Estimates of Southern White-tailed Ptarmigan daily nest survival from multiple sites in the Southern Rocky Mountains of Colorado

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INTRODUCTION
Population changes are attributable to variation in demographic rates contributing to growth (reproduction and immigration) and decline (death and emigration;Gotelli 2008).In avian population studies, researchers are often interested in underlying drivers of variation in each of these rates so they can predict how populations are likely to respond to environmental changes (e.g., habitat), management policies (e.g., hunting), and predator communities.The reproductive process is of particular interest in avian studies because a major component is a nesting stage directly observable through field studies (Deeming and Reynolds 2015).Furthermore, rates of nest success or failure can be highly influential contributors to annual variation in population numbers, which in turn may inform conservation strategies (Hagen et al. 2009).For species with shorter lifespans and higher reproductive rates, variation in population growth may be more responsive to reproductive rates than breeding-age survival (Sandercock et al. 2005).Therefore, gaining insights into nesting ecology can be beneficial to management, particularly if variation in rates of nest success is an important contributor to population change.
Nesting ecology is particularly interesting for birds in ecosystems defined by cold climates, such as the alpine and tundra biomes.In these extreme seasonal systems, breeding periods are restricted to a narrow temporal window and there are limited opportunities for second breeding attempts (Camfield and Martin 2009).Individuals must cope with a variety of environmental factors (Martin and Wiebe 2004), including limited nesting potential in years with high snowfall that lingers on mountain peaks (Clarke andJohnson 1992, Frederick andGutiérrez 1992) and inclement weather (Novoa et al. 2008, Martin et al. 2017).Studying birds in alpine ecosystems during the nesting season is often challenging due to limited accessibility caused by winter snowpack or the general remoteness of breeding areas (Chamberlain et al. 2011).This challenge has likely constrained the number of studies on nesting alpine birds and restricted inference to a limited set of geographic areas accessible for field observations (Chamberlain et al. 2011).Therefore, our understanding of larger-scale variation of vital rates in alpine birds is reduced due to sampling limitations.
There are only a few bird species that breed exclusively in alpine environments in North America (Martin 2001).These species demonstrate both altricial (e.g., passerines) and precocial (i.e., ptarmigan) nesting strategies.Most alpine breeders are passerines (e.g., Horned Lark Eremophila alpestris; American Pipit Anthus rubescens; Brown-capped Rosy-finch Leucosticte australis) that seasonally migrate upward from lower elevation habitats below treeline (Martin 2001), but White-tailed Ptarmigan (Lagopus leucura) spend their full annual life cycle in the sub-alpine and alpine elevation zones (Martin et al. 2015).White-tailed Ptarmigan are ground nesting birds that form pair bonds that generally last through the breeding and early incubation periods.Female White-tailed Ptarmigan raise precocial young through early summer, but broods may remain together into early fall (Martin et al. 2015).Females can renest if their first nesting attempt is unsuccessful during the laying or early incubation stages, but renesting may be infrequent and the number of eggs in second clutches is usually lower than in first nests (Giesen and Braun 1979a).The general breeding behavior and nesting ecology of White-tailed Ptarmigan have been extensively described from populations studied at two sites in Colorado (Giesen and Braun 1979b, Giesen et al. 1980, Martin et al. 2000), multiple sites on Vancouver Island (Fedy and Martin 2011), and one site in the Yukon (Wilson and Martin 2008).These studies have informed our understanding of White-tailed Ptarmigan reproductive biology, but insights from additional areas would add valuable information on geographic variability in nest survival.Furthermore, there have been extensions to statistical models since several of these foundational studies were published that allow for estimation of daily nest survival rates.Daily nest survival rates provide a way to estimate derived rates of nest success and will generally be more accurate compared to those estimated as a percentage of monitored nests that successfully hatched (i.e., apparent nest success), which is known to produce positively biased estimates because nests that fail early are never discovered (Dinsmore et al. 2002).
We analyzed nest monitoring data from six study areas in the Southern Rocky Mountains of Colorado collected as part of two radio-telemetry studies to estimate daily survival of Southern White-tailed Ptarmigan (L.l. altipetens) nests.Our objective was to estimate daily survival rates and evaluate potential differences between study areas by fitting a hierarchical survival model.Furthermore, we wanted to estimate nest success as a derived parameter for comparison to previously published estimates (Giesen and Braun 1979a, Giesen et al. 1980, Sandercock et al. 2005).We included several covariates in our model that represented environmental conditions that were potential drivers of daily nest survival (e.g., daily weather events and landcover at nest sites).Finally, we evaluated the influence of variation in nest success on the finite rate of population growth using a simulation from an age-structured transition matrix.We discuss the implications of our findings for applied management in terms of the effectiveness of targeting nest survival to influence the finite rate of growth.

Study area
We monitored nests at six alpine sites located throughout the Southern Rocky Mountains of Colorado (Fig. 1).These sites were, from north to south: Trail Ridge and Mount Blue Sky, in the Front Range in northcentral Colorado; Independence Pass and Mt.Yale, in the Collegiate Range of central Colorado; and Mesa Seco and Ice Lake, in the San Juan Mountains of southwestern Colorado.The mean of site-level average elevations was 3637 m and ranged from 3437 m (Trail Ridge) to 3789 m (Independence Pass).Alpine in the Southern Rocky Mountains consists of open areas with landcovers ranging from willow (Salix sp.) and spruce (Picea engelmannii) communities in mesic basins at lower elevations, mixed herbaceous sedge-grass communities at middle elevations, cushion plant communities in wind-exposed areas at higher elevations, and exposed gravel and rock along ridges and talus slopes.The landforms at our study areas were characterized by variable mountainous topography, with plateaus, steep slopes and cliffs, and lower elevation basins interlaced with lakes and streams.Climate patterns at our study areas were highly seasonal, with precipitation primarily in the form of snow in the non-growing season (Sep-Apr), and rain or sleet throughout the growing season (May-Aug).Average nesting season climate conditions based on monthly 4-km gridded climate data (PRISM 2014), subset to years and areas of our study extents, were as follows.Average cumulative precipitation during the breeding and broodrearing season (mid-May to early-Aug) was 19.5 cm and ranged from 13.5 cm (Mesa Seco) to 22.0 cm (Ice Lake).Average minimum and maximum temperatures over this same period were 0.89°C and 13.9°C, respectively, and the site-level ranges (low to high) varied from -0.03-13.1°Cat Mount Blue Sky, and 2.4-15.2°Cat Mesa Seco.Several of our sites had different forms of disturbance.The Mesa Seco site had domestic sheep grazing during summer and fall, and Trail Ridge, Independence Pass, and Mount Blue Sky sites each had a surface road bisecting the study area boundaries.The Trail Ridge and Ice Lake sites experienced high human foot traffic in summer, although foot traffic at the Trail Ridge site was heavily managed and largely relegated to designated trails, while the Ice Lake site was not.Ptarmigan hunting was prohibited at Trail Ridge and prohibited within onehalf mile of the road at Mount Blue Sky.At all other sites, hunting was regulated based on statewide season and bag limits set by Colorado Parks and Wildlife, with the season beginning 9 September, after nests were no longer active, and ending either 1 October (Mount Blue Sky, Independence Pass, Mt.Yale) or 26 November (Mesa Seco, Ice Lake).

Field surveys
We conducted field work during the spring and summer from 2013-2016 at all sites, and one additional year (2017) at a subset of sites (Independence Pass and Mt.Yale).Data were collected for research projects run by Colorado State University (Trail Ridge and Mount Blue Sky) and Colorado Parks and Wildlife (remaining sites).At all sites, we initially located birds in spring (mid-May to mid-Jun) using a combination of broadcasting male territorial calls (Braun et al. 1973) and searching exposed vegetation and open areas above snowpack, often around the edges of snowfields.Males located from territorial callbacks were often paired with females.We captured females using a 60-lb nylon-coated steel-wire noose placed at the end of a telescoping pole (5.5-m length), modified slightly from the design described in Zwickel and Bendell (1967).Females were classified as yearlings or adults based on the presence of pigmentation in primary feathers 9 and 10 and primary shape (Braun and Rogers 1971).All females were banded with a numbered aluminum State of Colorado band and 1-4 plastic colored bandettes (ProTouch Engraving, Inc.) for identification.Females were fitted with a 9g very high frequency (VHF) radio collar attached with an elastic neck loop (model RI-2DM; Holohil, Carp, Ontario).
We relocated females using a 3-element antenna and VHF receiver to obtain visual observations until a hen was confirmed to be on a nest, after which time we used triangulation from a distance of 20-30 m to determine if a female was still nesting.Across all sites, the average relocation rate of females occurred once every 4.0 days (SD = 2.29).Nest contents were inspected approximately 10 days after nest discovery at a subset of sites and years (Mesa Seco, Mount Blue Sky, and Trail Ridge from 2013-2016).During nest inspections, we wore nitrile gloves and weighed each egg and recorded its dimensions to calculate egg volume.During a subset of years in 2014-2016 (Mesa Seco, Mount Blue Sky, Trail Ridge), two small temperature loggers (Thermochron iButton DS1921G; Maxim Integrated) were pinned to the bottom of nest bowls to record the exact date a nest hatched or failed based on changes in temperature patterns (Wilson and Martin 2012).Nests were inspected visually any time a female was located off nest and the nest contents were recorded.We tested for a potential effect of both the iButton and nest measurements by comparing nest fates among nests that had survived at least 10 days (to avoid a potential selection bias if older nests survive at higher rates).We fit a logistic regression model to nest fate with either iButton or inspection as a binary covariate and compared it to an intercept-only model using a likelihood ratio test.Significance of this test (α = 0.1) would indicate an effect of the covariate on nest fate.

Daily nest survival
We used known-fate models applied to nest data to estimate daily nest survival rates (Royle and Dorazio 2008).These models depend on the following information: (1) the date a nest was found; (2) the date a nest was last observed active; (3) the date a nest was last visited; and (4) the nest fate (hatched or failed).The date of hatch for successful nests is assumed to be precisely known and equal to the date last observed alive.In contrast, failed nests do not require precise dates of failure, which is only assumed to occur between the date the nest was last observed alive and the date the nest was last visited, with no assigned outcomes for dates in between.We typically did not know the precise date of hatch for nests that lacked temperature loggers.For these nests, we assigned the hatch date as the mid-point date between the last date the nest was observed active and the date last checked.We assigned both hatch and failure dates using information collected from the temperature loggers for all other nests.
We created a nest history array in which each nest corresponded to a row, and each column corresponded to an ordinal day.We evaluated covariates that varied daily or were constant across all days a nest was under observation.We included daily precipitation, daily minimum temperature, and an interaction between the two to represent weather conditions, collected from gridded spatial layers (Daymet daily surface weather data on a 1km grid for North America, v. 4; Thornton et al. 2020).We calculated the age of each nest, defined as the number of days elapsed since the estimated date the first egg was laid, for every day the nest was under observation.We included covariates for percent shrub cover (Rigge et al. 2020) and elevation (USGS 3DEP 1 arc second digital elevation model), summarized as the mean of 30-m pixel values within a 100-m radius buffer around nests, and hen age (coded as yearling = 0 and adult = 1).Sites varied considerably in elevation, so within each site we centered elevation by subtracting the mean to make inference on the relative elevation of nests compared to others within the same site.We initially treated elevation as unscaled in our model, but we had difficulty achieving model convergence for the associated slope coefficient, potentially due to a correlation between elevation and the factor levels of site (i.e., both contain redundant information).However, as additional justification, we also hypothesized that a hierarchy in the quality of breeding territories might vary as a function of elevation, and relativizing elevation within each site was a useful way to capture this information.We centered and scaled all other covariates by subtracting the mean and dividing by the standard deviation.We confirmed that pairwise correlations between covariates were low (Pearson |r| < 0.6 for all pairwise comparisons) prior to model fitting due to effects multicollinearity can have on coefficient interpretation (Dormann et al. 2013).
We fit nest survival models in a Bayesian hierarchical modeling framework using a Markov-chain Monte Carlo (MCMC) algorithm to sample from the posterior probability distribution.We specified the model likelihood using a Bernoulli distribution, in which the probability of the binary outcome was a function of K covariates on the logit scale: The indexing refers to individual nest i, covariate k, site s, and time t (daily time scale).We used the vague normal prior specification recommended by Northrup and Gerber (2018) for covariate coefficients fit on the logit scale as β k ~ normal (0, 1.5).
We treated site as a random effect, α s , with prior distribution α s ñormal (μ, σ site ²) and hyperpriors for mean and variance specified as μ ~ normal (0, 1.5) and σ site ² ~ inverse gamma (0.001, 0.001), respectively.Therefore, the random effects parameters α s represents site-level intercepts.We exponentiated the daily nest survival rate by the combined duration of egg-laying and incubation (31 days) to obtain nest success as a derived parameter.The full mathematical expression of the posterior and joint distributions is presented in Appendix 1.
We did not conduct model selection because each covariate (excluding the site-level effects) had prior biological support for White-tailed Ptarmigan or other alpine nesting birds and because we were interested in the coefficient estimates for each covariate to evaluate the magnitude of their effects on daily nest survival and success.However, we were interested in the amount of shrinkage induced by the random effects model structure we included in our model, particularly given the limited number of levels in the site (6) effect.To evaluate the influence of random effects, we fit an alternative version of our model with fixed site effects and compared the marginal posterior distributions of sitelevel daily nest survival between the two models.A low amount of shrinkage and similar site-level estimates between the fixed and random effects models would indicate the statistical site units have different daily nest survival, whereas high shrinkage would indicate the opposite, or alternatively, that there are inadequate numbers of observations per site to draw such a conclusion.We fit models using the statistical software R (v4.0.2;R Core Team 2021) and the "rjags" library (Plummer 2013).We ran 3 chains for 5000 iterations after an initial burn-in of 10,000 (fixed effects model) or 40,000 iterations (random effects model) and saved every 5 th sample to obtain final marginal posterior samples of 3000 for each parameter.We confirmed parameter convergence by checking that the Gelman-Rubin statistic was less than 1.1 (Gelman and Rubin 1992) and visually inspecting trace plots for evidence of chain mixture for all parameters.

Nest success and finite growth rate
After fitting models, we examined the likely effect of variation in nest success on the finite population growth rate λ obtained using published field estimates of vital rates.We did a simple simulation using the age-structured transition matrix from a pre-breeding census model presented in Sandercock et al. (2005) and the means and variances of vital rates estimated in that study.However, we used breeding-age survival estimates obtained from radio telemetry of breeding-age females presented in Seglund et al. (2018) and the nest success estimates derived from the daily nest survival random effects model for the corresponding parameters in the transition matrix.We used the survival estimates from Seglund et al. (2018) because they were obtained from knownfate data, rather than apparent survival estimates obtained from mark-recapture data (Sandercock et al. 2005, Wann et al. 2014), the latter of which may be negatively biased in the presence of site infidelity.We randomly generated transition matrices with different vital rate values using a lognormal (rates ≥ 0) and beta (rates between 0-1) distribution and the associated mean and variance estimates of the vital rates, which we moment matched for beta distributions to calculate the corresponding shape parameters (Hobbs and Hooten 2015).We regressed the simulated growth values against their corresponding nest success rates, similar to a life stage simulation analysis (Wisdom et al. 2000).We lacked information to include covariances between vital rates in our simulation, but we acknowledge the presence of such correlations could lead to bias in our simulations (Morris and Doak 2002).Additional details on the simulation are presented in Appendix 2.

RESULTS
We estimated daily nest survival from 198 nests produced by 128 females observed from 2013-2017.We monitored 74 out of 198 nests (37%) with iButton temperature loggers, and we conducted nest inspections on 131 out of 198 nests (66%).The likelihood ratio tests did not indicate an effect on nest fate for nests with iButtons (df = 1, χ² = 1.50, P = 0.22) or nest inspections (df = 1, χ² = 2.25, P = 0.13).The number of observed nests monitored varied considerably by site and year (Table 1), which was mostly a function of sampling effort and the number of females marked and monitored with VHF transmitters.Across all sites and years, 109 nests hatched, for an apparent nest success rate of 55.1% (95% CI: 48.0-62.1%).We attributed all failed nests to predation based on the presence of crushed eggshells, missing eggs, and predatorkilled hens.Our derived estimates of nest success from daily survival were lower than the apparent nest success estimate.We estimated a mean derived nest success rate of 45.6% (95% CI: 31.2-59.6%)across all sites and years for the full model that included random effects, and 44.6% (95% CI: 37.4-52.4%)for the model with fixed effects.The site at Ice Lake had the lowest nest success, and Independence Pass had the highest, with random effects inducing considerable shrinkage toward the grand mean population estimate (Fig. 2).We did not find evidence that any of the covariates in our model strongly affected variation in daily nest survival (parameters presented are from the model with random effects); the marginal posterior distributions largely overlapped 0 for most covariate coefficients (Fig. 3).However, the slope coefficient for relative elevation was mostly negative (β elevation = -0.002;[P < 0] = 0.908), and the coefficient for nest age was positive (β nage = 0.230; [P > 0] = 0.980).The marginal posterior means for all other model parameters are presented in Table 2.
We estimated that λ increased 18.7% when evaluated across the 95% credible interval range of nest success (Appendix 2, Fig. A2.1), which was conditional on other estimated parameters in the transition matrix.A stable or increasing finite population growth rate (λ ≥ 1) was achieved when nest success was above 65.7%.Boxplot whiskers represent the 95% quantiles of parameter estimates.We obtained estimates for site-level fixed and random effects by predicting to the mean site-level covariate values and factor levels, which are shown in separate boxplots.The the overall mean effects (solid horizontal lines) and corresponding 95% credible intervals (dashed horizontal lines) are provided for random effects (light gray) and fixed effects (black).

DISCUSSION
Nest success has been identified as an important driver of population growth rates in many Gallinaceous species (Wisdom and Mills 1997, Sandercock et al. 2005, Taylor et al. 2012).
Understanding the sources of underlying variation in daily nest survival rates, or lack thereof, can provide useful information for developing applied management strategies (Hagen et al. 2009), or predicting changes in daily survival rates under different environmental scenarios (Skagen and Yackel Adams 2012, Grisham et al. 2013).Our work expands upon previous field studies of White-tailed Ptarmigan nesting ecology (Giesen et al. 1980, Wiebe and Martin 1998a, b, Sandercock et al. 2005) and provides estimates of daily nest survival rates from new areas in the southern portions of the White-tailed Ptarmigan occupied range.Our findings provide important information on site-level variation in daily nest survival rates, and how these rates relate to environmental effects thought to influence White-tailed Ptarmigan reproduction.Importantly, because we estimated daily nest survival rates directly, our estimates are likely to be less susceptible to biases that can occur when nest success is directly estimated from observed proportions of hatched nests to monitored nest, and when exposure times are not considered (Jehle et al. 2004).

Comparison to past studies
Several studies have provided important context for our estimates of nest success derived from daily nest survival.Clarke and Johnson (1992) monitored 94 White-tailed Ptarmigan nests (nest location methodology not reported) in the Sierra Nevada mountains of California and presented data indicating 36.9% apparent nest success (calculated from Tables 1 and 2 in Clarke and Johnson 1992).In Colorado, Giesen et al. (1980) monitored 60 nests across multiple sites throughout the state by locating hens during feeding bouts shortly before dusk and following their movements back to nests.They observed an apparent nest success rate of 56.7%.Sandercock et al. (2005) evaluated reproductive data collected from prior studies of White-tailed Ptarmigan in Colorado at Mount Blue Sky and three nearby sites via radiotelemetry tracking of hens (Wiebe andMartin 1998a, b, Martin et al. 2000).Nests were limited to those found early in the egglaying stage, thereby reducing potential bias of nest age on the resulting estimates of nest success.Across age classes and nesting attempts, the apparent nest success rate was 34.6% (calculated from results presented in Table 1 of Sandercock et al. 2005), similar to our estimate of 39.9% at Mount Blue Sky.Using some of the same data from Colorado presented in Sandercock et al. (2005), Wilson and Martin (2011) derived nest success from daily nest survival and obtained a much lower estimate of 24%.Our derived estimate of 45.6% nest success (combined across all sites and years) is higher than most but lies within the range of these prior findings.Differences in nest success between our work and past studies may have been due to differences in the years and locations observations were collected (i.e., there was a considerable lack of overlap in these factors between studies).Furthermore, comparing apparent nest success to estimates obtained from daily survival rates can lead to different estimates.For example, Giesen et al. (1980) may have missed nests lost early in the laying stages because nests were found using behavior associated with the incubation stage (hens stopping incubation to feed).Presumably this effect could positively bias nest success, particularly in light of the positive effect of nest age on daily survival.
We estimated site-level nest success using both fixed and random effects.Under fixed effects, the site estimate was of direct interest.Importantly, we found that the Ice Lake site had the lowest derived nest success.In contrast, differences among the other sites were relatively small.When we included random effects in our model, the underlying "global" population (i.e., the Southern White-tailed Ptarmigan population) was of interest, and sites were considered random samples from this population.Importantly, random effects induced site-level shrinkage toward the population mean.This effect was strongest on the Ice Lake daily survival rate, which correspondingly had the fewest number of nests monitored.This is expected behavior from random effects that pull group levels with smaller numbers of observations more toward the global mean.Alternatively, sites with daily nest survival that strongly differs from others under fixed effects may be of special interest.For example, Ice Lake may be experiencing unique conditions related to human recreation or other disturbance factors that we did not capture in our covariate set, but the small number of nests monitored at this site limits us from drawing a firm conclusion.Overall, the global population estimates of nest success obtained under random effects are the most general (and therefore most widely applicable) information we have on Southern White-tailed Ptarmigan daily nest survival and nest success.

Environmental effects
Variation in daily nest survival rates was not strongly driven by factors we thought were likely to be important.With the exception of nest age and elevation, the coefficients for the other covariates in our model all had posterior distributions largely overlapping 0, suggesting their effects were either not particularly strong or absent.We found only a weak indication of a negative precipitation effect, and no evidence of a temperature or interactive effect between temperature and precipitation.Despite there being three ptarmigan species occupying large distributions throughout the northern Holarctic, we are aware of no studies that have reported strong links between variation in daily nest survival and weather events in any species of ptarmigan.1983).Perhaps the range of precipitation conditions under which the nests we observed were too limited to detect a clear effect.For example, the snowstorm of 1995 described by Martin et al. (2000) would presumably have produced a signature in daily nest survival, but our nests were not under observation during any extreme weather events comparable to 1995.
Our model indicated that daily nest survival was negatively related to relative elevation, i.e., the difference between the mean site-level elevation and elevation at a specific nest location.In areas where White-tailed Ptarmigan sympatrically overlap with Rock Ptarmigan (L.muta), they occur at higher elevations with marginal cover and vegetation structure (Wilson and Martin 2012), but they experience higher nest success and number of hatched young than Rock Ptarmigan (Wilson andMartin 2010, 2012).At our study sites, we found a negative correlation between relative elevation and shrub cover (Pearson r = -0.481).Although shrub cover was only weakly related to daily nest survival, ptarmigan preferentially select shrub cover when it is available (Spear et al. 2020), and previous studies have reported higher nest success with shrub concealment (Wiebe and Martin 1998b).On average, we also expect that higher elevations may be associated with lower-quality territories in terms of shrub food and concealment availability, which could have negative effects on the body condition of ptarmigan hens and subsequent fitness (Robb et al. 1992).
Relationships between daily nest survival and nest age are seemingly equivocal in the grouse literature, with studies reporting positive (e.g., Moynahan et al. 2007, Wilson et al. 2007) and negative relationships (e.g., Davis et al. 2015, Zhao et al. 2020, Barker et al. 2022).A positive relationship may be a result of progressive vegetation growth (and subsequent concealment) around nests as they age (Gibson et al. 2016), or due to females spending progressively longer periods on nests resulting in reduced opportunities for predators to detect them.
Our results suggest that daily nest survival of White-tailed Ptarmigan at the sites we studied were largely invariant to the environmental conditions we examined.Nonetheless, site-level variation in daily nest survival did exist, but the drivers of this variation were not well explained by our model.We observed no abandoned nests in our sample, and we attributed all nest losses to predation by either mammals or birds.Management implications Sandercock et al. (2005) reported that variation in breeding-age and juvenile survival were the strongest drivers of finite growth rates in White-tailed Ptarmigan, suggesting those rates are of particularly high relevance to target if populations are directly managed.Nonetheless, we still found that the finite rate of population growth was predicted to increase by 18.7% when evaluated across the 95% range of estimated values of nest success, indicating that management targeting the nesting stage can be beneficial to increase growth rates, even though it is not the strongest driver of growth.Furthermore, our pooled (across sites) estimate of nest success during the 2013-2017 period was considerably higher than a previous estimate obtained from 1986-1997(Sandercock et al. 2005)).During this period, Sandercock et al. (2005) estimated that the vital rates at Mount Blue Sky and surrounding areas were insufficient to support a stable population (λ = 0.73).Our use of those vital rates in the simulation probably explains why our estimated threshold of nest success required for population stability was higher (65.7%) than our statewide estimate (45.6%).
An important challenge in managing for nest success is the lack of any obvious environmental factors that would be amenable to management manipulation.Although the environmental variables we fit to explain daily nest survival did not strongly drive variation in this rate, we note that the dataset that represented shrub cover was fairly coarse (30-m pixel) and derived from satellite imagery, which can miss important microhabitat conditions at nest sites.Future studies can likely add valuable insights by recording field-based measurements of vegetation and visual obstruction at the nest.Furthermore, there was evidence that nest age led to higher rates of nest success, and that nests at higher relative elevations were less likely to survive.These results indicate that habitat at lower elevations, potentially representing areas with suitable nesting habitat conditions, such as concealment cover, are important for Southern White-tailed Ptarmigan (but see Wiebe and Martin 1997 for findings related to trade-offs in concealment cover and female survival).Our finding that all failed nests were likely due to predation indicates that future studies of White-tailed Ptarmigan nesting ecology could greatly benefit from studies that pair nest monitoring with estimation of local predator abundance.Additionally, camera traps at nests could be a useful tool to classify the species responsible for nest loss.
Although daily nest survival may be largely determined by local predator communities more so than any specific habitat configurations or conditions in ground nesting birds (Stanley et al. 2015, Smith et al. 2020, Zhao et al. 2020), focusing on nesting habitat near treeline is likely still beneficial, not only to increase potential nesting habitat, but also as an important source of food and cover in early spring.Shrub cover at our sites was a combination of spruce and willow, the latter of which is critical both as a source of food and nest cover for White-tailed Ptarmigan, which can be improved in terms of establishment and regeneration through applied habitat management (Zeigenfuss et al. 2011).
the slope of the relationship.There are important caveats to this simulation.First, we lacked the necessary annual estimates to consider correlations between vital rates, which could modify the relationships.Second, the identified thresholds for λ ≥ 1 are expected to change with different underlying vital rates (e.g., if vital rates vary by site).For example, Sandercock et al. (2005) found that the internal demographics of the white-tailed ptarmigan population at Mount Blue Sky and surrounding areas were insufficient to sustain the population (λ = 0.73), which indicates that using vital rates from this population to simulate λ will result in a high identified threshold for nest success to stabilize the population.We therefore suggest that the percent change across the range of nest success values is the most informative piece of information to come from this simulation.Nonetheless, the vital rates in this simulation were estimated from field data and represent a realistic scenario for some white-tailed ptarmigan populations in Colorado.

Fig. 2 .
Fig. 2. Estimates of derived nest success for Southern Whitetailed Ptarmigan (Lagopus leucura altipetens) in Colorado.Study areas were Ice Lake (IL), Independence Pass (IP), Mount Blue Sky (MB), Mesa Seco (MS), Mt.Yale (MY), and Trail Ridge (TR).Derived nest success was obtained by exponentiating the daily survival rates of each site by 31 days.Boxplot whiskers represent the 95% quantiles of parameter estimates.We obtained estimates for site-level fixed and random effects by predicting to the mean site-level covariate values and factor levels, which are shown in separate boxplots.The the overall mean effects (solid horizontal lines) and corresponding 95% credible intervals (dashed horizontal lines) are provided for random effects (light gray) and fixed effects (black).

Fig. 3 .
Fig. 3. Marginal posterior distributions of slope coefficients and standard deviation of site-level random effects estimated for daily nest survival of Southern White-tailed Ptarmigan (Lagopus leucura altipetens) nests monitored at study areas in Colorado.Vertical gray lines are placed at 0.

Figure A2- 1 .
Figure A2-1.Change in finite growth rate (λ) as a function of nest success probability.Nest success probability was derived from daily nest survival estimated for southern white-tailed ptarmigan (Lagopus leucura altipetens) nests monitored across 6 study sites in Colorado.Each point represents a simulated growth rate from a transition (Leslie) matrix with randomly generated vital rate values.The blue line represents the predicted relationship from a linear regression, and horizontal and vertical red lines indicate the intersection of stable λ (1) and nest success probability (0.657).

Table 1 .
Southern White-tailed Ptarmigan (Lagopus leucura altipetens) nests monitored at six study areas in Colorado from 2013-2017.The number of nests monitored is provided for each site-year (number of hatched nests is indicated within parentheses).

Table 2 .
Summary statistics of marginal posterior distributions for parameters estimated from a daily nest survival model with random effects fit to Southern White-tailed Ptarmigan (Lagopus leucura altipetens) nests monitored at six study areas in Colorado.The mean, standard deviation, 95% credible intervals, and probability of covariate coefficients being below or above 0 (P).Study areas were Trail Ridge (TR), Mount Blue Sky (MB), Independence Pass (IP), Mt.Yale (MY), Mesa Seco (MS), and Ice Lake (IL).The parameter S represents daily survival, and the parameter MNS represents mean nest success.
(Wilson et al. 2007)005)d low rates of nest abandonment in White-tailed Ptarmigan (2%) and similarly attributed nest loss to predation.We documented a moderate rate of 86.7% hatchability in nests (95% CI: 80.0-93.6%),indicatinginfertilitywaslikelynot strongly limiting the nesting component of reproduction.We also found no impact of hen age on nest success.Older females lay more eggs and are more likely to renest but are not more likely to have successful nests(Sandercock et al. 2005).Overall, lack of hen age effects, nest predation, and annual variability between sites are common themes in our work and previous studies of nesting ptarmigan(Wilson et al. 2007), suggesting ptarmigan daily nest survival and nest success are largely driven by ecological factors outside the scope of the environmental effects we evaluated (e.g., predators, disturbance, and severe climatic influences).