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