Effort Corrections

Netting effort varied between years as a result of adding netting periods in April (starting in 2012) and missing periods or truncating days in response to inclement weather or other logistical constraints. Because of this variation, the intended effort (10 nets run for 6 hours per period or 60 intended net-hours per period) in a survey was not always met. The timing of missed or gained effort during a season or period can alter capture rate estimates and thus skew vital rate calculations. For example, the ratio of juveniles to adults resulting from not capturing adults during times when nets were closed before young-of-the-year fledge or not capturing juveniles during times when nets were closed after fledging, could result in over- or under-estimating productivity, respectively.

We followed methods developed by DeSante and others (2015) to summarize effort and capture data for a single station and to correct capture data for inconsistencies in seasonal effort with modifications for time of capture during the day. Effort corrections began by dividing the banding day into five time bins relative to sunrise: (1) 1 hour before sunrise to 1 hour after sunrise; (2) 1‒2 hours after sunrise; (3) 2‒3 hours after sunrise; (4) 3‒4 hours after sunrise; and (5) more than 4 hours after sunrise. We then compiled the actual effort expended (number of hours nets were open multiplied by number of nets that were open) for each time bin, each sampling period, and each year (A_b,p,t, where b is time bin [1‒5], p is sampling period [1‒13], and t is year [2009‒20, excluding 2016 when the station was not operated]). Second, we summed actual effort for all time bins within a period to get the total actual effort per period:

where Third, we calculated the proportion of total actual effort per period represented by each time bin: where Fourth, we set intended effort (I_b,p,t) as 10 net-hours for time bins 1‒4 and 20 net-hours for time bin 5. Finally, we calculated the proportional difference between intended and actual effort to produce a correction for missed or gained effort within each period for each time bin. If actual effort was less than intended effort, a positive correction would be generated. where

Captures per year were calculated by age and by species for all year-unique captures (including birds of undetermined age). To calculate captures per year using effort correction, we began by summing the number of year-unique captures for each species by time bin (n^A_b,p,t for adults, n^J_b,p,t for juveniles, and n^T_b,p,t for all captures). Next, we summed the total number of year-unique captures for each species by period by year:

where where where Then, we calculated the proportion of period captures represented by each time bin for each species: where where where We then calculated an effort correction factor to approximate the proportion of birds missed or gained in a time bin in each period and year that were a result of missing or extra effort: where where where Finally, we calculated the corrected numbers of adults, juveniles, and all captures by species for each year based on the observed number of year-unique captures and effort correction factors: where where where For all analyses and results, captures=year-unique effort-corrected captures, unless otherwise indicated.

In table 2, we present an example of effort correction for a hypothetical period 5 banding day in 2016. For this example, 10 nets were open for 5 hours each, and all nets were closed 1 hour early because of excessive wind. Total actual effort (e_5,2016) was 50 hours, and total year-unique captures in period 5 (N^T_5,2016) was 100. For this example, the actual effort in time bin 5 (that is, more than 4 hours after sunrise) was 10 hours, while the intended effort was 20 hours. This corrected the number of captures (n^T_5,5,2016) upward for that time bin, from 10 captures to 12.5 captures. Therefore, the total number of effort-corrected captures for period 5 in 2016 (C^T₂₀₁₆) was 103 (rounded from 102.5).

Climate Variables

A number of climate variables had the potential to influence productivity and survival of the seven species we selected for these analyses. We selected climate variables based on their potential to explain annual life stages of the focal species. Specifically, we selected bio-year precipitation, or total precipitation from July 1 _{(year x−1)} to June 30 _{(year x)}, a date range which encompasses the entire winter, the typical period of high rainfall in southern California. We also divided annual precipitation into two periods, early winter precipitation (October 1_{[year x−1]}–December 31_{[year x−1]}) and late winter precipitation (January 1_{[year x]}–March 31_{[year x]}), which likely influences the timing of increased availability of food resources (seeds, fruits, and insects). We also selected mean maximum daily temperature in August_{[year x−1]} and mean minimum daily temperature in December_{[year x−1]} to represent the hottest and coldest periods of the year. Mean breeding season temperature (mean temperature from March 1_{[year x]} to June 30_{[year x]}) had the potential to influence breeding productivity. Mean bio-year temperature (mean temperature from July 1 _{[year x−1]} to June 30 _{[year x]}) provided an annual measure of potential climate change within the same period as bio-year precipitation, and it can be useful in comparing with results from other regions. Daily temperature and precipitation data were gathered from the Brown Field Municipal Airport (National Oceanic and Atmospheric Administration, 2022), 11 km east of the MAPS station, for the years that the MAPS station was operated. Daily temperature and precipitation data also were gathered from Brown Field Municipal Airport for the years prior to station operation, when available, including 1945–46, 1954–61, and 1997–2008, to compare historical trends to trends during station operation. We used two-sample Student’s t-tests and Wilcoxon signed-rank tests to compare the means of precipitation and temperature before and during station operation. Any P-values less than 0.10 indicated that precipitation and temperature were significantly different before station operation than they were during station operation.

Annual Productivity

We used generalized linear models with a gaussian probability structure to model the effects of climate variables on annual productivity. Annual productivity is defined as the ratio of effort-corrected young (juvenile) captures to effort-corrected adult captures (C^J_t/C^A_t). For each of the seven focal-plus species, we created models relating annual productivity (the response variable) to mean breeding season temperature, mean bio-year temperature, bio-year precipitation, early winter precipitation, and late winter precipitation (predictor variables). To simplify interpretation of model results, we standardized the predictor variables before analysis by subtracting the mean and dividing by the standard deviation. We excluded 2018 Wrentit productivity from our analyses because unique-year captures were unusually low (5 individuals), and 80 percent (4/5) were juveniles, creating an artificially high productivity estimate for that year.

We created a set of a priori models containing the predictor variables and used an information-theoretic approach (Akaike’s Information Criterion for small sample sizes, or AIC_c) to evaluate support for each model (Burnham and Anderson, 2002). To build our model set, we first generated a constant (null) model to serve as a reference and a set of simple models, each of which contained a single predictor variable. Next, we began creating more complex models by adding other predictor variables to each of the simple models and evaluating them relative to the simpler model, eliminating those that did not improve on the simpler model by at least 2 AIC_c. All remaining models were ranked such that the highest-ranked model had the lowest AIC_c. Models were considered well supported if the ΔAIC_c (difference in AIC_c from the highest-ranked model) was less than 2. Only models with an AIC_c weight of at least 0.05 were presented in the final model set. After finalizing our model set, we evaluated the contribution of predictor variables to each model by examining the 90-percent confidence interval associated with the beta estimate for each variable. If the 90-percent confidence interval did not include 0, we had 90-percent confidence that the beta estimate differed from 0, and therefore, we determined that the variable likely contributed to the model. Models were created and summarized using the MuMIn package (version 1.43.17; Bartoń, 2020) in R (R Core Team, 2022).

Annual Survival

We analyzed annual survival of adults for the seven focal-plus species in Program MARK (White and Burnham, 1999) using the RMark package (Laake, 2013) in R (R Core Team, 2022). Survival analysis in Program MARK accounts for individuals that were present but not captured by modeling both survivorship and recapture probability. We estimated adult survival but not first-year survival because first-year survival was low for all species, and therefore, we could not differentiate the probability of survival from recapture probability. Birds that originally were banded as juveniles (during their hatching year) were included in analyses as adults in subsequent years. We created encounter histories for each year from 2009 to 2020, coding capture or recapture as 1 and no capture as 0.

Effort was not constant across years because no nets were opened in early banding periods in some years (2009, 2010, 2011, and 2020). To determine whether differences in effort had an effect on survival analyses, we modeled recapture probability in two ways for each species: (1) one model with constant recapture probability and (2) one model with time-varying recapture probability (allowing recapture probability to vary by year), using constant survival in both models. We compared the AIC_c of the two models and selected the model with the lowest AIC_c. Models with constant recapture probability ranked well above models with time-varying recapture probability for all species except Orange-crowned Warbler. Therefore, for all species except Orange-crowned Warbler, we used constant recapture probability in all models. For Orange-crowned Warbler, we allowed recapture probability to vary by year in all models. Because the MAPS station was not operated in 2016, annual survival for 2015–16 and 2016–17 was estimated by MARK by interpolating from other years.

Survival models were created to examine the effects of sex and climate variables on annual survival of adults. Climate variables included bio-year precipitation, early winter precipitation, late winter precipitation, mean bio-year temperature, mean maximum daily temperature in August, and mean minimum daily temperature in December. For species that remained at the MAPS station during the winter (Bushtit, Orange-crowned Warbler, Song Sparrow, Common Yellowthroat, Wrentit, and House Wren), survival models were created with precipitation and temperature during the bio-year ending in the current MAPS season. For species that migrated away from the MAPS station during the winter (Least Bell’s Vireo), survival models were created with precipitation during the bio-year ending in the previous MAPS season because migrants were absent from the MAPS banding station from September to March of the current bio-year and, thus, their survival likely was more influenced by precipitation at the MAPS banding station during the previous bio-year than the current bio-year. Similarly, we did not include mean minimum daily temperature in December in models for Least Bell’s Vireo because the species was not present at the MAPS banding station during December. Model sets were created and evaluated using information theoretic approach (AIC_c; see the “Annual Productivity” section).

Predictors of Population Change

Breeding productivity and annual survival are inherently linked to changes in bird populations. Absent other influences, higher breeding productivity and higher annual survival should result in increased population size. We used multiple regression to evaluate the contribution of breeding productivity and annual survival to population change (λ, or N_{[year x+1]}/N_{[year x]}) for each of the seven focal-plus species. First, we estimated λ using Pradel reverse-time capture-mark-recapture models (Pradel, 1996) in Program MARK. For all Pradel models, we used constant survival and recapture probabilities to isolate annual λ. Then, we used annual productivity in year_x−1 and annual survival estimates from year_x−1 to year_x as predictors, and λ from year_x−1 to year_x as the response variable in multiple regression analysis. For each predictor within a multiple regression model, P-values less than 0.10 indicate that the predictor, in isolation, significantly influenced the population change of that species. An overall P-value less than 0.10 for the overall multiple regression model indicates that population change was influenced by the combination of predictors.

Data were analyzed using Program R. Analyses were considered significant if P≤0.10. Means are presented with standard deviations. All data from NOLF 2009 to 2013 used in analyses can be found in Lynn and others (2015).