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Lesser Scaup Population Dynamics: What Can Be Learned from Available Data?
^{1}Montana State University, ^{2}Canadian Wildlife Service, ^{3}Institute for Wetland and Waterfowl Research, ^{4}Ontario Ministry of Natural Resources, ^{5}U.S. Fish and Wildlife Service, ^{6}University of Wyoming
Les populations de Petit Fuligule (Aythya affinis) montrent un déclin marqué en Amérique du Nord depuis le début des années 1980. Lorsque l'on considère les options permettant de redresser la situation, il serait utile de comprendre la relation fonctionnelle entre le taux d'accroissement de la population et les taux vitaux, de même que les taux vitaux qui affectent le plus ce taux d'accroissement (qui sont présumément ceux qui ont entraîné le déclin historique des effectifs). Afin d'établir un fondement quantitatif pour comprendre l'histoire naturelle et la dynamique des populations de Petit Fuligule, nous avons compilé les estimés (publiés ou non) de taux vitaux mesurés entre 1934 et 2005 et développé à partir de ces données des modèles matriciels de cycle de vie pour les femelles nichant dans la forêt boréale, la forêtparc des prairies et les deux régions combinées. Ensuite, nous avons utilisé l'analyse des perturbations afin d'évaluer les effets de changements dans divers taux vitaux sur le taux intrinsèque d'accroissement des populations et l'abondance. Comme chez le Fuligule milouinan (Aythya marila), le taux d'accroissement des populations obtenu pour le Petit Fuligule était particulièrement sensible aux variations unitaires ou proportionnelles du taux de survie des femelles adultes durant la saison de nidification ou le reste de l'année, mais beaucoup moins sensible aux variations des paramètres de fécondité. Curieusement, le taux d'accroissement des populations était aussi très sensible aux variations unitaires ou proportionnelles du succès d'éclosion moyen et des taux de survie des canetons ou des juvéniles. Étant donné les faibles effectifs d'échantillons disponibles pour certains aspectsclé du cycle de vie du Petit Fuligule, nous recommandons que des travaux additionnels soient effectués sur les taux vitaux qui ont une influence majeure sur l'accroissement des populations et leur effectif (ex. taux de survie des adultes). Nos modèles de cycle de vie devraient être testés et mis à jour régulièrement afin de guider l'étude et la gestion des populations de Petit Fuligule dans un contexte adaptatif.
Breeding numbers of Lesser and Greater Scaup (Aythya affinis and A. marila), which are surveyed collectively, have declined markedly since the early 1980s and, in 2006, the continental estimate was 48% below the North American Waterfowl Management Plan (NAWMP) goal of 6.3 million scaup (Wilkins et al. 2006). Greater Scaup primarily breed in Alaska and tundra regions of northern Canada (Kessel et al. 2002) where scaup numbers have remained stable or increased since the early 1980s (Afton and Anderson 2001). Scaup numbers have also remained stable on the prairies and most parts of the parkland region, which are breeding grounds for Lesser Scaup but not Greater Scaup (Afton and Anderson 2001). Much of the decline in scaup numbers has occurred in Canada’s western boreal forest and isolated parts of the parkland region where primarily Lesser Scaup breed (Austin et al. 1998, 2000, Afton and Anderson 2001, Koons and Rotella 2003a). Waterfowl biologists and managers strive to understand what can be done to reverse this trend and increase abundance of Lesser Scaup (Austin et al. 2006, Wilkins et al. 2006). Although general lifehistory information exists (e.g., Afton 1984, Austin et al. 1998), there is no published model of the Lesser Scaup life cycle. The potential uses of lifecycle models are many (see Caswell 2001). For example, parameterization of a lifecycle model forces an objective examination of the amount and quality of existing demographic data (e.g., sample size, spatial and temporal coverage, etc.), which helps identify information gaps. Lifecycle models also help managers and scientists understand how vital rates (e.g., clutch size, duckling survival, adult survival, etc.) and age structure affect population abundance and growth rate. Crude predictions about these functional relationships can be derived from basic attributes of a species’ life history (Sæther and Bakke 2000). Compared with rates for prairie dabbling ducks such as the Mallard (Anas platyrhynchos) (Hoekman et al. 2002), reproductive effort (e.g., renesting probability) and net fertility may be much lower for Lesser Scaup (Trauger 1971, Afton 1984). Thus, given avian lifehistory patterns (Sæther and Bakke 2000), we might predict that adult female survival should be an important determinant of population growth rate in Lesser Scaup, as was found for Greater Scaup breeding in Alaska (Flint et al. 2006). However, such a prediction could be tenuous for a declining population (Mertz 1971), variable environments (Tuljapurkar 1990), or when vital rates covary with one another (Caswell 2000, van Tienderen 2000), all of which may apply to Lesser Scaup. By generating a lifecycle model, it is possible to more objectively develop and explore alternative hypotheses about which vital rates and age classes contribute most to population dynamics. Without a guiding population model, it is not obvious which management tool might be employed most effectively (e.g., habitat conservation, habitat manipulation, harvest regulation, predator management, or various combinations) to reverse population declines by targeting specific vital rates. Prospective analysis of a lifecycle model developed from available lifehistory data can be used to estimate the effect of hypothetical changes in various vital rates on the short or longterm rate of population growth in a constant environment (Caswell 1978, Yearsley 2004, Koons et al. 2005), a variable environment (Tuljapurkar 1990, Doak et al. 2005), as well as the effects of alterations to age structure on short and longterm population size (Fox and Gurevitch 2000, Koons et al. 2006a,b). Such information provides insight as to which aspects of the life cycle are the most appropriate targets for management (e.g., Akæakaya and Raphael 1998, Cooch et al. 2001, CluttonBrock and Coulson 2002), with the confidence in inferences contingent on the quality of available data. To provide a basis for understanding Lesser Scaup population dynamics, we summarize the available lifehistory data between 1934 and 2005 in the form of matrix lifecycle models (Caswell 2001) for Lesser Scaup breeding in the boreal forest, the prairieparklands, and both regions combined using all available data. We used lifecycle perturbation analysis to evaluate the functional contribution of the various vital rates, variation in vital rates, and age structure to finite population growth rate and abundance. Using the model, we were able to identify important data limitations and prioritize vital rates for which future research is needed to guide management using a more biologically informed approach. Vital Rate Data We developed a comprehensive vitalrate database for Lesser Scaup by extracting estimates from government reports and the peerreviewed literature published between 1934 and 2005. We also included unpublished estimates from recent and ongoing studies (RGC, SS). For each study, we recorded years of study, vital rates estimated, estimated vitalrate statistics (mean, precision, and sample size), methods used, and region (boreal forest or prairieparkland). When reported, agespecific variation in a vital rate was also recorded. If reported estimates were pooled across years (i.e., yearspecific estimates were not provided), we used the pooled estimate for a given study location as a datum point. When estimates were provided for each year of study, we recorded the timespecific estimates for each study location as data points because we were interested in estimating variation in vital rates across time and location. If a particular pooled or timespecific estimate of a vital rate appeared in multiple publications, we only recorded the estimate once to avoid duplicates. To develop databased lifecycle models for Lesser Scaup, we calculated the weighted mean of each vital rate across all study locations and years for the boreal forest (eight study locations, 1951–2005), prairieparklands (16 study locations, 1934–2001), and for the composite of both regions (24 study locations, 1934–2005). We calculated weighted means using two different methods. For each region, we first calculated vitalrate means by weighting each datum point equally, and then by weighting each datum point by the reported sample size. For each vital rate, we then took the biaverage (i.e., the arithmetic mean) of the two weighted estimates and used this mean in the lifecycle models. For the two regions combined, we calculated the total variance of a vital rate across all study locations and years using standard methods. When ≥4 data points were available for a vital rate (all vital rates except juvenile survival), we estimated the vitalrate process variation (σ^{2}_{process}) using variancedecomposition methods described in Burnham et al. (1987). This method involves 1) estimating overall variance of mean estimates across studies, 2) using standard errors from each study to estimate the proportion of 1 that is due to sampling error, and 3) subtracting 2 from 1 to yield σ^{2}_{process}. We believed that existing vitalrate sample sizes within each of the boreal forest and prairieparkland regions were generally too small to calculate process variation of the vital rates on a regionspecific basis. Model Structure and Parameters We approximated the annual life cycle of female scaup breeding in the boreal forest (BF), prairieparklands (PP), and composite (CP) of all data using matrix models (A) with two stages indicative of age:
where F_{s} and P_{s} represent stagespecific fertilities and survival probabilities, respectively, and the superscript on A denotes the region that the model represents (Caswell 2001). The number of stagespecific vital rates appearing in our models was based on evidence of agerelated variation reported in the published documents, primarily based on Afton (1984). The two stage classes were 1) females entering their second calendar year of life (SY; i.e., individuals are just shy of their first birthday when censused) and 2), older females, which we denote as “after second year” females (ASY). We focused our modeling efforts on females because sex ratio data indicate that they are the limiting sex (Afton and Anderson 2001). The matrix models were parameterized with a prebreeding census (conducted in May) assuming birthpulse reproduction (Caswell 2001). We used stagespecific values for a vital rate if available data indicated agerelated variation in that rate. We parameterized all lifecycle models using a set of vital rates that we believe are relevant to Lesser Scaup life history and meaningful to waterfowl management (Rockwell et al. 1997). Specifically, we calculated per capita fertility for females in stage class s as:
which assumes a maximum of two nesting attempts and allows renesting only if the first nesting attempt fails. In this equation, 0.5 accounts for the female offspring only (assuming a 50:50 sex ratio at birth), BP_{s} is the breeding probability of females in stage s (i.e., the proportion of mature females that nest in a given year); BS represents breedingseason survival for both SY and ASY females; CS_{s} is the clutch size of females in stage s; NS is nesting success (i.e., the proportion of nests that hatch at least one egg); RP_{s} represents the renesting probability for females in stage s (i.e., the probability of producing a second clutch given total failure of the first clutch); DS is duckling survival (i.e., the proportion of ducklings that survive to fledging); and JS represents juvenile survival (the proportion of fledged ducklings that survive to the prebreeding census in May). We converted Apparent NS estimates to approximate Mayfield estimates using the Green conversion (Mayfield 1975, Green 1989, see especially Johnson 1991) so that all estimates were comparable. We calculated the probability of annual survival for females in each stage as:
where NBS represents the probability of surviving the nonbreeding season for both SY and ASY females. In practice, NBS was calculated as NBS = P_{s} / BS (Rotella et al. 2003; RGC unpublished data). The fertility equation presents the pathway through which individuals can be recruited into the SY stage during each time step. The complexities of the F_{s} and P_{s} transition equations were based on empirical data. We included BS within the fertility equation because we believe that females must survive the breeding season to fledge young, and we were interested in evaluating the impact of female mortality during the breeding season on population dynamics. By its presence in the fertility equation, BS accounted for nests that failed and ducklings that died due to mortality of breeding females. Available estimates of NS and DS were obtained from studies that did not distinguish nest or duckling losses due to female mortality from other sources. Thus, it was necessary to increase the mean NS and DS estimates in the models to avoid underestimating fertility (Hoekman et al. 2006). It was not necessary to adjust estimates of RP_{s} because available estimates were derived from females that survived the breeding season (A. D. Afton, personal communication). The appropriate adjustments to NS and DS were achieved by dividing NS by the probability of females surviving the nesting period and DS by the probability of females surviving the broodrearing period. To approximate these periodspecific estimates of BS for each region, we used a proportional hazards model (Agresti 1990, Cox 1972). The ratio of the hazard for the broodrearing period relative to that for the nesting period was estimated from survival probabilities for these two periods reported in Koons and Rotella (2003b). The resulting mean values of NS and DS used in our models were 18%–19% and 6% greater, respectively, than the biaverages estimated from available data (Table 1). Based on published evidence of agerelated variation in Lesser Scaup vital rates, we only used stagespecific values for BP_{s}, CS_{s}, and RP_{s}. We used composite estimates, pooled across ages, for the remaining demographic parameters (Table 1). The decision was straightforward for all rates except NS. Using Afton’s (1984) data, we developed NS estimates for SY (0.26, 95% CI = 0.13 to 0.42) and ASY females (0.33, 95% CI = 0.23 to 0.43). Given that these confidence intervals were largely overlapping, we did not believe that use of separate estimates was warranted, although we acknowledge that agerelated variation may exist. To approximate stagespecific estimates of CS_{s} for each region, we assumed that CS_{ASY} was 1.86 eggs greater than CS_{SY} as in Afton (1984). Analysis of Deterministic LifeCycle Models We developed deterministic matrix lifecycle models for each region, A^{BF}, A^{PP}, and A^{CP}, by parameterizing each model with the relevant mean values of each vital rate (Table 1), and adjusted NS and DS according to the method described above. We assumed densityindependent vital rates, a stable stage distribution, and no (co)variation among the vital rates over time (i.e., constant environments). For each model, we calculated λ_{1}, the population’s finite rate of growth in a constant environment, as the dominant eigenvalue of each matrix model. The projected stable stage distribution and stagespecific reproductive values were calculated with the corresponding right w_{1} and left v_{1} eigenvectors, respectively (Lefkovitch 1965, Caswell 2001). Although densitydependence should be incorporated into models designed for making longterm forecasts about population growth and abundance, empirical information about density regulation of Lesser Scaup vital rates is lacking (Boomer and Johnson 2005). Rather than attempting to make forecasts about Lesser Scaup population dynamics, our main objective was to estimate the functional relationship between vital rates and population growth rate with sensitivities and elasticities. Fortunately, densityindependent population models can provide accurate estimates of vitalrate sensitivities and elasticities for both densityindependent and densityregulated populations (Grant and Benton 2000, Caswell 2001). To measure the effect of changes in each vital rate on λ_{1}, we calculated the sensitivity of λ_{1} to unit changes in the lowerlevel vital rate means θ_{v} (e.g., NS) using chainrule differentiation (Caswell 1978):
where a_{ij} is the i, jth entry of A^{k} (e.g., F_{ASY}). Furthermore, we calculated “elasticities” as the sensitivity of λ_{1} to proportional changes in the lowerlevel vital rates (Caswell et al. 1984, de Kroon et al. 1986):
Elasticities measure the proportional change in λ_{1} resulting from a proportional change in θ_{v} and provide for a straightforward ranking of the functional contribution of the different vital rates to λ_{1}, given the data and modeling assumptions (de Kroon et al. 1986, 2000, Horvitz et al. 1997, but see Link and Doherty 2002). Nevertheless, sensitivities and elasticities are derivatives, and thus give the “local” slope of population growth rate as a function of a vital rate at its estimated mean value. Several of the vital rates used in our models were estimated from just a few studies (e.g., BP and RP) and others could be biased (e.g., annual survival probability). Because population growth rate is a nonlinear function of vital rates, sensitivities and elasticities could change if estimates of the underlying vital rates were substantially different. To test the robustness of sensitivities and elasticities to perturbation size and vital rate values, we examined the slope of population growth rate across a large range of absolute (±0.5) and proportional (±50%) changes in the vital rates for the composite model (de Kroon et al. 2000). Because (st)age structure is generally not expected to be stable to current vital rates if environmental conditions or harvest rates have recently changed (Hauser et al. 2006), we evaluated how unstable stage distributions might affect Lesser Scaup population dynamics. Using the same set of vital rates (A^{CP}), we projected dynamics forward in time from initial stage distributions n(0) ranging from all SY to all ASY individuals with the following equation:
where n(t) is a 2 × 1 vector representing abundance of SY and ASY females at time t, respectively. The total abundance in each of the initial populations was the same. For each projection, we numerically measured the time required for the stage distribution to converge to the stable stage distribution, after which λ_{1} becomes the population growth rate (Caswell 2001). Before this time, an unstable stage distribution causes transient fluctuations in the population growth rate (see Koons et al. 2005). We also measured the relative effect of unstable stage distributions on longterm population size using Tuljapurkar and Lee’s (1997) stable equivalent ratio (SER):
where  _{1} indicates the 1norm (i.e., the vector sum) and the subscript stable denotes projection from the stable stage distribution. Thus, the SER measures the actual longterm population size projected from any stage distribution relative to that from an initially stable population (Tuljapurkar and Lee 1997), and is very similar to population momentum (Keyfitz 1971, Koons et al. 2006a,b). Analysis of a Stochastic LifeCycle Model Constant environments are not likely to occur in nature (Fox and Gurevitch 2000). Rather, vital rates and (st)age distribution fluctuate over time as environmental conditions change. To examine the consequence of temporally fluctuating vital rates and stage distribution on population dynamics, we developed a stochastic version of the composite model (A^{CP}(t)). We did this by first generating probability distributions for each vital rate according to its estimated mean and process standard deviation: σ_{process} = √(σ^{2}_{process}). For modeling purposes, we assumed that process variation for both BS and NBS were equivalent to that calculated from annual survival probabilities. We assumed equivalent process variation across the two stage classes for the stagestructured vital rates (i.e., BP_{s}, CS_{s}, and RP_{s}). Furthermore, because just two estimates of JS existed, we assumed that the process standard deviation of JS was twice that of the adult survival parameters. Because all vital rates except clutch size were probabilities bounded between 0 and 1, we assumed that they conform to a Beta distribution and that clutch size parameters conform to a stretched Beta distribution. We then generated a time sequence of 100 000 randomly selected values for each vital rate from its Beta or stretchedBeta distribution. Because information on correlation amongst the vital rates did not exist, values for each vital rate were selected independently. Next, we generated a sequence of timespecific matrices composed of the randomly selected vitalrate values and projected the population forward in time from an arbitrary initialstagedistribution:
We used this stochastic sequence of population dynamics and discarded the first 10 000 time steps to estimate the stochastic population growth rate (Heyde and Cohen 1985, Caswell 2001:396):
where r(t) = log(n(t + 1)_{1} / n(t)_{1}) and T = 100 000. We also estimated the variance of these r(t) values. Ergodic theorems of random matrix products assure us that any stochastic projection of a Markovian model will approach λ_{s} as t → ∞ (Furstenberg and Kesten 1960, Oseledec 1968). We estimated the stochastic analogues of stable stage distribution and reproductive value using the procedure laid out in Caswell (2001:402–407; see also Tuljapurkar 1984, 1990). In a stochastic environment, the sensitivity and elasticity of λ_{s} to changes in the lowerlevel vital rates (θ_{v}) cannot be found using chainrule differentiation. Fortunately, Caswell (2005) recently derived formulas for these perturbation measures. Based on Caswell’s formulas, we calculated the sensitivity of λ_{s} to unit changes in the θ_{v} as:
and the elasticity of λ_{s} to proportional changes in the θ_{v} as:
We also estimated the sensitivity of λ_{s} to unit changes in the temporal variation of each vital rate using the process standard deviations and methods developed by Doak et al. (2005):
where σ_{v, process} is the process standard deviation of vital rate v (i.e., of θ_{v}), subscript x denotes any other vital rate, and ρ_{v,x} is the correlation coefficient between vital rates v and x. In Eq. 12, λ_{1}, S_{v}, and S_{x} are all measured from the deterministic lifecycle model A^{CP} (parameterized with mean vitalrate values) defined above. The elasticity analogue of Eq. 12 was approximated as:
and together, Eqs. 12 and 13 are useful for examining the effect of changes in the actual or estimated level of temporal variation in a vital rate on λ_{s}. Because we did not include correlation structure among vital rates in the stochastic model, the ρ_{v,x} term equals 0 and cancels out the summation term on the far righthand side of these equations (Doak et al. 2005). Deterministic LifeCycle Models For many vital rates, only a single estimate was available within each region, whereas many estimates were available for other vital rates (e.g., prairieparkland NS: n = 41; (Table 1)). Estimates of agestructured vital rates were largely derived from a single study within the prairieparklands (Afton 1984). Too few estimates of BP_{s}, adult annual survival, BS, and thus NBS, were available to make robust comparisons across regions. In general, vitalrate estimates from studies conducted in the boreal forest were similar to those from the prairieparklands, but mean values of CS_{s}, DS, and NBS in the boreal forest were lower (Table 1). The projected population growth rates for the boreal forest, prairieparkland, and composite lifecycle models were vastly different (λ_{1} = 0.79, 1.06, and 0.97 respectively), but each model was parameterized with data coming from a diverse spatial and temporal setting. Thus, these estimates of population growth rate are not representative of actual breeding populations. Nevertheless, the underlying dynamics related to population growth rate provided general insight into the demography of Lesser Scaup for each region. For example, the low population growth rate of the boreal forest model led to a stable stage distribution (w_{1}) that was skewed more toward ASY individuals, w_{1}^{BF} = (0.33, 0.67), relative to estimates for the prairieparkland and composite models: w_{1}^{PP} = (0.43, 0.57), w_{1}^{CP} = (0.38, 0.62) (note that each w_{1} should be a column vector). Estimated reproductive values (v_{1}) were similar across the three models: v_{1}^{BF} = (0.46, 0.54), v_{1}^{PP} = (0.45, 0.55), and v_{1}^{CP} = (0.46, 0.54). Because each lifecycle model had a different λ_{1}, the sensitivity and elasticity values for each vital rate necessarily differed across models. The qualitative pattern (i.e., ranking) of vitalrate sensitivities was very similar across models, and the pattern of vitalrate elasticities was identical for all three models (Table 2). For each lifecycle model, λ_{1} was always most sensitive to unit and proportional (indicated by elasticities) change in BS followed by NBS, except in the prairieparkland model where the sensitivity for NBS was ranked 3^{rd} and that for NS was ranked 2^{nd}. Except for the prairieparkland model where λ_{1} was highly sensitive to unit changes in NS, λ_{1 }was moderately sensitive to unit and proportional changes in the offspring survival vital rates (i.e., NS, DS, and JS). Although λ_{1} was always more sensitive to unit and proportional changes in the fecundity vital rates (BP_{s }, CS_{s }, and RP_{s}) of the ASY stage relative to those for the SY stage, λ_{1} was much less sensitive and elastic to changes in these vital rates compared with adultsurvival and offspringsurvival vital rates (Table 2). In addition, the slope of the relationship between population growth rate and each vital rate was nearly constant across a wide range of unit or proportional changes in each vital rate (Fig. 1), indicating that estimates of sensitivity and elasticity were quite robust to large deviations (e.g., bias) in vitalrate values (Fig. 1). Projections from initially unstable stage distributions with the A^{CP} model indicated that even initial stage distributions consisting of all SY, or all ASY individuals would reach nearexact convergence by the 5^{th} time step (equal to stable stage distribution in the 4^{th} decimal place; (Fig. 2)). Therefore, the effect of an unstable stage distribution on future stage distribution and population growth rate is expected to be short lived. However, large deviations from the stable stage distribution could have a substantial effect on population size. For the A^{CP} model, initially unstable stage distributions led to longterm population sizes that were as much as 10.4% smaller (SER = 0.896) and 6.4% greater (SER = 1.064) than that for a population with an initially stable stage distribution (Fig. 3). Stochastic LifeCycle Model For some vital rates, process variation was estimated from just a few data points (e.g., BP_{s} and RP_{s}), and for other vital rates it was estimated for many data points (e.g., CS_{s} and NS; (Table 1)). The process variation of JS could not be estimated because just two estimates existed (see Methods for assumed value). Therefore, the stochastic lifecycle model for the composite of both regions (A^{CP}(t)) was based on limited information about the process variation of several vital rates (Table 1). As expected, the projected population growth rate in a temporally stochastic environment was lower (λ_{s} = 0.906, 95% CI: 0.903 to 0.908) than in a constant environment (λ_{1} = 0.97). Yet, the large amount of processvariation in the underlying vital rates makes it difficult to actually predict future population growth rate (95% prediction interval: 0.45 to 1.81; see Neter et al. 1996 for definition of prediction interval). The stable stage distribution in a stochastic environment was skewed more toward ASY individuals (0.31, 0.69), and the reproductive values were similar (0.47, 0.53) to those for the deterministic model (A^{CP}; see above). In addition to reducing population growth rate, the introduction of temporally fluctuating vital rates into the composite model generally reduced the sensitivity and elasticity values as well. However, the NS and NBS stochastic sensitivity values, as well as the NBS stochastic elasticity value, were actually higher than the corresponding deterministic values (Table 2). Nevertheless, the qualitative patterns (i.e., ranking) of vitalrate sensitivities and elasticities were identical for the stochastic and deterministic lifecycle models (Table 2). The sensitivities and elasticities of λ_{s} to changes in σ_{v, process} were all negative, indicating that increased σ_{v, process} decreased λ_{s} (and vice versa). Furthermore, the absolute value of these sensitivity and elasticity values was smaller than corresponding values for changes in θ_{v}, indicating that change in σ_{v, process} had a smaller functional effect on λ_{s} than changes in θ_{v} (Table 2). Nevertheless, on top of the important effect that change in NS and BS had on λ_{s}, λ_{s} was moderately sensitive to changes in temporal variation of NS and BS as well (Table 2). By summarizing available demographic vital rates, we identified gaps in our knowledge of Lesser Scaup life history and population dynamics, and estimated the potential impact of changes in demographic statistics on population growth rate and size. Our estimates of the sensitivity and elasticity of the projected population growth rate to changes in mean values of vital rates were similar across models (i.e., boreal forest, prairieparkland, and composite), and were robust to large deviations in vitalrate values (Fig. 1) as well as the inclusion of temporal variability in the vital rates (Table 2). Sensitivities also indicated that including small amounts of correlation structure among vital rates would have a negligible effect on stochastic growth rate (unpublished results; method described in Doak et al. [2005]). Therefore, even our simple deterministic models, where we assumed constant vital rates and no correlation among vital rates, can provide a great deal of insight into Lesser Scaup population dynamics. Nevertheless, large departures from a stable (st)age distribution could have an important impact on population abundance (Fig. 3), which cannot be predicted from vital rates alone (Keyfitz 1971). Thus, managers should develop ways to reduce uncertainty in age structure (e.g., harvest age ratios) and assess its potential impact on population dynamics (e.g., Hauser et al. 2006, Koons et al. 2006a). Our sensitivity and elasticity analyses provided compelling evidence that changes in the mean value of both breeding and nonbreedingseason survival of adult females would have strong impacts on Lesser Scaup population growth (Table 2). Increased temporal variation of breedingseason survival would have a detrimental impact as well (Table 2) (temporal variation of a vital rate could be affected by global warming, change in habitat or predator community, etc.). Published capturemarkrecapture estimates of annual survival for adult female Lesser Scaup breeding in the Canadian parklands (Rotella et al. 2003) are 25% lower than capturemarkrecapture estimates for Greater Scaup breeding in Alaska (Flint et al. 2006). In addition, estimates of Lesser Scaup breedingseason survival are low compared with other duck species (Koons and Rotella 2003b, Rotella et al. 2003, Brook and Clark 2005), and evidence from the parklands indicates that it is especially costly for females to attend nests where a number of predators pose a threat to their survival (Afton 1984, Koons and Rotella 2003b). During the nonbreeding season Lesser Scaup must survive two migrations, hunting, and harsh weather conditions in order to breed again. Unfortunately, there is a great deal of uncertainty in estimates of Lesser Scaup survival at the continental scale, and the effects of hunting on Lesser Scaup survival (i.e., additive vs. compensatory) are poorly understood (Boomer and Johnson 2005). Recent unpublished data, however, indicate no relationship between harvest rates and annual survival probabilities since the 1950s (C. A. Nicolai, J. S. Sedinger, A. D. Afton, and C. D. Ankney unpublished data). Nevertheless, increased banding efforts at several times of the year, and across a wide spatial scale, are needed to improve our ability to more precisely estimate seasonal survival of Lesser Scaup, and thus improve our knowledge of population dynamics. Our sensitivity and elasticity analyses also indicated that changes in the mean value of nesting success, duckling survival, and juvenile survival would strongly affect Lesser Scaup population growth rate, and increased temporal variance of nesting success would have a deleterious impact (Table 2). The landscape that these birds use for breeding, migrating, and wintering has undergone considerable anthropogenic change, which may have altered vital rates. Climate and habitat change in the boreal forest, decreased quality of food resources on wintering and spring stopover areas, accumulation of contaminants, and harvest have all been proposed as possible factors contributing to the decline in Lesser Scaup numbers (Austin et al. 2000, Afton and Anderson 2001). However, we do not know how these factors affect the mean level, (co)variation, and density dependence of the aforementioned vital rates across space and time, especially those affecting adult females and eggs at the nest site. Therefore, if we are to understand factors limiting Lesser Scaup population growth, and design effective conservation actions to overcome these limitations, we must understand which of the vital rates are currently constrained and why. In addition to being a useful tool for examining population dynamics and guiding management, population models also serve as a powerful tool for learning about lifehistory evolution (Roff 1992, Stearns 1992). For example, the population growth rate of arcticnesting geese is much more elastic to changes in adult survival than to changes in net fertility (Rockwell et al. 1997, Schmutz et al. 1997, Cooch et al. 2001), indicating that they have evolved a “slow” life history adapted to low rates of reproduction but long lifespan (see Sæther and Bakke 2000). The population growth rates of Northern Pintails (Anas acuta) and Greater Scaup breeding in Alaska are more elastic to changes in adult survival than to changes in net fertility, but the difference between these elasticities is not as great as in the geese (Flint et al. 1998, 2006). At the other end of the spectrum, the population growth rate of Mallards breeding at lower latitudes is highly elastic to changes in net fertility, especially nesting success (Hoekman et al. 2002, 2006), indicating Mallards evolved a “faster” life history adapted to relatively rapid reproduction and shorter lifespan (Sæther and Bakke 2000). Our results for Lesser Scaup (all models) indicate that their life history is slightly slower than the Mallard but faster than Greater Scaup and pintails, and much faster than geese breeding at high latitudes. Nevertheless, Lesser Scaup breeding propensity, and renesting intensity are poorly understood, especially in the boreal forest where these rates may be lower (Trauger 1971) than in the prairieparklands region (where most estimates come from: Afton 1984). More data for these vital rates and others are needed for birds breeding in the boreal forest to determine whether or not their lifehistory strategy truly differs from their counterparts breeding in the prairieparklands (where most existing vitalrate data come from (Table 1)). If so, Lesser Scaup breeding in the boreal forest may need to be managed in slightly different ways than those breeding in the prairieparklands. Although existing lifehistory data were too disconnected across space and time to determine which vital rates were responsible for historical declines in Lesser Scaup numbers, our models can serve as a template to be built upon for understanding scaup life history and to help create management plans aimed at reversing population declines. Herein, we identified vital rates most likely to affect scaup population dynamics if changed. However, at this time, the lack of longterm demographic studies prevents us from accurately predicting how particular management actions (e.g., changes in harvest regulation or land management) will affect Lesser Scaup population dynamics. So before management actions are implemented, we urge that longterm studies of Lesser Scaup breeding biology, seasonal survival, crossseasonal habitat use, and foraging ecology be in place to test the effects of any management action on demographic vital rates and population dynamics. Only within this framework can models and management plans be updated adaptively (Williams et al. 2002).
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ACKNOWLEDGMENTS J. J. Rotella was funded by a research grant from Ducks Unlimited’s Institute for Wetland and Waterfowl Research. We thank Hal Caswell and Mark Lindberg for invigorating discussion about population modeling and those who collected and published the demographic data used in our analyses. We also thank Hannu Pöysä and two anonymous reviewers for their comments on our manuscript.
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