Divergent estimates of herd‐wide caribou calf survival: Ecological factors and methodological biases

Abstract Population monitoring is a critical part of effective wildlife management, but methods are prone to biases that can hinder our ability to accurately track changes in populations through time. Calf survival plays an important role in ungulate population dynamics and can be monitored using telemetry and herd composition surveys. These methods, however, are susceptible to unrepresentative sampling and violations of the assumption of equal detectability, respectively. Here, we capitalized on 55 herd‐wide estimates of woodland caribou (Rangifer tarandus caribou) calf survival in Newfoundland, Canada, using telemetry (n = 1,175 calves) and 249 herd‐wide estimates of calf:cow ratios (C:C) using herd composition surveys to investigate these potential biases. These data included 17 herd‐wide estimates replicated from both methods concurrently (n = 448 calves and n = 17 surveys) which we used to understand which processes and sampling biases contributed to disagreement between estimates of herd‐wide calf survival. We used Cox proportional hazards models to determine whether estimates of calf mortality risk were biased by the date a calf was collared. We also used linear mixed‐effects models to determine whether estimates of C:C ratios were biased by survey date and herd size. We found that calves collared later in the calving season had a higher mortality risk and that C:C tended to be higher for surveys conducted later in the autumn. When we used these relationships to modify estimates of herd‐wide calf survival derived from telemetry and herd composition surveys concurrently, we found that formerly disparate estimates of woodland caribou calf survival now overlapped (within a 95% confidence interval) in a majority of cases. Our case study highlights the potential of under‐appreciated biases to impact our understanding of population dynamics and suggests ways that managers can limit the influence of these biases in the two widely applied methods for estimating herd‐wide survival.


| INTRODUC TI ON
Population monitoring is fundamental to species conservation and management (IUCN, 2012) and can be used to track the abundance of wildlife populations through time so that managers can adjust management actions accordingly (Gibbs, Snell, & Causton, 1999;Nichols & Williams, 2006). Indeed, many jurisdictions rely on monitoring initiatives to inventory and manage large mammal and big game species (Flather, Knowles, & Brady, 2009;Manitoba Sustainable Development, 2018;Resources Inventory Committee, 2002).
Insufficient or inadequate data on population trends can hamper conservation efforts (e.g., Blake & Hedges, 2004). Even long-term, seemingly well-designed monitoring programs can lead to poor conservation practices (Gibbs et al., 1999;Karanth et al., 2003).
There are numerous biases, most of which we are unaware of, that can threaten our ability to accurately monitor population change through time. It is therefore prudent that we attempt to identify and correct biases in monitoring programs. This is especially important for vulnerable and at-risk species.
Caribou (Rangifer tarandus; Figure 1) are becoming a global flagship species of concern due to climate and other anthropogenic causes of population decline (Festa-Bianchet, Ray, Boutin, Côté, & Gunn, 2011;Vors & Boyce, 2009). In Newfoundland, Canada, woodland caribou (R. t. caribou) have been monitored nearly continuously for over 35 years, revealing large changes in population abundance that mirror the declines in caribou populations in the circumpolar north (Festa-Bianchet et al., 2011;Vors & Boyce, 2009). In Newfoundland, woodland caribou population abundance was comparatively low during the 1960s and 1970s, increased rapidly during the 1980s to mid-1990s, and has since declined sharply (Bastille-Rousseau, Schaefer, Mahoney, & Murray, 2013). This decline, from approximately 94,000 woodland caribou at its peak to an estimated 31,000 in 2013, led the Committee on the Status of Endangered Wildlife in Canada to designate the woodland caribou population in Newfoundland as "Special Concern" (COSEWIC, 2016).
In an attempt to understand the cause of woodland caribou population declines in Newfoundland, managers estimated calf survival from two independent and occasionally concurrent sets of monitoring data: recruitment rates (calf:cow ratio, hereafter, C:C) from herd composition surveys (e.g., Bender, 2006) and individual estimates of calf survival from telemetry (e.g., Olson, Fuller, Schaller, Lhagvasuren, & Odonkhuu, 2005). As originally interpreted, trends of herd-wide woodland caribou calf survival in Newfoundland derived from herd composition surveys and telemetry generally agreed during the population growth phase (1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997), but appeared to diverge during the population decline phase (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014); the telemetry data suggested a gradual increase in calf survival over time, while the herd composition surveys suggested that C:C remained low (Weir, Morrison, Luther, & Mahoney, 2014;Figures 2 and 3). This discrepancy in estimates of calf survival for the same herds during the same time period suggests that there are biases in the data because we would expect both methods to show the same trend in herd-wide calf survival through time. These biases would otherwise have gone undetected if we did not have two datasets to compare; these datasets thus allow us the unique opportunity to evaluate biases that could influence management.
Herd composition surveys and telemetry are common methods for estimating calf survival in ungulates, and both can be prone to biases that may lead to erroneous management or conservation actions (Elphick, 2008;Gilbert, Lindberg, Hundertmark, & Person, 2014;Murray, 2006). Calf:cow estimates derived from herd composition surveys depend on the critical assumption that different demographic groups are equally detectable at the time of the survey. Violations to this assumption can arise if: (a) the probability of detection varies among demographic groups (McCorquodale, 2001); (b) if some demographic groups are more likely absent (e.g., variation in the timing of herd aggregation for different demographic groups); or (c) if some demographic groups are present but difficult to numerate or are misclassified due to habitat type (Bonenfant, Gaillard, Klein, & Hamann, 2005;Samuel, Garton, Schlegel, & Carson, 1987) or physical similarities among demographic groups (Citta, Quakenbush, & Taras, 2014). Equal detectability during herd composition surveys of woodland caribou could be affected by survey date if different demographic groups (e.g., cows with calves and cows without calves) aggregate at different times. Similarly, larger herd sizes might hinder the detection of certain demographic groups. Survival estimates derived from telemetry studies assume that marked individuals represent the whole herd and that the collaring and monitoring processes do not influence survival (Cattet, Boulanger, Stenhouse, Powell, & Reynolds-Hogland, 2008). Efforts to collar woodland caribou calves might only occur on a few days of the calving season; thus, the distribution of calf collaring dates (typically an index of calf birth date) in a telemetry sample is unlikely to represent the distribution of calf birth dates in the herd.
This violation of the assumption of representative sampling (i.e., only monitoring calves born during a few days of the calving season) could generate a biased estimate of survival if woodland F I G U R E 1 Woodland caribou (Rangifer tarandus caribou) cow and calf on Fogo Island, Newfoundland on 28 June 2016 taken by Maegwin Bonar caribou calves that were born later in the calving season have a lower probability of survival; indeed, this pattern is evident across several ungulate species (Festa-Bianchet, 1988;Gaillard, Festa-Bianchet, Yoccoz, Loison, & Toïgo, 2000). While several studies have examined the potential biases of herd composition surveys (e.g., Caughley, 1974;McCullough, 1994) and survival analyses (e.g., DeCesare, Hebblewhite, Lukacs, & Hervieux, 2016;Gilbert et al., 2014;Murray, 2006), and examined how vital rates themselves might influence age ratios derived from herd composition surveys (Harris, Kauffman, & Mills, 2008), rarely have both methods been evaluated concurrently on the same herd. Violations of these assumptions could lead to the divergent estimates of woodland caribou calf survival that we observed.
The goal of our analysis was to identify and attempt to reconcile the methodological challenges that cause divergent estimates of herd-wide calf survival from herd composition surveys and telemetry datasets, therefore lending increased confidence to potential management and conservation practices. Our first objective was to determine how the date that calves were collared influenced estimates of calf survival and how survey date and herd size influenced C:C across both the population growth and decline phases of woodland caribou in Newfoundland. Our second objective was to determine whether modification of herd-wide calf survival estimates (based on the relationships identified in the first objective) could reconcile trends in herd-wide calf survival derived from telemetry and herd composition surveys ( Figure 4). F I G U R E 2 Estimates of herd-wide woodland caribou (Rangifer tarandus caribou) calf survival. Estimates were derived from telemetry (triangle and dashed line) and herd composition survey (circle and solid line) datasets for herds in (a) La Poile, (b) Northern Peninsula, and (c) Middle Ridge during the population decline (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014) in Newfoundland, Canada. Estimates represent unmodified data and demonstrate the lack of congruence in estimates of herd-wide calf survival from the two data sources F I G U R E 3 Weighted trend line (using the inverse sample variance) and 85% confidence intervals (for clarity) of estimates of herd-wide woodland caribou (Rangifer tarandus caribou) calf survival. Data were derived from telemetry (triangle and light gray ribbon) and herd composition survey (circle and dark gray ribbon) datasets for herds in (a) La Poile, (b) Northern Peninsula, and (c) Middle Ridge during the population decline (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014) in Newfoundland, Canada. Estimates represent unmodified data and demonstrate the lack of congruence in estimates of herd-wide calf survival from the two data sources 2 | ME THODS  (2013), we categorized woodland caribou population dynamics into two distinct phases based on estimated population abundance: growth (1979-1998) and decline (2002-2014). Accounting for phases of population growth and decline in demographic studies is critical because such phases are typically density-dependent, and as such, age structure, reproductive rate, and other demographic and ecological processes can vary (Festa-Bianchet, Gaillard, & Côté, 2003;Festa-Bianchet, Gaillard, & Jorgenson, 1998). In our first objective, we used data from 10 woodland caribou herds across Newfoundland that were monitored with telemetry (8 herds and 540 calves during the population growth phase and 5 herds and 635 calves during the population decline phase; Appendix A) and from 26 herds monitored with herd composition surveys (18 herds and 107 C:C estimates during the population growth phase and 24 herds and 142 C:C estimates during the population decline phase; Appendix A). For our second objective, we focused on three herds that were studied most extensively during the population decline phase: La Poile, Middle Ridge, and Northern Peninsula (17 concurrent estimates of annual herdwide calf survival from 448 calves and 17 estimates of calf:parous F I G U R E 4 Schematic diagram of our methodology for producing modified estimates of herd-wide woodland caribou (Rangifer tarandus caribou) calf survival and trends from telemetry data (left column) and herd composition survey data (right column) across three herds (La Poile, Northern Peninsula, and Middle Ridge) during the population decline (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014) in Newfoundland, Canada cow ratio [derived from autumn and spring herd composition surveys; see Section 2.3]; Figure 5).

| Calf collar date as an index of calf birth date
Our first objective was to determine how the date that calves were collared influenced estimates of calf survival. Woodland caribou calves were typically collared when they were only a few days old; calves were difficult to catch beyond five days old. We therefore used the number of days since an individual was collared as an index of age. We assumed that all calves were the same age when they were collared, regardless of collaring date. An estimate of calf age, based on size and calf development, was collected in the field for some calves (38%); however, these data were not estimated consistently (e.g., age, when reported, was recorded as a closed (i.e., 2-5 days) or open (i.e., >1 day) range). Thus, we could not directly assess our assumption that calves were collared within the first few days of life. Instead, we assessed our assumption indirectly by examining the relationship between calf weight and collaring date using available calf weight data for a subset of our sample from five herds during the population decline phase (n = 625). We did not detect a relationship between calf weight and calf collaring date across all five herds (Appendix B), suggesting that calves collared later in the season were not heavier and thus unlikely to be significantly older than calves born earlier in the season, supporting our assumption that calves were collared within the first few days of life. Other studies have linked caribou birth timing to birth weight and found that individuals born earlier weighed more than individuals more later (Adams & Dale, 1998;Côté & Festa-Bianchet, 2001). When we examined this relationship in our data for individual herds, we did find a negative relationship between calf collar date and calf weight in the Northern Peninsula herd (Appendix B). Furthermore, when looking at animals collared on the same date in the same herd, most animals were within 2 kg of each other (IQR < 2 kg); however, the weight difference between some outliers was as high as 5 kg (Appendix B).
Together, these data suggest that most animals were collared within the first few days of life, but some individuals might have been collared at ages > 5 days. To minimize this effect, we removed obvious violations to this assumption from our analyses: calves that were collared after the calving season as older individuals or calves that weighed more than 12 kg when collared (cutoff value based on conversations with staff from the Government of Newfoundland and Labrador).

| Delineating the woodland caribou calving season
Woodland caribou calves tend to be born within the same general time frame in late spring and early summer (May-June) every year, referred to as the calving season. In Newfoundland, Canada, conventional wisdom is that the calving season begins roughly in late May and concludes by mid-June, and the start of the calving season may vary by a few days among the different herds on the island; this could be due to variation in climate and land cover (Post, Boving, Pedersen, & MacArthur, 2003). There have not been any recent studies on the timing of woodland caribou calving in Newfoundland. Bergerud (1975), however, found that in the late 1950s and early 1960s, the calving season in Newfoundland began on 24 May.
Recent work by DeMars, Auger-Méthé, Schlägel, and Boutin (2013) has shown that ungulate parturition dates can be estimated from telemetry data on adult females. However, we did not use this method across our dataset for two reasons: (a) Adult telemetry data were not available for all of the herds and years that we had calf mortality data, and (b) recent work by Bonar, Ellington, Lewis, and Vander Wal (2018) has shown that estimating migratory woodland caribou parturition dates from telemetry is not as reliable as estimating parturition for sedentary woodland caribou.
To assess the potential influence of collaring date on calf mortality risk, we defined the calving season for each herd separately using the calf collaring dates in the telemetry dataset . We defined the start and end of the calving season as the earliest and latest day of the year that a calf was collared for each herd across all years. We excluded herds with low sample size (n < 50). Using these criteria, the start date of the calving season varied between 25 May and 29 May, depending on the herd. The average start of the calving season was 27 May, and we used this date for herds that had low sample size. The end date of the calving season ranged from 8 June to 18 June for the herds for which we had large sample sizes (n > 50).
Interestingly, the herd with the earliest collaring date, Grey River (25 May), also had the latest collaring date (18 June). The collaring dates for Grey River suggest a calving season of 25 days, while the collaring dates of the other herds (with large sample sizes, n > 50) suggest a calving season that ranged between 10 and 22 days. Indeed, Bergerud (1975) found that woodland caribou calving seasons in Newfoundland lasted around 25 days, although most of calving (90%) occurred during the first 12 days. Among the collared calves in our dataset, 92% were collared during the first 12 days of the calving season. Given that calves are much more likely to be born and thus collared in the first days of the calving season, we were less likely to collar a calf on the last day of the calving season. To avoid underestimating the length of the calving season, we assumed that the calving season was 25 days for each herd, which was the maximum estimated length of the calving season from any herd and in line with estimates by Bergerud (1975)

| Monitoring collared calves
The monitoring of collared calves by Newfoundland government staff declined in intensity within a year: Calves were monitored every 1-3 days in the first few months postcalving (when calves were most vulnerable) and monitoring declined to once per month through the autumn and winter. We censored all animals after 1 October, when monitoring became less frequent.

| Herd composition survey data
The herd composition surveys had more coverage, both chronologically and across herds, than the telemetry datasets. In total, 249 herd and we did not necessarily know the exact methodology used for a specific herd-year. We summarize below a broad picture of the methods used. Between the months of September and December, observers (typically two plus the pilot) flew rotary-wing (and perhaps in earlier years, fixed-wing) aircraft over an area believed to be where herds were currently located. Occasionally, telemetry data were used to estimate where a woodland caribou herd was located, and in other years, the historic position of the herd was used. Herd composition surveys were typically conducted over one day, but occasionally, surveys were conducted over multiple days if weather was poor or woodland caribou were difficult to locate. For larger herds, the herd composition survey was a sampling effort, but for smaller herds, total counts were occasionally conducted. The crew counted the number of woodland caribou within basic demographic groups: adult male, adult female, and calf, and if needed, the pilot would use the aircraft to separate large groups into more manageable subgroups for counting.
Prior to 2009, the crew attempted to maximize sample size and minimize flight distance by applying a haphazard sampling designthis was practiced due to budget, time, and logistical constraints. As such, the crew focused on larger groups of woodland caribou on the landscape and in open areas. The underlying assumption (which is not necessarily supported) was that demographic make-up of large groups in open landscapes was representative of the demographic make-up of the entire herd. More recently, there has been a concerted effort to recognize and attempt to minimize some of the biases inherent in the haphazard sampling effort, with the use of line transect sampling that is representative of landscape type and group size (Saunders & Strickland, 2009).
As C:C represented the joint contribution of fecundity and calf survival, herd composition surveys were also conducted during the months of May and June to estimate the proportion of parous cows (an estimate of fecundity). Cows with calves close by or with visible signs of pregnancy were considered parous. With both C:C and proportion of parous cows, one can estimate the calf:parous cow ratio, which is analogous to a herd-wide estimate of calf survival. It should be noted that cow survival rate between the two survey periods could also influence the estimate of herd-wide calf survival; however, natural adult mortality during this time period was rare (Mahoney & Weir, 2010;Weir et al., 2014). Lewis and Mahoney (2014)  Furthermore, most hunted caribou in Newfoundland are male due to focus on trophy hunts (Weir et al., 2014), so it is possible that hunting mortality of adult females was even lower than 2%. For our analysis, we assumed no cow mortality occurred between survey periods. We estimated 95% confidence intervals for herd composition survey ratios following Czaplewski, Crowe, and McDonald (1983).

| Estimating missing data with multiple imputation
There were two different types of missing data in herd composition surveys: missing survey date (5% of surveys) or the presence of unknown adults in the count data (26% of surveys; median number of unknown adults in these surveys was 3, range was 1-23). In both cases, we used multiple imputation to estimate these missing data (Appendix D). We averaged, across all the imputed datasets, model weight (w i ), adjusted R 2 , p-value, and other parameters reported from analyses of C:C; these values therefore have an associated standard error (SE). We averaged results across imputed datasets after we calculated model selection metrics (AICc, ΔAICc, w i ); thus, we do not report AICc and ΔAICc, as averages of these values could have been influenced by shifting baselines (lowest AICc values and model with lowest AICc value). Model coefficients would normally have an associated SE, so we always reported SE with these estimates.

| Modeling method
For the herd composition survey dataset, we used linear regression models to examine how different factors might influence C:C with the lme4 package (Bates, Mächler, Bolker, & Walker, 2014) in R. We generated eight models of C:C based on the fixed effects of survey date, herd size, and year. In each model, we included herd as a random effect on the intercept. To avoid confounding the random effect of herd with fixed effects, when a herd had less than three surveys during a population phase, we collapsed it into an "other herd" category. For the telemetry dataset, we used Cox proportional hazards models to estimate mortality risk and the factors that influence mortality risk. We generated ten models of woodland caribou calf mortality risk, focused mainly on calf collar date (an index of calf birth date) and year (as both a linear fixed effect and a random effect). We ran additional models that included herd as a random effect on the intercept. We conducted all Cox proportional hazard analyses with the package survival (Therneau, 2015b) and coxme (Therneau, 2015a) in R (R Core Team, 2018).
For both datasets, we also included models with year and herd, as these factors could index temporal or spatial changes in mortality risk and C:C. Individual herds often vary in population demographics and persist in areas with different climates and land cover; thus, it is possible that the response of calf mortality risk and the C:C to different factors might vary among herds. For both datasets, we conducted model selection with AICc (Burnham & Anderson, 2002) using the package AICcmodavg (Mazerolle, 2016) in R. We considered models with AICc model weights (w i ) ≥ 0.50 as a top model, and when there was not a top model, we considered all models with w i ≥ 0.05 as having some support. As additional metrics for model support and fit, we calculated concordance values (c) for fixed-effects models of calf mortality risk, likelihood-ratio tests (LRT) for all models of calf mortality risk, and conditional R 2 for our models of C:C.

| Modified mortality risk and calf:cow ratios
For our objective 2, we used data from three herds to compare modi-  Figure 4). First, we generated modified estimates of mortality risk and C:C based on factors identified in the first objective (using hazard ratios for calf mortality risk and β coefficients for C:C from the population decline phase; see results). Then, we converted the modified estimates of calf mortality risk (measured at the individual level) obtained from the telemetry dataset and C:C obtained from the herd composition survey dataset to comparable estimates of herd-wide calf survival. We again used multiple imputation to estimate the demographic identity of unknown adults in herd composition survey data (see Section 2.3.1 and Appendix D).
To convert the telemetry data to an estimate of herd-wide calf survival, we generated an estimate of calf mortality risk within each herd-year to match the date that the corresponding autumn herd composition survey was conducted (i.e., we censored all calves on the day of the corresponding herd composition survey). In herdyears where multiple herd composition surveys occurred, we used the survey conducted later in the year. We then calculated the cumulative mortality risk and converted this value to calf survival probability. Cumulative mortality risk (and calf survival probability) on a given day would be different for calves born on different days because these calves would be different ages. Thus, each different aged cohort of calves would have a different survival probability estimate. We estimated the proportion of calves born on each day of the calving season across all herds and years and then modified this estimate to a Gaussian mixture curve in R. We then generated herdwide calf survival estimates by averaging the different age survival probabilities weighted by the estimated proportion of different ages in a herd.
To convert the herd composition survey data into an estimate of herd-wide calf survival, within each herd-year, we used the proportion of parous cows (obtained for the corresponding spring herd composition survey conducted during May or June; Appendix A) to adjust our modified C:C to the calf:parous cow ratio. When an estimate of the proportion of parous cows was not available, we did not estimate the calf:parous cow ratio. We equate the calf:parous cow ratio to herd-wide calf survival because it is an estimate of the number of calves that survive from the first spring survey, which, weather permitting, took place just before the calving peak, until the autumn survey.

| Estimating trends in herd-wide calf survival
We plotted the two estimates of herd-wide calf survival with 95% confidence intervals for each herd during the population decline phase. Finally, we conducted a weighted regression of herd-wide calf survival estimates within each herd using the inverse variance to estimate trends in herd-wide calf survival. We did this for both unmodified estimates and modified estimates. We plotted an 85% confidence interval around these estimated trend lines; the choice of an 85% confidence interval allowed for easier interpretation than the large 95% confidence intervals.

| Biases in calf mortality risk estimated with telemetry data
The date that a calf was collared was an important predictor of calf mortality risk during both the population growth (n = 540 calves) and decline phases (n = 635 calves), as it was present in all the models with the some support (w i > 0.05; Table 1). During the population growth phase, there was not a sole top model (w i > 0.50); rather, there were five models with some support (w i > 0.05). In addition to collar date (which was present in all 5 of these models), these models contained an effect of linear year (2 of 5 models), random effect of year (1 of 5 models), and random effect of herd (2 of 5 models). Interestingly, the hazard ratios for collar date and linear year (when present) were very similar across all five models (Appendix E). Given the similarity between the coefficients in all the supported models, we focused our interpretation on the two models with the most support (collar date and linear year + collar date). These two models not only had the highest w i , they also had concordance index values (c) > 0.50, and the LRT values indicated these models provided significantly more explanatory power than the null model (Table 1; Appendix E). During the population decline phase, we found a sole top model, linear year + collar date (w i = 0.55; c = 0.57; LRT = 30.61), and focused our interpretation on this model (Table 1; Appendix E). We found a consistently significant, positive relationship between woodland caribou calf mortality risk and the collaring date of the calf during both the population growth and decline phases (Table 2). For each day later in the calving season that a calf was born, calf mortality risk increased by 6% (hazard ratio = 1.06, 95% CI = 1.02 to 1.09) during the population growth phase and by 6% (hazard ratio = 1.06, 95% CI = 1.02 to 1.10) during the population decline phase (Table 2). Conversely, we detected a significant, negative effect of year on calf mortality risk only during the population decline phase, whereby woodland caribou calf mortality risk decreased by 6% per year (hazard ratio = 0.94, 95% CI = 0.90 to 0.99; Table 2). TA B L E 1 Cox proportional hazards models of woodland caribou (Rangifer tarandus caribou) calf mortality risk during the population growth (n = 540 calves from 8 herds from 1979 to 1997) and decline phases (n = 635 calves from 5 herds from 2003 to 2013) in Newfoundland, Canada

| Biases in calf:cow ratios estimated with survey data
There was a single top model (linear year + survey date + herd (random); w i = 0.59, R 2 = 0.41) for C:C during the population growth phase (n = 107 estimates of C:C); therefore, we focused our interpretation on only this model (Table 3; Appendix E). During the population growth phase, we detected a significant, positive relationship between C:C and survey date, such that for every 30 days later in the year that a survey was conducted, the C:C was 0.10 higher (95% CI = 0.05 to 0.14; Table 4). We also detected a significant, negative relationship between C:C and year, such that during the population growth phase, the C:C decreased by 0.006 each year (95% CI = −0.010 to −0.002), equivalent to a 0.12 decline in the C:C over the entire population growth phase (Table 4). Conversely, during the population decline phase (n = 142 estimates of C:C) there was not a sole top model (w i > 0.50), but all eight models had some support (w i > 0.05; Table 3). The model with the most support was herd (random) (w i = 0.20; R 2 = 0.30). Furthermore, in all other models the effects of survey date, linear year, and herd size were nonsignificant (Table 4, Appendix E).

| Reconciling herd-wide calf survival estimates from two types of data
We modified our estimate of calf mortality risk by the coefficient identified in the top model of calf mortality risk during the population decline phase (Table 2). We also modified our estimates of the C:C by the coefficient for survey date derived from the model survey date + herd (random) during the population decline phase.
The effect of survey date from this model during the population decline phase was nonsignificant, but we still used it to modify our estimates of C:C for two reasons. First, survey date had a significant positive effect on C:C during the population growth phase, and while the trend was nonsignificant and weaker, it was positive during the population decline phase, suggesting a potential link. Second, not only did we modify our estimates by the coefficient, but also by the bounds of the 95% confidence interval. Thus, we were not only accounting for the potential effect but also the uncertainty around this potential effect.
When we applied the modifications to the concurrent estimates of herd-wide calf survival during the population decline phase, we found that the 95% confidence intervals for 11 of 17 estimates overlapped (Figure 7), which is an increase from the unmodified es-

| D ISCUSS I ON
The two most common methods for quantifying herd-wide calf survival are herd composition surveys and telemetry. Here, we capitalized on a large, long-term woodland caribou population monitoring dataset to compare these two methods and explore potential biases that could represent violations of equal detectability (herd composition surveys) and representative sampling (telemetry). The genesis of our study was the mismatch in calf survival estimates generated from telemetry and herd composition survey datasets. These differences cast doubt on our understanding of the state of the herd and hinder conservation and management decisions. We found that calves born later in the calving season had higher mortality risk, and this effect was consistent across both the population growth and decline phases. We also found that herd composition surveys conducted later in the year had higher estimates of C:C-we detected a significant effect during the population growth phase and a smaller, nonsignificant effect during the population decline phase. Using these relationships, we attempted to account for nonrepresentative sampling of calves (relative to calf birth date) and survey date (which might represent a violation of equal detectability). We were able to reconcile some estimates of herd-wide calf survival by compensating for these biases in the datasets (11 of 17). In the Middle Ridge herd, the herd for which we had the most data, we were also able to reconcile the trends: Between 2005 and 2012, herd-wide calf survival was low but showed an increasing trend.  (Rutberg, 1987). Within the birthing season, fawn survival might be higher for those individuals born close to the peak birth date (Jarnemo, Liberg, Lockowandt, Olsson, & Wahlström, 2004) or higher for those individuals born farther from the peak birth date (Aanes & Andersen, 1996). Finally, diel timing of birth could also influence survival (Patterson, Mills, Middel, Benson, & Obbard, 2016). These nuances further the argument that monitoring efforts should carefully consider the ecology of the species and the ecosystem in which they occur and plan sampling methods accordingly.

| Monitoring population demographics with telemetry data
For woodland caribou in Newfoundland, our results indicated that the effect of calf birth date on mortality risk was equivalent during the population growth and decline phases. The increased mortality risk for calves born later in the season could be driven by access to resources, vulnerability to predators, or both, and therefore, we might expect the magnitude of this risk to vary depending on climatic conditions or fluctuations in predator populations.
Among some ungulate species, it has been suggested that when predation rates are high, birth date has no influence on fawn survival (Fairbanks, 1993). However, in Newfoundland we found evidence of birth date influencing calf survival, despite predation being the dominant source of mortality for collared woodland caribou calves (Mahoney et al., 2016). Indeed, calves were more susceptible to predation during the population decline phase than during the population growth phase (Mahoney et al., 2016), and this was driven by the relationship between maternal body condition, susceptibility to climatic events, and predation risk (Bastille-Rousseau et al., 2016).

| Monitoring population demographics with herd composition surveys
We also found some evidence that herd composition survey data could be biased by survey date for woodland caribou in Newfoundland. We found evidence suggesting that timing of the herd composition survey can influence the C:C, whereby surveys conducted later in the autumn tended to have a higher C:C. One potential explanation for this counterintuitive result is that different demographic groups might ag-  (Caughley, 1974). It should be noted that managers can attempt to minimize these biases, for example, by using route and timing standardization for herd composition surveys (McCullough, 1994). Such strategies are not uniformly adopted, however, and can be cost-prohibitive in certain systems. While we were only able to explore how survey date and herd size might have Patterson, Drake, Allen, and Parent (2014), however, found that many of these factors did not influence C:C for caribou in Ontario, Canada. Additionally, a preliminary analysis did not reveal a relationship between C:C and the number of woodland caribou groups or the average group size (Ellington, 2015).

| Analytical considerations
With an analysis of this scale and scope, there are bound to be limitations. We assumed that collar date was an index of calf birth date, and we demonstrated that there was no relationship between calf birth weight (an index of calf age) and calf collar date. There could, however, have been violations of this assumption (Appendix B).
Indeed, other studies have concluded that lighter birth weight and/or later birth date could be linked via maternal condition (Adams, 2005;Cameron, Smith, Fancy, Gerhart, & White, 1993;Festa-Bianchet, 1988;Verme, 1989). Broadly speaking, caribou calf birth weight may have been higher in Newfoundland during the population growth phase than during the population decline phase (Mahoney & Weir, 2010), which is similar to other caribou herds (Couturier et al., 2009).
If there were individuals in our dataset that were collared as older individuals (i.e., individuals born earlier in the calving season masquerading as individuals born later in the season), then we would have underestimated the effect of calf birth date on calf mortality risk.
To properly account for unrepresentative sampling bias of calves relative to calf birth date within a season, the distribution of calf birth dates within a season must be known. We generated this using the average distribution across all herds and years, but an independent estimate of this distribution would be preferable. Some po-  et al., 2018). While the parturition date among some ungulates is highly repeatable (Plard et al., 2013), future work should examine whether the distribution of caribou calf birth dates within a calving season varies with climate, population density, herd, and maternal age, condition, and sociality. Indeed, date of the calving season has changed over time in the George River caribou herd in Quebec and Labrador, Canada (Couturier, Brunelle, Vandal, & St-Martin, 1990), and recent work has shown that caribou calves in Newfoundland are occasionally born beyond the typical 25-day calving season (Bonar, Laforge, & Vander Wal, 2017). Such variation, if not properly accounted for, would also result in biased estimates of herd-wide calf survival.
The proportion of parous cows that we used to transform C:C into estimates of herd-wide calf survival could themselves be biased by violations of equal detectability, as they were also derived from Furthermore, telemetry studies could also examine herd aggregation patterns after calving relative to different demographic groups and such studies could form an important link between the relationship between survey date and equal detectability of demographic groups.
Herd composition surveys are a traditional and relatively inexpensive way to monitor a multitude of demographic parameters but there could be hidden variability. We caution that future interpretations of herd composition survey data are cognizant of this limitation.
Misclassifying individuals in composition surveys will lead to bias; when observers are uncertain about the demographic classification, they should classify these individuals as unknown. By using multiple imputation, we were able to avoid masking the effect of unknown individuals on our ratios while at the same time accounting for the variability caused by unknown individuals in herd composition survey data. We also note that herd composition surveys cannot provide the additional data, such as timing and cause of death, that telemetry can provide; without telemetry data, the mechanisms underlying population changes are difficult to understand. Further, as suggested by Citta et al. (2014), understanding and mitigating some of the biases of herd composition surveys likely requires occasional comprehensive telemetry studies. Finally, more broadly, Harris et al. (2008) found that C:C performed poorly at detecting declines in calf survival and argue that the inclusion of independent estimates of calf survival, such as from telemetry, is important when populations need to be monitored closely.
Our study would not have been possible without the long-term monitoring datasets collected on woodland caribou herds across Newfoundland over the last 40 years. While our study found issues with both monitoring methods, we did not assess the validity of past research using these datasets and we caution against dismissing past studies and conclusions using these datasets without a thorough reassessment. We do not, however, support one monitoring method over the other. Instead, we recommend improvements to both monitoring methods. Ultimately, a comprehensive multi-approach monitoring program produces higher quality data, which could lead to more concrete management recommendations.

| Concluding thoughts
Ecological data are inherently noisy. Numerous ecological processes can influence calf mortality risk and recruitment rate (C:C), and moreover, they can vary among populations and ecosystems, and in response to climate change (Osinga, Pen, de Haes, & Brakefield, 2012), food availability (Bowen, Ellis, Iverson, & Boness, 2003), or human interactions (Gamelon et al., 2011). Demographic factors such as birth date can have impacts beyond juvenile survival; they can impact dispersal patterns (Jansen & Jenks, 2012) and overall fitness (Green & Rothstein, 1993), and can in some instances have stabilizing effects (e.g., Schultz, 1993). Not accounting for methodological biases when using different sampling methods to estimate ecological phenomenon and population demographics could have unexpected and unknown impacts. Even if we could control for or eliminate methodological biases, there would still be, and should be, a measure of uncertainty around estimates of herd-wide calf survival, some of which may be ecological and some merely stochastic.

ACK N OWLED G M ENTS
We thank the Government of Newfoundland and Labrador for supporting this work and the many employees over the past 40 years who have contributed their time, knowledge, and dedication both in the field and in the office. C. Doucet and G. Luther offered critical reviews in various stages of this analysis. This manuscript was also improved by the careful reviews from two anonymous reviewers and an associate editor. F. Norman and J. Guy helped organize and convert data into more accessible forms. Finally, we thank T. Bergerud and S. Mahoney for their vision in initiating much of the work on woodland caribou in Newfoundland.

CO N FLI C T O F I NTE R E S T
We declare we have no competing interests.

DATA S U M M A R I E S
This appendix contains summary data on telemetry studies used to estimate woodland caribou (Rangifer tarandus caribou) calf mortality risk (Table A1), summary data on autumn herd composition surveys used to estimate woodland caribou calf:cow ratio (Table A2), and summary data on spring herd composition surveys used to estimate woodland caribou parous cow:cow ratio (Table A3). This appendix also includes summary data on the telemetry studies and herd composition surveys used to compare estimates and trends of herd-wide calf survival (Table A4). This appendix also shows the difference between calf:cow ratio and calf:parous cow ratio

A PPE N D I X B R E L ATI O N S H I P B E T WE E N C A LF WE I G HT A N D CO LL A R DAT E
This appendix explores the relationship between the collar date May 2011, some outlier calves were more than double the weight of some other outlier calves ( Figure B2).

E S TI M ATI N G C A R I B O U C A LV I N G S E A S O N
This appendix explores collar date of woodland caribou calve (Rangifer tarandus caribou) in our telemetry dataset. We report the day of the year that the first caribou calf was collared and the last day of the year a caribou calf was collared for each herd (Table C1)

M U LTI PLE I M PUTATI O N O F H E R D CO M P OS ITI O N S U RV E Y DATA
Two types of missing or incomplete data were present in woodland caribou (Rangifer tarandus caribou) herd composition survey data in Newfoundland, Canada. The first type of incomplete or missing data was the date of the survey: Either the month of the survey or the day of the survey was missing. When the month of the survey was unknown, we could not be certain whether the survey was conducted during the autumn; thus, we removed these data from the analysis.
When the month was known but the day of the survey was missing, we used multiple imputation to estimate the missing day. We first converted day to a proportion of day of the month (i.e., the 15th