Data were derived from the Monitoring Avian Productivity and Survivorship (MAPS) program, a network constant-effort mist-netting and bird-banding stations that extends across the continental United States and, generally, the more southerly portions of Canada. Over 1,175 MAPS stations have been established since the inception of the MAPS program in 1989, of which 982 were operated for at least one year during the 15-year period (1992-2006) considered here.
The design of the MAPS program and field methods were standardized in 1992 and are described in DeSante (1992) and DeSante et al. (1995, 1996, 2004, 2015). MAPS stations were established by operators in areas where long-term mist netting was practical and permissible. Typically, ten net sites were established rather uniformly throughout the central 8 ha of a 20-ha study area (station) at locations where breeding landbirds could be captured efficiently. One mist net, usually 12m x 2.5m, 30mm-mesh, was erected at each net site. Locations and orientations of nets were kept consistent over all days and years that the station was operated. Nets were operated in a constant-effort manner, typically for six hours per day beginning at local sunrise, for one day per 10-day period, and for 6-10 consecutive 10-day periods beginning between May 1 and June 10 (starting later at more northerly latitudes) and continuing through the 10-day period ending August 8 (thus, with fewer periods at more northerly latitudes). To facilitate the collection of constant-effort data, nets were opened, checked, and closed in the same order on all days of operation. Nets were occasionally closed (or not opened) due to inclement weather, especially high capture rates, or for other logistical reasons.
With few exceptions, each bird captured was marked with a uniquely-numbered aluminum leg band provided by the U.S. Geological Survey or the Canadian Wildlife Service. Band number, capture status, species, age, sex, ageing and sexing criteria (skull pneumatization, breeding condition [cloacal protuberance and/or brood patch], feather wear, body and flight-feather molt, molt limits, and plumage characteristics), physical condition (body mass, wing chord, and fat content), date, capture time, station, and net number were recorded using standardized codes for all birds captured, including recaptures. Ageing and sexing followed guidelines developed by Pyle (1997). The times of opening and closing the nets and beginning of each net run were standardized and recorded each day so that netting effort could be calculated for each 10-day period each year. The breeding (summer residency) status of each species seen or heard while the station was being operated (including species that were not captured) was determined by the station operator using methods similar to those employed in breeding bird atlas projects.
Following computer entry, all MAPS data were run through extensive vetting routines that verified: (1) the validity of the codes used in all records; (2) the internal consistency of each banding record by comparing the ageing and sexing criteria and physical condition data to the resulting species, age, and sex determinations; (3) the consistency of species, age, and sex determinations for all records of each band number; and (4) the consistency among banding, effort, and breeding status data for all records. These vetting routines were conducted on data from about 60% of the stations by the station operators themselves through the use of MAPSPROG, a Visual dBASE entry, verification, and error-tracking program (Froehlich et al.2006); data from the remainder of the stations, including stations operated by IBP interns, were verified by IBP staff biologists.
We used capture-mark-recapture (CMR) models and generalized linear mixed models (GLMMs) to model temporal (annual) and spatial (at the scale of North American Bird Conservation Initiative [NABCI] Bird Conservation Regions [BCRs]) variation in demographic parameters.
We only included in analyses data from stations and years for which we considered data to be adequate for both constant-effort capture GLMMs and CMR analyses. Because estimation of survival rates from transient Cormack-Jolly-Seber (CJS) CMR models (i.e., models that correct for the presence of transient individuals among the birds captured; Pradel et al. 1997, Nott and DeSante 2002, Hines et al. 2003) requires four years of data, we only included data from stations that were operated for at least four years during the 15-yr period 1992-2006, and that had no more than two consecutive missed years within those four years. If a station met this minimum number and distribution of years but had other longer gaps during which it was not operated, data from all years during which it was operated were included in the analyses. In addition, to include data from a station for any given year, we required that the station was operated during that year with sufficient effort for the data to be usable for both survival and productivity analyses. For a station to be considered "operated with sufficient effort" for a given year, at least half of the standardized sampling-period effort for that station had to be completed for that year during at least three early-season sampling periods (adult superperiod) and two late-season sampling periods (young superperiod). Adult and young superperiods are defined in the MAPS Manual (DeSante et al. 2015) for each starting period of operation, which varies by latitude from Period 1 (May 1-10; for stations located in the southern parts of California, Arizona, Texas, or Florida) to Period 5 (June 10-19; for stations located in Alaska [except the SE part] or Boreal Canada). Although MAPS protocol calls for just 1 day of mist-netting per 10-day sampling period, a few stations operate nets more frequently. For these stations, we used a subset of the capture data that included all data from the first day of operation of each 10-day MAPS sampling period. By discarding data from additional effort within a sampling period we aimed to provide greater standardization of effort among stations and minimize bias in capture indices due to net-avoidance and effort saturation (DeSante et al. 2004). A total of 628 stations fulfilled these requirements during 1992-2006; data from these stations comprised the basis for the analyses reported here. Although some stations dropped out and new stations entered the program each year, many stations were operated for long time spans (e.g., 231 [37%] of those 628 stations were operated for ten or more years).
We included data for a species from all stations at which the breeding status of the species was determined to be "usual breeder" whereby one or more individuals of the species were present at the station during summer (i.e., in territories overlapping station boundaries) and presumably attempted to breed there during more than half of the years that the station was operated during 1992-2006. Finally, we limited analyses to 158 species with \(\geq\) 75 adult individuals captured, marked (banded), and released during 1992-2006, and for which at least 14 between-year recaptures were recorded during 1993-2006. Because of the difficulty of distinguishing Alder (Empidonax alnorum) from Willow (E. traillii) flycatchers, and Pacific-slope (E. difficilis) from Cordilleran (E. occidentalis) flycatchers, in the hand, we combined data for each of these species pairs and analyzed them as two super-species, "Traill’s" Flycatcher (TRFL) and "Western" Flycatcher (WEFL), respectively.
Population change (\(\lambda\); Lambda). An estimate of the annual net change in adult population size, \(N\), typically measured between years \(t\) and \(t+1\) as \(N_{t+1}/N_t\). Here we estimate \(\lambda\) using Pradel reverse-time CMR models (Pradel 1996). In the context of time-constant temporal analyses and all of our spatial analyses, \(\lambda\) can be interpreted as an estimate of average population change over the 15-year time period (i.e., trend). Pradel reverse-time CMR models also provide estimates of recapture probability (Pradel_p) and adult apparent survival (Pradel_phi). Estimates of adult apparent survival from these models are biased low, however, because of the presence of transients (because transients, by definition have zero survival probability; Pradel et al. 1997). Thus, we do not use Pradel_phi in our interpretations of results.
Adult apparent survival probability (\(\phi\); Phi). An estimate of the annual probability that a resident bird that was alive and present at the station in year t will also be alive and present in year t+1. Adult apparent survival (TM_PhiR) was estimated from ad hoc length-of-stay transient Cormack-Jolly-Seber (CJS) CMR models (Pradel et al. 1997, Nott and DeSante 2002, Hines et al. 2003). Adult apparent survival estimated in this way is unbiased with respect to transients. Transient CJS models also provide estimates of recapture probability (TM_p) and first-interval annual survival of birds of unknown residency status (U_Int1_Phi). Adult apparent survival probability represents a mixture of true survival (the complement of which is mortality) and site-fidelity (the complement of which is emigration).
Residency (\(\tau\); Tau). An estimate of the proportion of newly-captured adults that are residents at the station. The estimate of the proportion of newly-captured birds of unknown residency that are resident at the station (Tau) is estimated from the ratio of U_Int1_Phi to TM_PhiR, both of which are estimated from transient CJS CMR models. When the proportion of newly-captured birds that are residents is expanded to include the presence of newly-captured known residents (individuals that were recaptured at least 7 days later during their first year of capture), we define the parameter as \(\tau1\) (Tau1).
Recruitment (\(f\)). An estimate of the annual number of new individuals in year t+1 relative to the total number of individuals in year t. Recruitment (\(\hat{f}\)) is calculated as \(\hat{\lambda}-\hat{\phi}\). Recruitment includes two age-class components, second-year (SY) birds hatched the preceding year and after-second-year (ASY) immigrant birds. Note that, because of natal dispersal, the SY birds that recruit at any station are generally not the young birds that were produced the previous year at that station.
Index of adults per station (Ad). We estimate of the annual number of captures of adults per station to provide an index of station-scale adult population size. The index of adults per station is estimated from effort-corrected Poisson generalized linear mixed modes (GLMMs). Because MAPS stations are established to be approximately the same size (20 ha), the index of adults per station (Ad) could be considered an index of population density (adults per 20 ha). This index will be positively biased to some extent due to the presence of transient individuals and negatively biased due to imperfect detection.
Index of young birds per station (Yg). An estimate of the annual number of captures of young (hatching-year [HY]) birds per station. The index of young per station, like the index of adults per station, is estimated from effort-corrected Poisson GLMMs. Unlike Ad, however, many young birds captured at a station are likely dispersing juveniles fledged from nests outside the boundaries of the station.
Productivity (reproductive index; RI). An index of the annual number of young (hatching-year [HY]) birds produced per adult. Because most HY birds captured at MAPS stations are likely dispersing juveniles that are independent of their parents, the reproductive index represents the end result of a complex mixture of components including: proportion of adults attempting to breed, number of nesting attempts and broods, clutch size, egg hatchability, survival of eggs and nestlings, and survival of fledglings to independence from parents. Productivity is estimated independently from effort-corrected binomial GLMMs (i.e., it is not simply calculated as Yg/Ad).
Post-breeding effects (PBE). An index calculated as \(f\)/RI. Because recruitment (\(f\)) includes two age-class components, SY birds hatched the preceding year and ASY immigrant birds, post-breeding effects (PBE) reflects both first-year survival of young birds and immigration of adults, although it seems likely that the major effect arises from first-year survival.
1. Temporal analyses. We used capture-mark-recapture (CMR) models to estimate population change (lambda [\(\lambda\)]) and adult apparent survival rate (\(\phi\)) and to calculate estimates of recruitment rate (\(f\)), and residency (the proportion of residents among newly captured adults [\(\tau1\)]). We ran all CMR models with Program MARK (White and Burnham 1999) using the RMark package (Laake and Rexstad 2008) in R ver. 2.10.1 (R Development Core Team 2009). We considered three parameterizations of temporal models for each of the four demographic parameters: 1) time-dependent (\(t\)), for which a year-specific estimates is produced for each of the 14 years or intervals); 2) a linear function of time (\(T\)), for which an intercept and slope (\(\beta\)) are estimated for the 15-yr period, and year-specific estimates are calculated from the intercept and slope); and 3) time-constant (\(\cdot\)) for which a single (mean) estimate is estimated for the entire 15-yr period). We used Akaike’s Information Criteria for small samples (\(AIC_c\)) for model selection (Burnham and Anderson 1992) and for reporting model-averaged parameter estimates using \(AIC_c\) model weights (\(w_i\); Burnham and Anderson 1998).
Pradel models. We estimated population change (\(\lambda\); where \(\lambda < 1\) indicates a declining population and \(\lambda > 1\) indicates an increasing population) by applying Pradel reverse-time CMR models to MAPS data (Pradel 1996). We used the '\(\lambda\) and \(\phi\)' version of the likelihood in Program MARK (White and Burnham 1999). In addition to three temporal models each for \(\lambda\) and \(\phi\), we considered four temporal models for the 'nuisance' parameter, \(p\), recapture probability: (1) time-constant (\(\cdot\), in which a single estimate is calculated over the entire 15-yr period), (2) time-dependent (\(t\), in which a year-specific estimate is calculated for each of the 15 years), (3) as a linear function of the mean number of within-season captures of individual birds over the entire 15 year period (CAPCOV), and (4) as a linear function of year and the station-specific mean number of within-season captures of individual birds (CAPCOV + t). There were thus, a total of 36 models in the Pradel reverse-time CMR model set, 3 for \(\lambda\) \(\cdot\) 3 for \(\phi\) \(\times\) 4 for \(p\).
Cormack-Jolly-Seber models. Estimates of adult apparent survival, \(\phi\) from Pradel reverse-time capture- recapture models will be biased low if transient individuals (e.g., passage migrants, dispersing birds, and 'floaters' [sensu Brown 1969]) that have zero probability of returning to the station are present in populations. Because of this potential bias, we used ad-hoc length-of-stay transient Cormack-Jolly-Seber (CJS) models that account for the presence of transients (Pradel et al. 1997, Nott and DeSante 2002, Hines et al. 2003) to estimate unbiased (by transients) adult apparent survival rates (\(\phi^{R}\)). We also used these modified CJS models to estimate the 'nuisance' parameter, \(\tau\), the proportion of residents among newly-captured adults of unknown residency status (i.e., those individuals not recaptured 7 or more days later in their first year of capture). By using additional information on the number of newly-captured birds that were known residents (i.e., that were recaptured 7 or more days later in their first year of capture), we calculated the proportion of residents among all newly-captured adults, \(\tau1\), and suggest that this parameter might contain useful biological information.
Length-of-stay transient models estimate \(\tau\) based on a ratio of two survival rates: \(\phi^{U1}/\phi^{R}\), where \(\phi^{U1}\) is the first interval survival rate for individuals not captured 7 or more days apart in their first year of capture (a mixture of residents and transients), and \(\phi^R\) is the survival rate of residents.
Then, letting '\(\cdot\)' indicate time-independence, '\(t\)' indicate time-dependence, and '\(T\)' indicate a linear function of time, and letting '\(\times\)' indicate that the two parameters vary independently of each other (i.e., temporal effects nested within residency classification, U1:t + R:t) and '+' indicate that the two parameters vary in concert (i.e., an additive U1 + t model), there are 11 biologically meaningful models describing time variation (or lack thereof) in \(\phi^{U1}\) and \(\phi^{R}\) as follows:
| Model | U1 | R | |
|---|---|---|---|
| 1 | \(\cdot\) | \(\cdot\) | |
| 2 | \(t\) | \(\cdot\) | |
| 3 | \(\cdot\) | \(t\) | |
| 4 | \(t\) | \(\times\) | \(t\) |
| 5 | \(t\) | + | \(t\) |
| 6 | \(T\) | \(\cdot\) | |
| 7 | \(\cdot\) | \(T\) | |
| 8 | \(T\) | \(\times\) | \(T\) |
| 9 | \(T\) | + | \(T\) |
| 10 | \(t\) | \(\times\) | \(T\) |
| 11 | \(T\) | \(\times\) | \(t\) |
We modeled time variation in recapture probability, \(p\), using the same four models that we used in the Pradel models, that is, as time-constant (\(\cdot\)), as time-dependent (\(t\)), as a linear function of the mean number of within-season captures of individual birds over the entire 15 year period (CAPCOV), and as a linear function of year and the mean number of within-season captures of individual birds (CAPCOV + t). There were thus, a total of 44 models in the transient Cormack-Jolly-Seber CMR model set, 11 for (\(\phi^{U1}\) and \(\phi^R\)) \(\times\) 4 for \(p\).
Recruitment rate. Despite (negative) bias in survival-rate estimates from Pradel reverse-time models, estimates of population growth rate from these models are unbiased if we assume that under-estimation of survival rate is balanced by over-estimation of recruitment rate (i.e., transience in survival and recruitment are of equal magnitude). Based on this assumption, we calculated year-specific estimates of recruitment rate as:
\[\hat{f}^{R}_{t}=\hat{\lambda}_t-\hat{\phi}_{t}^{R}\;,\]
where \(\hat{f}^{R}_{t}\) represents an estimate of the year-specific number of new individuals in the population in year \(t\), per individual in year \(t-1\), based on \(\hat{\lambda}_{t}\) from Pradel reverse-time models and \(\hat{\phi}_{t}^{R}\) from the length-of-stay transient CJS models. Note that \(\hat{\lambda}_{t}\) and \(\hat{\phi}_{t}^{R}\) are model-averaged estimates derived from model sets whereby \(\lambda_t\) (for Pradel models) or \(\phi_{t}^{R}\) (for CJS models) are constrained to be annually varying, but all possible parameterizations of other parameters are allowed. Although inference regarding demographic contributions to trend can be based on survival and recruitment estimates derived solely from Pradel reverse-time models (Saracco et al. 2008), we feel that combining information from Pradel and transient CJS models, as we have done here, provides a more appropriate basis for assessing demographic components of trends.
2. Spatial analyses. We used CMR models to provide time-constant estimates of population growth rate (\(\lambda\)) and adult apparent survival rate (\(\phi\)), and to calculate estimates of recruitment rate (\(f\)), and residency (the proportion of residents among newly captured adults [\(\tau1\)]) at the program-wide (i.e., continental) scale, and at the scale of North American Bird Conservation Initiative Regions (BCRs). As in temporal CMR models, we used Akaike Information Criteria (\(AIC_c\)) for model selection (Burnham and Anderson 1992) and, in addition to reporting program-wide and BCR-specific parameter estimates, also report model-averaged parameter estimates using \(AIC_c\) weights (\(w_i\); Burnham and Anderson 1998).
Pradel models. We again estimated population growth rate, \(\lambda\), by applying Pradel reverse-time CMR models to MAPS data (Pradel 1996), and used the '\(\lambda\) and \(\phi\)' likelihood formulation in Program Mark (White and Burnham 1999) to obtain estimates of \(\lambda\) and \(\phi\). We considered two spatial models each for \(\lambda\) and \(\phi\): BCR-constant (whereby a single mean estimate is calculated over all of the BCRs, thus, program-wide), and BCR- dependent (in which a time-constant estimate is calculated for each BCRs, thus, BCR- specific). We considered four spatial models for recapture probability, \(p\): BCR-constant (\(\cdot\)), (2) BCR-dependent (BCR), (3) as a linear function of the mean number of station-specific within-season captures of individual birds (CAPCOV), and (4) as a linear function of BCR and the mean number of within-season captures of individual birds (CAPCOV + BCR). There were thus, a total of 16 models in the spatial Pradel reverse-time CMR model set, 2 for \(\lambda\) \(\times\) 2 for \(\phi\) \(\times\) 4 for \(p\).
CJS models. We again used ad-hoc length-of-stay transient models to provide adult apparent survival rate estimates that were unbiased with respect to transient individuals, and estimates for \(\tau\), the proportion of residents among newly captured birds that were not recaptured 7 or more days later in their first year of capture. We modeled \(\phi^{U1}\) and \(\phi^{R}\) using five biologically meaningful models to describe spatial variation (or lack thereof). Again using '\(\cdot\)' to indicate BCR-independence, 'BCR' to indicate BCR-dependence, and '\(\times\)' to indicate that the two parameters vary independently (i.e., a nested U1:BCR + R:BCR model), and '+' to indicate that the two parameters vary in parallel (i.e., an U1 + BCR additive model), these five models are as follows:
| Model | U1 | R | |
|---|---|---|---|
| 1 | \(\cdot\) | \(\cdot\) | |
| 2 | BCR | \(\cdot\) | |
| 3 | \(\cdot\) | BCR | |
| 4 | BCR | \(\times\) | BCR |
| 5 | BCR | + | BCR |
We again considered the same four spatial models for p as in the Pradel spatial models, so that there were a total of 20 models in the spatial transient Cormack-Jolly-Seber CMR model set, 5 for (\(\phi^{U1}\) and \(\phi^{R}\)) \(\times\) 4 for \(p\).
Recruitment rate. As with temporal CMR analyses, we calculated BCR-specific estimates of recruitment as:
\[\hat{f}^{R}_{BCR}=\hat{\lambda}_{BCR}-\hat{\phi}_{BCR}^{R}\;,\]
where \(\hat{\lambda}^{R}_{BCR}\) represents the estimated (average, or time-constant) number of new individuals in the population in year \(t\) per individual in year \(t-1\) based on \(\hat{\lambda}^{R}_{BCR}\) from Pradel reverse-time models and \(\hat{\phi}_{BCR}^{R}\) from the length-of-stay transient CJS models.
We modeled observed yearly capture data of adult and young birds as Poisson random variables and used a binomial model whereby productivity represented the probability of a captured bird being a young bird. We used generalized linear mixed models (GLMMs) to assess temporal (by year) and spatial (by BCR) variation in adult and young capture indices and modeled productivity using a logistic model. We used regional spatial replication of sites to calculate correction offsets for missed or excess effort and incorporated the offsets into the linear models. Because all MAPS stations are approximately the same size (20 ha) and typically have the same number (10) and distribution (throughout the central 8 ha of the station) of nets, we used the effort-corrected capture index of adults (Ad) as an index of population density (adults per 20 ha), and the reproductive index (RI, young/adult), based on the probability of a captured bird being a young bird, as our measure of breeding performance or productivity.
Despite best efforts, MAPS stations are not always operated in a 'constant effort' manner among years. In most cases when effort differed in a given year from what is typical for a particular station, effort was less than intended (e.g., due to weather or logistical problems); however, in some cases effort was slightly higher than normal. To correct our analyses of capture data for these inconsistencies, we included offsets in generalized linear mixed models examining spatial and temporal variation in adult captures, young captures, and productivity. We calculated offsets based on regional scale distribution of effort and captures across the MAPS season for each year. Accounting for within-season timing of missed effort, rather than just the amount of effort missed is critical for calculating this offset in a meaningful way (Peach et al. 1998, Nott and DeSante 2002). Data from years with complete data for a particular station could be used to estimate individuals (or fractions of individuals) missed due to missed effort in a particular sampling period. Such an approach has been pioneered and advocated as part of standard analyses of the British Trust for Ornithology‘s Constant Effort Sites scheme (e.g., Peach et al. 1998, Robinson et al. 2007). Here we use regional spatial replication of sites to calculate effort corrections rather than temporal replication of a given station. We feel that spatial replication within geographic regions provides a more appropriate means of correcting our data for annual variation in sampling effort because annual variation in the timing of captures in North America can be high.
Calculation of correction offsets involved summarizing annual effort and capture data for 17 groups based on MAPS region and intended starting period (ISP). MAPS regions were defined based on biogeographic and meteorological considerations and included: Northwest, Southwest, North-central, South-central, Northeast, Southeast, Alaska, and Boreal Canada regions (see map in DeSante et al. 1993, 2015). Initiation of the MAPS season should ideally begin after most northward migration has been completed, and MAPS protocols provide recommended starting periods based (largely) on latitude (see DeSante et al. 2004). Because recommendations do not match MAPS regions exactly, and because some individual stations deviate slightly from these recommendations (e.g., due to local conditions), there can be 2-3 ISPs represented by stations within any given MAPS region (except for the Alaska and Boreal Canada regions, which always had intended starting period 5 [Jun 10-19]).
Our calculations to correct for annual effort inconsistencies are as follows. First we completed a set of summaries of the effort data. For i in \(1,\cdots,M\) MAPS stations, we summed the net-hours completed across p in \(1,\cdots,P\) sampling periods (where P = 5-10 periods represents the entire MAPS season) in each of G = 17 region-ISP groupings and \(t = 1,\cdots\,T = 15\) years. We represent this quantity as \(e_{g[i],p,t}\). We then calculated \(H_{g[i],p,t}\) as the proportion of the total annual net-hours represented by group i and sampling period p as:
\[H_{g[i],p,t}=e_{g[i],p,t}/\sum_{p=1}^{P}e_{g[i],p,t}\;.\]
We then calculated \(h_{i,p,t}\), the proportion of the total intended net hours actually represented by the difference between intended effort, \(I_{i,p,t}\), and actual completed effort, \(A_{i,p,t}\) in each sampling period (where intended net-hours is based on numbers of nets typically operated and typical numbers of hours of operation, and is defined by the station operator after the end of the first year of station operation) at the station-scale:
\[h_{i,p,t}=(I_{i,p,t}-A_{i,p,t})/\sum_{i=1}^{M}I_{i,p,t}\;.\]
We then completed a series of summaries of the capture data. For each species, region-ISP, and year we summed numbers of adult and young individuals captured (a small number of unknown-aged birds were excluded from the analysis), which we denote as \(N_{g[i],t}^{A}\) and \(N_{g[i],t}^{Y}\) for adult and young birds, respectively. We then calculated a set of reduced summaries representing the total number of individuals of each age class captured with data from individual sampling periods removed. We denote these as \(n_{g[i],p,t}^{A}\) and \(n_{g[i],p,t}^{Y}\). The proportion of the overall annual catch lost by removal of individual periods was then calculated as:
\[\delta_{g[i],p,t}^{A}=n_{g[i],p,t}^{A}/N_{g[i],t}^{A}\]
for adult birds, and
\[\delta_{g[i],p,t}^{Y}=n_{g[i],p,t}^{Y}/N_{g[i],t}^{Y}\]
for young birds. Correction factors representing the proportion of birds missed (positive values) or gained (negative values) at a station, period, and year due to missing or extra effort can then be approximated as:
\[c^{A}_{i,p,t}=\frac{\delta^{A}_{g[i],p,t}h_{i,p,t}}{H_{g[i],p,t}}\;\textrm{and}\;c^{Y}_{i,p,t}=\frac{\delta^{Y}_{g[i],p,t}h_{i,p,t}}{H_{g[i],p,t}}\]
for adults and young, respectively, and the corrected numbers of adult and young at a particular station and year can then be calculated based on these correction factors and the observed numbers (i.e., numbers captured) of adults and young captured in each sampling period at the station:
\[C^{A}_{i,t}=\sum_{p=1}^{P}(N^{A}_{i,p,t}+c^{A}_{i,p,t}N^{A}_{i,p,t})\; \textrm{and}\; C^{Y}_{i,t}=\sum_{p=1}^{P}(N^{Y}_{i,p,t}+c^{Y}_{i,p,t}N^{Y}_{i,p,t})\;.\]
We modeled observed yearly capture data of adult and young birds at the station-scale, \(N^{A}_{i,t}\) and \(N^{Y}_{i,t}\), as Poisson random variables with mean (and variance) parameters \(\lambda^{A}_{i,t}\) and \(\lambda^{Y}_{i,t}\); i.e.,
\[N^{A}_{i,t}\sim\textrm{Pois}(\lambda^{A}_{i,t})\; \textrm{and}\; N^{Y}_{i,t}\sim\textrm{Pois}(\lambda^{Y}_{i,t})\;,\]
and we used a binomial model for productivity with \(N^{Y}_{i,t}+N^{A}_{i,t}\) trials and probability parameter, \(p_{i,t}\), representing the probability of a captured bird at a given station and year being a young bird:
\[N^{Y}_{i,t}|(N^{Y}_{i,t}+N^{A}_{i,t})\sim\textrm{Bin}(N^{Y}_{i,t}+N^{A}_{i,t},p_{i,t})\;.\]
We used generalized linear mixed models (GLMMs) to assess spatial (BCR) and temporal (annual) variation in adult and young capture indices and productivity. As with CMR models, we modeled temporal variation in our estimates of the capture index of adults (Ad), capture index of young (Yg), and reproductive index (RI) as time- constant (\(\cdot\)), time-dependent (\(t\)), and as a linear function of time (\(T\)). We modeled spatial variation in Ad, Yg, and RI as BCR-constant (\(\cdot\), essentially program-wide) and BCR-specific (BCR). As in temporal and spatial CMR models, we used \(AIC_c\) weights to assess support for temporal or spatial variation in these parameters. We used time- and BCR-specific models to compare to CMR estimates of demographic parameters, and so describe those in detail here. Poisson models for temporal variation in adult and young captures were defined as:
\[\textrm{log}(\lambda^{A}_{i,t})=\beta_{0}+S_{i}+Y_{t}+\textrm{log}(\frac{N^{A}_{i,t}}{C^{A}_{i,t}})\;\textrm{and}\;\textrm{log}(\lambda^{Y}_{i,t})=\beta_{0}+S_{i}+Y_{t}+\textrm{log}(\frac{N^{Y}_{i,t}}{C^{Y}_{i,t}})\;,\]
respectively. We modeled productivity using a logistic model:
\[\textrm{logit}(p_{i,t})=\beta_{0}+S_{i}+Y_{t}+\textrm{log}(\frac{N^{Y}_{i,t}C^{A}_{i,t}}{C^{Y}_{i,t}N^{A}_{i,t}})\;.\]
In each of the above, the \(\beta_{0}\) represents the mean for the year during which the most adults were captured, \(S_{i}\) represent random station effects distributed as \(S_{i}\sim\textrm{Norm}(0,\sigma^{2})\), and the \(Y_{t}\) represent fixed year effects for years relative to the year during which the most adults were captured. The \(\textrm{log}(N^{A}_{i,t}/C^{A}_{i,t})\), \(\textrm{log}(N^{Y}_{i,t}/C^{Y}_{i,t})\), and \(\textrm{log}(N^{Y}_{i,t}C^{A}_{i,t}/C^{Y}_{i,t}N^{A}_{i,t})\) terms are offsets to correct for annual effort variation. The offsets for models of adult and young captures represent ratios of observed captures to estimates of the numbers of captures that would have been observed under complete intended effort (see above Correcting capture data for annual variation in mist-netting Effort for detail). The offset for productivity was derived from the following expression, which denotes the difference in the proportion of young captured between observed and corrected catches:
\[\textrm{logit}\frac{N^{Y}_{i,t}}{N^{Y}_{i,t}+N^{A}_{i,t}}-\textrm{logit}(\frac{C^{Y}_{i,t}}{C^{Y}_{i,t}+C^{A}_{i,t}})=\]
\[\textrm{log}(\frac{\frac{N^{Y}_{i,t}}{N^{Y}_{i,t}+N^{A}_{i,t}}}{1-\frac{N^{Y}_{i,t}}{N^{Y}_{i,t}+N^{A}_{i,t}}}) - \textrm{log}(\frac{\frac{C^{Y}_{i,t}}{C^{Y}_{i,t}+C^{A}_{i,t}}}{1-\frac{C^{Y}_{i,t}}{C^{Y}_{i,t}+C^{A}_{i,t}}})=\]
\[\textrm{log}\frac{N^{Y}_{i,t}C^{A}_{i,t}}{N^{A}_{i,t}C^{Y}_{i,t}}\;.\]
We defined analogous models for our spatial analysis by replacing the \(Y_{i}\) term in the temporal models with an effect to indicate differences among BCRs, \(BCR_{i}\). Models were implemented using the glmmML package (Brostrom 2009) in the R statistical package (R Development Core Team 2009). Model parameters were estimated using Laplace approximation, which is more accurate than quasi-likelihood methods and appropriate for application to data such as ours, with Poisson (young and adult captures) and binomial (reproductive index) responses and a single random effect (Bolker et al. 2009).
We present capture indices and indices of productivity for the first year of the study and for the BCR that representing the lowest BCR factor level (i.e., the lowest-numbered BCR) as the inverse-log transformed point estimates of model intercepts, \(\textrm{exp}(\hat{\beta_{0})}\). For remaining years and BCRs, we added year and BCR effects to intercepts; e.g., for the temporal model, year-specific indices for 1993-2006 would be \(\textrm{exp}(\hat{\beta_{0}}+\hat{Y_{t}})\). We estimated standard errors (SEs) of these year- and BCR-specific indices using the delta method (Oehlert 1992; implemented in R using Jackson 2010). We approximated 95% confidence intervals approximated as \(\textrm{exp}(\hat{\beta_{0}}+\hat{Y_{t}}\pm{1.96}({\widehat{SE}}(\beta_{0}+Y_{t}))\).
Breeding performance in a given year is not the only factor driving the recruitment of new individuals into breeding populations in the subsequent year. The survival of young through their first winter, the ability of surviving young to recruit into a breeding population, and the extent of immigration of adults will also have post-breeding effects on recruitment. In an attempt to get a handle on these effects, we created a parameter we called post-breeding effects (PBE) by dividing year- or BCR-specific estimates of recruitment by the corresponding reproductive index estimate (e.g., \(f/RI_{t}\)). Again, in the temporal analyses, we provided time-constant (\(\cdot\)), time-dependent (\(t\)), and linear function of time (\(T\)) estimates for PBE, while in the spatial analyses, we provided BCR-constant (\(\cdot\), program-wide) and BCR-specific estimates for PBE.
We examined the year-specific and BCR-specific estimates obtained for population change (\(\hat{\lambda}_{t}\) and \(\hat{\lambda}_{BCR}\)), adult apparent survival (\(\hat{\phi}_{t}^{R}\) and \(\hat{\phi}_{BCR}^{R}\)), recruitment (\(\hat{f}_{t}\) and \(\hat{f}_{BCR}\)), and residency (\(\hat{\tau1}_{t}\) and \(\hat{\tau1}_{BCR}\)) from temporal and spatial CMR models; and the indices of adults (Ad) and young (Yg), productivity (RI), and post-breeding effects (PBE) from GLMM analyses; and excluded estimates with unrealistic values as follows.
We excluded population change estimates that had standard errors (SEs) of 0, had lower 95% confidence limits (LCLs) of 0 or upper 95% confidence limits (UCLs) of infinity, had SEs that were larger than the estimate, or were < 0.3 (the approximate value of lambda if all three demographic rates contributing to it [productivity, survival of young, and survival of adults] were simultaneously 60% lower than the previous year) or > 2.1 (the approximate value for lambda if all three demographic rates were simultaneously 60% higher than the previous year); or were associated with recruitment estimates that were < 0. If we excluded a \(\hat{\lambda}\), we also excluded the corresponding \(\hat{f}\).
We excluded adult apparent survival estimates (either survival of resident birds or first period survival of unknown residency birds), that were 0 or 1, had SEs of 0, or had LCLs of 0 or UCLs of 1; were associated with residency estimates that were > 1; or (in the case of survival of residents) were associated with recruitment estimates that were < 0. If we excluded an adult apparent survival estimate of resident birds, we also excluded the corresponding residency and recruitment estimates. If we excluded a first-period survival estimate of unknown residency birds, we again excluded the corresponding residency estimate but not the associated recruitment estimate.
We excluded residency estimates that were > 1, or were associated with adult apparent survival estimates (either survival of resident birds or first period survival of unknown residency birds) that were excluded. If we excluded a residency estimate that was > 1, we also excluded the corresponding survival estimate of resident birds and the first-period survival estimate of unknown residency birds.
We excluded recruitment estimates that were < 0, or were associated with lambda or adult apparent survival estimates of resident birds that were excluded. If we excluded a recruitment estimate that was < 0, we also excluded the corresponding lambda estimate and survival estimate of resident birds.
We excluded productivity (RI) index estimates that were 0, that had LCLs that were 0, or UCLs that were > 10. We excluded Ad and Yg index estimates that were 0, that had LCLs that were 0, or UCLs that were > 1000. Finally, we excluded post-breeding effects (PBE) estimates that were associated with recruitment or productivity estimates that were excluded.
We then conducted weighted (by number of year-unique individual adult birds captured) pairwise correlation analyses among the index of adult population density, lambda, adult apparent survival, recruitment, productivity, and post-breeding effects using the wtd.cor function in the 'weights' package (Pasek et al. 2014) in R (R Core Development Team 2009), and examined scatterplots and pairwise correlation matrices for both temporal (annual) and spatial (BCR-scale) correlations. Because preliminary analyses yielded mean (for all species) temporal correlations between residency (\(\tau{1}_{t}\)) and each of the other demographic parameters that were very weak (ranging from -0.056 for post-breeding effects to 0.123 for adult apparent survival), and yielded no consistent patterns in any of these temporal correlations, we did not present results of temporal (or spatial) correlations between \(\tau{1}\) and any other demographic parameter in the scatterplots and pairwise correlation matrices for any species.
To facilitate comparisons among species, we calculated weighted arithmetic means (after excluding unreliable estimates as described above) for each demographic parameter from each temporal and spatial model that was employed in its estimation (and for model- averaged estimates from CMR models), along with corresponding standard deviations and coefficients of variation (CVs). This allowed us not only to compare mean values for these important vital rates among various species, but also to examine and compare the annual and spatial variabilities of a given vital rate among various species, and to compare the annual and spatial variabilities of various vital rates for a single species. Weighting for calculations of means for all parameters estimated from CMR analyses and for the index of post-breeding effects was by the number of year-unique captures of adults. Weighing for calculations of means for all parameters estimated from GLMM analyses (population indices of adults (Ad) and young (Yg) and reproductive index (RI) was by number of stations at which the species was captured.
To elucidate potential patterns in relationships between lambda and other demographic parameters, we grouped species according to their overall population trend (decreasing, stable, increasing) and their migration strategy (Neotropical-wintering migrant, temperate-wintering migrant, permanent resident). We calculated and used the weighted (again, by number of year-unique individual adult birds captured) geometric mean of the fully model- averaged lambda estimates (from either temporal or spatial analyses) as our measure of overall population trend, and used the standard errors of the individual year- or BCR-specific lambda estimates and the delta method to calculate a standard error of the geometric mean and subsequent 95% lower and upper confidence limits (LCL and UCL, respectively). We then established the following population trend species groups:
DS: Significantly decreasing: \(\hat{\lambda}\) < 1.0 and \(\hat{\lambda}\) UCL < 1.0
DE: Non-significantly decreasing: \(\hat{\lambda}\) < 0.99 and \(\hat{\lambda}\) UCL > 1.0
ST: Stable: 0.99 < \(\hat{\lambda}\) < 1.01 and 95%confidence interval containing 1.0
IN: Non-significantly increasing: \(\hat{\lambda}\) > 1.01 and \(\hat{\lambda}\) LCL < 1.0
IS: Significantly increasing: \(\hat{\lambda}\) > 1.0 and \(\hat{\lambda}\) LCL > 1.0
Finally, we defined the geographical border between Neotropical wintering and temperate wintering to follow approximately the southern boundary of the United States, and used migration strategy species groups developed for MAPS data by DeSante and Pyle (unpublished MS) as follows:
R: Permanent resident species
RT: Permanent resident species with irregular, irruptive, or minor (<< 50% of individuals) temperate-wintering migrations
T: Temperate-wintering migratory species
TI: Mainly temperate-wintering migratory species, but < 50% of individuals are Neotropical-wintering migrants
NI: Mainly Neotropical-wintering migratory species, but < 50% of individuals are temperate-wintering migrants
N: Neotropical-wintering migratory species
For general discussions and overall classifications, we considered all species classed as R or RT as permanent resident species, all species classed as T or TI as temperate-wintering migratory species, and all species classed as NI or N as Neotropical-wintering migratory species.