Environmental covariates.
Hourly ambient temperature (°C) was collected using Thermocron ® iButton loggers (Maxim Integrated) from 25 May to 31 July 2016, 2018, and 18 May-3 August 2019 and 2021. Loggers were placed at long-term GPS coordinates (Duclos et al., 2019) that represented the elevation gradient we were interested in and corresponded with bins used for nests (280m, “BEF”; 550m, “Low Jeff”; 800m, “Mid Jeff; and 1,200m, “High Jeff”). Loggers were held in a Holden shield to protect the iButton from direct solar exposure (Holden et al., 2013). Daily average temperature, minimum daily temperature, and temperature range was calculated and used to analyze the effect on daily nest survival. Precipitation data were collected in 2019 and 2021 using Onset ® HOBO ® RG3-M rain gauges. To capture the daily cumulative rainfall across the elevation gradient, we placed three rain gauges at Mt. Jefferson at locations similar to the iButton loggers (500m, “Low Jeff”; 800m, “Mid Jeff”; and 1,200m, “High Jeff”) in open areas with no tree canopy. We used precipitation data collected in BEF (250m, “BEF”) from the NSF National Ecological Observatory Network (NEON), an open-sourced data platform. Within each rain gauge is a tipping bucket that measured how much cumulative precipitation fell each day throughout the season. Precipitation data were not collected in 2016 and 2018 and, therefore, will not be analyzed with nest survival data from those years. Rain intensity was quantified by how much rain (mm) was recorded per hour per day.
Due to equipment malfunctions from the HOBO Rain Gauge placed at 500m (i.e., “low-Jeff), precipitation data from 1 July – 3 August 2021 was lost. To estimate the missing daily precipitation at this location for the remainder of the 2021 season, we used the Random Forest (RF) machine-learning algorithm. When tested against other algorithms to estimate large amounts of missing precipitation data, the RF was the most preferred method (Aguilera et al., 2020), in the context of our data. The RF algorithm is a non-parametric imputation method that takes observed values of each variable, and predicts the missing values, without having any assumptions about the distribution of data or imputation models. We followed the recommendations from Aguilla, Guardiola-Albert and Serrano-Hidalgo (2020) and included dummy variables to account for no rain days, a Hanssen-Kuipers (HK) score to distinguish between occurrences and non-occurrences of a rain event (Hanssen and Kuipers 1965), and an NRMSE (normalized root error mean squared error) error metric to allow for the comparison of the average relative differences between the observed and imputed missing values (Supplementary Figure 1).
Dummy variables were produced by randomly assigning the missing data matrix with presence (1) or absence (0) of rain days. For each day we considered the dates where the dummy variable was 0 and input 0 for that day, and only the days the dummy variable predicted a value of 1 did we input the numeric value estimated from the RF algorithm. The HK score ranges between -1 to +1, where 0 represents no skill or a random estimate, and 1 indicates a perfect estimate, and has been widely used to evaluate yes/no meteorological forecasts (Woodcock 1976, Teegavarapu 2014, Kim and Ryu 2016). We used the package missForest in R Studio (version 2022.07.0; R Core Team 2022) for the RF algorithm to input missing precipitation values.

Statistical analysis.

Daily survival rate. We measured the daily survival rate (DSR), i.e., the probability that a nest survives one day (Dinsmore et al., 2002; Mayfield, 1961) to better understand how abiotic factors (temperature and precipitation), nest initiation date, elevation, and other temporal variables influence nesting survival of Swainson’s thrush. We analyzed DSR using the RMark package (Laake et al., 2013) in R Studio (v. 2022.07.0). This package calculates estimates of DSR using a maximum likelihood estimator with the logit-link function with predictor variables. The assumptions are that DSR is the same for all nests on all days and for all nest ages (nest fates are independent and identically distributed: iid ; Rotella, 2006) though there is currently no goodness-of-fit test for nest survival models in rMark (Dinsmore et al., 2002; Laake et al., 2013), and rMark cannot run mixed models (Rotella et al., 2004). Daily survival probabilities were calculated by taking the beta parameter estimate and raising it to the power of the number of nesting days (i.e., 28 for Swainson’s thrush). See Rotella et al. (2004) for a more in-depth description of how MARK interprets the temporal covariates as an encounter history. We included nests in our analysis when they met the following criteria: 1) known day the nest was found, 2) the last day the nest was active, 3) the last day the nest was checked, and 4) known nest fate (i.e., fledged or failed). We standardized the ordinal dates to be the duration that nests were first active (i.e., initiation date) which translated to 0 (1 June) until the last known active nest date, 63 (2 August) over the four years (number of occupancy days, NOCC = 63).
Environmental covariates. We used cumulative daily precipitation (mm; 2019, 2021), categorical rain events denoted as either no rain (0), “light” rain (0.1-6.9mm) or “heavy” rain (>7mm), and rain intensity (mm per hour) as predictor variables in our daily survival models. Rain event parameters were determined by examining the data in a frequency plot and categorizing “light” and “heavy” rain days accordingly. Average daily temperature, minimum daily temperature, and daily temperature range (°C; 2019, 2021) were separately modeled against daily survival to better understand how temperature in the White Mountains affects daily survival probability. Nests from 2016 and 2018 were excluded from precipitation and temperature analysis because we did not collect climate data from those years. Nests were binned in four groups (“BEF” = 200-300m; “Low Jeff” = 500-700m; “Mid Jeff” = 701-900m; “High Jeff” = 901-1,250m) to correspond with the matching spatial precipitation and temperature data that was collected along the elevation gradients.
Model selection. We began the model building stage by testing pairwise correlation comparisons in our predictor variables for our nest survival data (elevation, nest age, initiation date) and the environmental covariates (elevation, daily average temperature, minimum daily temperature, temperature range, daily cumulative precipitation, and rain intensity). This comparison revealed a negative correlation coefficient with elevation and daily temperature range (p =-0.46) and, therefore, these variables were not included in the same model.
We created 14 a priori DSR univariate models that examined the effects of temporal variables including nest age, julian date, and year, as well as initiation date, elevation, and our weather covariates on the daily nest survival of Swainson’s thrush (Table 1; models 2-3, 5-13). We also included an intercept model (model 1) in which only daily survival rate was estimated, and a quadratic time trend (model 4), which allows for nest survival to fit a curvilinear pattern, since survival over time is not always linear. We included several other models (Supplementary Table 1) in the initial stages of model building to test for any relevant additive or interaction effects, including a global model, but because they did not perform well, they were removed from our final analysis.
After evaluating variables a priori models above, and removing necessary models that performed poorly, we added two additional models with interaction effects (year and elevation) with seasonal time. This predictor variable performed the best against DSR (Table 1; models 15 and 16). We then built four more models that included biological interaction and additive effects we were interested in (models 17-23) to explore all potentially important relationships between our variables and DSR. In the final stage of model building, we used AIC (Akaike’s Information Criterion) to find support for the most parsimonious model that best described DSR (Anderson & Burnham, 2002) and compared models 1-5 (Table 1) between all years, and models 6, 8-13, and 19-20 for 2019 and 2021 (Table 1). We considered the best model to have a ∆AICc value of zero, variables in models that were within 4 ∆AICc of the best model with 95% confidence intervals not including zero to be strongly supported (Arnold, 2010), and variables in models within 4 ∆AICc with 90% confidence intervals to have some support (Hein et al., 2008; Long et al., 2008). Model outputs are reported with 95% confidence intervals otherwise noted.

Results