Publisher Correction: Linking landscape-scale conservation to regional and continental outcomes for a migratory species

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, with a difference of 0.028 between these averages. Likewise for these scenarios, age ratio ranged from 0.440 (SE = 0.042) to 0.509 (SE = 0.049), with a difference of 0.069.
Harvest rate. Assuming a daily bag limit of one pintail, a common and restrictive policy for this species 32,45 , percent of all individuals harvested (henceforth, harvest rate) averaged 9% (95% confidence interval [CI]: 5-15%) out of all pintails alive in the fall (i.e., pooled across age and sex cohorts). This corresponds with an average baseline harvest rate for adult females of 6% (95% CI: 3-10%).
A priori scenarios. Under all a priori scenarios for habitat conservation (regardless of harvest) and average parameter values, the predicted number of male and female pintails at the start of breeding across all regions at equilibrium (henceforth, population) was predicted to reach <3 M individuals (Table 3 and Fig. 2). Under No Conservation and no harvest, we predicted a population of 1.8 M (95% CI: 54 K-3.5 M) pintails when using the lower 95% confidence limits (CLs) for the focal parameters. While still assuming average parameter values ≥5% baseline harvest led to extirpation across all of these scenarios, and 3% baseline harvest led to a population exceeding 1 M individuals under none of the scenarios except Increase Conservation (Fig. 2). The 10-year cost of this scenario was estimated at $588 M. The North American Waterfowl Management Plan (NAWMP) goal of 4 M pintails 46 was reached under limited conditions: Increase Conservation scenario, no harvest, and upper 95% CLs of parameter values. With a bag limit of one pintail, this goal was not reached under these scenarios.
Across the a priori scenarios, habitat conservation affected 2 to 6% of the Canadian portion of the PPR (henceforth, Canadian Prairies; Table 1). Total cost of the observed conservation delivery (i.e., Observed Conditions scenario) during the 10-year study period was $313 M ( Table 1). The remaining scenarios differed from Observed

Observed Conditions
Conversion of spring-seeded cropland to hayland/pasture 2,994 0. 52 34 Conversion of spring-seeded cropland to idle grassland 380 0.07 75 Winter wheat included in cropland rotation 2,724 0. 47 19 Protection of existing grasslands 3,910 0. 68    www.nature.com/scientificreports www.nature.com/scientificreports/ conserved equal to 11 K km 2 . Under Observed Conservation, nearly 3000 km 2 of spring-seeded cropland (ca. 1% of total) was converted to idle grassland at a cost of $75 M during the 10-year study period. We estimated a total of 250,200 km 2 of spring-seeded cropland in the Canadian Prairies, with a one-time cost of $197,931 km −2 ($801 ac −1 ) when converting this cropland to idle grassland. post hoc scenarios. Achieving a population of >2 M pintails under the restricted bag limit would require $9.9B to convert 20% of spring-seeded cropland (50,040 km 2 ) to idle grassland, assuming 23 K km 2 of cropland includes winter wheat in the rotation and the lower CL for harvest rate along with averages for the other parameters (Fig. 3). Under the same conditions, half the spring-seeded cropland (125,100 km 2 ) would need to be converted at a total cost of $24.8B to ensure that the lower 95% CL exceeds 2 M pintails. Reaching the NAWMP goal of 4 M pintails while assuming a bag limit of one pintail and average parameter values would require converting 90% of the spring-seeded cropland (225,180 km 2 ) at a total cost of $44.6B. Converting all spring-seeded cropland to idle grassland at a cost of $49.5B while annually harvesting 5% of pintails (i.e., the lower 95% CL under restrictive harvest) would yield a population of 5.3 M (95% CI: 4.2 M, 6.7 M) while assuming average reproduction and male breeding survival.
Uncertainty. Population estimates differed by −11 K to 25 K individuals and 0 to 18% when varying adult breeding survival between its lower and upper CLs (i.e., 0.89 and 0.99) across combinations of fixed values for age ratio (corresponding with habitat conservation scenarios in the PPR) and harvest rate (Fig. S1). Combinations of absolute and proportional differences in the population estimates were maximized when age ratio was lowest (i.e., Figure 3. Predicted relationship between conversion of spring-seeded cropland to idle grassland within the Prairie Pothole Region and the equilibrium population size of northern pintails at the start of the breeding season. The population size at the x-intercept (i.e., % converted = 0) corresponds with the Increase Winter Wheat scenario. Panels represent predicted relationships under particular proportions of all pintails harvested (i.e., harvest rate; h). A harvest rate of zero represents a closed hunting season, and the remaining represent the uncertainty about harvest rate expected under a bag limit of one pintail. Cost of habitat conversion (secondary x-axis) is given in 2016 USD. Solid line is based on mean values for all parameters, and the dashed lines are based on the upper and lower 95% confidence intervals for parameters derived from available empirical data.
www.nature.com/scientificreports www.nature.com/scientificreports/ No Conservation) and harvest rate was 1-3%. For example, when harvest was 2% under the No Conservation scenario, the absolute difference was 25 K and the proportional difference was 5%.
By contrast, population estimates differed by 0 to 4.6 M individuals and 47 to 200% when varying age ratio in the PPR between its lower and upper CLs (Table 3) across values for mean age ratio and harvest rate (Fig. S2). Here, the absolute and proportional differences in the population estimates reached their maxima when mean age ratio was lowest (i.e., No Conservation) with no harvest.

Discussion
Tools are needed to quantify and understand impacts from the expansion of intensive agriculture on migratory species, especially in agriculturally dominated regions. Likewise, methods are needed to account for the influence of conservation and harvest management on populations of economic or cultural importance. We have developed a novel modeling framework for linking landscape-scale habitat conservation with continental population dynamics of a migratory bird. In our case study, we found that existing conservation practices and realistic alternatives appear to be insufficient to maintain population viability of this species under a restrictive hunting-bag limit. Based on model predictions accounting for parameter uncertainty, enormous increases in habitat conservation within the focal region and possibly eliminating harvest of the species would be necessary to allow for achieving population goals at the continental scale. Increased agricultural intensification, driven by the conversion of ca. 9 M hectares of idled cropland (summer fallow) to continuous spring-seeded cropland under minimum tillage, has occurred over the past three decades 47,48 . The resultant increase in availability and use of spring-seeded versus idle cropland for nesting is the likely driver of declining reproduction levels 49,50 . At the observed level of annual funding for waterfowl habitat conservation ($31.3 M yr −1 ), it would take >100 years to cover the cost of habitat conversion ($35.7B) needed to achieve a predicted population size meeting the NAWMP goal of 4 M pintails. This assessment assumes average parameter values and that future conservation activities are focused on the pintail 51,52 .
The predicted decline in continental-scale abundance of pintails under observed habitat conditions contradicts our previous findings using the same population model with regional age ratios based on expert elicitation 19 . We previously assumed that age ratios in breeding regions were negatively correlated with abundance due to density-dependent reproduction within each region. On further review we now believe that reproduction is only density-dependent at a continental scale, whereby a greater proportion of pintails settle in areas with lower reproduction as the spring population increases. This spring fly-over effect was part of the original population model 19 and was retained in the current version. Thus, linking scales between landscape-level conservation and continental-level dynamics has provided new insights about the scale of density-dependent reproduction for this species.
In addition to our own modeling work based on a large dataset of individual nests and broods, evidence from PPR banding studies indicates that pintail reproduction has declined. For example, the trend in age ratio of pintails banded at the end of breeding in the Canadian Prairies decreased from 1.5 to 0.5 from 1960 to 2014 coincident with population decline 45 . Similar results have been found using such banding-based age ratios for regressing changes in reproduction with agricultural intensification in the Canadian Prairies 50 . Our estimates of reproductive rate based on long-term studies of nests, and assumptions regarding lack of density-dependent reproduction at regional scales, are therefore supported by models using independent data.
As with any multi-scale modeling framework, ours carries several assumptions about the accuracy of parameter values. There are several possible sources of bias, some of which are discussed elsewhere 19 , and it is beyond the scope of this study to address all of these. For predicting continental-scale abundance, we found that uncertainty about reproduction was three orders of magnitude more important than was uncertainty about male breeding survival. We therefore highlight two parameters with potential for inducing bias in the reproduction estimate. There are concerns that estimates of nest survival are biased low due to disturbance caused by human observers 53 , but this hypothesis was not supported for any guild of birds considered in a meta-analysis on this topic 54 . Further, there was no evidence of visitation effects on nest survival of radio-tagged female mallards in the Canadian Prairies 55 . We therefore expect that bias induced by nest observation was negligible in our study.
Second, we assumed the land-cover map provided an accurate assessment of the proportion of spring-seeded crops and grassland in the landscapes. Errors with remote sensing can induce biased estimates, such that percentage of crops in the landscape is underestimated and grassland is overestimated in the PPR 56 . If present, this bias would make pintail persistence even less likely than in our current predictions. In our previous work 19 , we identified several other sources of uncertainty for predicting continental-scale abundance of pintails as a function of management. Although we have addressed uncertainties about variables for which empirically based confidence intervals were estimable (i.e., harvest rate, reproduction, and male breeding survival), many remain to be examined.
Further, our estimated impact of conservation efforts on pintail reproduction is based on information collected in the Canadian Prairies. When modeling population dynamics at the continental scale, we assumed similar conservation efforts and effects on reproduction on both sides of the U.S.-Canada border bisecting the PPR. This assumption was necessary, as we were unable to acquire similar data for the U.S. portion. There is evidence suggesting that age ratio has responded similarly to agricultural intensification in the US portion as it does in the Canadian Prairies 50 . A critical need then is to obtain comparable information about habitat conservation and pintail reproduction within the U.S. portion, so that our predictions can be further validated.
When comparing the U.S. and Canadian portions of the PPR, another important difference is the trend in funding for conservation of waterfowl habitat. Based on our concurrent study on annual funding for conservation of waterfowl habitat in the PPR, finances in the Canadian Prairies were quite stable during the study period (range: $26 M-$46 M annually) 57 . By contrast in the U.S. portion, funding was greater and growing (range: $61-$163 M annually). We may have therefore underestimated reproduction in the PPR under Observed Conditions, www.nature.com/scientificreports www.nature.com/scientificreports/ considering that the U.S. portion may have conserved more habitat compared to the Canadian Prairies. Taken together, there are important contrasts between countries in documenting conserved habitats and consistency of funding for the conservation work. Future analyses in ecoregions straddling an international border must therefore account for international differences in conservation funding and resultant habitat management.
Despite calls to integrate the management of habitat and harvest under NAWMP 19,58 , optimal policies for harvesting waterfowl in North America are based on estimates of abundance and distribution as state variables rather than habitat metrics 59 . Our predictive framework provides the means necessary for this formal integration. Specifically, we link landscape-scale conditions of habitat conservation throughout the PPR to pintail reproduction and a continental-scale forecast for trend in population size. These elements are the necessary ingredients for formally integrating harvest and landscape-scale conservation to achieve population goals at the continental level. Until now, this essential link has been missing.
A precautionary approach to hunting regulations entails projecting population outcomes under alternative harvest policies while accounting for uncertainty, which is an important consideration in the adaptive harvest management of waterfowl 60,61 . The current harvest strategy for pintails focuses on uncertainty about the strength of density dependence for post-harvest survival 59 . Although addressing this uncertainty can improve predictions about continental dynamics 19 , we believe that uncertainty about the effect of habitat conservation on reproduction (along with the magnitude of the age ratio) is an equally if not more important concern. By considering alternate forms of density-dependent survival and of conservation-dependent reproduction, the key sources of uncertainty for dynamics of the pintail population can be addressed through adaptive management.
Explicitly accounting for costs of habitat conservation can help inform strategies to maintain or increase at-risk populations of migratory birds. Applying a cost constraint when investigating alternative strategies 62,63 is a simple method to address limited funds for conserving migratory species. Accurate accounting for spatial variation in cost of habitat conservation was important for finding an optimal strategy that would save money while conserving breeding habitat for bobolinks (Dolichonyx oryzivorus) 64 . The bobolink study also revealed that cost determined the optimal mixture of habitat protection and restoration. Similarly, cost savings were revealed by a study that used management costs when optimizing conservation of stopover habitats of the pink-footed goose (Anser brachyrhynchus) 65 . Optimization with cost as a constraint, however, may not reveal a clear relationship between expenditures and population-level outcomes. Based on estimated costs in our study, we found that achieving the desired population size and harvest level at the continental scale would require multiple decades under the current level of investment. This timeline may be insufficient given the predicted decline in abundance.
New approaches are needed to overcome the challenge of conserving habitats for migratory birds in the face of limited budgets. The emerging field of biodiversity-based agriculture may hold some promise 66 . Methods in this field include model-based games 67 that investigate scenarios for conserving both local and migratory biota. Our modeling approach can be used to support such investigations. Biodiversity-based agriculture requires advances in participatory methods for engaging stakeholders 22,68,69 along with predictive models for species response 19,21 . Frameworks exist for integrating knowledge and stakeholder processes to inform decisions for conserving highly mobile species, including collaborative decision analysis 70 and adaptive management 60,61 . These frameworks must be tested for improving the practice of conserving migratory species.
Across the annual cycle, migratory birds span multiple jurisdictions ranging over large extents. Linking landscape and continental scales is therefore needed when modeling population-level outcomes under realistic scenarios of habitat conservation. Such linkages are rarely modeled when investigating effects of habitat changes on migratory populations [71][72][73] . Modeling populations at extreme scales is challenging as it requires the integration of conceptual models and mathematical approaches along with diverse data sets 71,74 , which we have experienced in our work. This approach however can address important ecological questions in ways that were until now not possible.
Addressing scale mismatches between management and ecological processes is a critical factor limiting effective conservation 75 . Tools for developing multi-scale models and obtaining the necessary data are being increasingly refined and used 44 . A particular opportunity is extending our framework for other species and in novel contexts. Continental-scale population models and necessary data are now available for migratory species representing multiple taxonomic groups, including waterfowl 20,21 , passerines 76-79 , shorebirds 35,80 , butterflies 40 , and bats 38 . Landscape-level models are relatively common 69 , and so there is a great opportunity for linking landscape-level changes to continental-scale dynamics of migratory species. A future challenge for multi-scale modeling is forecasting annual changes in population size while accounting for shifts in weather and land cover induced by global change and nonstationarity 81,82 . Multi-scale modeling that links landscape-scale changes to continental-level outcomes offer an important means for closing the gap between the practices of management and science of conserving migratory species.

Methods
Study system for case study. The PPR of Canada and the northcentral U.S. comprises the formerly glaciated and wetland-rich region serving as the primary breeding area for many North American waterfowl [83][84][85] (Fig. 4). Historically, extensive grasslands along with abundant and diverse wetlands provided ideal habitat for successful waterfowl reproduction in this region 86 . Since human settlement, however, a majority of the PPR has become an important agricultural production area for cereal grain, oil seed and row crops. This region is one of the most productive agricultural landscapes in the world 87 with a high potential for expansion of cropland and agricultural intensification 4 . Conversion of grassland to annual cropland and drainage and degradation of wetlands have significantly altered the landscapes in which waterfowl settle to breed 88,89 . These habitat losses represent the primary conservation concern for NAWMP 90,91 .
www.nature.com/scientificreports www.nature.com/scientificreports/ Conversion of grasslands to cropland and associated alteration of predator communities in the PPR are thought to be the leading cause of long-term declines in waterfowl production in this region 88,[92][93][94] . In addition, the intensity of cropping practices on existing cultivated lands has increased in recent decades. The largest and most economically and environmentally significant change in agricultural land use since the 1970s has been the decline in summer fallow. Through this practice, cropland was removed from production during alternate growing seasons for moisture accumulation, nitrogen release, and weed control 47 . In the Canadian Prairies, summer fallowing declined by approximately 90 K km 2 from 1971 to 2016 95 . In its place, the prevailing approach is continuous cropping with minimum and zero-tillage practices (hereafter, 'conservation tillage') requiring high nutrient and pesticide inputs 47,48 . While beneficial for soil conservation, reduced stubble disturbance in combination with spring seeding operations may create ecological traps for breeding birds 96 .
Migratory waterfowl are one of the most intensively managed groups of vertebrates in North America. Ongoing restoration and protection of habitats throughout the annual cycle along with annual regulation of harvest rates comprise modern waterfowl management 60 . Every year, millions of dollars are invested in conservation efforts within the PPR 51,97,98 . Improving the effectiveness of waterfowl management depends on a better understanding of how changes in habitat as a result of conservation activity will affect achievement of continental-level goals for species abundance 19,58,99 .
Conservation programs for breeding waterfowl in the PPR are generally targeted toward habitat for dabbling ducks in general, not to any particular species 100 . Primary conservation activities in this region include conversion of cropland to forage grass (hay or pasture) and idle grass, protection of existing grassland and wetlands, restoration of drained wetlands, and converting spring-seeded cropland to fall-seeded varieties 51 . These habitat manipulations serve multiple objectives; they not only maintain or restore the carrying capacity of the landscape to attract and hold breeding ducks, but they also increase breeding success through improved nest survival 88,101,102 . These conservation investments are expected to provide benefits for migratory ducks over the long term, assuming recurring use of these habitats by target species 100,103 . focal species. The pintail is of particular interest in its response to conservation actions. A significant population decline in the 1970s and 1980s caused concerns for hunters and bird enthusiasts, leading to its classification as a species of conservation concern 104 . Although the initial decline has been attributed to widespread prairie drought in the 1980's, the leading hypothesis for lack of population recovery is agricultural intensification leading to reduced reproduction in the PPR 19 . Wetland loss, especially loss of small and shallow basins preferred by pintails, may have reduced the carrying capacity of the region to attract and hold pintail pairs 105,106 . Further, and likely more influential, have been changes in land use that have reduced the ability of pintails to successfully hatch nests [107][108][109] . Since 1990, the number of pintails at the start of breeding in North America has remained between 1.8 M and 3.6 M except for 2011 when the population was estimated at 4.5 M 110 . www.nature.com/scientificreports www.nature.com/scientificreports/ Based on a population model for the PPR, declining productivity has been a main driver of changes in pintail abundance over the past five decades 50 . This study also found that productivity was negatively correlated with agricultural intensification at the subregional scale. Indeed a growing body of evidence from North America suggests that the decline in abundance of the pintail, a species that readily nests in residual crop stubble prior to seeding, may be linked to the increase in conservation tillage practices that reduce the availability of undisturbed stubble provided by fallowed cropland 49,50,108 . The economic value of birding and hunting associated with pintails in North America is estimated at >$100 M (2014 USD) annually 10 . A declining population is therefore not only a concern for biodiversity but also for society.
Unlike other dabbling ducks, pintails use croplands for nesting and begin nesting before crops are plan ted 102,104,111,112 . They therefore uniquely benefit from the high nest survival afforded by rotating crops between spring-seeded and fall-seeded crops such as winter wheat 102,111 . Pintails tend to settle opportunistically within the PPR in association with variably available wetlands, especially temporary and seasonal wetlands [113][114][115] . Predicting the impact of habitat conservation on the pintail population therefore requires an accounting of their distribution and habitat associations along with resultant changes in breeding success in affected landscapes. Such effects of amount and spatial targeting of conservation investments have until now not been investigated.
Modeling frameworks have been developed for predicting outcomes of habitat management for pintails at landscape to regional scales 49 and regional to continental scales 19 . In addition, methods are emerging for explicitly quantifying the sources and patterns of funding for conservation of wildlife habitat in North America 57 . These developments render a great opportunity for linking modeling frameworks to predict the outcomes of funding scenarios for population dynamics of this migratory species.
Our study builds from previous work 19 that used a FAC-PP model to investigate shifts in continental-scale population size and maximum sustainable yield caused by simulated changes in habitat quality within the PPR and within the Gulf Coast wintering region. The present study focuses on effects of landscape-scale habitat conservation within the PPR, as the previous study showed that increased age ratio in the PPR was more important than reducing the strength of density dependence for post-harvest survival in the Gulf Coast. The FAC modeling approach is needed to simultaneously account for effects of habitat conservation in the breeding grounds during summer and harvest across regions in the fall. overview of modeling approach. Before giving a detailed description, we provide an overview of the modeling framework for linking landscape-scale conservation of habitat to continental dynamics of the pintail population. Our general approach was to relate landscape-level alterations to expected changes in the breeding population at equilibrium while accounting for parameter uncertainty. As such, we altered the observed landscape according to alternative conservation scenarios. More specifically, we updated a land-cover map to characterize the current composition of the landscape as it pertains to waterfowl in the PPR. We then used existing models for estimating pintail distribution, hen success, and ultimately age ratio throughout the PPR. Here, we accounted for uncertainty in multiple reproductive parameters. Next, we developed alternative scenarios for conservation of pintail habitat in the PPR along with an uncertain harvest rate of pintails at the continental scale. As a final step we adapted an existing approach for modeling population dynamics at the continental level as a function of varying age ratios, mediated by landscape-scale conservation, while accounting for harvest during fall across all core regions of North America. We ran the model three times for each scenario based on the mean and 95% confidence limits of parameters for which we could quantify uncertainty based on empirical data.

Land-cover map and landscape-level habitat composition. We used Agriculture and Agri-Food
Canada's (AAFC) 2016 annual, 30-m crop raster (http://open.canada.ca/data/en/dataset/ba2645d5-4458-414d-b196-6303ac06c1c9) to estimate landscape composition in 2016 for eight habitat classes (spring-seeded cropland, fall-seeded cropland, idle grassland, grazed grassland, hayland, wetland, trees/shrubs, and other). Because wetlands are poorly captured in AAFC's crop mapping layer, we recalculated base habitat composition after including estimated wetland habitat area from the CanVec hydrology layer 116 after adding small wetlands missed by the AAFC and CanVec layers 49 . This approach yielded the 2016 land-cover map for modeling pintail distribution and reproduction throughout the PPR. To conduct the spatial analysis, we used ArcGIS version 10.4 (Environmental Systems Research Institute, Redlands, California, USA). Detailed methods for developing the land-cover map are provided elsewhere 49 .
From this layer, we estimated proportional habitat composition in each of 49 conservation-planning landscapes (henceforth, landscapes) covering 574 K km 2 comprising the Canadian Prairies (Fig. 4) 51 . All except three of these are target landscapes that delineate areas of high breeding duck density. The landscapes range in size from 1.68 K-12.7 K km 2 and collectively cover an area of 168 K km 2 . The remaining three landscapes, representing area outside target landscapes in each province, are much larger and range from 58.6 K-183 K km 2 .
Reproduction model. To quantify the impact of conservation scenarios on pintail reproduction in the PPR, we estimated the age ratio (R) as the number of juvenile females divided by the number of adult females alive at the end of the breeding season. In particular, we estimated R using a reproduction model that was structured as follows: where S h is proportion of hens having hatched a nest (i.e., hen success), C is mean clutch size at hatching, S d is the probability a duckling survives 30 days after hatching (i.e., to the end of the breeding season), θ is the proportion of hatchlings that are female, and S f is the probability that an adult female survives during the breeding season. This approach mimics that applied for estimating reproduction in previous avian population models 117 .
www.nature.com/scientificreports www.nature.com/scientificreports/ We estimated parameters for the reproduction model based on existing predictive models fit to empirical data from 992 nests that were monitored throughout the Canadian Prairies from 1993-2011 49,112,118 . Hen success (S h ) was estimated as a function of habitat conditions. Specifically, we first accounted for the spatial variation in pintail breeding pair density within each landscape based on a species distribution model 49,118 (Fig. 4) from which we extracted the estimated long-term average (1961-2009) abundance of breeding pairs in each landscape 51 . Estimated number of breeding pairs and proportional habitat availability in each landscape were used in an existing deterministic model of pintail nest habitat selection, habitat-specific nest survival, and breeding effort (nesting and renesting propensity) in the Canadian Prairies 49,112 to estimate the number of hatched nests across the region. We divided hatched nests by the number of breeding pairs to estimate hen success (S h ), which was then entered in Eq. 1 to estimate age ratio. Age ratio was subsequently used as an input parameter for the continental population model (see "Population model structure and parameters" below). As comparable information is missing from the U.S. portion of the PPR, we assumed that age ratios were equal on both sides of the border.
The remaining parameters for Eq. 1 were directly estimated from empirical data. Average clutch size (C = 8.0, SE = 0.05) was based on direct observations of 2925 nests monitored throughout the Canadian Prairies during 1993-2011 by Ducks Unlimited Canada (DUC; unpubl. data). Mean duckling survival (S d = 0.505) was based on the average of annual estimates from pintails monitored with radio telemetry in southern Alberta during 1995 to 1996 119 . Consistent with other models of bird reproduction based on nesting studies 117 , we assumed that 50% of hatchlings are female. The survival rate for adult females (S f = 0.81) during breeding was based on a telemetry study of pintails in an agricultural landscape within southern Saskatchewan during 1998-2000 120 . We estimated standard errors of duckling survival (0.020) and adult female breeding survival (0.016) based on respective coefficient of variation estimates from a large sample of radio-marked mallards in the Canadian Prairies from 27 sites during 1993-2000 103 .

Scenarios for habitat conservation and pintail harvest.
We used the reproduction model to explore the impact of scenarios representing alternate landscape compositions throughout conservation areas of the Canadian Prairies during 2007-2016 ( Table 1). The 2016 land-cover map represented the Observed Conditions scenario of empirically derived habitat conditions resulting from investments in habitat conservation. Alternatives to Observed Conditions reflect scenarios varying the amount and spatial distribution of conservation investments targeted at waterfowl habitat. With the exception of including winter wheat in crop rotations (which is limited to areas with spring-seeded wheat), we varied conservation amounts throughout the 46 target landscapes. Each scenario was treated as an instantaneous realization of habitat conditions in the Canadian Prairies that remained constant during the study period and provided the basis for estimating reproduction.
Although the land-cover map provides a comprehensive snapshot of land cover, it does not explicitly identify habitats modified by conservation activities. For simulating alternative scenarios, we made assumptions about habitat composition in each landscape and then manipulated habitat proportions to accommodate specific scenarios. For example, we increased the proportion of pasture and decreased the proportion of spring-seeded cropland by equal amounts to simulate the conversion of cropland to grassland. Sufficient data on land cover and conservation activities throughout the study period were not available for the U.S. portion of the PPR. We therefore assumed that reproduction in the U.S. portion paralleled that of the Canadian Prairies throughout the scenarios.
Two alternatives to Observed Conditions represented changes across all conservation areas. To create the No Conservation scenario (Table 1), we altered landscapes in the 2016 land-cover map to reflect a hypothetical lack of habitat conservation over the 10-year period. Specifically, we reverted all restored or protected nesting habitat (i.e., grasslands, wetlands, and winter wheat) to spring-seeded cropland to represent a landscape before observed conservation activities were applied. The number of pintails per landscape were then reduced based on the area of restored wetlands lost using models developed by Bartzen 121 . We generated the Increase Conservation scenario by doubling the acreage per conserved habitat type except winter wheat, which was held at the same acreage as for Observed Conditions.
Because of its importance to nesting pintails, we developed three scenarios focused on winter wheat (Table 1). Under No Winter Wheat, all winter wheat on the 2016 land cover map was reverted to spring-seeded cropland to reflect expected conditions in the absence of funding for winter wheat. The Increase Winter Wheat scenario reflects the stated goal of the Prairie Habitat Joint Venture 51 , to have 30% of the spring-seeded wheat acreage in the Canadian Prairies converted to rotations with winter wheat. We also examined an Increase Winter Wheat -Targeted scenario. Here, we modified the previous scenario by only applying winter-wheat rotations in landscapes with >2.3 pintail pairs km −2 (>6 pairs mi −2 ) according to estimated population densities predicted from the species distribution model.
In addition to these a priori scenarios, we conducted a post hoc analysis to determine the amount of spring-seeded cropland that would need to be converted to idle grassland in order to achieve specific population sizes at the continental scale. In particular, we adjusted the amount converted while assuming that winter wheat was included in 23 K km 2 of crop rotation congruent with the Increase Winter Wheat scenario (Table 1).
Cost estimates for each scenario were based on financial data provided by DUC. Total costs incurred over the 10-year study period were itemized according to the main types of habitat conservation: conversion of spring-seeded cropland to hayland/pasture or idle grassland; increasing amount of cropland with winter wheat in the rotation; protection of existing grasslands and wetlands; and restoration of wetlands.
Along with scenarios for habitat conservation, we considered a range of harvest rates according to existing strategies for harvesting pintails along with the associated uncertainty about actual harvest levels resulting from these strategies. The first strategy assumes a policy of no harvest and closed seasons for hunting pintails. The second assumes a daily bag limit of one pintail. To estimate the range of harvest rates expected under the latter www.nature.com/scientificreports www.nature.com/scientificreports/ policy, we used annual harvest rates 122 for years when the daily bag limit for pintails was set to one (i.e., 1988-1996 and 1998-2008) based on yearly rulings in the federal registry e.g. 123 . We fitted a generalized linear mixed model to these harvest data, using a logit link function and year as a random intercept. We determined the baseline (i.e., for adult females) harvest rates that respectively yielded the simulated total harvest rates matching the empirically estimated harvest rate. This baseline harvest rate was used as an input to the population model, which accounts for differential vulnerabilities among age and sex cohorts and crippling loss 19 . population model structure and parameters. We examined effects of changes in age ratio, as mediated by scenarios for harvest and habitat conservation, on equilibrium population size of pintails across their core breeding and wintering regions in North America (Fig. 4). We now briefly summarize the structure of the population model, as the details are described elsewhere 19 . The population model includes two age classes, both sexes, and the five core regions. Core breeding regions include the entire PPR (including portions in Canada and in the U.S.), Alaska, and the northern unsurveyed area. The latter region includes low-quality habitats within the PPR and in northern boreal portions of Canada beyond the PPR. Although this area spatially overlaps the PPR, it is modeled as a separate region to reflect important characteristics of the species distribution and behavior. The western wintering region includes the Pacific Flyway states of California and Oregon, and the central breeding region includes the Central Flyway states of Texas and Louisiana. We updated the structure and parameters of the original model to match current understanding about pintail population dynamics.
First, we changed the initial population size at the start of breeding from 3.2 M to 4.0 M as the sum across all three regions. The latter value is the long-term average of the breeding population based on annual surveys , which is the NAWMP 46 population goal for pintails. We then removed density-dependent reproduction within breeding regions. The only evidence for density dependence on the breeding grounds is at the continental scale 19 , and regional-scale density dependence has not been detected during long-term studies within the PPR 112 nor within Alaska (P. L. Flint 2010, oral communication). This modification renders the model with two density-dependent mechanisms. One occurs during spring migration when an increasing proportion of adults settle in poor-quality breeding habitat as abundance increases. The other density-dependent process in the model is the reduction of post-harvest survival with increasing abundance on the wintering grounds 19 .
The estimated age ratio (computed from the reproduction model) for the Observed Conditions scenario was significantly lower than the one used in the original population model. We therefore rescaled age ratios for the remaining breeding regions based on our new estimate for PPR from the Observed Conditions scenario. In particular, we multiplied the original age ratio R i by ′ R R / PPR PPR , where i indexes the other two breeding regions, R PPR ′ is the estimate of age ratio for PPR based on the Observed Conditions scenario in the current study, and R PPR is the baseline estimate used in the original population model. This calculation is based on the assumption that age ratios in the original model were being overestimated by the same percentage across regions.
Last, we modified several survival rates. We computed a breeding-season survival rate for males of 0.96 (Agresti-Coull 95% confidence interval: 0.89, 0.99) 124,125 , which was based on 76 of 79 radio-marked pintails who survived from early April through early July in landscapes within southern portions of Manitoba and Saskatchewan during 1998 and 1999 126 . This is lower than the original estimate, which was only based on paired males. We also reduced natural mortality rate during fall (i.e., from the start of fall migration to the end of the hunting season) for all cohorts by 0.04. This reduction in fall mortality leads to an annual female survival rate of 0.67, which matches the estimate for the Western and Central Flyways 32 . The modified population model allowed us to estimate equilibrium abundance at the continental scale under each scenario.
Analysis. For each scenario, we estimated the following parameters within the PPR: conservation cost, habitat availability, hen success, and age ratio at the end of the breeding season. At the continental scale, we projected equilibrium population size at the start of breeding across all three core breeding regions as a function of age ratios. The set of age ratios was based on the modeled estimate for each of the a priori scenarios for habitat conservation along with those predicted under the post hoc scenarios.
Although the model is deterministic, we ran each scenario using the mean and 95% confidence limits for age ratio, male survival during breeding, and harvest rate. We held the remaining parameters constant, because empirical data for computing confidence intervals for these are lacking. To estimate standard error for age ratio, we integrated uncertainties about clutch size, hen success, duckling survival, and female breeding season survival within the reproduction model by using the delta method 127 . We then multiplied this standard error by 1.96 to obtain the upper and lower prediction intervals for age ratio under each habitat conservation scenario. To model the 95% confidence interval for harvest rate for all individuals under a daily bag limit of one, we extracted the 2.5 th and 97.5 th quantiles from 1000 bootstrap iterations of the mixed logistic regression using the bootMer function in program R 128 . The method for estimating the confidence interval breeding survival of adult males is given under "Population model structure and parameters", above.
The analysis was conducted using SAS version 9.4 (SAS Institute, Cary, North Carolina, USA8) for the reproduction model and program R 128 for the remaining parameters and population model. All monetary values are given in 2016 USD.

Data availability
The data and code used for the analysis in this study are available from the corresponding author upon request. www.nature.com/scientificreports www.nature.com/scientificreports/ www.nature.com/scientificreports www.nature.com/scientificreports/ www.nature.com/scientificreports www.nature.com/scientificreports/