Study site and general methods

The study was conducted at Hemlock Hill Field Station in Crawford County, Pennsylvania, USA (41.8°N, 79.9°W). The study site comprises 125 ha of primarily beech-maple-hemlock forest located within a complex rural matrix of agricultural land, abandoned fields, and forest fragments. Data for the present study come from the 8 years 2013–2020, when intensive efforts were made to capture and color-band all breeding adult Hooded Warblers and find and monitor all nests during the May–August nesting season. Nests were checked every 3–5 days, and more frequently around expected dates of hatching and fledging. About half (48%) of all nests were found before the onset of incubation, but when a nest with a complete clutch of eggs or nestlings was found, the date of nest initiation (date the first egg was laid) was estimated based on either the date of hatching, assuming eggs were laid on consecutive days and a 12-day incubation period (Mumme et al. 2023), or the date a previous nesting attempt by the same female had failed. These estimated dates of nest initiation were likely accurate to within 1–2 days. In total, 847 nests were included in the complete dataset.

Statistical analysis

The date of nest initiation, which we defined as the day the first egg is laid (FEDay) and recorded as the number of days elapsed since 30 April, is an important determinant of several Hooded Warbler reproductive variables, including probability of nest parasitism, clutch size, and probability of nest predation (Harrod 2021, Lignac 2022). We therefore examined the effects of cowbird parasitism on Hooded Warbler nesting success with generalized linear mixed models (GLMM) or generalized linear models (GLM) that included FEDay as a fixed factor. Year was included in these models as either a random effect in a GLMM or a fixed factor in a GLM; the latter approach was used when we encountered model convergence or singularity issues with GLMM. All statistical analyses were conducted using JMP Pro 15.2 (SAS Institute, Cary, North Carolina, USA) and R version 4.2.1 (R Core Team 2022) with package lme4 version 1.1-30 (Bates et al. 2015).

Timing of parasitism, clutch size, and nest abandonment. We analyzed the relationship between the date of nest initiation (FEDay) and probability of parasitism using a logistic GLMM with year included as a random effect. We used a Poisson GLM to examine the effects of cowbird parasitism on the number of Hooded Warbler eggs in the complete clutch. The number of cowbird eggs in the nest, FEDay, and year were included as fixed factors. A logistic GLM was used to examine the probability of nest abandonment, with cowbird parasitism, FEDay, and year entered as fixed factors.

Nest survival to hatching and hatching failure. The effect of cowbird parasitism on the probability of nests surviving to hatching was examined using a logistic GLMM, with cowbird parasitism and FEDay as fixed factors and year as a random effect. This analysis was limited to 356 nests found before the onset of incubation that were not abandoned. To examine the effects of cowbird parasitism on Hooded Warbler hatching failure and egg loss during incubation, we used Poisson GLMs to analyze the effect of cowbird parasitism on both the number of eggs that failed to hatch and the number of warbler eggs that disappeared during incubation. In these analyses, the number of cowbird eggs, FEDay, and year were entered as fixed factors, with the total number of Hooded Warbler eggs in the clutch serving as the offset variable. These analyses were limited to a sample of 373 nests that were found no later than the fourth day of the 12-day incubation period and did not experience abandonment or complete nest failure before hatching.

Nest and nestling survival from hatching to fledging. We used a logistic GLM to examine the probability of nests with and without a cowbird nestling surviving to fledging. This analysis was limited to 492 nests found before hatching that were not abandoned and included FEDay, year, and the presence/absence of a cowbird chick as fixed factors. We also created Kaplan-Meier survival curves to examine the pattern of nest survival during the nestling period. For 359 nests that survived from hatching to fledging, a Poisson GLM was used to determine if the presence of a cowbird chick increased the number of Hooded Warbler hatchlings that disappeared and presumably died before fledging; the number of warbler nestlings that hatched was used as the offset variable in this analysis, and FEDay and year were included as fixed factors.

Cumulative effects of cowbird parasitism on success per nest

We estimated the cumulative effects of cowbird parasitism on mean success per nest at Hemlock Hill by calculating its separate impacts on five components of per-nest success: (1) the number of Hooded Warbler eggs in the final clutch, (2) the probability that the nest is not depredated, abandoned, or a victim of complete nest failure prior to hatching, (3) the proportion of Hooded Warbler eggs in surviving nests that hatch successfully, (4) the probability that the nest is not depredated, abandoned, or a victim of complete nest failure between hatching and fledging, and (5) the proportion of Hooded Warbler nestlings in surviving nests that fledge successfully. We used GLMs to estimate the effect of cowbird parasitism on the five components of nest success listed above while simultaneously controlling for the potentially confounding effects of FEDay.

An additional complication of calculating the cumulative effect of nest parasitism is including the probability that the cowbird egg (or eggs) in a parasitized nest will fail to hatch, effectively turning a parasitized nest into a non-parasitized nest during the nestling stage. We incorporated this probability into our calculations, using a 0.75 probability that each cowbird egg would hatch (McMaster and Sealy 1997) and our finding that 15.6% of parasitized nests contain more than one cowbird egg.

Effects of cowbird parasitism on seasonal fecundity

Because we removed cowbird eggs from some Hooded Warbler nests late in incubation as part of other experimental studies, and because some females move onto or off of the study between nesting attempts, we do not have unbiased data that allow a direct assessment of the impact of cowbird parasitism on female reproductive histories and population productivity. Instead, we generated a realistic female-based stochastic simulation of Hooded Warbler reproduction to extend our estimates of the per-nest impacts of cowbird parasitism to both per-season effects on individual females, and population-level effects on the reproductive performance of entire populations. We used data from the Hemlock Hill study population to parameterize the simulation with realistic variation in the timing of first reproduction, the probability of nest parasitism, clutch size, hatching success, the probability of complete nest failure, nestling survival, the timing and probability of renesting after nest failure, and the timing and probability of attempting a second brood following a successful nest. One baseline simulation was created to mimic the parasitism and reproductive characteristics of the Hemlock Hill study population, and this simulation was used to estimate the effect of cowbird parasitism on per-season success of individual females. However, we also created 7 additional simulations that altered the overall nest parasitism rate by realistically modifying the logistic regression equation relating the probability of nest parasitism to the date of nest initiation (see Results). Collectively, the 8 simulations allowed us to explore the population-level reproductive consequences of simulated variation in the overall rate of nest parasitism.

For each of the 8 simulations, we ran 25 replicates of 400 females; we chose 400 females for these replicates because 400 approximates the number of females whose reproductive histories we followed each year (~50) multiplied by the number of complete breeding seasons (8, 2013–2020) used in our analyses. In addition, for each of the 8 simulations we also ran one replicate based on a much larger simulated population of 40,000 females. All simulations were created with JMP Pro 15.2 (SAS Institute, Cary, North Carolina, USA).

Complete details on the simulation models and their validation are provided in Supplementary Materials 1. However, we note here that the baseline simulation consistently replicated important reproductive characteristics of the Hemlock Hill study population that were not explicitly built into the simulation, including overall mean ± SD of nest initiation dates (13 June ± 18 days simulated vs. 14 June ± 18 days observed), overall mean ± SD of Hooded Warbler clutch size (3.00 ± 0.97 simulated vs. 3.02 ± 0.93 observed), overall rate of cowbird parasitism (29.7% simulated vs. 30.3% observed), and overall mean ± SD number of young fledged from successful non-parasitized nests (2.78 ± 0.88 simulated vs. 2.83 ± 0.88 observed).

The baseline simulation

To explore the effects of Brown-headed Cowbird nest parasitism on the annual reproductive output of Hooded Warbler females and populations subjected to varying levels of parasitism, we created a realistic female-based stochastic simulation of Hooded Warbler reproduction. We used data from our Hemlock Hill study population to parameterize the simulation with realistic variation in the timing of the initial nesting, the probability of nest parasitism, clutch size, hatching success, the probability of complete nest failure, nestling survival, the timing and probability of renesting after nest failure, and the timing and probability of attempting a second brood following a successful nest. 

Initial nest

We simulated the date of nest initiation (laying of the first egg, FEDay) for the first nest with a four-parameter sinh-arcsinh (SHASH) distribution that closely fit our observed data:

23.24 + 8.30(SinH((ArcSinH(RandomNormal) + 0.70)/1.61))

In our baseline simulation of 40,000 females, the simulated first egg date for the initial nesting attempt was 27 May ± 5 days (mean ± SD), range 15 May–15 June. 

For each of the 40,000 simulated initial nests, we then simulated whether it was parasitized based on the logistic regression equation relating the probability of cowbird nest parasitism to the date of nest initiation (FEDay; Figure 2A); 45.1% of the 40,000 initial nests in our baseline simulation were parasitized. Host clutch size was then simulated based on both the date of nest initiation (FEDay) and whether the nest was parasitized (Figure 2B); this approach therefore accounted for both the seasonal decline in clutch size and the reduction in host clutch size associated with nest parasitism (Figure 2B).

The probability of the nest surviving to hatching was simulated based on our observed logistic regression equation relating nest survival to both FEDay and whether the nest was parasitized; all causes of complete nest failure prior to hatching (e.g., abandonment, clutch predation, nest destruction) were included in the logistic regression analysis. If a simulated nest did not survive to hatching, a simulated failure date was assigned, based on a uniform random distribution over the time period between laying of the first egg and expected hatching date (12 days after clutch completion). If the nest did survive to hatching and was not parasitized, the number of Hooded Warbler eggs hatching was simulated based on the observed hatching probability of eggs in surviving non-parasitized nests, 0.89 (Figure 3C). If the nest was parasitized, hatching probability for each Hooded Warbler egg was set at the observed value of 0.72 (Figure 3C). For parasitized nests, the probability of a cowbird nestling hatching in a surviving nest was set at 0.784, based on a 0.75 probability that each cowbird egg would hatch (McMaster and Sealy 1997) and our finding that 15.6% of parasitized nests contain more than one cowbird egg. 

For nests that survived to hatching, we then simulated whether the nest would survive to fledging, based on the logistic regression relating the probability of post-hatching nest survival to both FEDay and whether a cowbird nestling was present in the nest (see Figure 4); all causes of complete post-hatching nest failure were included in the logistic regression analysis. In our baseline simulation, the probability of survival from hatching to fledging was 0.733 for 13,621 simulated non-parasitized nests and 0.524 for 5616 simulated nests where a cowbird nestling was present. For surviving nests, we also simulated the probability that each Hooded Warbler nestling fledged successfully, using the observed probability of 0.96 for nestlings from successful nests without a cowbird chick, and 0.85 for those from successful nests with a cowbird chick. For nests that did not survive from hatching to fledging, we simulated a failure date based on a uniform random distribution over the time period between hatching and the expected date of fledging, 9 days after hatching.

Subsequent nests

If the initial nesting attempt failed before fledging, we simulated renesting as follows. First, because data from Hemlock Hill indicate that renesting females require 6 days from failure of the previous attempt to laying of the first egg for the subsequent nest, we added 6 days to the simulated failure date described above for the female’s new estimated date of nest initiation (FEDay). If this new date was before June 30, we considered the probability that the female would renest to be 100%. However, if the new date was July 1 or later, the probability of renesting was set to (number of days remaining in July/31); July 31 is the latest nest initiation date ever recorded for a nest at Hemlock Hill, so this linear decrease in the probability of renesting through the month of July is realistic and closely matches the observed breeding biology of Hooded Warblers at Hemlock Hill. 

If the initial nesting was successful, we simulated the laying of a second brood as follows. Because females who attempt a second brood at Hemlock Hill average 12 days between fledging and the first egg of the subsequent nest, we added 12 days to the date of fledging of the prior attempt to estimate the first egg date for the second brood. If this new date was before June 30, we considered the probability that the female would attempt to nest again to be 100%. However, if the new date was July 1 or later, the probability of renesting was set to (number of days remaining in July/31), as described above.

For each subsequent attempt we modeled the probability of cowbird parasitism, clutch size, nest survival to hatching, hatching success, nest survival to fledging, and nestling survival to fledging using the same approaches as described above for the initial nest, adjusting for the date of nest initiation (FEDay) to account for the seasonal changes in nest parasitism (Figure 2A), clutch size (Figure 2B), and nest predation. Because 5 nesting attempts in a single season is the most we have ever observed by an individual female at Hemlock Hill, we set 5 as the maximum number of nesting attempts that a female might make. However, in our baseline simulation, <1% (308 of 40,000 simulated females) made 5 nesting attempts, and the mean ± SD was 2.6 ± 0.7 attempts per season. 

Simulation validation

The simulation realistically models Hooded Warbler reproduction and accurately reflects the breeding biology of our Hemlock Hill study population. This conclusion is best illustrated by Figure S1, which shows the observed and simulated distribution of nest initiation dates. The two distributions are remarkably similar; overall mean ± SD nest initiation date was 14 June ± 18 days (range 17 May–31 July) for 847 observed nests, vs. 13 June ± 18 days (range 15 May–30 July) for 103,258 simulated nests. Most impressively, our simulation also produced the bimodal distribution observed in our study population, with a smaller second peak of nesting occurring in late June and early July (Figure S1). This second peak of nesting was not explicitly built into the simulation, but emerged from the realistic parameterization of the simulation with data on the timing and probability of renesting following failure, and the timing and probability of attempting a second brood following a successful nesting attempt.

Our baseline simulation also replicated other important reproductive characteristics of the Hemlock Hill study population that were not explicitly built into the simulation, included overall Hooded Warbler clutch size (Figure S2), overall rate of cowbird parasitism (30.3% observed vs. 29.7% simulated), and overall mean ± SD number of young fledged from successful non-parasitized nests (2.83 ± 0.88 observed vs. 2.78 ± 0.88 simulated).

Simulating variation in rates of nest parasitism

After creating the baseline simulation to mimic the parasitism and reproductive characteristics of the Hemlock Hill study population, we then created 7 additional simulations that altered the overall nest parasitism rate by realistically modifying the intercept and slope of the logistic regression equation relating the probability of nest parasitism to the date of nest initiation (Table S1, Figure 2A). All 7 of the modified logistic regression equations retained the essential feature that the probability of cowbird nest parasitism was highest early in the nesting season and declined to low levels in July (Figure 2A). Collectively, the 8 simulations allowed us to explore the population-level reproductive consequences of simulated variation in the overall rate of nest parasitism. 

JMP Pro 15.2 (SAS Institute, Cary, North Carolina, USA) and R version 4.2.1 (R Core Team 2022) with package lme4 version 1.1-30 (Bates et al. 2015).