Identification and synthetic modeling of factors affecting American black duck populations

We reviewed the literature on factors potentially affecting the population status of American black ducks (Anas rupribes). Our review suggests that there is some support for the influence of 4 major, continental-scope factors in limiting or regulating black duck populations: 1) loss in the quantity or quality of breeding habitats; 2) loss in the quantity or quality of wintering habitats; 3) harvest, and 4) interactions (competition, hybridization) with mallards (Anas platyrhychos) during the breeding and/or wintering periods.

These factors were used as the basis of an annual life cycle model in which reproduction rates and survival rates were modeled as functions of the above factors, with parameters of the model describing the strength of these relationships. Variation in the model parameter values allows for consideration of scientific uncertainty as to the degree each of these factors may be contributing to declines in black duck populations, and thus allows for the investigation of the possible effects of management (e.g., habitat improvement, harvest reductions) under different assumptions.

We then used available, historical data on black duck populations (abundance, annual reproduction rates, and survival rates) and possible driving factors (trends in breeding and wintering habitats, harvest rates, and abundance of mallards) to estimate model parameters. Our estimated reproduction submodel included parameters describing negative density feedback of black ducks, positive influence of breeding habitat, and negative influence of mallard densities; our survival submodel included terms for positive influence of winter habitat on reproduction rates, and negative influences of black duck density (i.e., compensation to harvest mortality). Individual models within each group (reproduction, survival) involved various combinations of these factors, and each was given an information theoretic weight for use in subsequent prediction. The reproduction model with highest AIC weight (0.70) predicted black duck age ratios increasing as a function of decreasing mallard abundance and increasing acreage of breeding habitat; all models considered involved negative density dependence for black ducks. The survival model with highest AIC weight (0.51) predicted nonharvest survival increasing as a function of increasing acreage of wintering habitat and decreasing harvest rates (additive mortality); models involving compensatory mortality effects received ≈0.12 total weight, vs. 0.88 for additive models.

We used the combined model, together with our historical data set, to perform a series of 1-year population forecasts, similar to those that might be performed under adaptive management. Initial model forecasts over-predicted observed breeding populations by ≈25%. Least-squares calibration reduced the bias to ≈0.5% under prediction. After calibration, model-averaged predictions over the 16 alternative models (4 reproduction × 4 survival, weighted by AIC model weights) explained 67% of the variation in annual breeding population abundance for black ducks, suggesting that it might have utility as a predictive tool in adaptive management.

We investigated the effects of statistical uncertainty in parameter values on predicted population growth rates for the combined annual model, via sensitivity analyses. Parameter sensitivity varied in relation to the parameter values over the estimated confidence intervals, and in relation to harvest rates and mallard abundance. Forecasts of black duck abundance were extremely sensitive to variation in parameter values for the coefficients for breeding and wintering habitat effects. Model-averaged forecasts of black duck abundance were also sensitive to changes in harvest rate and mallard abundance, with rapid declines in black duck abundance predicted for a range of harvest rates and mallard abundance higher than current levels of either factor, but easily envisaged, particularly given current rates of growth for mallard populations.

Because of concerns about sensitivity to habitat coefficients, and particularly in light of deficiencies in the historical data used to estimate these parameters, we developed a simplified model that excludes habitat effects. We also developed alternative models involving a calibration adjustment for reproduction rates, survival rates, or neither. Calibration of survival rates performed best (AIC weight 0.59, % BIAS = -0.280, R²=0.679), with reproduction calibration somewhat inferior (AIC weight 0.41, % BIAS = -0.267, R²=0.672); models without calibration received virtually no AIC weight and were discarded. We recommend that the simplified model set (4 biological models × 2 alternative calibration factors) be retained as the best working set of alternative models for research and management.

Finally, we provide some preliminary guidance for the development of adaptive harvest management for black ducks, using our working set of models.