Life-history tradeoffs and reproductive cycles in Spotted Owls

Abstract

The study of tradeoffs among life-history traits has long been key to understanding the evolution of life-history strategies. However, more recently, evolutionary ecologists have realized that reproductive costs have the potential to influence population dynamics. Here, we tested for costs of reproduction in the California Spotted Owl (Strix occidentalis occidentalis), and assessed whether costs of reproduction in year t − 1 on reproduction in year t could be responsible for regionally synchronized biennial cycles in reproductive output. Logistic regression analysis and multistate mark–recapture models with state uncertainty revealed that breeding reduced the likelihood of reproducing in the subsequent year by 16% to 38%, but had no influence on subsequent survival. We also found that costs of reproduction in year t − 1 were correlated with climatic conditions in year t, with evidence of higher costs during the dry phase of the El Niño–Southern Oscillation. Using a simulation-based population model, we showed that strong reproductive costs had the potential to create biennial cycles in population-level reproductive output; however, estimated costs of reproduction appeared to be too small to explain patterns observed in Spotted Owls. In the absence of strong reproductive costs, we hypothesize that observed natural cycles in the reproductive output of Spotted Owls are related to as-yet-unmeasured, regionally concordant fluctuations in environmental conditions or prey resources. Despite theoretical evidence for demographic effects, our analyses illustrate that linking tradeoffs to actual changes in population processes will be challenging because of the potential confounding effects of individual and environmental variation.

Resumen

El estudio de los compromisos entre rasgos de la historia de vida es considerado clave para entender la evolución de las estrategias de historia de vida. Sin embargo, recientemente los ecólogos evolutivos se han dado cuenta de que los costos reproductivos tienen el potencial de influir sobre las dinámicas de la población. Aquí probamos los costos reproductivos de Strix occidentalis occidentalis y determinamos si el costo de la reproducción en el año t – 1 sobre la reproducción en el año t podría ser responsable de la sincronización regional bianual en el rendimiento reproductivo. Análisis de regresión logística y modelos multiestado de marca-recaptura con incertidumbre de estado revelaron que la cría redujo la probabilidad de reproducción en el año subsiguiente entre el 16% y 38%, pero no tuvo influencia sobre la supervivencia. También encontramos que los costos de reproducción en el año t – 1 estuvieron correlacionados con las condiciones climáticas del año t, con evidencia de mayores costos durante la fase seca del fenómeno de El Niño. Usando un modelo de la población basado en simulaciones, mostramos que el alto costo reproductivo tuvo el potencial de crear ciclos bianuales en el rendimiento reproductivo a nivel de la población; sin embargo, los costos estimados de reproducción parecieron ser muy bajos como para explicar la variación observada en S. occidentalis. En la ausencia de costos reproductivos altos, formulamos la hipótesis de que los ciclos naturales observados en el rendimiento reproductivo de S. occidentalis están relacionados con fluctuaciones regionales en las condiciones ambientales o en los recursos alimenticios que aún no han sido medidas. A pesar de la evidencia teórica a favor de efectos demográficos, nuestros análisis ilustran que relacionar los compromisos con los cambios reales en los procesos de la población es difícil debido a los efectos de la variación individual y ambiental.

Palabras clave: Búho moteado, ciclos reproductivos, compromisos de historia de vida, costos reproductivos, demografía, incertidumbre de estado, Strix occidentalis

Introduction

Life-history theory predicts that the allocation of resources to current reproduction reduces the energy available for future reproduction and survival (Williams 1966, Stearns 1992, Roff 2002). While it is generally accepted that such tradeoffs exist, manifestations of reproductive costs are complex and can vary owing to a variety of extrinsic and intrinsic factors in natural populations (Robert et al. 2012). Current reproduction may covary in a positive manner with other life-history traits in high-quality individuals, such that reproductive costs are only apparent in low-quality individuals (Cam et al. 1998, 2002, Hamel et al. 2009, Lescroël et al. 2009). Moreover, reproductive costs may be more severe in young individuals (Tavecchia et al. 2005, Proaktor et al. 2007, Aubry et al. 2009) or harsh environmental conditions (Messina and Fry 2003, Reid et al. 2003, Barbraud and Weimerskirch 2005, Bears et al. 2009). Such mitigating factors challenge the detection of reproductive costs in natural populations, but understanding the mechanisms resulting in tradeoffs has helped to explain the evolution of the diverse array of life-history strategies in nature.

While the study of reproductive costs has long been a central theme in evolutionary ecology, the realization that life-history tradeoffs have the potential to influence population dynamics is more recent. Perhaps most broadly, species that have evolved long lifespans at the expense of reproductive rates typically exhibit more stable population growth rates than shorter-lived and more fecund species (Morris et al. 2008). In addition, Proaktor et al. (2008) recently used a simulation-based population model to demonstrate that the costs of reproduction on survival in red deer (Cervus elaphus) are expected to produce age structures skewed toward young individuals and to reduce population density. Similarly, Kuparinen et al. (2011) used a simulation-based population model to show that observed costs of reproduction on survival in Atlantic cod (Gadus morhua) are expected to reduce population growth rates. However, both of these studies examined the expected impacts of life-history tradeoffs on population dynamics using prospective population models. To the best of our knowledge, no study has attempted to determine whether observed population-level processes were related to life-history tradeoffs.

Here, we tested for costs of current reproduction on future reproduction and survival of Spotted Owls (Strix occidentalis), and assessed whether potential reproductive costs influenced population dynamics in this species. Previous studies of Spotted Owls suggest that reproduction in year t − 1 may come at a cost to vital rates in year t (Anthony et al. 2006, Forsman et al. 2011, Mackenzie et al. 2012), but these studies were based on annual mean vital rates or territory occupancy metrics, and thus were not designed to detect reproductive costs at the individual level (where costs occur). Moreover, many Spotted Owl populations exhibit regionally synchronized, annual cycles in reproductive output, in which good reproductive years tend to be followed by bad reproductive years (i.e. an “even–odd” pattern; Anthony et al. 2006, Blakesley et al. 2010, Forsman et al. 2011) that may represent the emergent effect of reproductive costs (Forsman et al. 2011). Following a “good” year in which most individuals in the population breed, impacts to body condition stemming from reproductive costs could reduce breeding propensity in a large segment of the population during the subsequent year, resulting in low population-level output. Under this hypothesis, few individuals would experience additional reproductive costs in year t, allowing “recovery” from previously incurred reproductive costs, such that most of the population would breed in year t + 1. The “reproductive cost hypothesis” is appealing because prey species and weather conditions that influence Spotted Owl reproduction are not known to vary according to a biennial cycle (Forsman et al. 2011).

Our specific objectives in this study were to assess: (1) whether costs of current reproduction may affect future reproduction and survival in Spotted Owls using individual-based statistical models; (2) whether intrinsic and environmental factors may have mediated costs of reproduction; and (3) whether observed biennial cycles in reproductive output could have been driven by costs of reproduction. We used a 20-year (1991 to 2010) dataset collected as part of a long-term demographic study of California Spotted Owls in the central Sierra Nevada (Seamans et al. 2001, Seamans and Gutiérrez 2007) to test these hypotheses. Previous studies have shown that our study population exhibits biennial cycles in reproductive output (Blakesley et al. 2010), a finding that was supported by an analysis of the 20-year dataset we considered here (Appendix A, Appendix A Figure 4).

Methods

Field Methods

We used standard, well-described field methods to capture and band Spotted Owls, determine sex, assign age class, and estimate reproductive status of individuals (Seamans et al. 2001). Briefly, we surveyed Spotted Owl territories using vocal imitations of their calls to locate territorial individuals during their breeding season (April to August). Unbanded owls were captured with a noose pole, mist net, or by hand, and fitted with a unique color band combination on one leg and a uniquely numbered aluminum band on the other leg. Previously banded owls were identified visually based on their color band combination and gender. Reproductive status was determined by the presence of juveniles in the owl's territory, the owl's behavior (e.g., attendance at a nest), and the owl's response to live mice (Franklin et al. 1996, Seamans et al. 2001).

Testing for Costs of Reproduction

We tested for costs of reproduction in year t − 1 on reproduction and survival in year t and evaluated factors that may have modulated reproductive costs using both logistic regression (Agresti 2013) and multistate closed robust design mark–recapture models with state uncertainty (MSCRD-SU models; Kendall et al. 2003, 2004, 2012). We used these two approaches because of differences in model complexity and the ability to account for imperfect detectability, both of which could influence inferences about life-history tradeoffs. The logistic regression approach used consecutive observations of individual breeding in a generalized mixed model framework to determine if breeding state in year t was related to breeding state in year t − 1. Because consecutive observations of breeding state were required, observations were discarded when information on breeding state was not available from the preceding or the following year, potentially resulting in a significant loss of information. The logistic regression approach also required making the assumption that breeding state had been determined without error. In contrast, MSCRD-SU models used joint probabilities of individual capture histories to estimate state-specific and time-specific apparent survival probabilities (ϕ) and transition probabilities among breeding states (ψ). This approach also provided a framework for estimating individual detection probabilities (p), detection probability of state (δ), observed state structure of the population (π), and true state structure of the population (ω); doing so allowed for the incorporation of all data, including observations of unknown breeding state (“u”), and thus relaxed the assumption of perfect state assignment (Kendall et al. 2012). Moreover, MSCRD-SU models allowed for the testing of hypotheses about costs of current reproduction on future survival as well as on future reproduction. However, logistic regression models were able to accommodate random effects and thus controlled for individual and temporal variation with fewer parameters than MSCRD-SU models.

We considered two “true” breeding states for both modeling frameworks: breeders (individuals that established a nest regardless of the outcome of the nesting attempt; “B”) and nonbreeders (individuals that did not establish a nest; “N”). In principle, five states were possible based on our field data: nonbreeders, failed breeders (nested, but nest failed), and breeders that produced one, two, or three offspring. However, preliminary modeling indicated that sample sizes within each state were not sufficient to support the estimation of all pairwise transition probabilities. Therefore, we pooled the five potential states into breeders and nonbreeders, and thus tested the hypothesis that initiating nesting in a given year influenced the probability of nesting the following year. Doing so resulted in approximately equal sample sizes in each of the two states (see below). In addition, only 14% of observed nesting attempts failed; thus, the majority of individuals in the breeder state incurred costs associated with successfully fledging young.

We developed five a priori hypotheses about costs of current reproduction on future reproduction and survival in Spotted Owls and tested these: (1) by estimating transition probabilities between breeding states in year t − 1 to breeding states in year t; and (2) by estimating state-dependent survival probabilities from year t − 1 to year t. We present hypotheses in terms of cost of current reproduction on future reproduction, but these can be translated to hypotheses about survival by substituting the term “future reproduction” with the term “future survival” (Table 1). Hypothesis 1 stated that a cost of current reproduction on future reproduction existed such that owls which bred in year t − 1 were less likely to breed in year t than were owls that did not breed in year t − 1. This hypothesis was tested by evaluating the level of support for the categorical Breed_t−1 effect (i.e. breeding status in year t − 1, where 0 = nonbreeder [N] and 1 = breeder [B]) in logistic regression models and the Breed_t−1 state in the MSCRD-SU models. Hypothesis 2 posited the same cost of reproduction, but predicted that it was higher in subadults than in adults, as subadult Spotted Owls typically have lower reproductive rates than adults (Anthony et al. 2006); this relationship was tested by evaluating the interaction term Breed_t−1*Age_t−1 (where Age_t−1 was a categorical covariate, with A = adult [≥3 years] and S = subadult [1–2 years]). Hypothesis 3 stated that costs on future reproduction would be higher following breeding in a “poor” year than breeding in a “good” year. Breeding conditions in year t − 1 were indexed using mean annual fecundity, MnFec_t−1 (the number of female offspring per territorial female, assuming a 1:1 sex ratio among offspring); support for this hypothesis was assessed based on the interaction term Breed_t−1*MnFec_t−1. Like the previous hypothesis, Hypothesis 4 stated that a cost of reproduction was mediated by environmental conditions, but that the intensity of the cost was dependent upon weather conditions indexed by the mean Southern Oscillation Index (SOI). We calculated the mean SOI from August through November preceding the breeding season, SOI_Aug–Nov (data downloaded from the National Center for Atmospheric Research, http://www.cgd.ucar.edu/cas/catalog/climind/SOI.signal.ascii), which predicted weather conditions in the vicinity of our study area four months into the future (i.e. the winter prior to the breeding season of interest; Redmond and Koch 1991). Negative values for the Southern Oscillation Index were correlated with occurrences of El Niño events, which result in high precipitation in our study area, whereas positive values were correlated with La Niña events, which result in low precipitation (Redmond and Koch 1991). In our study area, previous demographic analyses incorporating SOI_Aug–Nov revealed a significant relationship between this covariate and fecundity of owls (Seamans and Gutiérrez 2007). Support for this hypothesis was tested by evaluating the significance of the term Breed_t−1*SOI_Aug–Nov. Hypothesis 5 mirrored Hypothesis 4 in that a cost of reproduction existed and that this was mediated by El Niño–La Niña conditions, but invoked a one-year lag effect for the Southern Oscillation Index (SOI_{Aug t−1–Nov t−1}).

Table 1.

A priori hypotheses regarding the cost of reproduction in year t − 1 on reproduction in year t for California Spotted Owls.

In the logistic regression analysis, we treated breeding status in year t as the binomial dependent variable (N or B) based on 418 breeding attempts by 117 females (185 and 233 of which were breeders and nonbreeders in the previous year, respectively). We limited the logistic regression analysis to females to avoid a lack of independence in breeding histories between paired males and females. We considered all of the covariates described in Hypotheses 1 through 5 and treated year and individual as random effects (Year and Individual, respectively) to account for repeated observations of individuals over time. Prior to investigating fixed effects, we evaluated the importance of random effects using Akaike's Information Criterion corrected for small sample size (AIC_c; Burnham and Anderson 2002) in a means-only model, and verified that the lower 95% confidence limits of selected variance components excluded zero. We used both approaches to evaluate support for random effects because model-selection methods by themselves may not adequately identify important random effects (Müller et al. 2013). We retained the best random effects for subsequent incorporation of fixed effects in a mixed-effects framework. We evaluated support for fixed effects by comparing the AIC_c ranks of all hypothesized models (Table 1), nested additive models, single covariate models, and the null model (Burnham and Anderson 2002). For hypotheses 1, 3, 4, and 5, we evaluated these models with and without Age_t−1 as an additional additive covariate. Further, we examined support for covariates by assessing the 95% confidence intervals around slope parameters, β (Graybill and Iyer 1994).

MSCRD-SU modeling was based on 764 breeding attempts by 204 females (309 and 339 of which were breeders and nonbreeders in the previous year, respectively) and 750 breeding attempts by 168 males (309 and 324 of which were breeders and nonbreeders in the previous year, respectively). Both males and females were included in the MSCRD-SU analysis to allow for testing of sex-specific costs of reproduction on survival, treating sex as a grouping variable when necessary to limit pseudoreplication in the data. Capture histories were constructed by assigning detected individuals to breeding state (B, N), or state unknown (u); individuals that were not detected were assigned “0”. The sampling design was based on primary sampling periods (i.e. the approximate Spotted Owl breeding season: April 1 to August 20) as well as two secondary occasions occurring within each primary sampling period (April 1 to June 15 and July 16 to August 20). Secondary sampling periods within the robust design allowed for the probabilistic assignment of breeding state in cases where it was unknown (Kendall et al. 2012, Reichert et al. 2012).

Given the number of structural parameters in MSCRD-SU models (ϕ, ψ, p, δ, π, and ω), we took a stepwise approach to identify sets of covariates that best explained variation in each parameter. We first modeled variation in the four “nuisance” parameters (δ, p, π, and ω; methods described in Appendix B). For the two parameters of interest, apparent survival probability (ϕ) and state transition probability (ψ), we tested the five hypotheses about costs of reproduction (Table 1) by evaluating Breed_t−1 and its interactions with Age_t−1, MnFec_t−1, SOI_Aug−Nov, and⁠. We also ran static and time-variable models, allowing structural parameters to vary by primary period (ϕ, ψ, π, ω, δ, p) and by secondary period (δ, p). Initially, we incorporated sex as a grouping variable in all structural parameters, but we retained it only when it improved model support. Once we evaluated nuisance parameters, we used AIC_c to determine the best covariate substructure for survival probabilities (built upon a global model for state transition probabilities) and then the best covariate substructure for state transition probabilities. We also examined support for hypotheses by assessing the 95% confidence intervals around slope parameters, β. To estimate the strength of potential costs of reproduction on future reproduction, we examined the difference between and⁠, where the first and second superscripts indicated breeding states in year t − 1 and year t, respectively (sensu Nichols et al. 1994). Goodness-of-fit tests have not been developed for robust design mark-recapture models, and existing tests cannot be conducted on models using individual covariates or on models with state misclassification (e.g., observations of “u”). Therefore, we tested goodness of fit on a more generalized global model using the median-ĉ goodness-of-fit test in Program MARK (White and Burnham 1999); specifically, we used an age- and time-variable multistate model in which observations were summarized by primary period and records of “u” were replaced by “N”. This method provided a conservative assessment of fit.

Simulating Effects of Costs of Reproduction on Annual Variability in Reproductive Output

We used a stochastic, simulation-based population model to determine: (1) whether cost of reproduction could generate biennial cycles in reproductive output; and (2) whether these patterns could be detected in the presence of environmental variability. To do so, we first simulated populations in which breeding individuals experienced a reproductive cost in the year after breeding, and then tested statistically for biennial cycles in reproductive output in the simulated populations. We used a three stage-class, postbreeding, female-based model, in which subadult and adult individuals could move between breeding states according to transition probabilities (⁠and⁠; Figure 1). For simplicity, we combined subadults and adults of each breeding state into a single stage class (breeder or nonbreeder) and assumed no mortality. Thus, individuals were present throughout the simulation and the abundance of adults was constant. We felt that this simplification was reasonable given that our focus was on evaluating annual variability in fecundity rather than population size.

Figure 1.

Life-cycle diagram for a California Spotted Owl population model with three stage classes: juveniles, nonbreeders, and breeders. R = fecundity and ψ = state transition probability (B = breeder and N = nonbreeder).

For each annual time-step in a given model run, we randomly sampled from a normal distribution described by the mean and temporal process variance of obtained from the top-ranked MSCRD-SU model (following Burnham et al. 1987). We constrained to be a function of based on the observed Spearman's rank correlation between real parameter estimates ofand obtained from the top-ranked MSCRD-SU model (r_s = 1.0). Each year, we calculated the number of breeders as and calculated the number of nonbreeders as⁠, where was the combined number of breeders and nonbreeders in year t. We set to 50 individuals (the approximate number of territorial females in our study area) in all years of the projection, and projected populations forward in time for t = 20 years (the duration of our study). For year t = 0, and were specified as described below. We calculated reproductive output in year t as R_t = × P_t, where P_t was productivity, i.e. the number of young produced per breeder, in year t. We calculated P_t as a function of based on the observed Spearman's rank correlation coefficient between empirical P_t estimates from field data (P̄ = 0.684, SE = 0.228) and real parameter estimates of obtained from the MSCRD-SU analysis (r_s = 0.58).

When assessing the effect of reproductive cost on patterns of reproductive output, we considered three scenarios for the potential magnitude of the reproductive cost by varying the difference between and⁠: “weak” (Δψ = 0.08), “medium” (Δψ = 0.40), and “strong” (Δψ = 0.80). We used Δψ = 0.08 to represent the smallest cost scenario as this value represented the magnitude of the reproductive cost estimated with MSCRD-SU models for Spotted Owls (see Results). We anticipated that the effect of reproduction in year t − 1 on reproduction in year t could be masked if only half of the population bred in the initial year; this would happen if, in the following year, a greater breeding propensity of the previous year's nonbreeders counteracted a reduced breeding propensity of the previous year's breeders. Therefore, for each cost magnitude, we considered three scenarios in which environmental conditions might initiate oscillations in reproductive output: (1) “good” conditions, under which all owls bred in year 1 (⁠ = 1); (2) “bad” conditions, in which no owls bred in year 1 (⁠ = 0); and (3) “recurring bad” conditions, where there was a 20% chance each year that no owls bred. Scenarios 1 and 2 were realistic given that all territorial owls bred in 1992 and that there were several years in which almost complete reproductive failure occurred. We developed scenario 3 to determine whether periodic extreme events, such as El Niño events, which occur at 3–7 year intervals (Redmond 1998), could maintain annual cycles in reproductive output that might otherwise attenuate over time. We simulated 1,000 populations for all nine factorial combinations of cost-of-reproduction (weak, moderate, and strong) and environmental (good, bad, and recurring bad) scenarios. For all simulations, we set to 50 individuals (the approximate number of territorial females in our study area), and projected populations forward in time for t = 20 years (the duration of our study). For a given scenario, we estimated the probability of detecting annual cycles in reproductive output by calculating the proportion of simulated datasets within which a fixed even–odd year factor was statistically significant using one-way ANOVA.

Results

Costs of Reproduction—Logistic Regression

Using a means-only model, we retained Year (⁠ = 1.76, SE = 0.87), but not Individual (⁠ = 0.01, SE = 0.16), as a random effect in logistic regression models. The highest-ranked fixed-effects model was:

$$$$

in which the random effect of Year was slightly smaller than in the means-only model (⁠ = 1.49, SE = 0.74). This model accounted for nearly half of the AIC_c weight in the 95% confidence set (Table 2). A cost of breeding was supported by the significance of the Breed_t−1 covariate, which indicated that the probability of breeding in year t was lower for females that bred in the previous year (⁠ = −0.63; 95% CI = −1.15 to −0.12). Least-squares means indicated that nonbreeders were 38% more likely to breed in year t than breeders (nonbreeders: mean = 0.44, 95% CI = 0.29 to 0.62; breeders: mean = 0.32, 95% CI = 0.18 to 0.50). The top-ranked model also indicated that the probability of breeding was negatively correlated with the mean monthly SOI from August to November of year t (⁠= −0.34; 95% CI = −0.80 to 0.12), such that females were less likely to breed after dry La Niña winters than after wet El Niño winters, although the 95% CI for this estimate overlapped zero. The interaction between breeding state in year t − 1 and the SOI indicated that costs of reproduction were greatest during La Niña conditions (⁠ = −0.32; 95% CI = −0.64 to 0.01; Figure 2). Lastly, this top-ranked model indicated that breeding was positively related to the age class of females, with subadults being less likely to breed in year t, regardless of their previous year's breeding state, than adults (⁠ = −1.14; 95% CI = −1.85 to −0.43). Little support existed for the other hypothesized covariates; all models containing MnFec_t−1 and ranked at least 4.5 AIC_c units below the top model and individually accounted for ≤5% of the weight within the candidate model set (Table 2, Appendix C Table 9).

Table 2.

95% confidence set of AIC_c-ranked logistic regression models depicting the relationship between breeding status in year t and breeding status in year t − 1 for female California Spotted Owls in the central Sierra Nevada (Year included as a random variable in all models). AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight. The complete model set is provided in Appendix C Table 9.

Figure 2.

Probability of breeding by California Spotted Owls in the central Sierra Nevada in year t as a function of the Southern Oscillation Index (SOI) in the previous winter and breeding status in year t − 1 based on logistic regression analysis. Dashed lines represent 95% confidence intervals.

Costs of Reproduction—MSCRD-SU Model

Goodness-of-fit testing on the global MSCRD-SU model indicated that our model fit the data well (median ĉ = 1.01; 95% CI = 0.96 to 1.05). Primary sampling period detection probabilities were high (>0.8; Appendix B). The best model for state transition probability (representing study year 1991) was:

$$$$

,

wherewas the probability of transitioning to being a breeder in year t regardless of breeding state in year t − 1. This model accounted for 68% of the weight in our candidate model set (Table 3), and indicated that breeding propensity depended on breeding state in year t − 1, differed across age classes, and varied among years. Similar to the logistic regression analysis, breeders from the previous year were less likely to breed in year t than nonbreeders from the previous year (⁠ = −0.39; 95% CI = −0.71 to −0.08). Mean transition probabilities based on real parameter estimates indicated that nonbreeders were 16% more likely to breed in year t than breeders (⁠= 0.51, 95% CI: 0.39 to 0.63; = 0.43, 95% CI: 0.31 to 0.55). As with logistic models, subadults were less likely than adults to breed in subsequent years (⁠ = −1.13; 95% CI = −1.62 to −0.64). No other models were within 2.0 AIC_c of the top model (Table 3), and there was little support for SOI_Aug−Nov,⁠, or MnFec_t−1 (Table 3, Appendix C Table 10). Individually, SOI_Aug−Nov,⁠, and MnFec_t−1 explained only 8.5%, 12.9%, and 0.1% of the variance, respectively, in breeding probability, based on analysis of deviance (using the method of Iles et al. 2013).

Table 3.

AIC_c-ranked Multistate Closed Robust Design with State Uncertainty models testing the relationship between: (i) breeding state in year t − 1 and breeding state in year t (95% candidate model set); and (ii) breeding state in year t − 1 and apparent survival in year t (80% candidate model set) for California Spotted Owls in the central Sierra Nevada. AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight. Complete model sets are provided in Appendix C Table 10.

We did not detect a cost of current reproduction on future survival with MSCRD-SU models, as Breed_t−1 was absent from the four top-ranked survival models (Table 3). Together, these models accounted for 50% of the weight in the candidate model set, each containing either the full or a nested subset of Sex, Age, and Year covariates. The best survival model, accounting for 14% of model weight, contained only Sex and Year effects, with females exhibiting slightly lower survival than males (β_Sex=F = −0.21; 95% CI = −0.48 to 0.05). For year 1991, this model was:

$$$$

.

According to this model, mean annual survival was 0.81 for females (range: 0.57–0.90) and 0.84 for males (range: 0.63–0.92).

Detecting Annual Cycles in Reproductive Output

We found that the cost of breeding on reproduction in consecutive years could result in biennial cycles in population-level reproductive output (Figure 3). However, when the cost of reproduction was weak or moderate, expected oscillations attenuated and became negligible within 1–5 years of being induced by good or bad environmental conditions. As a result, statistical power to detect oscillations induced by weak or moderate costs of reproduction was low, ranging from 0.03 to 0.13 (Figure 3). Under weak or moderate costs of reproduction, recurring bad environmental conditions resulted in greater annual variability in reproductive output, but failed to consistently generate regular cycles (Figure 3); statistical power to detect annual cycles was low under both scenarios (0.06 and 0.15, respectively). Biennial cycles in reproductive output were more obvious when the cost of reproduction was strong than when the cost was small or moderate, but the pattern attenuated to low levels after approximately 10 years under both good and bad initial environmental conditions (Figure 3); statistical power to detect cycles was greater for these scenarios (0.20 and 0.38 when cycles were induced by good and bad environmental conditions, respectively). Recurring bad years appeared to generate the most consistent cycles when the cost of reproduction was strong (Figure 3), but power to detect cycles remained low (0.40).

Figure 3.

The top nine panels show projected variation in the fecundity of California Spotted Owls under three cost-of-reproduction scenarios (“Strong,” “Moderate,” and “Weak” costs) as well as two scenarios about the fecundity in year 1 (“Good” and “Bad”) and one scenario with recurring bad years (20% chance of recurrence, “Recurring bad”). In each panel, the black line represents expected fecundity in the absence of environmental variation, whereas the blue, red, and green lines show examples of simulated fecundity when environmental variation is added. The bottom panel shows statistical power to detect biennial cycles in fecundity under each scenario. “COR” is cost of reproduction.

Discussion

We detected a cost of current reproduction on future reproduction in Spotted Owls, such that individuals that bred in year t − 1 were less likely to breed in year t, using both logistic regression and MSCRD-SU models. The fact that we detected reproductive costs using both methods suggests that our results were robust to potential violations of assumptions and limitations specific to each modeling approach (e.g., assumptions of homogeneous detection probabilities in the logistic regression model and lack of independence of paired individuals in the MSCRD-SU model). Moreover, statistical support for reduced breeding propensity in individuals that bred in year t − 1 was strong given that (i) models containing the Breed_t–1 term explained 87% and 90% of the weight in the logistic regression and MSCRD-SU model sets, respectively, and (ii) nested models without the Breed_t–1 term always ranked more than 2.0 AIC_c units below the “parent” model containing Breed_t–1. Thus, results from our individual-based modeling effort were consistent with previous studies which suggested that current reproduction can come at a cost to future fitness in Spotted Owls, based on negative correlations between mean vital rates in consecutive years (Anthony et al. 2006, Forsman et al. 2011) and territory occupancy analyses (Mackenzie et al. 2012).

Estimated costs of reproduction were modest, as nonbreeders were 16–38% more likely to breed in the subsequent year than breeders, depending on the modeling approach. Estimated differences in costs of reproduction between breeders and nonbreeders, however, were similar to reproductive costs estimated for other bird species (Robert et al. 2012). Moreover, when integrated over an individual's lifetime, estimated annual reproductive costs may translate to meaningful differences in fitness given that Spotted Owls can live up to 20 years (R. J. Gutiérrez personal observation). We also suspect that the estimated reproductive costs were biologically meaningful because they were evident despite high variation in Spotted Owl reproduction due to weather conditions and habitat quality (Franklin et al. 2000, Franklin and Gutiérrez 2002, Seamans and Gutiérrez 2007). Lower subsequent breeding propensity in breeders could result from reductions in body condition that prevent individuals from breeding in consecutive years or that serve as a cue for individuals to forgo breeding in consecutive years (Drent and Daan 1980). In addition, similar to biennially breeding albatross species (Langston and Rohwer 1996, Prince et al. 1997), Spotted Owls exhibit a partially biennial molt, during which all retrices are replaced within a roughly two-week period every other year (normally in July; Forsman 1981). Thus, the energetic demands of molting may affect the energy available for reproductive investment in the same year. Regardless of the mechanism, observed reproductive costs may be symptomatic of low mean fitness given that our study population has declined markedly over the past two decades (Tempel and Gutiérrez 2013).

Although subadults were less likely to breed than adults, we did not find statistical support for a mediating effect of age on reproductive costs as has been observed in other species (Tavecchia et al. 2005, Proaktor et al. 2007, Aubry et al. 2009). However, sample sizes of subadults, particularly breeding subadults, were relatively small and it is possible that we did not have sufficient power to detect age-related reproductive costs. Life-history studies in other species also have demonstrated that reproductive costs were stronger in low-quality than in high-quality individuals (Cam et al. 1998, 2002, Hamel et al. 2009, Lescroël et al. 2009). Such interindividual heterogeneity in costs could occur in Spotted Owls as well, but we did not explore this possibility because clear morphological measures of individual quality were not available and because we expected that heterogeneity would dampen, rather than magnify, population-level reproductive cycles (e.g., if high-quality individuals breed every year).

Based on logistic regression analysis, reproductive costs were most evident when the winter preceding the breeding season in year t was characterized by La Niña conditions (Figure 2), which in our study area are associated with relative dry conditions (Redmond and Koch 1991). The mechanism by which La Niña conditions may increase reproductive costs in Spotted Owls is uncertain, but dry winter weather could limit primary productivity, which in turn could limit rodent abundance in the spring and ultimately reduce the breeding propensity of owls that had bred in the previous year. It is noteworthy that reproductive costs were influenced by weather conditions prior to breeding in year t rather than by weather conditions presumably affecting breeding in year t − 1. Thus, the cumulative effects of the energetic demands of reproduction in the prior year and the impacts of environmental conditions in the current year may influence an owl's ability to breed. We note that the interaction between breeding in year t − 1 and El Niño–Southern Oscillation (ENSO) conditions was not supported in MSCRD-SU analysis, and we cannot rule out the possibility that the interaction supported in logistic regression models was due to the effects of ENSO conditions on detectability rather than on reproduction. However, post-hoc modeling indicated that little support existed for a relationship between SOI_Aug–Nov and detection probability, as a post-hoc model of detection probability containing SOI_Aug–Nov ranked 1.93 AIC_c lower than a time-constant model.

While current reproduction came at a cost to future reproduction, breeding did not appear to influence the probability of surviving to the subsequent year. This finding is consistent with the hypothesis that reproductive costs are influenced by “life speed,” where fitness components with high temporal variance are generally more likely to be sacrificed than fitness components with low temporal variance (Hamel et al. 2010). Indeed, Spotted Owls apparently have evolved a bet-hedging life-history strategy characterized by high and stable adult survival rates to mitigate low and temporally variable reproduction (Franklin et al. 2000). Thus, a cost of reproduction on survival would likely have a disproportionate effect on fitness given that population growth in Spotted Owls is considerably more sensitive to adult survival than reproductive rates (Noon and Biles 1990). Stable survival in adult Spotted Owls may be the result of a similar proximate mechanism that occurs in Barn Owls (Tyto alba), in which parents with experimentally enlarged broods do not increase foraging effort and instead risk the survival of their young by parsing food among members of the enlarged brood (Roulin et al. 1999).

Influence of Reproductive Costs on Cycles in Reproductive Output

Animal population cycles have long fascinated ecologists (Elton 1942), with the majority of studies of cycles focusing on fluctuations in the abundance of a primary consumer and the numerical response of its predator(s) (Turchin 2003). Both biotic and abiotic forces have been proposed to explain the emergence of multiannual population cycles, including the mechanism of density dependence with time lags. Indeed, when reinforced by large-scale environmental conditions, density dependence appears to generate and sustain cyclic dynamics in some systems (Yan et al. 2013). However, mechanisms responsible for multiannual population cycles are likely system-dependent and involve complex interactions among multiple endogenous and exogenous factors (Berryman 2002, Ims et al. 2007, Krebs 2011, Iles et al. 2013). Our study differed from typical investigations of cyclic population dynamics in that we investigated possible causes of biennial reproductive cycles in a predator that does not exhibit cyclic changes in abundance (our study population experienced a gradual but steady decline over the study period; Tempel and Gutiérrez 2013, Tempel et al. 2014). Thus, density dependence seemed unlikely to be the cause of biennial fluctuations in reproductive cycles in Spotted Owls, which motivated us to explore the potential impacts of year-to-year reproductive costs and annual fluctuations in large-scale environmental factors in this system.

Our simple population model indicated that, in principle, strong costs of reproducing in year t − 1 on reproducing in year t could generate temporary biennial cycles in population-level reproductive output, the so-called even–odd year effect observed in many Spotted Owl populations (Franklin et al. 2004, Anthony et al. 2006, Blakesley et al. 2010, Forsman et al. 2011). However, the amplitude of expected cycles was almost negligible when the population model was parameterized with the magnitude of the reproductive cost detected in this study. Thus, we consider it unlikely that the observed cycles in the reproductive output of California Spotted Owls reflect life-history tradeoffs. While the nature of such tradeoffs may vary among populations (Glenn et al. 2011), we also doubt that reproductive costs are sufficiently strong in Northern Spotted Owls to have generated the cycles observed in the Pacific Northwest (Anthony et al. 2006, Forsman et al. 2011, Glenn et al. 2011) given that even a 0.40 difference in breeding probability between breeders and nonbreeders was insufficient to generate meaningful periodicity in fecundity of simulated populations (Figure 3).

In lieu of reproductive costs, we consider it more likely that reproductive cycles in Spotted Owls are related to unknown (i.e. unmeasured) fluctuations in resources or large-scale environmental processes. Populations of small mammals exhibit periodic cycles in abundance in other systems (Krebs 1996) and reproductive parameters of other owl species are known to track such cycles (Brommer et al. 2002, Millon et al. 2010). However, quantifying long-term variability in Spotted Owl prey such as dusky-footed woodrats (Neotoma fuscipes), northern flying squirrels (Glaucomys sabrinus), and deer mice (Peromyscus maniculatus) is difficult (Ward et al. 1998), and whether these species cycle biennially in the Sierra Nevada is unknown. Weather conditions related to the El Niño–Southern Oscillation, which are correlated with Spotted Owl reproduction in the Sierra Nevada (Seamans and Gutiérrez 2007, this study), typically vary on three-year to seven-year timescales (Redmond 1998) and thus do not seem likely to generate biennial cycles in reproductive output. However, other large-scale, but less well-studied, climatic processes such as the Quasi-Biennial Oscillation (Baldwin et al. 2001) do vary on timescales consistent with the biennial cycles observed in Spotted Owl reproduction. Regardless, it is clear that more detailed studies of spatial and temporal variation in prey abundances, climatic processes, and other factors are needed to understand the specific mechanisms responsible for reproductive cycles in Spotted Owls.

While previous studies have used population models to show that life-history tradeoffs are expected to influence population dynamics (Proaktor et al. 2008, Kuparinen et al. 2011), to the best of our knowledge ours is the first to attempt to link estimated tradeoffs to observed population dynamics. Matching observed changes in population-level processes to predictions from models parameterized with empirically based costs of reproduction will be essential to understanding whether life-history tradeoffs generate measurable demographic changes in natural populations. However, linking life-history tradeoffs and population dynamics will be challenging due to a number of factors, particularly the confounding effects of environmental variability on population processes. Experimental manipulation of reproductive effort, either by preventing individuals from breeding or by artificially increasing fecundity, and monitoring subsequent potential changes in population-level fecundity could be effective ways to test for emergent, population-level effects of life-history tradeoffs.

Acknowledgments

We thank Douglas Tempel, William Berigan, Sheila Whitmore, Christine Moen, and Mark Seamans for leading field work and providing previous syntheses of the data. In addition, we thank the numerous field technicians who have contributed to this study. Jim Baldwin provided invaluable statistical advice. Two anonymous reviewers provided feedback that greatly improved this paper. Work was funded by the USDA Forest Service, the USDI Fish and Wildlife Service, the California Department of Fish and Wildlife, the California Natural Resources Agency, the University of Wisconsin–Madison, the University of Minnesota Agriculture Experiment Station Project MIN-41-036, and the Sierra Nevada Adaptive Management Project. We also thank the Blodgett Forest Research Station for logistical support. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Appendix A Confirming Previously Detected Biennial Cycles in the Fecundity of California Spotted Owls

Methods

We used a general linear mixed model to test for biennial cycles in Spotted Owl reproduction at our study site in the central Sierra Nevada from 1991 to 2010 and to confirm that cycles detected previously in this population were still evident. We treated the number of females fledged (NFF, assuming a 50:50 sex ratio) as the dependent variable and the following temporal covariates as independent variables: EO (a categorical fixed effect coding an even–odd pattern across years with even years coded as 0 and odd years coded as 1), T (a categorical fixed effect coding a linear trend in time), TT (a categorical fixed effect coding a quadratic trend in time), and lnT (a categorical fixed effect coding a log-linear trend in time), based on Blakesley et al. (2010). We also included Age (age, a categorical covariate with A = adult [≥3 years] and S = subadult [1–2 yrs.]) in our models; Year (Year) and individual (Individ) were modeled as categorical random effects, with Individ as a blocking factor within Year, to account for repeated measures across time. Prior to testing relationships with the above fixed covariates, to account for possible dependence of error terms in the dataset, we modeled variance–covariance structures with restricted maximum likelihood in a means-only model for the random effects. Covariance structures considered were first-order autoregressive, heterogeneous autoregressive, log-linear variance, compound symmetric, heterogeneous compound symmetric, Toeplitz and heterogeneous Toeplitz (each also with estimates for the first two and for the first three off-diagonal bands), and unstructured (Littell et al. 2006). To assess the necessity of covariance structure and random effects coding, we assessed standard errors of random effects and compared these models against models without covariance structures specified, and against models dropping either or both of the random effects. We used Akaike's Information Criterion corrected for small sample size (AIC_c) to rank models (Burnham and Anderson 2002), incorporating the covariance structure from the top-ranking model into subsequent analyses of fixed effects.

Results

Using a means-only model, with random effects of Year and Individ (treated as a blocking factor), we found significant temporal covariance within the fecundity dataset and—of covariance structures tested—that this was best modeled by a Toeplitz matrix with two off-diagonal bands. This structure indicated that mean fecundity of the population in years t − 1 and t − 2 covaried in constant relationships with fecundity in year t, but that the magnitude and/or direction of the covariance depended upon the time lag between years. Over this structure, fixed effects modeling revealed a significant even–odd pattern in fecundity (from top model with 53% weight: β_EO = 0.20; 95% CI = 0.03 to 0.38), and further explained temporal variation in the data with a declining log-linear trend and age-class-dependent reproductive success (Appendix A Table 4, Appendix A Figure 4). The similarly structured second-best model showed an equivalent effect size for an even–odd pattern (β_EO = 0.20; 95% CI = 0.01 to 0.39), substituting only a declining linear trend for the log-linear trend, and together with the top model accounted for 69% of the weight in the candidate model set. The next model, nested within the structure of the first by not having an even–odd effect, ranked significantly lower than the top model (ΔAIC_c = 2.60).

Appendix A Table 4.

95% confidence set of AIC_c-ranked mixed regression models testing for even–odd year oscillations in number of California Spotted Owl females fledged (NFF; n_observations = 459; Year included as a random variable with subject = Individ in all models). AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight.

Appendix A Figure 4.

Annual estimates of fecundity (0.5 * reproductive output) in California Spotted Owls in the central Sierra Nevada, 1991–2010. Line represents a modeled log-linear declining and annually cyclic pattern in fecundity.

Thus, we confirmed that previously noted biennial cycles in Spotted Owl reproduction (Blakesley et al. 2010) remained evident at the Eldorado Study Area from 1991 to 2010. Even though the effect was most evident from 1998 to 2005 (Appendix A Figure 4), biennial cycles have been detected at several other Sierra Nevada study areas (Blakesley et al. 2010), as well as in several populations of Northern Spotted Owls (Anthony et al. 2006, Forsman et al. 2011). We conclude that the so-called “even–odd” pattern in reproduction appears to be a biologically important phenomenon characteristic of many Spotted Owl populations.

Appendix B Modeling Nuisance Parameters in the Multistate Closed Robust Design with State Uncertainty (MSCRD-SU) Model

Methods

Given the number of structural parameters contained in the MSCRD-SU model (p, δ, π, ω, ϕ, and ψ, defined in the Methods section of the main text, under “Testing for Costs of Reproduction”), we took a stepwise approach to identify sets of covariates that best explained variation in these parameters. Starting with the global covariate model (age, sex, and time), we sequentially constrained structural parameters based on hypothesized covariate relationships, using AIC_c to rank covariate structures within each structural parameter. For detection probability (p) and detection probability of state (δ), we considered Breed_t, Age_t, Sex, Secondary Occasion (Apr 1–Jun 15 vs. Jun 15–Aug 20), Capture_t,_j (a time-varying individual covariate indicating whether the individual was captured or resighted in breeding season t and secondary period j), Effort_t,_j (a continuous covariate indexing survey effort and calculated as the total number of unique territories surveyed in a given secondary period multiplied by the total number of survey hours that period divided by 1,000), Year, and the interactions Age_t*Sex, Breed_t*Sex, Breed_t*Age_t, Breed_t*Capture_t,_j, and Breed_t*Effort_t,_j. For stage structure of the observed sample (π) and stage structure of the population (ω), we considered Age_t, Sex, and Year. After a final model was settled upon for all structural parameters, primary period detection probabilities (p^*) were summarized from secondary period estimates of p and δ using the equations of Kendall (2009:767–768).

Results

Secondary period detection probabilities, p and δ (Appendix B Table 5 and Appendix B Table 6). In general, estimates of detection probabilities of individuals (p) were higher for breeders than for nonbreeders, for adults than for subadults, for captured vs. resighted birds, and for males than for females, regardless of secondary period. The more effort expended, the more likely a bird was to be seen, and lowest detection probabilities coincided with the year of lowest survey effort (1995). Capture probabilities for adult and subadult breeders and nonbreeders were near 1.0 (range: 0.93–0.99). Because birds typically were captured only one time (during banding), the following individual detection probabilities represent resighted birds: For adults during any given secondary period, mean estimated detection probabilities, ⁠, were ∼0.83 for breeders and ∼0.61 for nonbreeders; for subadults, these values were ∼0.73 for breeders and ∼0.47 for nonbreeders. Similarly, on average, estimates of state detection probabilities (δ) were higher for breeders than for nonbreeders and for adults than for subadults, but were higher for females than for males, higher in the first half of the breeding season than in the second half of the breeding season, and showed no effect of capture vs. resight. Mean estimated state detection probabilities, ⁠, for adult breeders during the first and second secondary periods were ∼0.93 and ∼0.87, while those for adult nonbreeders were ∼0.70 and ∼0.54, with the highest values observed after 1996. For subadults, these values were ∼0.91, ∼0.85, ∼0.66, and ∼0.48.

Appendix B Table 5.

95% confidence set of AIC_c-ranked Multistate Closed Robust Design with State Uncertainty (MSCRD-SU) models depicting individual detection probability, p, for California Spotted Owls in the central Sierra Nevada. AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight.

Appendix B Table 6.

95% confidence set of AIC_c-ranked Multistate Closed Robust Design with State Uncertainty (MSCRD-SU) models depicting state detection probability, δ, for California Spotted Owls in the central Sierra Nevada. AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight.

Primary period detection probabilities, p*

Summarizing individual and state detection probabilities within primary period revealed that our ability to detect breeders and nonbreeders was high, with little chance of mistaking breeders for nonbreeders. The average probability that an adult female breeder was resighted at least once with her offspring within a primary period, ⁠, was 0.92 (range: 0.71–0.99). The average probability that an adult female breeder was resighted at least once without her offspring within a primary period, ⁠, was 0.04 (range: 0.00–0.17). The average probability that an adult female nonbreeder was resighted at least once during a primary period, ⁠, was 0.81 (range: 0.67–0.94). For adult males, these values were 0.93 (range: 0.74–1.00), 0.04 (range: 0.00–0.19), and 0.88 (range: 0.77–0.97), respectively. For subadult females, these values were 0.84 (range: 0.55–0.98), 0.06 (range: 0.00–0.21), and 0.66 (range: 0.49–0.87), respectively. For subadult males, these values were 0.87 (range: 0.60–0.99), 0.07 (range: 0.00–0.24), and 0.76 (range: 0.60–0.92), respectively.

State structure, π and ω (Appendix B Table 7 and Appendix B Table 8)

Covariate relationships proved inestimable for state structure of the observed population, π (e.g., standard errors for all β's tested were zero). However, AIC_c ranking retained age class, Age_t, in the best model; this was biologically reasonable given that differential experience and/or competitive ability could cause subadults and adults to differ in the proportion of breeders within their respective “populations.” Thus, for this reason, and because we expected age class to affect parameters that had not yet been constrained—namely, state structure of the true population (ω) and state transition probability (ψ)—we retained this covariate in our substructure of π. As predicted, Age_t was significantly correlated with ω, as was Year, such that a lower proportion of subadults than adults were breeders in any given breeding season. Ten out of 19 years showed significantly lower proportions of breeders than average, with 1999 exhibiting the most extreme value (≥2× lower than any other year). No years had significantly higher proportions of breeders than average (although the point estimate for 1992 was conspicuously high, high standard error obscured this relationship). Mean adult state structure, ⁠, was equal to 0.459 (SE = 0.245).

Appendix B Table 7.

95% confidence set of AIC_c-ranked Multistate Closed Robust Design with State Uncertainty (MSCRD-SU) models depicting state structure of the observed population, π, for California Spotted Owls in the central Sierra Nevada. AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight.

Appendix B Table 8.

95% confidence set of AIC_c-ranked Multistate Closed Robust Design with State Uncertainty (MSCRD-SU) models depicting state structure of the true population, ω, for California Spotted Owls in the central Sierra Nevada. AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight.

Appendix C Complete AIC_c Tables for Multistate Closed Robust Design (MSCRD) Modeling of Breeding Probability (ψ) and Apparent Survival (ϕ)

Appendix C Table 9.

Full set of AIC_c-ranked logistic regression models depicting the relationship between breeding status in year t and breeding status in year t − 1 for female California Spotted Owls in the central Sierra Nevada (Year included as a random variable in all models). AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight.

Appendix C Table 10.

Full model set of AIC_c-ranked Multistate Closed Robust Design with State Uncertainty (MSCRD-SU) models testing the relationship between: (i) breeding state in year t − 1 and breeding state in year t; and (ii) breeding state in year t − 1 and apparent survival in year t for California Spotted Owls in the central Sierra Nevada. AIC_c is Akaike's Information Criterion adjusted for small sample sizes, and ΔAIC_c is the difference in AIC_c between the current model and the top model. K = the number of model parameters, −2lnL is the maximum loglikelihood, and w_i = AIC_c model weight.