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Assessment of a Mallard Model in
Minnesota's Prairie Coteau

Discussion


Some intermediate predictions from both the default and customized models were similar to our field estimates, but many differed. Predictions of important endpoints such as number of nests per hen, hen success, and number of successful nests from both models exceeded our field estimates. For some parameters, the differences were substantial. Predicted number of successful nests, for example, were 94-133% greater than the field average depending on the model being considered. Differences of this magnitude could lead to predictions of recruitment and population growth that would be severely inflated.

To truly validate the mallard model, the null hypothesis of no significant difference between a predicted parameter and its true value would be predicated on the existence of a single alternative that the predictions departed significantly from true values because of an incomplete or misspecified model. In our assessment, 2 other alternatives were possible: 1) one or more of the model inputs (e.g., Robel readings which control habitat attractiveness to nesting hens) could have been inappropriate or 2) field estimates (i.e., "known" value) could have been biased.

Model Inputs

Model executions for 14 habitats required 495 inputs. Concurrent independent estimation of the value of the inputs would have been ideal, but it was clearly beyond the reach of our study. Consequently, we relied on default values. Whereas, defaults may adequately represent long-term average conditions in western Minnesota, they might have been inappropriate for our study area and the years during which we worked. We attempted to address this possibility by making a priori modifications to the defaults (customized model) to better represent our study sites. Overall, predictions from the customized model deviated only slightly less from the field estimates than did those from the default model. Possibly, the customized inputs still did not adequately represent our study conditions or the predicted outputs were not sensitive to the particular defaults we changed.

Johnson et al. (1987:266-272) reported that certain inputs had more effect on output predictions than others. Furthermore, importance of each input varies with makeup of landscapes being modeled. Daily nest mortality, for example, was one of the most influential input variables for which they measured sensitivity. As such, accurate input estimates of daily nest mortality would be critical for habitats that, by virtue of their attractiveness or their areal extent, contained a high proportion of the nests from the landscape.

Nest Mortality.--Our field estimates and predictions from both models all agreed as to the relative importance of CRP habitat to nesting mallards. The predicted nest success for a habitat approximates, subject to stochastic variation, the nest success derived from the input daily nest mortality. Although nest success in CRP predicted by both models fell within the field estimate confidence interval, we believe the input for daily nest mortality in CRP (i.e., equivalent to 20% nest success) was too low. The confidence interval for the field estimate was relatively large, but the observed mean nest success was only 13.2%. Thus, a higher input daily mortality rate for nests in CRP might have been more realistic for our assessment. Because CRP contained most of the nests, a lower input CRP nest success rate would have resulted in lower predictions for several parameters defining mallard recruitment. In habitats other than CRP, our sample sizes were small and we have no other information with which to judge the appropriateness of input nest mortality rates.

Female Body Mass.--Mallard reproductive performance is in part dependent on the condition of females in the spring (Krapu 1981, Eldridge and Krapu 1988, Gloutney and Clark 1991). Female body mass is used as an index of hen condition in the model. Information regarding mass can be viewed as a model assumption or an input that is not specified by the user. A mathematical function of mass is employed to determine maximum egg-laying potential, and mass also provides a partial basis for the function controlling nest initiation and renesting by the hypothetical population being modeled (Johnson et al. 1987). Mass of adults in the hypothetical population are assumed to follow a normal distribution with mean of 1200 g and a variance of 640. Yearlings are assumed to have a mean of 1100 g and the same variance as adults. Reproductive performance related to female age is then modeled through assumptions regarding changing female mass.

Average mass for adult and yearling females in the hypothetical population fell outside the confidence intervals for our field estimates. Possibly, mallards in our study entered the nesting season in poorer condition than would be typical of those in much of the Prairie Pothole region during most years. For example, hen mallards in North Dakota were lighter during drought years than during years with average water conditions (Lokemoen et al. 1990). Hens in relatively poorer body condition would likely lay smaller clutches and renest less tenaciously than those in better condition (Krapu 1981). Further, Gloutney and Clark (1991) determined that heavier mallard hens were more successful than lighter ones. Thus, the greater weights attributed to hens in the modeled populations may explain why both models predicted values for nests per hen, clutch size, and hatched nests that exceeded our field estimates.

Hen Mortality.--Our estimated summer hen mortality was much greater than that predicted by the model. Our study also coincided with a period during which red fox (Vulpes vulpes) populations were at near record highs (W. Berg, Minn. Dep. Nat. Resour., unpubl. data). Drought effects via food web influences on body condition (Nichols et al. 1982) and fox predation (Sargeant et al. 1984) both reduce hen survival. The model prediction of summer hen mortality reflects inputs for conditional hen mortality plus daily hen mortality, subject to stochastic variations. The model input for conditional hen mortality was similar to our field estimate. However, the difference between the predicted summer hen mortality and our field estimate suggests that either the input for daily hen mortality was too low or our estimate of summer hen survival was biased.

Field Estimates

Nondetection of Nests.--Numerous nest initiations likely were undetected by our telemetry. Evaluating the implication of nondetection is difficult. Mallard hens use a variety of cover for nesting, and the difficulty of equally searching all habitats for nests is widely recognized (e.g., Greenwood et al. 1987). Nests found using radiotelemetry have been assumed to be an unbiased sample of nests from all habitats (cf., Cowardin et al. 1985:6, Arnold et al. 1993:580). However, this is not necessarily true. The age at which we detected nests varied significantly among habitats and study sites. As a consequence, our nesting data may be biased in ways that are difficult to assess.

Bias could result because nests with short survival times were under- represented in the sample. Pollock (1989) described this as the staggered entry problem when estimating survival rates. More generally, statisticians label it lower- or left-truncation (London 1988) because the operant hazard (i.e., daily nest mortality) truncates observations early in the underlying survival distribution. When estimating the number of nest initiations in different habitats, more bias will accrue when nest detection is difficult and nest survival is low compared to situations where nests are easily detected and survival is high (M. Zicus, unpubl. data). In addition to biased estimates of nests per hen and habitat-specific proportional nest occurrence, left truncation could bias estimates of habitat-specific nest survival if the daily survival rate of undetected nests differed from that of nests that were detected. Theory and analytical methods to address these potential problems are being developed (D. Heisey, Univ. of Wis., Dep. of Surgery, pers. commun.), but are not yet available.

Other Influences.--Radiotelemetry has been used to study mallard biology for many years; however, researchers remain concerned about the possible influences of transmitters on bird behavior. Early work with captive mallards and blue-winged teal (A. discors) suggested that birds equipped with transmitters lost more weight than control birds (Greenwood and Sargeant 1973). More recently, Houston and Greenwood (1993) observed no effects from transmitter attachment on average clutch size and renesting intervals of captive mallard hens, although their power to detect differences between radiomarked and control birds was low due to small sample size. In contrast, Pietz et al. (1993) reported that radiomarked wild mallards fed less and preened more than nonradioed hens, that they nested later, and that radiomarked hens laid smaller clutches of lighter eggs. Indications of a radiopackage effect were also observed by Rotella et al. (1993) who reported that a smaller proportion of wild mallard hens with harnesses nested than did hens with transmitters attached in other ways. Hens with transmitter harnesses also initiated fewer nests than those with radios attached by other means. Possibly, our estimates of clutch size and number of nests per female were biased negatively by the influence of harness-attached transmitters. In addition, our estimate of summer hen mortality might have been biased positively because of effects of the radiopackage. Transmitter packages have contributed to mortality of mallards wintering in the San Luis Valley (Jeske 1991). Transmitter influences also could have been exacerbated by drought conditions in southwest Minnesota.

Other aspects of our study may have biased some of the field estimates. Because we were interested in detecting all nest initiations, we confirmed the existence of suspected nests as soon as possible. As a result, we sometimes caused hens to abandon nests discovered early in the laying period. This disturbance could have caused hens to initiate more nests than they otherwise would have. Consequently, and contrary to the possible bias resulting from transmitter attachment, our field protocol had the potential to bias positively the estimated number of nests per hen.

Model Specification

We did not rigorously assess the model specification. Because we suspected that the differences between model predictions and our field data were primarily the result of inappropriate inputs, we superficially examined the model specification and our suspicion that certain key inputs were inappropriate by executing an ad hoc model. We used inputs derived from the field data and compared the resulting predictions with our field estimates. We recognized that this would not be a true evaluation because the "known" values against which we compared model predictions would not be independent of the inputs used in the model, but we believed the ad hoc model would be informative.

We executed the ad hoc model after replacing 3 inputs to the customized model. We 1) changed the daily nest mortality rate in CRP to the study mean (i.e., decreased nest success by 7%), 2) modeled the nesting population as all yearlings to account for the lighter mass of our study hens, and 3) increased the input daily hen mortality rate so that, when combined with conditional hen mortality rate, predicted summer hen mortality would approximate the study mean (i.e., reduced predicted summer hen survival by approximately 27%). For the ad hoc model, four of the 5 predicted reproductive parameters listed in Table 11 fell within the confidence intervals of our estimates. Only nests per hen (1.25) did not and it was barely outside its respective confidence interval. Furthermore, hen success (12.3%) was exactly equal to the observed mean and numbers of hatched nests (2.0) exceeded the observed mean by only 11%. The ad hoc model also suggested that the default and initial customized models may have overestimated the actual recruitment rate by a minimum of 122 and 82% respectively (M. Zicus, unpubl. data).

Application of the Model

Our assessment of the model's performance was inconclusive because we could not attribute the difference between model predictions and our field data to a single cause. Thus, an apparent lack of agreement between model predictions and field estimates could not be interpreted unambiguously as a failure of the model. Likewise, apparent agreement between the ad hoc model predictions and field estimates is not incontrovertible evidence that the model performed well. Nonetheless, we believe the relationships incorporated into the mallard model are biologically sound and have been well documented (cf. Johnson et al. 1986, 1987) and that the model has been appropriately specified. Although we did not assess fully the possible bias in our field data, there is reason to believe that biases in our field data were either small or offsetting. Thus, we believe use of inappropriate values for some important inputs was likely the overriding reason model predictions and our field data differed to the extent that they did.

In practice, there may be a desire to overextend the model. Both Johnson et al. (1986:29) and Cowardin et al. (1988:24) cautioned potential users about the model's limitations. Predictions are simply solutions from a series of mathematical equations reflecting current knowledge of mallard biology and can be no better than the inputs to the model no matter how sound the modeled relationships are.

Managing for mallard recruitment in heterogeneous landscapes is complex and can be understood best by first exploring the relationships among various management options. Recruitment in different landscapes may be limited by factors requiring a mix of management prescriptions. To realize the maximum benefit from management, care must be taken to assure that different management practices complement rather than compete with each other. The mallard model can help explore these relationships.

Future Needs

There is no substitute for appropriate inputs to any model. Usefulness of the mallard model can be improved most by developing management programs that ensure ongoing collection of data to describe conditions expected in different landscapes. Inputs to the model must be as appropriate as possible for the area of concern, and they should reflect long-term average or median conditions and not unusual or episodic events in the various habitats.

We previously noted that model predictions are sensitive to input values for habitat-specific nest mortality (Johnson et al. 1987:266-272). For example, what value should be used as an estimate of daily nest mortality over the long-term in Minnesota CRP? Nest success in CRP can be variable and often may be less than 20% (Kantrud 1993, M. Zicus, unpubl. data). Where other habitats dominate a landscape, are suggested default values for these habitats reasonable? Current date-specific estimates of daily nest survival are important inputs needed to realize the maximum benefit from use of the model in Minnesota. Considering the transitory nature of changes continually occurring in the landscape, developing programs to monitor nest success for a variety of habitats will be a challenge.

Questions also exist regarding the spring mass of Minnesota hens. Mallard hen mass in our study was substantially less than that assumed in the model. Food availability, precipitation, and wetland conditions in winter can affect hen condition and reproductive performance in spring (Heitmeyer and Fredrickson 1981, Delnicki and Reinecke 1986, Dubovsky and Kaminski 1994) as can factors during spring migration (LaGrange and Dinsmore 1988). Do Prairie Coteau mallards, or Minnesota hens in general, typically return to nesting areas in poorer condition than those in other areas of the Prairie Pothole region? Or was lighter mass simply a manifestation of the extended drought that was ending as our study began? Adult (n = 202) and yearling (n = 33) mallard hens caught in Minnesota's Border Prairie PPJV target area in 1981 weighed 1090 and 1048 g, respectively (J. Bladen, U.S. Fish Wildl. Serv., pers. commun.). These body masses were nearly identical to those measured in our study. However, dry conditions prevailed in 1981 (Maxson and Pace 1989) possibly precluding hens from attaining normal weights. Unfortunately data from 4 remaining years of the Stabilized Regulations Program appear to have been lost (R. Eberhardt, Minn. Dep. Nat. Resour., pers. commun.; R. Reynolds, U.S. Fish Wildl. Serv., pers. commun.; R. Blohm, U.S. Fish Wildl. Serv., pers. commun.; J. Bladen, U.S. Fish Wildl. Serv., pers. commun.). Hen weight data from Minnesota also were collected as part of a U.S. Geological Survey small unit management study. This study was conducted in the Border Prairie PPJV target area, but it ran concurrently with ours and the Border Prairie also experienced severe drought during these years. These data have not been compiled into a useable format (G. Krapu, U.S. Geol. Survey, pers. commun.), but they could provide a comparison from another part of Minnesota. Other Minnesota data are needed to determine appropriate hen weights for the model.

We know of no sensitivity analyses examining the influences of hen survival in the model. Our modeling suggested that predictions of recruitment rate and proportional population change are likely quite sensitive to changes in hen survival. Considering the difference between our field estimate of seasonal hen survival and that predicted by the model, what should the model input for daily hen mortality be? Blohm et al. (1987) determined that spring-summer survival of female mallards in the prairie provinces of Canada was 0.603. Reynolds et al. (1995) used the same data and estimated spring-summer survival of adult females to be 0.574. Both values are closer to our estimate than to the prediction resulting from the default inputs, especially considering that our sample was largely adults. Default inputs for hen survival used in the model were arrived at by iteratively running the model until predictions of summer mortality were 0.25 - 0.30 as reported in Johnson and Sargeant (1977) (T. Shaffer, U.S. Geol. Survey, pers. commun.). Annual mallard survival has been shown to vary spatially and temporally (Anderson 1975, Chu and Hestbeck 1989). An east-west gradient across the Prairie Pothole region also has been detected for nest success (Klett et al. 1988). Sargeant et al. (1984) reported on the high rate of hen mortality that is often associated with nest destruction by predators. Perhaps a regional gradient in summer hen survival also exists because of the influence of additional hen mortality associated with a greater loss of nests in more easterly parts of the Prairie Pothole region. Alternately, the low hen survival that we observed may have been a biased estimate or simply unique to our study. Regardless, more information about summer hen survival is needed to obtain the greatest value from use of the model.

Date- and habitat-specific Robel readings, combined with the areal extent of habitats, control the distribution of simulated nests among habitats. Predicted recruitment rate is sensitive to the simulated distribution of nests when habitat-specific nest mortality varies markedly among habitats or within the season. Robel measurements from some Minnesota habitats may exceed defaults by appreciable amounts (Appendix B). Default Robel readings for ROWs, in particular, may be too low. In addition, we are uncertain about the appropriateness of the Robel readings suggested for wetland vegetation. Potential biases notwithstanding, we found somewhat fewer nests in wetland vegetation than the model predicted. This suggested Robel readings for wetland vegetation might have been too large, at least during our study.

In a study of overwater duck nests, Maxson and Riggs (1996) also found relatively few mallard nests in overwater cover in northwest Minnesota. However, in other locations, the proportion of all mallard nests occurring in wetland cover has been reported as 49-74% (Evans and Black 1956, Jessen et al. 1964, Krapu et al. 1979b, Arnold et al. 1993). The significance of these high rates of wetland nesting with respect to the appropriateness of Robel readings for wetland vegetation is unclear because the attractiveness and extent of competing cover was not assessed in these earlier studies. Possibly, inherent attractiveness of wetland habitats varies regionally, and thus Robel readings for wetland vegetation should vary as well. If Minnesota wetland vegetation defaults are too large relative to those of other habitats, then the importance of wetland habitats for nesting will be overemphasized in model predictions. Because wetland vegetation may be a large part of the cover suitable for nesting in parts of Minnesota's intensively cropped landscape, knowledge of the attractiveness of wetland habitats for nesting is important.

As new habitat management practices evolve, data will be needed to describe the resulting conditions. These data will need to be expressed in a manner useful in the model. For example, various types of mallard nest structures are becoming popular (Johnson et al. 1994). Date-specific estimates of the relative attractiveness of these structures to nesting mallards and estimates of daily nest mortality in structures are needed. Mack (1991) suggested default values for nest structures; however, the appropriateness of these is unknown because the use of structures as a management practice is new and many different types are employed. For example, paired fiberglass and flax-straw hen houses were used at significantly different rates (Kowalchuk 1996). Thus, different Robel readings would be needed for each structure type to model them correctly. Relative attractiveness of nest structures in the model is indexed by a false Robel measurement and cannot be measured directly (Mack 1991). Determination of appropriate input values for practices such as nest structures will require additional studies.

Our assessment focused on Minnesota's PPJV Prairie Coteau target area, an area that was physiographically more similar to North and South Dakota where the mallard model was developed than is much of Minnesota. As a result of our study, we gained an understanding of the performance of the mallard model and the appropriateness of model inputs in the Prairie Coteau. This knowledge is lacking for other Minnesota target areas where approximately 91% of Minnesota's PPJV mallards breed (J. Lawrence, Minn. Dep. Nat. Resour., pers. commun.). Clearly, data needs are greatest for target areas in Minnesota's prairie-forest transition zone where most PPJV mallards occur.

Conclusions

Hanley (1994) recently discussed the expectations from research by natural resource professionals. He cautioned against undertaking studies asking questions that were too big and could not be answered unambiguously. To an extent, our effort is guilty on this count. Nonetheless, our assessment has identified additional data needed to improve the mallard model's usefulness in Minnesota's Prairie Coteau. It was not surprising that model predictions failed to agree with our field estimates. That predictions of important endpoints from both models differed as much as they did warrants caution in the way the model is used. The model's ability to predict mallard production during the extreme conditions of our study appeared poor given inputs that we used. Much greater agreement was realized with an ad hoc model following changes to only 3 key inputs. Although not validation in the modeling sense (Conroy et al. 1995), this is reassuring and suggests the model's structure is appropriately specified.

Conroy et al. (1995) noted that models usually have 2 complementary goals: understanding processes and forecasting the effects of human activities. They further suggested that models should not be judged solely on either ability. Cause and effect relationships incorporated into the mallard model are complex, and the model relies on gross oversimplifications of many ecological processes. Cowardin et al. (1988) acknowledged this when they quoted Box (1979) as saying that "models of course are never true, but fortunately it is only necessary that they be useful." The mallard model is useful because it provides a means whereby the relative merits of various management activities can be compared. Continuous efforts must be made to improve any model's inputs (Conroy et al. 1995). As inputs improve, model usefulness and accuracy also should improve. Because the model is landscape-based, most data needs focus on gaining a better understanding of the habitats being managed or the consequences of altering these habitats. Acquisition of these data should become an integral part of an adaptive process (Holling 1978, Walters and Holling 1990) for management of waterfowl habitats.


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