Demographic response to perturbations: the role of compensatory density dependence in a North American duck under variable harvest regulations and changing habitat


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1. Most wild animal populations are subjected to many perturbations, including environmental forcing and anthropogenic mortality. How population size varies in response to these perturbations largely depends on life-history strategy and density regulation.

2. Using the mid-continent population of redhead Aythya americana (a North American diving duck), we investigated the population response to two major perturbations, changes in breeding habitat availability (number of ponds in the study landscape) and changes in harvest regulations directed at managing mortality patterns (bag limit). We used three types of data collected at the continental scale (capture–recovery, population surveys and age- and sex ratios in the harvest) and combined them into integrated population models to assess the interaction between density dependence and the effect of perturbations.

3. We observed a two-way interaction between the effects on fecundity of pond number and population density. Hatch-year female survival was also density dependent. Matrix modelling showed that population booms could occur after especially wet years. However, the effect of moderate variation in pond number was generally offset by density dependence the following year.

4. Mortality patterns were insensitive to changes in harvest regulations and, in males at least, insensitive to density dependence as well. We discuss potential mechanisms for compensation of hunting mortality as well as possible confounding factors.

5. Our results illustrate the interplay of density dependence and environmental variation both shaping population dynamics in a harvested species, which could be generalized to help guide the dual management of habitat and harvest regulations.


In nature, the environment is never stable. Climate fluctuates, random catastrophes occur and human activities alter environmental conditions. These perturbations influence the population dynamics of wild animals, both spatially and temporally (Stenseth et al. 1999; Benton & Beckerman 2005; Koons et al. 2005; Dodd, Ozgul & Oli 2006; Grosbois et al. 2008; and references therein). While life-history strategy (e.g. Gaillard et al. 1989) determines to a large extent the sensitivity of populations to a given type of perturbation (Beissinger & Westphal 1998; Pfister 1998; Stahl & Oli 2006), this needs to be understood within the broader framework of density regulation (Saether et al. 2005; Bonenfant et al. 2009). Compensatory density dependence is indeed a major mechanism enabling populations to offset the effect of perturbations of anthropogenic or environmental origin (Burnham & Anderson 1984; Sinclair & Pech 1996; McCann, Botsford & Hasting 2003; Benton & Beckerman 2005; McGowan et al. 2011). In other words, when a perturbation reduces the population size or local population density, the remaining individuals, freed from the negative effects of density, may perform better than if no perturbation had occurred, thereby ‘buffering’ environmental variation. On the other hand, the absence of compensatory density dependence can have dramatic consequences on population size. For example, lesser snow goose Chen caerulescens caerulescens populations are currently in a phase of exponential growth, mostly because density dependence in winter mortality was reduced because of increased food availability, and regulation via density-dependent breeding success proved to be inefficient in this long-lived species (Alisauskas et al. 2011). Another contrasting example is provided by least Bell’s vireo Vireo belli pusillus, which can locally decline at a rapid rate because brood parasitism by invasive brown-headed cowbirds Molothrus ater reduces offspring production (Kus 2002) without density dependence in adult survival later compensating the losses in this short-lived species. By contrast, density dependence can also be part of the mechanism through which perturbations impact population size. In particular, adverse conditions generally reduce available resources, exacerbating competition between individuals. For example, Tule elk Cervus canadensis nannodes from Point Reyes, California, only experience density dependence during the years of poor vegetation productivity (Howell et al. 2002).

To sum up, the extent to which a population will respond to environmental or anthropogenic forcing is driven by: (i) which demographic parameter(s) the perturbations affect and whether these parameters are important for the species’ life-history strategy; (ii) whether the population is below or above carrying capacity each year; and (iii) which demographic parameter(s) are density regulated. Despite these clear-cut predictions and an abundant theoretical literature, large uncertainties still exist about the actual functioning of most wild animal populations. The analysis of time series of population counts remains the major tool biodemographers use to study population dynamics and choose between competing hypotheses (Stenseth et al. 1999; Creel & Creel 2009). More rarely is a fully mechanistic model (i.e. describing, as a function of environmental conditions and density, the demographic processes of fecundity, survival and transition between stages) designed, tested and calibrated using field data (Coulson, Milner-Gulland & Clutton-Brock 2000; Oli & Armitage 2004; Jenouvrier et al. 2009). As a result, in most populations, density dependence and environmental forcing are known to exist to some extent, but without quantification of all the pathways through which density can offset (or not) the effect of perturbations.

Here, we studied the dynamics of the mid-continent population of redhead Aythya americana, a North American diving duck. This breeding population encompasses a high proportion of the world population of the species and includes the famed Prairie Pothole Region. Mid-continent redheads could be affected by two major perturbations: (i) changes in the availability of breeding habitat and (ii) changes in the intensity of hunting. For redheads, availability of breeding habitat is measured by the number of ponds within the landscapes used by the mid-continent population. Redheads are habitat specialists and require ponds for building floating nests, as well as foraging and rearing broods, which makes them an ideal study species for our purpose. Hunting intensity is measured through the proxy of hunting regulations, and bag limit in particular, which is the most influential variable upon which managers can act (Conroy, Miller & Hines 2002). The issue of identifying the relative influence of these two perturbations on population dynamics has come to the forefront of waterfowl ecology and management in North America (Conroy, Miller & Hines 2002; Runge et al. 2006; Mattsson et al. 2012), but empirical studies are lacking, especially on the topic of compensatory density dependence. Here, for the first time, we simultaneously investigate the relative influence of variability in habitat availability, harvest regulations and compensatory density dependence on both survival and fecundity, and how these shape the population dynamics of a harvested species.

Materials and methods

We used capture–recovery data (CR; information on the age and time at which individually marked redheads were shot by hunters), population surveys (aerial counts of the breeding population on stratified transects of habitat), and age- and sex-ratio data (from the plumage features of wings of redheads shot by a subsample of hunters). To combine these three types of data and extract information about density dependence and response to perturbations, we used integrated population models (IPM; Besbeas et al. 2002; Brooks, King & Morgan 2004). This method makes it possible to analyse the three data sets at once and simultaneously estimate survival, fecundity and population size. Below we (i) present the data sets, which are available to the scientific community in the form of online data bases; (ii) describe our use of IPMs to address our objectives; and (iii) describe our assessment of how trustworthy the estimates from the IPMs were compared to more standard analyses of single data sets.

Capture–recovery data

We attained redhead banding and recovery data over the period of 1960–2009 (50 years) from the GameBirds data base (Bird Banding Lab, USGS Patuxent Wildlife Research Center). Data from mid-continent states and provinces were selected (Alberta, Saskatchewan, Manitoba, Montana, North and South Dakota, Minnesota and Iowa). The analysis was restricted to normal wild birds released in the same 10-min block as the banding location. Moreover, we removed birds of unknown sex or age, and ducklings marked with plasticine bands. We used data for birds that were banded in July, August or September, which is after most ducks have completed nesting but generally before the opening of the hunting season. Band recoveries were restricted to birds shot and reported between September and January, and of which the date of death was reported to the nearest 10 days or more precisely.

We partitioned the data by sex and age class, where hatch-year (HY) birds are defined as those hatched in the calendar year they were banded, including ‘locals’ that were banded before fledging (see the section ‘IPMs: general structure and assumptions’ below for justification). After hatch year (AHY) birds are those that hatched in years previous to that of banding. These data filters resulted in a total of 21 340 banded and released AHY females, 19 966 AHY males, 20 920 HY females and 21 084 HY males, from which 1135 AHY females, 1480 AHY males, 1731 HY females and 1851 HY males were shot and reported (i.e. recovered). Hereafter, HY stands for birds in their first year of life from banding to first breeding season and AHY for all other (adult) birds.

Throughout we use the abbreviation HY to designate birds during their first twelve months of life, before their first breeding season, and AHY to designate all other (adult) birds. This is different from the standard North American bander terminology, which recommend the use of SY (second year) for all birds in their second calendar year, HY being restricted to the few months between hatching and December 31 of the calendar year of hatching.

Population surveys

We attained redhead breeding population surveys over the same 50-year period, 1960–2009, from the Waterfowl Breeding Population and Habitat Survey data base (Division of Migratory Bird Management, U.S. Fish & Wildlife Service). The analysis was restricted to the strata pertaining to the mid-continent population: 22, 26–49 and 75. A number of post hoc corrections needed to be brought to the raw count data. First, aerial surveys miss some of the birds that are visible to observers on the ground (Smith 1995). For each year and strata, a visibility correction factor is computed and we applied it to the strata-specific count data (these correction factors were treated as constants in our model). Second, many birds (mostly drakes) are recorded as single; following the guidelines based on the knowledge that the adult sex ratio is male-biased in this population, we considered that these birds were unpaired males (the alternative that these birds are the mates of hidden, nesting females is less likely because few nests are initiated before the surveys occur; Sorenson 1991). Thus, the population survey consisted of the count of all redheads seen (pairs, singles and groups of more than two birds), corrected for imperfect visibility and summed over strata.

Age- and sex ratios in the hunters’ bags

We attained redhead age- and sex-ratio data over the period of 1964–2009 (four missing years due to small sample size) from the USFWS. The USFWS computes range-wide age- and sex ratios in the harvest based on the plumage features of duck wings that a subsample of hunters mail back to the service.

Integrated population models: general structure and assumptions

The models were parameterized using:

  • 1 Survival probability S: the probability for a bird to survive for 1 year, starting October 1.
  • 2 Seber’s recovery probability r: the probability for a dead bird to have died from hunting and have been reported as such.
  • 3 Fecundity F: the number of offspring (of both sexes) per female, at the time of banding operations in late summer.
  • 4 Presence on the breeding ground τ: the proportion of 1-year-old (HY) females that are on the breeding grounds during the May survey. At the local scale, Arnold et al. (2002) estimated this proportion to be 0·71 ± SE 0·19 by comparing the detection probability of individually marked females of varying age. Here, we estimated this proportion at the mid-continent scale. We assumed that the remaining fraction of HY females (1−τ) either spent the breeding season in migratory stopover locations, or arrived after the population surveys. We also assumed that all males and all AHY females were present on the breeding grounds in May at the time of the surveys.
  • 5 Population size N: the number of individuals in each sex- and age-specific stage, at the time of the May surveys, and within the boundaries of the survey transects.

Integrated population models can be fit to a wide range of data but several assumptions were required. First, fecundity was measured as the total number, per female that was present on the breeding grounds, of offspring that reached the age at which they could be submitted to banding. Thus, this mixed together several parameters traditionally used in waterfowl productivity studies: breeding probability (probability for a present female to actually nest), nest success (probability for a nest to hatch at least one egg), hatching success (percent eggs hatching from successful nest), brood success (probability for a successful nest to fledge at least one duckling), fledging success (percent ducklings fledged from successful brood), re-nesting probability, as well as survival from fledging up to the date of banding operations. Second, the first-year survival of HY birds was assumed independent of whether or not they had fledged before banding (this assumption was supported by a preliminary analysis indicating that HY survival was not statistically different between pre- and postfledgling HY birds, though Hestbeck et al. 1989 found a ratio of 0·84 between the survival of pre- and postfledgling HY birds in mallards Anas platyrhynchos). Third, all birds within the same age- and sex class were considered equivalent in terms of survival, recovery probability and fecundity. Fourth, immigration and emigration fluxes in and out of the mid continental population were neglected. This was supported, as a first approximation, by the large fraction of the world population that is included in the mid-continent population, as well as by Johnson & Grier (1988) and Arnold et al. (2002); these two studies highlight the high rate of between-year site fidelity.

Model fitting

The philosophy underlying IPMs is to separately construct the likelihood of each data type and then find the maximum of the combined (product) likelihood (Besbeas et al. 2002). Although this method has been presented in detail elsewhere and is now widely in use, we detail below our procedure for building the likelihood.

Likelihood of the CR data

We used the m-array formulation of Seber’s capture–recovery models, as described in, for example Brooks, Catchpole & Morgan (2000) and Schaub et al. (2007). That is, we first computed for each pair of years (i,j), the number mi,j of individuals banded in year i and recovered in year j (= 51 was used for ‘not recovered’). Then we expressed the probability Pi,j of event ‘recovered in year j | banded in year i’ as a function of the time-specific survival and recovery probabilities. Next, the mi,j values were modelled as the realization of a multinomial process with the total number of individuals banded in year i as the number of trials and the probabilities (Pi,j)j1:51 as cell probabilities. The only modification we brought to the standard CR model formulation was that the recovery probability of newly marked AHY birds was modelled separately during the first year after banding relative to following years, to accommodate a potential transient effect because of, for example, some overlap between hunting and banding operations. We modelled the effect of ‘first year after banding’ on recovery probability as an additive component to other considered effects.

Likelihood of the survey data

We constructed a two-age class, sex-specific, prebirth-pulse Leslie matrix model. The state process was thereby (Besbeas et al. 2002; Brooks, King & Morgan 2004; Schaub et al. 2007):

image(eqn 1)

where the subscripts f, m and t stand for ‘female’, ‘male’ and ‘year t’, respectively, and other notations are as above. Because survival was estimated from October to October, but population size was surveyed in May, the HY survival in the above equation corresponded to the 7-month period from October to May, which we accommodated by using inline image, where k stands for either male or female. Demographic stochasticity (not shown in eqn 1) was modelled through a Poisson process for the HY compartments and a binomial process for the AHY compartments (Besbeas et al. 2002; Brooks, King & Morgan 2004; Schaub et al. 2007).

The observation process was assumed to induce a Gaussian noise around the count (eqn 2).

image(eqn 2)

where Yt is the breeding population count in year t, δt is normally distributed with mean 0 and standard deviation proportional to the count θt θ0·Yt (Véran & Lebreton 2008), and θ0 is a parameter to estimate.

Likelihood of the age- and sex-ratio data

Four likelihood terms were involved (female age ratio, male age ratio, AHY sex ratio and HY sex ratio) and were built in a similar way. For the female age ratio, we first computed the expected proportion of HY individuals among females shot by hunters in year t (denoted Af,t), as a function of survival, recovery, presence probability and fecundity.

image(eqn 3)

Then, we modelled the number of HY female wings sent by hunters in year t according to a binomial distribution with the total number of female wings sent by hunters in year t as the number of trials, and Af,t as the success probability. The other three likelihoods were built following a similar method.

Model selection for sex, age and time effects

We first ran a series of three models in which demographic parameters varied with time following a fully varying parameterization (one parameter per year). These three models differed in how age, sex and time effects interacted or added to each other. We considered models AGE*SEX*TIME (the four age- and sex-specific time series varied independently with time), AGE*(SEX + TIME) (the same time variation applied to males and females of a given age class) and AGE*SEX + TIME (the time variation in the different classes was parallel). In these three models, we used the same parameterization for both survival and recovery probabilities. Because the data did not allow the estimation of age-specific fecundity, the models always had a TIME-only structure for fecundity and a constant presence probability for first-year females. We used the deviance information criterion (DIC; Spiegelhalter et al. 2002) to select the preferred model out of the three considered and denote it ‘Model 1’ hereafter.

Temporal covariates

To examine density regulation within the mid-continent redhead population, we used population counts Yt, standardized to a mean of 0 and a standard deviation of 1, as a covariate affecting survival, fecundity, recovery probability or any combination of these parameters. Survival from October 1 of calendar year t to October 1 of year + 1 was regressed against population count in May of year t, and the effect of population count on recovery probability was modelled in similar fashion. The underlying assumption is that population size in May is representative of population density on the wintering grounds during the next winter. Fecundity in breeding season of year t was regressed against population count in May of year t. We used population counts rather than modelled population size Nt as the explanatory variable because of constraints on computational time. Because in our model, population count is a noisy measure of population size, doing this was expected to reduce the statistical power for detecting density dependence (by dragging the absolute value of the regression slope towards zero).

To examine the effect of habitat quality and its interaction with density dependence, we used the counts of pond number that are conducted during the May surveys (presented in Appendix S1, Supporting information). Pond number Pt, standardized to a mean of 0 and a standard deviation of 1, is an indicator of habitat availability (the more ponds, the more nesting locations, food availability, brood habitat, etc.). Survival from October 1 of year t to October 1 of year + 1 was regressed against pond number in May of year t, but we did not consider the effect of pond number on recovery probability. Fecundity in breeding season of year t was regressed against pond number in May of year t.

To examine the effect of changes in hunting regulations, we attained data about bag limit (the number of redheads a hunter is legally allowed to shoot on any given day during the hunting season; Appendix S1, Supporting information), hunting season length and hunting season opening date. These three regulations varied in a dependent fashion both among them and among flyways (ecological and administrative units relevant to hunting regulations). We used only the Central Flyway regulation data because this flyway is the one where many mid-continent redheads spend the winter (along the Gulf of Mexico coasts) and because variation in the hunting regulations of this flyway was for the most part mirrored in other flyways (Appendix S4, Supporting information). Preliminary analyses indicated that only the effect of bag limit was detectable, so we only included that variable in further analyses (see also Conroy, Miller & Hines 2002). Survival from October 1 of year t to October 1 of year + 1 was regressed against bag limit of the hunting season that spans over years t and + 1, and the effect of bag limit on recovery probability was modelled in similar fashion. We did not consider the effect of bag limit on fecundity.

To examine the effect of winter harshness, we used the U.S. state-specific average monthly temperatures, attained from NOAA. For each winter, we computed an average over the lower 48 states and over December to February (presented in Appendix S1, Supporting information) and standardized it to a mean of 0 and a standard deviation of 1. Survival from October 1 of year t to October 1 of year + 1 was regressed against average temperature during winter of year t to + 1, and the effect of winter temperature on recovery probability was modelled in a similar fashion. We did not consider the effect of winter temperature on fecundity, nor did we consider the interaction between winter temperature and May pond number or population counts.

Models with covariates and stochasticity

Departing from Model 1 (see Model selection for sex, age and time effects), we converted all time effects into a mixture of fixed temporal covariate effects (see the previous section) and temporal random effects. The random effects were normally distributed on the link functions scales and corresponded to the temporal variance in demographic parameters not explained by the effect of covariates. Model 2 was the model including all the covariates. Nonsignificant effects were those for which the 95% credible interval on the corresponding parameter included zero. After discarding the nonsignificant covariate effects in Model 2, our final model for making inference was called Model 3.

Bayesian inference

We fit all models in a Bayesian estimation framework using WinBUGS (Spiegelhalter et al. 2003). The likelihood components are assumed independent because banded birds and birds used in age- and sex-ratio computations represent a very small subset of the birds present on the surveyed strata. The product likelihood of the data sets was combined with prior probability distributions to obtain the joint posterior distribution of the parameters. For two of the model parameters (τ and F), normal prior distributions were built using the results of two studies conducted in Manitoba. These studies estimated first-year female breeding propensity to be 0·71 ± sampling SE 0·19 (Arnold et al. 2002) and fecundity to be 4·2 30-day-old ducklings per breeding female ± sampling SE 0·4 (Yerkes 2000). The latter estimate was considered abnormally high (partly because productivity was especially high during the study and partly because only females that built a nest were considered; see also Stoudt 1971). As such, we multiplied the sampling error by ten to obtain a ‘flatter’, less informative prior.

We used uninformative prior distributions for the remaining parameters: normal prior distributions of mean 0 and variance 1000 for the slopes of the regressions, uniform prior distributions between 0 and 1 for θ0, truncated positive normal prior distributions with mean 2000 and variance 10 000 for the initial population sizes, and uniform [0,2] prior distributions for the hyperparameters describing the normal distribution of the temporal random effects in demographic parameters. The latter distribution was chosen based on preliminary analyses indicating that these hyperparameters’ values were all below 1.

We generated two chains of length 200 000, discarding the first 100 000 as burn-in. Convergence of the chains was assessed using the Gelman–Rubin criterion described in Brooks & Gelman (1998), which was below 1·3 for all model parameters. The R package r2winbugs (Sturtz, Ligges & Gelman 2005) was used to call WinBUGS and export results into the R environment (R Development Core Team 2010). A practical note is that the fitting of the various models exceeded 2 months of computer time overall.

Performance assessment of the IPMs

A major caveat regarding IPMs is that if one of the data types is biased then, via the sampling covariance, the bias can propagate to estimate that would not have been affected if the different data types had been analysed separately. However, in the latter ad hoc approach, some estimates are sometimes used as inputs for the computation of other ones, which can cause even greater risk of cascading error and bias. For example, this is the case for the computation of fecundity from age-ratio data, which requires that age specificity in the vulnerability to hunting is accounted for through the use of age-specific recovery probability estimates (obtained from CR data). To address that issue within the IPM framework, we compared the estimated parameter values from three data configurations: (i) using the three types of data, (ii) discarding age- and sex-ratio data and (iii) using CR data only. We examined (i) whether 95% CI intersected, (ii) whether a potential bias in age-ratio data induced a bias in fecundity estimates that cascaded to survival estimates by forcing the compliance with population survey data. Lastly, (iii) we measured the reduction in sampling variance (precision of the estimates; e.g. Péron et al. 2010) in the IPM compared to the ad hoc approach.


Model selection for sex, age and time effects

The DIC-based model selection indicated that the model with a full age, sex and time interaction performed best, given the data [model AGE*SEX*TIME: DIC = 8179·5; vs. DIC of 8344·5 and 8530·8 for, respectively, model AGE*(SEX +  TIME) and model AGE*SEX + TIME]. Parameter estimates for this fully time-dependent population model (Model 1) are presented in Appendix S2 (Supporting information).

Models with covariates and stochasticity

The results from Model 2 (full covariate effect) are presented in Appendix S3 (Supporting information). Based on these results, we excluded: (i) the effect of pond number and average winter temperature on survival (all age and sex classes), and the effect of population size on male survival; (ii) the effect of average winter temperature on recovery (all age and sex classes), and the effect of population size on male recovery; (iii) the effect of bag limit on survival probability (all age and sex classes). The effect of bag limit was however significant for some bag limit × sex × age combinations (Appendix S3, parts A–f, Supporting information). All significant effects were nevertheless positive (indicating a better survival during years with higher bag limit). In addition, they were not consistent, neither between levels of harvest regulations (increasing bag limit did not have an increasing impact), nor between age and sex classes (all classes exhibited different responses to bag limit). Therefore, we considered all bag-limit effects on survival to be spurious and possibly linked to temporal covariance between bag limit and environmental conditions (see Discussion: ‘Perturbations by changes in mortality patterns and possible confounding effects’).

Estimates of demographic parameters at average population size and pond number are presented in Table 1. In the final Model 3, fecundity increased with pond number, but this effect was offset when population size was high (as indicated by the interaction term in Table 2; see also Appendix S4, Supporting information). Female survival decreased with population size (significant in HY birds only; Table 3). Population size also affected female recovery probability (interacting with age; Table 4). Recovery probability increased with bag limit in all sex and age classes (Table 4), suggesting a linkage between harvest regulations and the band recovery process, but not the survival process.

Table 1.   Back-transformed (identity scale) parameter estimates under average conditions of population size and pond number, from Model 3. For fecundity, ‘offspring per female’ stands for the number of duckling of both sexes surviving up to the banding operations in July–September, per female present on the breeding ground in May. ‘Presence of HY females’ stands for the probability for a hatch-year female to reach the breeding grounds before the May survey immediately preceding their first birthday, conditional on survival. For recovery, these values correspond to years with a bag limit of zero (see Table 4). Average population count on the survey area was 7649 individuals and average pond number was 27 618
 MeanSD95% Credible interval
  1. AHY, after hatch year; HY, hatch-year.

 Offspring per female (F)1·4990·1411·242; 1·776
 Presence of HY females (τ)0·5220·0990·404; 0·763
Survival probability (S)
 AHY males0·7070·0090·690; 0·725
 AHY females0·6480·0120·624; 0·669
 HY males0·4470·0230·401; 0·492
 HY females0·4660·0240·419; 0·511
Recovery probability (r)
 AHY males0·0360·0020·031; 0·041
 AHY females0·0210·0020·017; 0·026
 HY males0·0480·0050·039; 0·058
 HY females0·0360·0020·031; 0·041
Table 2.   Parameter estimates for the fecundity submodel (number of offspring of both sexes per female; F) in Model 3. All effects are on the log scale. Nonsignificant effects (95% credible interval encompassing 0) are indicated in italic font. Pond number and population counts were standardized, so that the intercepts correspond to the actual estimated value of demographic parameters at the average conditions of pond number of population counts
 MeanSD95% Credible interval
Intercept0·4000·0940·217; 0·575
Population count 0·063 0·068 0·194; 0·061
Pond number0·4770·0530·39; 0·589
Interaction of population count and pond number−0·1570·063−0·262; −0·024
Time random effect0·1880·0510·11; 0·306
Table 3.   Parameter estimates for the survival submodel (S) in Model 3. All effects are on the logit scale. Nonsignificant effects (95% credible interval encompassing 0) are indicated in italic font. Population counts were standardized. Sex- and age-specific intercepts are omitted for conciseness but are presented (after transformation into the identity scale) in Table 1
 MeanSD95% Credible interval
  1. AHY, after hatch year; HY, hatch-year.

Density dependence (effect of population count)
 AHY females0·065 0·074 0·233; 0·06
 HY females−0·2270·098−0·407; −0·031
Time random effects
 AHY males0·0330·0180·008; 0·076
 AHY females0·0560·0340·014; 0·139
 HY males0·0980·0670·016; 0·262
 HY females0·0490·0330·006; 0·126
Table 4.   Parameter estimates for the recovery probability submodel (r) in Model 3. All effects are on the logit scale. Nonsignificant effects (95% credible interval encompassing 0) are indicated in italic font. Population counts were standardized. Sex- and age-specific intercepts for bag limit of zero are presented (after transformation into the identity scale) in Table 1
 MeanSD95% Credible interval
  1. AHY, after hatch year; HY, hatch-year.

Effect of bag limit 1, shared or not with canvasback (similar species; Aythya valisineria)
 AHY males0·5640·1070·351; 0·768
 AHY females0·6670·1280·407; 0·929
 HY males0·7910·1240·549; 1·041
 HY females1·1510·0970·944; 1·322
Effect of bag limit 2, shared or not with canvasback
 AHY males1·1280·0940·932; 1·323
 AHY females1·2260·1580·894; 1·489
 HY males1·1650·1310·925; 1·431
 HY females1·4110·1221·14; 1·629
Effect of bag limit >2
 AHY males1·1180·1590·751; 1·404
 AHY females1·2370·2200·822; 1·677
 HY males1·6770·1821·349; 2·003
 HY females1·5630·2131·158; 1·954
Density dependence (effect of population count)
 AHY females0·057 0·076 0·202; 0·117
 HY females−0·2770·077−0·432; −0·134
Time random effects
 AHY males0·0380·0170·013; 0·078
 AHY females0·0520·0210·023; 0·105
 HY males0·0960·0390·046; 0·197
 HY females0·0880·0270·05; 0·152

Performance assessment of the IPMs

In all but one case, the 95% CI of parameters estimates from the three considered data configurations broadly intersected (presented and discussed in Appendix S4, Supporting information). There was no apparent ‘cascading bias’ (Appendix S4, Supporting information). We observed, on average over the ten parameters used to describe survival in Model 3, a decrease in the SD of the posterior distribution when using IPMs: −18% when comparing configuration A to C (Appendix S4, Supporting information), −5% when comparing B–C and −7% when comparing A–B. These results indicated that utilizing all of the available data in an IPM framework increased precision in our estimates without inducing significant bias.


By combining three types of data that are usually analysed separately, we could document simultaneously the variation in survival and fecundity of the mid-continent redhead population, in relation to changes in pond number (habitat availability), population size (density dependence) and harvest regulations (bag limit).

Perturbations by changes in habitat availability and model predictions

We found that availability of ponds affected only fecundity. Our data and analysis nevertheless did not allow us to decipher if the relationship was attributed to a direct effect of pond number (or other habitat attributes that covary with pond number) on breeding success per se or on breeding propensity. The interaction of the effect of pond number with the effect of population size on fecundity (Table 2) indicated that the positive influence of pond number could be offset in years of high population size. This suggests that density dependence in fecundity at least partly occurred via competition between females (crowding effects operating at local scales), but we cannot exclude regulation via variation in the use of suboptimal habitats (mechanisms operating at the landscape or larger scale). We also found some evidence for density dependence in female survival, but this was not related to the availability of May ponds.

Using the deterministic part of the matrix population model described in eqn 1, we estimated yearly female population growth rate (Caswell 2000). A large part of the pond number × population count space resulted in a declining population (Fig. 1a), suggesting that, especially when population count was above its temporal average (positive value of standardized population count in Fig. 1), the population was above carrying capacity. This result was congruent with the observed trend in population size over the period 1960–1990 (small-scale oscillations around a long-term stable trend, suggesting a population at carrying capacity), as well as with the more ample variation in population size observed since 1990 (possibly linked to the lasting effect of a series of wet years in the late 1990s and then again in the mid-2000s). Years with high pond numbers (standardized value above 1 in Fig. 1) were likely to produce ‘population booms’, such as recorded in 1999 (1998 being the year with highest number of pond). Overall, density regulation was strongest in wet years (standardized pond number above 0 in Fig. 1a), but mostly because drought years (standardized pond number below −1 in Fig. 1a) were always years of decline independently of population size. We note that such conclusions are limited by the absence in the data set of the combination ‘low pond number – high population size’. Our results nevertheless set the stage for developing more intricate population models and further investigating the implication of compensatory density dependence for population dynamics in redheads and other species. In particular, field crews distinguish ‘singles’, ‘groups’ and ‘pairs’, the latter being assumed to represent the breeding segment of the population, while others could be nonbreeders; this structure of the population survey data could be used to estimate temporal variation in parameter τ and provide deeper insight into the redhead reproductive strategy.

Figure 1.

 Female-only, prebreeding census, deterministic matrix population model based on the results of the integrated population model for mid-continent redheads. (a) Population growth rate. (b) Sensitivity of population growth rate to change in pond number. (c) Sensitivity of population growth rate to change in population count (density dependence). Population size and pond number have been standardized (mean of zero and standard deviation of one). Prediction standard errors are omitted for clarity.

Perturbations by changes in mortality patterns and possible confounding effects

Harvest regulations such as bag limit constitute a proxy for the realized hunting pressure, and they constitute the variable upon which managers can act (Johnson & Moore 1996; Conroy, Miller & Hines 2002). However, numerous other factors, from hunter numbers and behaviour, to epidemic disease outbreaks and variation in landscape features also play a role in shaping the actual proportion of deaths that is attributable to hunting (partial controllability; Nichols et al. 2007). Our result that bag limit did not correlate with survival in the expected negative direction, but was positively correlated with recovery probability as predicted, nevertheless suggests that under past hunting regulations, a large part of the variation in hunting-related mortality was compensated by decreases in others sources of mortality (Burnham & Anderson 1984; G. Péron, unpublished analysis). However, our analysis did not account for a probable effect of bag limit on hunters’ reporting behaviour. Indeed, in years with low redhead bag limit but higher limits for other duck species, hunters may inadvertently shoot redheads and be reluctant to report the bands found on these birds. Thereby, the observed effect of bag limit on recovery probability might at least partly stem from an effect of bag limit on reporting rate rather than on hunting pressure.

Compensation for hunting mortality is often thought to be linked to density dependence: in years with higher than average hunting pressure, population density is artificially lowered on the wintering grounds, enabling the individuals that escape hunters to experience lower natural mortality (Burnham & Anderson 1984). The lack of strong density dependence in redhead survival (especially in males) suggests that the lack of effect of bag limit on survival stems either from an inability of bag limit regulation to effectively modify hunting pressure, or from compensatory mechanisms other than density dependence (e.g. individual heterogeneity in vulnerability to hunting). However, note that our measurement of density dependence in survival was based on a measure of spring population size (before breeding) and may not have been representative of population density during the winter. A more precise alternative would have been to first model the transition from spring to autumn, then estimate the effect of autumn population size on survival from one autumn to the next–this analysis was however computationally prohibitive.

With respect to our results, we can furthermore point to several possible confounding factors. First, during all but three consecutive years, bag limit was ≤2. This limited variation in bag limit potentially lent more importance to variation in factors other than hunting regulation. Second, the decision for setting bag limits is in part based on the results of the May survey. Thus, even if there is considerable variation in population size that is not directly translated into variation in bag limit, the fact that bag limit and population size covaried positively is of concern. In addition, the power to test the effect of hunting closures (bag limit of zero) is compulsorily low (low number of recoveries), which was enhanced by the fact that all five closed seasons occurred at the beginning of the study period, when the number of ‘available’ banded birds was lower.

Link with waterfowl life history and management

Within Anatidae, the Aythya life-history strategy is close to the ‘bet-hedging strategy’ (Saether & Bakke 2000) of producing large number of offspring in occasional good years (Yerkes 2000). In other words, females are thought to capitalize on survival to experience at least one good year with good reproductive output in their lifetime. Our results tend to confirm this. First, the fecundity estimate was relatively low under average conditions but varied with the number of ponds and density. This suggested that redhead females were adjusting their breeding effort to encountered conditions, possibly by modulating their use of typical nesting as opposed to parasitic egg laying (Sorenson 1991). Second, the between-year variation in survival probability was moderate (Table 3: back-transformed estimates of temporal variation in survival indicate a temporal SD of less than 5% of the intercept value of survival in all age classes). This suggested the occurrence of environmental canalization as observed in bet-hedging, long-lived species (Gaillard & Yoccoz 2003; Nevoux et al. 2010). Given the large 95% CI on the estimates of temporal variation in redhead survival (Table 3), caution is however needed with such an interpretation. Bringing support to that theory, however, Sorenson (1991) found that during a local drought (1988 breeding season), the rate of parasitic egg laying by redhead females increased more than twofold, and the rate of skipping reproduction increased more than threefold, with a corresponding decrease in typical nesting behaviour. The less energetically costly (as well as less predation risky) behaviours were thereby predominant when breeding success prospects were lowest, as expected within the bet-hedging life-history strategy. Third, a high proportion (estimated 48%) of first-year females apparently did not breed during their first year. This is coherent with an overall pattern of a slower life history (Koons et al. 2006 in lesser scaup Aythya affinis) than, for example similarly sized mallard, in which most females attempt to breed at 1 year of age and repetitively attempt to re-nest after failure (Hoekman et al. 2002). HY redhead females may exhibit a slower spring migration than AHY females and thus arrive on the breeding grounds after the May surveys (Naugle et al. 2000), thus the low τ estimate, but this interpretation needs confirmation.

It has been previously found in other North American waterfowl that fecundity is an important driver of population dynamics. In declining populations of pintails Anas acuta and black brant Branta nigricans, survival is not the cause of the decline (respectively, Rice et al. 2010 and Sedinger et al. 2007), leaving fecundity responsible (because at the large spatial scales of the mentioned studies emigration and immigration are negligible). Similarly, most temporal variation in mid-continent mallard population growth rate is explained by changes in offspring production (Hoekman et al. 2002). In the mid-continent redhead population, population booms driven by fecundity were possible in very wet years (Fig. 1). However, smaller scale changes in pond numbers were largely compensated for by density dependence in fecundity, suggesting that the population typically fluctuates around its carrying capacity. Consequently, 10-year projections of the population trajectory based on auto-regressive predictions of pond number indicated a stable population size (result not shown). Overall, our study illustrates the insights that can be gained from a combined analysis of all demographic parameters in relation to environmental variables and density. Such insights can help document life-history variation and bring support to life-history theories (Gaillard et al. 1989; Pfister 1998; Saether et al. 2005) as well as be used to refine population models used in management schemes (McGowan et al. 2011). Our modelling approach seems especially useful for guiding the dual management of harvest regulations and landscape conservation policies for exploited species (Runge et al. 2006; Mattsson et al. 2012).


G.P. was supported by a Quinney post-doctoral fellowship. We are grateful to Todd W. Arnold and James D. Nichols for comments on an earlier version of this article.