4 (4)

To estimate (θt), we created a data set in which the treated and utreated habitats were equal in area and executed the stochastic model to estimate the nests initiated in each habitat. It was then simple to execute the deterministic model while varying the treated area. For these analyses, we expressed input as the proportion of the area managed and output as the number of incremental recruits. For the economic analyses, incremental recruits were converted to dollars, as explained later.


We assumed that successful hens and their progeny home to specific habitats (Lokemoen et al. 1990). The stochastic model was modified to account for homing by making the probability of a hen selecting a habitat an increasing function of nest success in that habitat. We assumed that brood survival was constant. In real situations brood survival is variable and can be an important component of recruitment (Sergeant and Raveling 1992:404). We assumed that nest success rate was not a function of the area of treated habitat. We assumed average water conditions and used the model default for average water conditions in all simulations. For simplicity we did not vary breeding population in these simulations.

For executing the model, we used the default breeding population of 1,000 hens in all simulations except the economic analysis, where we showed estimates for a range of breeding population sizes. This breeding population (1,000 hens) is much higher than what is normally observed for mallards, so we scaled the resulting recruits to a breeding population of 200 pairs, which is reasonable for years of average water. We averaged 8 executions of the stochastic model. Even at this sample size, model estimates were highly variable.

Costs and values

In the fencing example, we used a cost of $78.60/ha/year for fencing, based on data presented by Lokemoen (1984). For simplicity, we did not adjust for decreasing fencing costs as area fenced increased. The costs were amortized over a 20-year life of the fence and include purchase of the land at $617.74/ha. Placing CRP cover on the land has an annual cost of about $94/ha in the northern plains (Ribaudo et al. 1990). The primary purpose of the CRP is to protect the nation's crop base for food security and soil conservation; therefore, many wildlife agencies view the benefits of the CRP as free. However, we believe that some cost should be assigned for the wildlife benefits derived from the practice. We estimated the proportion of the benefits of CRP to wildlife, 0.125, by dividing wildlife benefits/ha derived by Ribaudo et al. (1989) by their total benefits/ha for the northern Great Plains. To estimate the proportion of wildlife benefits attributable to ducks, we divided expenditures for waterfowl hunting by the expenditures for all hunting in North Dakota and obtained 0.203 (U.S. Fish and Wildl. Serv. 1988). The product of the 2 proportions times the cost/ha/year was $2.38, which we used as a cost of CRP cover for ducks. These costs and benefits are arguable and have not been updated to present values but will serve to illustrate the principles.

Determining a dollar value for a duck is far more difficult. We valued mallards at $50/duck based on state estimates. Minnesota and Nebraska use $50/duck (R. T. Eberhart, Minn. Dep. of Natural Resources, Bemidji, Minn. and P. J. Gabig, Neb. Game Comm. Lincoln, pers. communs., 1993) and Texas uses $51-$75/duck (H. W. Miller, U.S. Fish and Wildl. Serv., Lubbock Tex., pers. commun., 1993).

Economic analysis

For economic analysis the benefit was $50 x Rinc and the cost was the cost of treating the entire plot times the proportion treated, At. Maximum net benefit was obtained from the deterministic model by setting the derivative of Rinc with respect to At,

Equation 5 (5)

equal to 1 and solving for At. We required an iterative solution, which we obtained with MathCad commercial software, (Math Soft, Inc. 1993; use of trade names does not imply endorsement by the federal government). To obtain At in terms of dollars spent and dollar value of ducks produced, we multiplied the derivative by the value of a duck divided by the cost of treating the entire plot.


Stochastic model

Executing the stochastic model on habitat data obtained from the 2 test plots revealed that fencing had the greatest effect on the total number of recruits produced in both plots because of high nest success in an attractive cover within the fence (Fig. 2). The addition of CRP cover increased the total number of recruits, but the increase was modest, especially on Plot 601, where there already was an abundance of attractive competing cover (Fig. 3). The number of recruits hatched in CRP cover rose rapidly from 0 and then leveled off. CRP cover is attractive, and hens shifted to CRP cover from other covers with estimated nest success almost as high as or higher than CRP cover (Table 1). This phenomenon was most obvious for Plot 601 where birds were attracted away from grassland on waterfowl production areas (WPA's) and wetlands. The competition among habitats for available hens sometimes caused unexpected results because nesting hens were attracted away from a cover with high nest success. The simulated result of increasing the amount of CRP cover on Plot 701 when the fence remained in place had a negligible effect on the total number of recruits produced because the dense CRP cover attracted hens away from the cover inside the fence (Fig. 4). Hens went from a cover with nest success of 54% to a cover with nest success of 20%.

Production curves (Figs. 2 and 3) are nonlinear, and there is a point beyond which increasing the amount of treatment produces few additional recruits. For a treatment with high nest success like fencing on Plot 701 (Fig. 2), inspection suggests that fencing more than 5-10 % of the area results in few additional recruits. For other treatments (e.g. adding CRP cover on Plot 601), the optimum is less obvious (Fig. 3). The problem is compounded because of variation from the stochastic model.

Deterministic model,

The deterministic model results were comparable to those obtained from the stochastic model although the estimates from the deterministic model were consistently higher (Table 2) for the following reason. For simplicity, we assumed that α, a measure of nesting intensity, equals 1.0 in the deterministic model. Cowardin and Johnson (1979:equation A2) showed that α equaled 1.0 when most basins contain ponds. The stochastic model did not include α, but results from the stochastic model indicated α of about 0.95. It is possible to modify equation 3 to include α = 0.95; however, for our purposes and the quality of the data we used, the difference was not important.

Management examples

Our graphic representations of a simple benefit-cost analysis (Figs. 5 and 6) are after Sewell et al. (1965) as presented by Pearse and Bowden (1968). Those authors presented an S-shaped function in which small costs yielded lower benefits than the costs. The function rose to a maximum benefit-cost ratio. From that point the function continued to increase, but the rate of increase declined. After the maximum benefit-cost ratio, the rate of increase declined until benefits equaled costs at the break-even point. The point at which the tangent to the curve was 45° (on a graph with identical scales on x- and y-axes) was the maximum net benefit, equal to equation 5 with the derivative equal to 1. This should not be confused with the maximum of a function where the slope of the tangent line is equal to 0. Our functions were not S-shaped because we had insufficient data to describe that portion of the function where costs were very small. Therefore, in our analysis the maximum benefit-cost ratio cannot be estimated.

Two examples illustrate the utility of our work. First, assume that a manager has an objective of producing 700 recruits, with an associated benefit of $35,000/year, by means of predator fencing given 500 breeding pairs as the average number expected from the current wetland base. It would be necessary to spend about $48,000 (Fig. 5) to meet the objective. The manager could also create, restore, or improve wetlands to increase the number of pairs, a strategy requiring additional cost, or select an alternative site. If the population could be raised to 600 pairs, the cost would drop to about $16,000 (Fig. 5). At about 675 pairs, the manager would achieve maximum net benefit. If raising the population above 600 breeding pairs were not possible, the objective of $35,000 worth of ducks is unrealistic. In the fencing example, a large benefit can be obtained at a large cost involving a small amount of the total area.

A second example evaluates the use of CRP cover with the same breeding population of 500 pairs (Fig. 6). An objective of $35,000 worth of ducks cannot be attained even by converting the entire plot to CRP cover and raising the breeding population to 1,000 pairs. However, at maximum net benefit the manager can produce about $ 11,000 worth of ducks at a cost of about $1,700. An obvious strategy for this type of inexpensive management would be to reach the maximum net benefit on 1 area and then move to a new area


The examples given are for illustrative purposes, but it should be possible to estimate required parameters from studies. The attractiveness of the treated cover (θt) is of crucial importance here and in any practical use of the stochastic model. We recommend field studies to estimate this parameter. The estimates of nest success in the various covers are also critical to evaluating a proposed management technique. Though there is much published information on nest success, especially for common treatments, data are scarce for unmanaged covers in many areas. Equation 5 can easily be used for other cost data by supplying a dollar value for a duck and a cost for treating the entire plot.

Our analyses relied heavily on model estimates. These models certainly do not entirely accurately portray real population functions nor are the parameter estimates used in the simulations necessarily accurate. However, use of the models demonstrates some concepts that must be true. Animals may compete for habitats, and in a certain sense, habitats may compete for available animals (e.g., hens selecting nesting sites). Our model produces the maximum number of recruits when all hens nested in the habitat with the highest nest success.

We demonstrated that as an attractive habitat with high nest success is added to a landscape, recruits produced will rise and then level off, approaching the maximum potential recruits that can be produced on that landscape from the available breeding population. Therefore, real management actions should involve addition or management of cover characterized by greater attractiveness to hens and higher nest success rates than in the existing unmanaged habitats. Thus, the curve will rise rapidly to a point where further management accomplishes little and effort can be directed to new areas. Managers must realize that the function is not linear (Johnson 1981), i.e., expressing results of an action as recruits/ha and multiplying proposed hectares to be managed by recruits/ha might greatly overestimate benefits to be derived from the management.

Recruitment rate, indexed by nest success in our example, may be a function of the amount of treatment. For example, it may be that as CRP cover is added to the landscape, predation would decrease (Kantrud 1993). For our examples, we assumed no relation between amount of treatment and nest success. If such a relation exists, then under some conditions it is possible that the number of recruits produced could continue to rise rapidly as more habitat is added. We concur with Clark and Diamond (1993), who identified the importance of determining the relation between amount, size, and configuration of nesting cover blocks and productivity of waterfowl

Management Implications

Our examples are from relatively small (51.8 km²) areas where breeding population is constrained primarily by the amount of wetland habitat present on the plot. However, size of the continental breeding population constrains the continental number of recruits that can be produced. Moving birds to an area by creation of wetlands does not increase the size of the continental breeding population unless recruitment and survival rates are higher in the new area than in the area they would have used otherwise. Further work on modeling such shifts in continental population (see Koford et al. 1992) is needed. Without data and appropriate models, the manager can use the following guidelines. In areas where recruitment is inadequate to maintain a stable population, management to increase recruitment should precede management to attract breeding pairs. Conversely, managers should attract pairs to areas characterized by high recruitment rate.

Our work clearly showed the importance of conducting benefit-cost analyses of management actions. Unfortunately, much of the data essential to such analyses are unavailable or subjective. For example, although we used a subjective value of $50/duck, the actual value of a duck to society is not clear nor do we know all of the other values such as soil and water conservation associated with each proposed management technique. As long as these economic judgements remain unclear, managers may fail to meet objectives or waste scarce funds. To avoid this, we suggest immediate action in 3 areas: continued study of basic biology of duck species, development of new models as well as testing and modification of existing models, and cooperative work with economists to give a sound economic basis for management actions.


P. M. Arnold, D. H. Johnson, R. R. Koford, J. T. Lokemoen, and R. E. Reynolds kindly reviewed earlier drafts of the manuscript. J. T. Lokemoen furnished advice on economic analyses. A. D. Kruse and R. E. Reynolds furnished information on CRP.

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This resource is based on the following source (Northern Prairie Publication 0924):

Cowardin, Lewis M., Terry L. Shaffer, and Kathy M. Kraft.  1995.  How much habitat management is needed to meet mallard production objectives?  Wildlife Society Bulletin 23(1):48-55.

This resource should be cited as:

Cowardin, Lewis M., Terry L. Shaffer, and Kathy M. Kraft.  1995.   How much habitat management is needed to meet mallard production objectives?   Wildlife Society Bulletin 23(1):48-55.  Jamestown, ND: Northern Prairie Wildlife Research Center Online. (Version 16JUL97).

GIF - Authors

Lewis (Lew) M. Cowardin (left) is a biologist with the National Biological Service Northern Prarie Wildlife Research Center. He received his Ph.D in Wildlife Management from Cornell University, and M.S. in Wildlife Management from the University of Massachusetts, and an A.B. in Biology from Harvard University. His research interests include, waterfowl ecology, wetland inventory and classification, remote sensing, and modeling.
Terry L. Shaffer (center) is Chief of Technical Services at Northern Prarie Wildlife Research Center. Mr. Shaffer received an M.S. in Applied Statistics from North Dakota State University and a B.S. in Mathematics and Computer Science from Moorhead State University. His area of expertise is statistical applications in ecological studies.
Kathy M. Kraft, (right) is currently a Professor of Mathematics at Jamestown College, North Dakota and was working as a statistician for Northern Prarie Wildlife Research Center when this paper was written. She recieved a Ph.D. from North Dakota State University, an M.S. from Northern Arizona University, and a B.S from Southwest Texas State University. Kathy's current research interests are in survival analysis and sampling.

All authors were with the National Biological Service, Northern Prairie Wildlife Research Center, 8711 37 Street Southeast, Jamestown, ND 58401-7317. Present address for Kathy M. Kraft: JC Box 6059, Jamestown, ND 58405.

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