Using Binomial Distance-Sampling Models to Estimate the Effective Detection Radius of Point-Count Surveys Across Boreal Canada

Abstract

We used binomial distance-sampling models to estimate the effective detection radius (EDR) of point-count surveys across boreal Canada. We evaluated binomial models based on 0–50 m and >50 m distance categories for goodness-of-fit and sensitivities to variation in survey effort and habitats sampled. We also compared binomial EDRs to Partners in Flight's maximum detection distances (MDD) to determine differences in landbird population sizes derived from each. Binomial EDRs had a small positive bias (4%) averaged across 86 species and a large positive bias (30–82%) for two species when compared with EDRs estimated using multinomial distance sampling. Patterns in binomial EDRs were consistent with how bird songs attenuate in relation to their frequencies and transmission through different habitats. EDR varied 12% among habitats and increased 17% when birds were counted to an unlimited distance, compared with a limited distance of 100 m. The EDR did not vary with the duration of surveys, and densities did not differ when using unlimited-distance versus truncated data. Estimated densities, however, increased 19% from 3- to 5-min counts and 25% from 5- to 10-min counts, possibly from increases in the availability, movement, or double counting of birds with longer counts. Thus, investigators should be cautious when comparing distance-sampling results among studies if methods vary. Population sizes estimated using EDR averaged 5 times (0.8–15 times) those estimated with MDD. Survey data from which to estimate binomial EDRs are widely available across North America and could be used as an alternative to MDD when estimating landbird population sizes.

Résumé

Nous avons utilisé des modèles binomiaux d'échantillonnages basés sur la distance afin d'estimer le rayon de détection effectif (RDE) des inventaires par points d'écoute en région boréale canadienne. Nous avons évalué des modèles binomiaux basés sur des catégories de distance de 0–50 m et >50 m pour en déterminer l'adéquation et les sensibilités aux variations de l'effort d'inventaire et les habitats échantillonnés. Nous avons aussi comparé les RDE binomiaux aux distances de détection maximales de Partenaires d'envol (DDM) afin de déterminer les différences dans les tailles de populations des oiseaux terrestres estimées. Les RDE binomiaux avaient un léger biais positif (4 %) en moyenne pour 86 espèces et un biais positif élevé (30–82 %) pour deux espèces lorsque comparés aux RDE estimés à l'aide d'un échantillonnage multinomial selon la distance. Les patrons des RDE binomiaux étaient consistants avec la façon dont les chants d'oiseaux s'atténuent en fonction de leur fréquence et de leur transmission à travers différents habitats. Les RDE variaient de 12 % entre les habitats et augmentaient de 17 % lorsque les oiseaux étaient dénombrés à une distance illimitée, comparativement à une distance limitée à 100 m. Les RDE ne variaient pas avec la durée des inventaires. Les densités ne différaient pas selon que l'on utilisait les données de distance illimitée ou les données tronquées. Cependant, les densités estimées augmentaient de 19 % pour les dénombrements de 3 à 5 minutes et de 25 % pour ceux aux 5 à 10 minutes, probablement en raison d'augmentations dans la disponibilité, le mouvement ou le double comptage des oiseaux avec des dénombrements plus longs. Ainsi, les chercheurs devraient être prudents lorsqu'ils comparent les résultats d'échantillonnages basés sur la distance si les méthodes varient entre les études. Les tailles de populations estimées à l'aide des RDE étaient en moyenne 5× (0,8–15 fois) plus élevées que celles estimées à l'aide des DDM. Les données d'inventaire permettant d'estimer les RDE binomiaux sont largement répandues à travers l'Amérique du Nord et peuvent être utilisées comme une alternative aux DDM pour l'estimation des tailles de populations des oiseaux terrestres.

IN NORTH AMERICA, all the major taxonomic initiatives for bird conservation set numerical targets for continental bird population sizes (Brown et al. 2001; Kushlan et al. 2002; North American Waterfowl Management Plan, Plan Committee 2004a; Rich et al. 2004). These population goals are often stepped down to regional or local levels to help direct on-the-ground conservation (North American Waterfowl Management Plan, Plan Committee 2004b; Will et al. 2005). Reliable estimators of density and population size are required to set defensible population goals and to judge the value of different geographic regions and habitats to birds. Estimating the population size of any bird species over a large portion of its range is challenging (Rosenberg and Blancher 2005, Lanctot et al. 2008). For landbirds this can be complicated by poor survey coverage over species' ranges (Bart et al. 2004) and the many issues of detectability associated with point-count surveys (Nichols et al. 2009, Simons et al. 2009). Here, we address the problem of incomplete detection of birds during point-count surveys, with a view toward developing new and reliable estimates of breeding population sizes and habitat-specific densities for landbirds across boreal Canada.

Recently, the continental population sizes of 448 species of breeding landbirds were estimated for the Partners in Flight North American Landbird Conservation Plan (Rich et al. 2004, Rosenberg and Blancher 2005, Blancher et al. 2007). These estimates relied primarily on data from the North American Breeding Bird Survey (BBS), a spatially extensive, roadside survey designed to monitor the population trends of a range of species breeding across Canada and the United States (Sauer and Link 2011). The BBS does not include ancillary data to correct the surveys for incomplete detection (O'Connor et al. 2000). However, Rich et al. (2004) and Rosenberg and Blancher (2005) adjusted BBS counts to account for two important forms of detection bias. Diurnal variation in the probability that birds are available for detection (P_avail) was modeled by a sixth-order polynomial regression fit to the tallies of the bird counts at each of the 50 survey stops in a BBS route. The probability of detecting available individuals (P_detect) was estimated using an expert-derived, species-specific maximum detection distance (MDD) within which birds could be heard by observers (Emlen and DeJong 1981, Wolf et al. 1995).

Maximum detection distance defines the effective area sampled by a survey (Rosenberg and Blancher 2005) and can be thought of as a modification of the effective detection radius (EDR) used in distance sampling (Buckland et al. 2001). In distance sampling, P_detect is derived from a detection function that models the decreasing probability that a bird is detected as a function of its increasing distance from the observer. The detection function can be rescaled to yield the EDR, the radius at which as many birds are detected beyond the EDR as remain undetected within the EDR during point-count surveys (Buckland et al. 2001). The EDR can be defined for unlimited- or fixed-distance point counts. Both MDD and EDR yield an effective sampling area that can be used to transform survey counts to estimates of density.

At the request of Partners in Flight, Thogmartin et al. (2006) and Thogmartin (2010) recently evaluated the methods that Rich et al. (2004) and Rosenberg and Blancher (2005) used to estimate landbird population sizes. The population size estimator was found to be particularly sensitive to changes in MDD—for example, a decrease from 200 m to 80 m resulted in a 6.3-fold increase in the estimated population size of the Golden-winged Warbler (Vermivora chrysoptera; Thogmartin 2010). Because area increases with the square of radius, even small differences in the effective sampling radius can markedly affect abundance estimates. It was recommended that population sizes be based instead on empirical estimates of detectability such as EDR. However, most available estimates of EDR are based on studies of limited geographic scope and do not account for the effects of habitat or survey methods (Buckland 2006, Pacifici et al. 2008, Reidy et al. 2011). Thus, there is a need for new, robust estimates of EDR that can be applied to broad-scale survey data.

Data from which to estimate EDR are widely available in North America from point-count surveys because observers often stratify detections within two broad distance intervals (i.e., 0–50 m and > 50 m; Ralph et al. 1993, 1995a). Such survey data are relatively easy to collect, and they minimize the difficulties of accurately estimating distances to birds that are far from the survey point (Alldredge et al. 2007a). They also lend themselves to the computation of EDR using binomial distance-sampling models (hereafter “binomial models”), the simplest form of the multinomial distance-sampling model for analyzing distance data grouped into intervals (Buckland 1987, Buckland et al. 2001:204–207). The goodness-of-fit of the binomial model cannot be directly measured. Comparisons of binomial estimates to those from distance models with three or more distances intervals are needed. In a simulation study, the binomial model produced estimates of EDR with bias and variance similar to those of models based on exact measurements of distances to birds (Buckland 1987, Buckland et al. 2001). This led Buckland (1987) to conclude that the binomial model “should not be underrated because of its simplicity.” Despite these promising findings and the widespread availability of appropriate data, binomial distance sampling has been used sparingly for analyzing avian point-count data in North America (but see Farnsworth et al. 2005, Laake et al. 2011).

In the present study, we used binomial distance sampling to estimate EDR for 94 species of boreal forest birds. We used point-count survey data compiled among 93 distinct projects conducted across Canada's boreal forest region (Cumming et al. 2010), which varied in the duration of counting time at each point, the maximum distance to which birds were counted, and the habitats surveyed. Many of the projects (n = 58) stratified bird observations during surveys as being within or beyond 50 m. We were able to exploit this and other features of the data to assess whether binomial models were robust to variations in sampling protocol. Specifically, we first analyzed subsets of our data with multiple distance and time intervals to examine (1) general goodness-of-fit of the binomial models and (2) whether binomial estimates of EDR and breeding density were sensitive to variation in the duration of point-count surveys (3, 5, and 10 min) or the maximum distance to which birds were surveyed (100-m fixed radius vs. unlimited distance). We then applied the binomial model to the larger data set to estimate habitat-specific EDRs, testing for patterns in detectability among species and habitats identified by acoustical studies (Date and Lemon 1993, Schieck 1997). Finally, we compared our estimates of EDR with Partners in Flight's MDD (Blancher et al. 2007) to examine the magnitude of difference in population sizes estimated from these different approaches.

Methods

Sampling

We used data from off-road point-count surveys conducted during the breeding season across the boreal forest region of Canada and compiled as part of the Boreal Avian Modelling Project (BAM; Cumming et al. 2010). These data were collected by 93 separate research, impact-assessment, and monitoring projects conducted between 1992 and 2010 (BAM Database, version 2.0). We analyzed data from 58 projects conducted between mid-May and early July, 1995–2010, in which detections of birds were tallied in relation to a 50-m cut point (0–50 m vs. 50 m to an unlimited distance [>50 m]) over a 5- or 10-min counting interval at each point. These data included 20,781 survey visits (v) to 10,864 survey points (k). The contributing studies were located in the following Bird Conservation Regions (U.S. North American Bird Conservation Initiative Committee 2000): Northwestern Interior Forest (BCR 4; 5 projects, v = 1,090, k = 895), Boreal Taiga Plains (BCR 6; 37 projects, v = 11,826, k = 7,040), Taiga Shield and Hudson Plains (BCR 7; 2 projects, v = 132, k = 132), Boreal Softwood Shield (BCR 8; 7 projects, v = 2,965, k = 1,420), Boreal Hardwood Transition (BCR 12; 4 projects, v = 2,745, k = 673), and the Atlantic Northern Forest (BCR 14; 3 projects, v = 2,023, k = 704). The number of total visits per project varied from 16 to 3,086. Survey points were geo-referenced in the field by the contributing projects using global positioning systems. We excluded from analysis all birds that were detected at previous points, counted as nestlings or juveniles, or only observed taking long directed flights over the survey point and not obviously tied to the sample location for display, breeding, or feeding.

We used ARCGIS, version 9.0 (ESRI, Redlands, California), and overlaid survey points on habitats defined by the 250-m resolution Land Cover Map of Canada 2005 (Latifovic et al. 2008). We collapsed the 39 cover classes into five general habitat types: non-forest (<25% cover by trees; k = 2,422 points), open-canopy forests (25–60% canopy cover) dominated by conifers (>50% tree cover by conifers; k = 2,763), open-canopy forests dominated by deciduous trees (k = 1,252), closed-canopy forests (>60% canopy cover) dominated by conifers (k = 2,901), and closed-canopy forests dominated by deciduous trees (k = 1,526). We predicted that EDR would decrease from non-forest, to open forest, to closed forest because of the increase in tree foliage available to absorb sound. We also expected that EDR would be higher in forests with conifers than in forests dominated by deciduous trees (Date and Lemon 1993, Schieck 1997, Pacifici et al. 2008).

Statistical Analyses

We used conventional distance sampling in DISTANCE, version 6.0 (Thomas et al. 2010), to estimate EDR (m) and breeding density (birds ha^-1; Buckland et al. 2001). We restricted our estimations of EDR and breeding density to cases in which we had ≥75 detections after truncation to support each estimate (Buckland et al. 2001:241). We grouped our survey data into distance intervals prior to analysis. Because the outermost interval was unlimited in sampling distance (>50 m or 100 m to an unlimited distance [>100 m]), we had to set an upper limit to this interval in order to analyze the data in DISTANCE. We defined this upper limit for each species as the distance beyond which few individuals would be detected. Specifically, we defined the upper limit for landbirds as the greater of 150 m or the species-specific MDD (Blancher et al. 2007, Partners in Flight 2007); we used a cut-off of 400 m for shorebirds. We defined the sample units for our analyses according to the survey design of the original projects. For projects in which the sample unit was the survey point, we used the number of replicate surveys per point across all seasons to assign survey effort to sample units. For projects in which the sample unit was a group of points along a transect, we multiplied the number of points per transect by the number of replicate surveys per transect across all seasons to assign survey effort to sample units.

We calculated means, standard errors, and 95% confidence intervals (CI) for EDR and breeding density from 999 bootstrap replicates of sampling units. In each replicate, we fit alternative robust formulations of the detection function (Buckland et al. 2001:45–48) and selected the estimates from the model with the lowest value of Akaike's information criterion adjusted for small sample size (AIC_c). When more than one model shared the lowest AIC_c value, we selected one at random. For binomial distance sampling (0–50 m, >50 m), we assessed four models: the half-normal and uniform key detection functions without expansion and the uniform function with one cosine or simple polynomial series expansion term. For trinomial distance sampling (0–50, 51–100, >100 m), we assessed six models: the half-normal function with and without one cosine or Hermite polynomial series expansion term, and the uniform function with and without one cosine or simple polynomial series expansion term. We calculated the 95% CI from the 2.5% and 97.5% quantiles of the 999 bootstrap estimates (Buckland et al. 2001:161–164). Thus, in all cases, we report model-averaged estimates of EDR and breeding density.

Preliminary evaluation of the binomial model.—We first examined a subset of data from 20 projects (v = 10,714, k = 3,952) that tallied avian detections into three distance intervals (0-50, 51–100, >100 m) and two time intervals (0–5 and 5–10 min) to assess (1) goodness-of-fit of binomial models, (2) whether binomial EDRs were biased in relation to our choice of the upper limit to the outermost distance interval (>50 m), and (3) whether binomialmodel estimates of EDR or breeding density varied with either truncation distance (100 m vs. unlimited distance) or count duration (5 vs. 10 min). We also examined a smaller subset of data collected from 14 projects (v = 3,851, k = 2,779) that tallied counts into shorter time intervals (0–3 and 3–5 min) to determine whether estimates of EDR or breeding density differed when calculated with data from shorter counts (3 vs. 5 min).

We followed the recommendations of Buckland (1987) and Buckland et al. (2001:206) to assess the goodness-of-fit of the binomial model by comparing estimates of EDR calculated from binomial and trinomial models. Specifically, we used data from 10-min counts collected for three distance intervals (0–50, 51–100, >100 m), and fit binomial (0–50, >50 m) and trinomial models of the detection function for each of 88 species. We applied a paired t-test to compare the estimates of EDR between binomial and trinomial models and then identified those species whose 95% CI for EDR did not overlap between binomial and trinomial models.

We were concerned that we might underestimate EDR when analyzing the unlimited-distance survey data because of our choice of the outer boundary to the outermost distance interval (>50 m; Thompson and La Sorte 2008). To evaluate this, we used the same data set and compared our binomial estimates of EDR, based on a limited outer survey boundary (bounded EDR), to EDRs estimated using the simple form of the binomial model with a half-normal key detection function and the outermost interval left unbounded (unbounded EDR; Buckland 1987, Buckland et al. 2001:204–207). We then compared bounded and unbounded EDRs across species using a paired t-test.

It is often advisable to withhold from analyses observations that are far from the point to improve model fit near distance zero and to minimize the number of estimated parameters in the detection function (Buckland et al. 2001). We therefore assessed the need for truncating observations of birds at outlying distances by examining the graphs of the detection functions from the best-fit trinomial models. We identified those species for which the fitted detection probability was <0.1 for the last distance interval (>100 m), a recommended cut-off for truncation (Buckland et al. 2001:151–153). We applied binomial models to estimate EDR and density for both the unlimiteddistance and truncated data using the same data set. We then used paired t-tests to compare the estimates, identifying significant differences as above. Unlike Thompson and La Sorte (2008) or Efford and Dawson (2009), we expected that birds could be consistently detected beyond 100 m during point-count surveys and that EDR would therefore vary with truncation. We also expected density estimates to be similar between unlimited-distance and truncated data if the data met the assumptions of distance sampling and if we used the proper model of the detection function (Buckland et al. 2001:105). Variation in density estimates in relation to truncation would therefore indicate problems with our data or models.

We assessed the effects of count duration on the estimates using two data sets of unlimited-distance surveys in which observations were tallied into subintervals. The first data set included 51 species from surveys 5 min in duration with subintervals of 0–3 and 3–5 min. The second data set included 81 species from surveys 10 min in duration with subintervals of 0–5 and 5–10 min. For each data set, we used binomial models to estimate species-specific EDR and density for the entire count duration and for the first subinterval. We then compared the estimates using paired i-tests and identified significant differences within species when 95% CIs of estimates (EDR or breeding density) did not overlap between 3-min versus 5-min counts and 5-min versus 10-min counts. We expected EDR to increase with count duration if birds close to the point were counted first and birds far from the point were counted last (Farnsworth et al. 2005). This would help balance the general increase in survey counts with the count duration and thereby minimize variability in densities with count duration. Conversely, we expected EDR to remain constant with count duration if detection distances were independent of count duration. This would result in density estimates that increase with count duration because the encounter rate typically increases with count duration.

Comparison of EDR and song frequency.—We used the binomial model and estimated EDR for 92 species using the survey data pooled across habitats (pooled estimates) from all 58 projects that tallied the birds detected at two distance bands, 0–50 m and >50 m. These data incorporated count durations of 5 and 10 min. We used species' EDRs and densities estimated from the unlimited-distance data in all subsequent analyses. These data specifications were based on the results of the analyses described in the previous section. We checked the validity of our methods by assessing the relationship between pooled estimates of EDR and the sound frequencies of species' vocalizations. Because high-frequency sounds attenuate more quickly than low-frequency sounds (Morton 1975, Date and Lemon 1993), we expected our estimates of EDR to be negatively correlated with sound frequencies. We recorded the minimum sound frequencies (kHz) for each species from spectrographs in the Birds of North America species accounts (Poole 2011), when available, or else from Robbins et al. (1983). When multiple spectrographs were provided for a species, we used the lowest frequency measured. We log-transformed species' EDRs to normalize the residuals and then treated the transformed EDRs as the response variable in a linear regression that included minimum sound frequency as the explanatory variable. This was possible only for the 83 species with spectrographs.

Habitat-specific EDRs and comparisons with MDD.—To evaluate the effects of nonrandom selection of habitats for sampling, we tested for habitat variation in EDR within species. First, we fit binomial models of EDR both with and without habitat class as a covariate, using the half-normal key detection function, and compared their relative fit using AIC_c. We restricted analysis to 48 species with at least 75 observations in at least four of the five habitat classes. As a broader test of habitat effects, we calculated modelaveraged bootstrap estimates of EDR by habitat for 83 species with at least 75 observations in at least one of the five habitat types. We analyzed the point-level data because habitat was assigned to each survey point. However, we resampled the original sampling units (points or transects depending on the study) during each bootstrap iteration to ensure that our estimates of EDR and associated variance were not biased by pseudoreplication (Buckland et al. 2001:83–84). We log-transformed the habitat-based estimates of EDR to normalize the residuals and then used a generalized linear mixed model to test for the fixed effect of habitat on EDR while controlling for species as a random effect.

We used a simple ratio, MDD²/EDR² (Thogmartin 2010), to calculate the magnitude of difference in population size that would result from using the two estimates to assign the effective sampling-areas for point-count surveys. This excluded the four species of shorebirds for which we did not have estimates of MDD. We used the maximum of the habitat-based estimates of EDR for 80 landbird species. For each of 8 other species, we used the EDR estimated from the data pooled across habitats because these species had too few observations to estimate habitat-specific EDRs. We used maximum EDR as a conservative comparison to MDD because birds might be heard at greater distances along roadside clearings sampled by the BBS than through dense vegetation in off-road areas.

We fit generalized linear models in SPSS, version 18.0 (SPSS 2008), considered statistical tests to be significant at α = 0.05, and present all statistics ± SE. The  Appendix includes the common and scientific names and four-letter species codes for the 94 species analyzed.

Fig. 1.

The effective detection radius (EDR, m) estimated from distance-sampling models with two distance intervals (0–50 m, >50 m; binomial model) versus three distance intervals (0–50 m, 51–100 m, >100 m; trinomial model). The EDR was estimated for 88 bird species detected on point-count surveys during the breeding season across boreal Canada, 1995–2010. The diagonal line references a 1:1 relationship between binomial and trinomial model estimates. Four-letter codes denote the species included in the analyses; the associated common and scientific names are provided in the  Appendix.

Results

Goodness-of-fit.—Species-specific estimates of EDR from binomial and trinomial models were highly correlated (r² = 0.922, P < 0.001; Fig. 1). However, binomial estimates ( = 81.7 ± 4.1 m) averaged 6.8% higher than trinomial estimates = 76.5 ± 3.1 m; difference = 5.2 ± 1.7 m; |t₈₇| = 3.1, P = 0.003, n = 88 species). The 95% CIs for EDR from binomial and trinomial models were non-overlapping for two species, the Common Raven (hereafter “raven”) and American Crow (hereafter “crow”). The binomial model clearly overestimated EDR for these two species (30% and 82%, respectively) compared with trinomial models. This was in contrast to the other 86 species analyzed (Fig. 1). These two outlier species had the smallest proportion of their observations within 50 m of the point (4.0% for crow, 6.5% for raven). With crow and raven removed, the binomial estimates ( = 77.3 ± 2.6 m) averaged 4.2% higher than trinomial estimates ( = 74.2 ± 3.1 m; difference = 3.1 ± 0.4 m; |t₈₅| = 7.2, P < 0.001). Thus, EDR estimated from binomial models had minimal positive bias compared with EDR from trinomial models in all but two cases (Fig. 1). We interpret this as evidence for reasonable goodness-of-fit by the binomial models for the majority of species. We removed the crow and raven from all subsequent analyses.

Outer boundary to unlimited-distance data.—Our estimates of EDR with and without an outer boundary to outermost distance interval (>50 m) were highly correlated (r² = 0.999, P < 0.001; Fig. 2). The bounded EDRs averaged 3.9% higher than the unbounded EDRs ( = 74.4 ± 2.6 m; difference = 2.9 ± 0.1 m; |t₈₅| = 24.9, P < 0.001), and the 95% CI of the estimates overlapped for all 86 species. Thus, our choice of the boundary to the outermost distance interval introduced minimal bias to our estimates of EDR. We therefore estimated EDR using the bounded outer interval in all subsequent analyses of the unlimited-distance data. This allowed us to fit different forms of the detection function and to use model averaging, both of which minimize bias from model selection when estimating EDR.

Fig. 2.

The effective detection radius (EDR, m) estimated using binomial distance-sampling models for 88 bird species detected on point-count surveys during the breeding season across boreal Canada, 1995–2010. The EDR was compared among models in which the outermost distance interval (>50 m) was bounded at an upper limit so that the data could be analyzed in the program DISTANCE (Thomas et al. 2010) versus those in which it was unbounded and, therefore, truly unlimited in distance (Buckland et al. 2001:204–207). The diagonal line references a 1:1 relationship between bounded and unbounded estimates. Four-letter codes denote the species included in the analyses; the associated common and scientific names are provided in the  Appendix.

Maximum survey distance.—For trinomial models, the third and last distance interval (>100 m) had an estimated detection probability of <0.1 for 69 of the 86 species (80%). Binomial model estimates of EDR for truncated and unlimited-distance data were highly correlated (r² = 0.918, P < 0.001; Fig. 3). Estimates of EDR based on the unlimited-distance data ( = 77.3 ± 2.6 m) averaged 17% higher than estimates from the truncated data ( = 66.2 ± 1.5 m; difference = 11.1 ± 1.4 m; |t₈₅| = 8.1, P < 0.001). The 95% CI for EDR from unlimited-distance and truncated data were non-overlapping for 18 of the 86 species (21%), with the unlimited-distance estimates ( = 107.2 ± 5.5 m; range: 80–153 m) higher in all cases. Their EDRs were, on average, 1.6× the unlimited-distance estimates for the other 66 species (= 66.4 ± 2.1 m; range: 38–127 m). The disparity between EDRs estimated from truncated and unlimited-distance survey data was greatest for species with larger EDRs (Fig. 3).

The resulting estimates of breeding density were highly correlated (r² = 0.999, P < 0.001; Fig. 3). Estimates of density from the unlimited-distance data ( = 0.072 ± 0.011 birds ha^-1) averaged 1.0% higher than those from the truncated data ( = 0.071 ± 0.011 birds ha^-1; difference = 0.0007 ± 0.0002; |t₈₅| = 3.5, P = 0.001). The 95% CI for densities estimated from truncated and unlimited-distance data overlapped for all 86 species. Thus, although our estimates of EDR were sensitive to truncation, the resulting estimates of breeding density appeared to be robust.

Fig. 3.

Estimates of (A) the effective detection radius (EDR, m) and (B) breeding density (birds ha^-1) calculated for 86 bird species using binomial distance-sampling models applied to unlimited-distance surveys and the same surveys with the observations of birds >100 m from the survey point withheld from analysis (truncated 100 m). The diagonal line references a 1:1 relationship between estimates. The data are from off-road point-count surveys conducted during the breeding season across boreal Canada, 1995–2010. Four-letter codes denote the species included in the analyses; the associated common and scientific names are provided in the  Appendix.

Survey duration.—Our point estimates from binomial models were highly correlated between pairs of durations (3 vs. 5 min; 5 vs. 10 min) for both EDR and breeding density (r² ≥ 0.990, P < 0.001; Figs. 4 and 5). Averaged across species, EDR increased 1.6% from 3- to 5-min counts ( = 69.7 ± 2.5 m, = 70.8 ± 2.4 m; difference = 1.1 ± 0.3 m; |t₅₀| = 3.1, P = 0.003, n = 51 species) and 1.7% from 5- to 10-min counts ( = 75.6 ± 2.7 m, = 76.9 ± 2.7 m; difference = 1.3 ± 0.4 m; |t₈₀| = 3.4, P = 0.001, n = 81 species). The 95% CI for EDR between pairs (3 vs. 5 min; 5 vs. 10 min) overlapped for all species. Thus, increasing count duration from 3 to 5 min or from 5 to 10 min appeared to have only a small positive effect on EDR (Fig. 4).

Fig. 4.

The effective distance radius (EDR, m) estimated from point-count surveys with different durations of the counting time. The EDR was estimated by applying a binomial distance-sampling model to survey data on (A) 51 bird species detected during 3-min versus 5-min surveys and (B) 81 bird species detected during 5-min versus 10-min surveys. Data are from off-road surveys conducted during the breeding season across boreal Canada, 1995–2010. The diagonal line in each graph references a 1:1 relationship between estimates. Four-letter codes denote the species included in the analyses; the associated common and scientific names are provided in the  Appendix.

Breeding density was more sensitive than EDR to changes in count duration. Among species, density increased, on average, by 19% between 3- and 5-min counts ( = 0.075 ± 0.012 birds ha^-1; = 0.089 ± 0.014 birds ha^-1; difference = 0.014 ± 0.002 birds ha^-1; |t₅₀| = 5.7, P < 0.001) and by 25% between 5- and 10-min counts ( = 0.060 ± 0.009 birds ha^-1; = 0.075 ± 0.011 birds ha^-1; difference = 0.015 ± 0.002 birds ha^-1; |t₈₀| = 6.6, P < 0.001). However, 95% CIs of densities estimated during 3- versus 5-min counts overlapped for all species, and CIs of densities estimated during 5-versus 10-min counts overlapped for all but three species: Yellowbellied Sapsucker, Swainson's Thrush, and Chipping Sparrow.

Fig. 5.

Avian breeding density (birds ha^-1) estimated from point-count surveys with counting times of different durations. Density was estimated for (A) 51 bird species detected during 3-min versus 5-min surveys and (B) 81 bird species detected during 5-min versus 10-min surveys. Data are from off-road surveys conducted during the breeding season across boreal Canada, 1995–2010. The diagonal line in each graph references a 1:1 relationship between estimates. Four-letter codes denote the species included in the analyses; the associated common and scientific names are provided in the  Appendix.

Habitat effects.—Stratification of EDR by habitat reduced AIC_c by at least 2 units for 30 of the 48 species (63%) with sufficient detections in at least four of the five habitats. The effect of habitat on EDR was highly variable among species (Table 1). However, we found a consistent effect of habitat class on EDR across species (n = 83) using a generalized linear mixed model (F = 12.7, df = 4 and 212, P < 0.001). Back-transforming the log-transformed fitted values to the response scale, the EDR in the reference category, nonforest ( = 78.4 ± 2.9 m), averaged 7.9 ± 1.5 m greater than the EDR in closed deciduous forest (|t₂₁₄| = 5.6, P < 0.001), 6.2 ± 1.5 m greater than the EDR in open deciduous forest (|t₂₁₃| = 4.3, P < 0.001), and 3.9 ± 1.4 m greater than the EDR in closed conifer forest (|t₂₁₂| = 2.9, P = 0.005). The EDRs for non-forest and open conifer forest were not significantly different (difference = -0.2 ± 1.4 m; |t₂₁₂| = 0.1, P = 0.88). Given equivalent counts during surveys, the EDR in closed deciduous forest would, on average, produce density estimates that were 24% higher than those from the EDR in non-forest habitat.

Comparisons of EDR to song frequencies and MDD.—Our pooled estimates of EDR based on unlimited-distance data averaged 77.7 ± 2.7 m over 92 species and ranged 4.4-fold from 39.0 ± 4.7 m for Golden-crowned Kinglet to 171.3 ± 24.4 m for Varied Thrush. When we transformed EDRs to detection probabilities within the survey area, P_detect averaged 0.18 ± 0.01 (range: 0.04–0.73). The minimum sound frequency of avian vocalizations explained 16% of the variation in the log-transformed estimates of EDR (F = 16.0, df = 1 and 82, P < 0.001, n = 83 species), with EDR negatively related to sound frequency (β_o = 4.5 ± 0.7, β_{sound_frequency} = -0.10 ± 0.03). Transforming the parameter estimates of the linear regression back to the original scale, EDR decreased 8.8 ± 2.3 m with each increase of 1 kHz in the minimum sound frequency.

Our point estimates of maximum EDR were positively correlated with Partners in Flight's MDD (r² = 0.50, P < 0.001) but were smaller for 87 of 88 species (Table 1). Our estimates of EDR averaged 95.4 ± 4.8 m (-6.7 to 278.7 m) less than MDD. Only the Ruffed Grouse had a larger maximum EDR (91.3 ± 6.0 m) than MDD (80 m). All other factors being equal, our estimates of EDR would result in estimated population sizes 5.1 ± 0.3 (0.8–14.6) times those resulting from MDD. The increase in population size estimated using MDD versus EDR was approximately an order of magnitude (≥9.5) for nine species (Table 1).

Discussion

Collecting point-count data in relation to a single 50-m distance cut point has been a standard for avian point-count surveys in North America for nearly 20 years (Ralph et al. 1993, 1995a). Our results demonstrate that these broadly available survey data can be used to calculate species-specific estimates of the EDR of surveys using relatively simple binomial distance-sampling models. Such estimates of EDR could be used in lieu of Partners in Flight's MDDs to improve estimates of North American landbird population sizes. However, we also found that our estimates of EDR or breeding density from binomial distance-sampling models were sometimes sensitive to survey methodology, particularly duration of the count. Researchers using distance-sampling models should therefore be cautious when comparing their results with those of other studies or when applying distance sampling to data compiled from studies using varying point-count methods.

Binomial distance-sampling models provided EDR estimates for point-count surveys of boreal forest birds that were very similar to EDRs estimated from trinomial distance-sampling models for 86 of 88 species (98%). Thus, the binomial model had reasonable goodness-of-fit for most species. Our binomial estimates of EDR were also negatively related to the sound frequencies of speciesspecific vocalizations, a validation of the distance-sampling approach because high-frequency sounds attenuate more rapidly and cannot be heard as far away as low-frequency sounds (Morton 1975, Date and Lemon 1993, Schieck 1997). Thus, binomial distance-sampling models appear to provide a simple adjustment for heterogeneity in avian detectability related to the distance of birds from observers. This bias is likely pervasive in avian point-count surveys but is not accounted for by abundance estimators that rely solely on surveys with multiple visits, observers, or time intervals (Efford and Dawson 2009, Laake et al. 2011).

When we transformed our binomial estimates of EDR to detection probabilities, we found the resulting estimates to be quite low for most species ( = 0.18; range: 0.04–0.73, n = 92 species), similar to findings from other studies that used distance sampling in the temperate United States (P_detect = 0.07–0.66, n = 14 species; Norvell et al. 2003, Thompson and La Sorte 2008, Reidy et al. 2011). The low values of P_detect from distance-sampling models often result in substantial adjustments to the raw survey counts that may be much larger than the adjustments for P_avail estimated from removal models based on singing frequency (Farnsworth et al. 2002, 2005; Thompson and La Sorte 2008; Handel et al. 2009; Reidy et al. 2011). Thus, the proper specification of P_detect is particularly important because of its large influence on estimates of avian abundance from point-count surveys. This was recently underscored by Thogmartin (2010), who found Partners in Flight's estimates of landbird population sizes (Rich et al. 2004) to be 39% more sensitive to changes in MDD than to the time-of-day adjustment for P_avail.

The application of MDD to BBS data was an important step in developing useful first approximations of population sizes for most landbird species breeding in North America (Rich et al. 2004, Rosenberg and Blancher 2005, Blancher et al. 2007). However, we found MDD to consistently overestimate the distance over which avian detectability can be assumed to be 100% during surveys in the boreal forest. MDD exceeded our estimates of EDR based on unlimited-distance data for all but one species (Ruffed Grouse), and averaged 95-m larger across the 88 landbird species we evaluated. All other factors being equal, our values for EDR would estimate population sizes that average 5× those resulting from MDD, with the difference an order of magnitude for nine species. These results are similar to regional and local estimates of avian abundance from spot-mapping data, which averaged 3× and 8× larger, respectively, than abundance estimated using the Partners in Flight approach (Rosenberg and Blancher 2005, Confer et al. 2008). Thus, the estimates of landbird population sizes by Rich et al. (2004) are likely conservative for many species and could be improved by replacing MDD with quantitative estimators, such as EDR, that account for the effective area sampled during surveys (Thogmartin et al. 2006, Confer et al. 2008, Thogmartin 2010). Data from which to estimate EDR in other regions of North America are being compiled by programs such as the Avian Knowledge Network and Coordinated Bird Monitoring. Estimating EDRs from such data would complement our values from the boreal forest region and could be used collectively to improve future estimates of landbird population sizes across North America.

We note that Rich et al. (2004) applied MDD to roadside survey data from the BBS, whereas we estimated EDR from off-road survey data. We did not have roadside survey data from which to estimate EDR, but we expect that (1) on average, birds can be heard and seen at greater distances across roadside clearings than through forest vegetation in off-road areas; and (2) roadside EDRs might be most similar to our maximum values of EDR, which were typically in non-forested habitats. Thus, our comparisons of MDD to our maximum values of EDR are likely reasonable. However, direct comparisons of EDR between on- and off-road surveys are needed, both to quantify the magnitude of roadside bias in detection rates and to develop adjustments that would strengthen extrapolation of abundance estimates from roadside surveys to off-road areas (Thogmartin et al. 2006).

Despite our encouraging results, binomial model estimates of EDR often varied with the habitats sampled and the maximum distance to which birds were surveyed, whereas estimates of breeding density were sensitive to variation in the length of the recording time during point-count surveys. Thus, there remain challenges in estimating EDR from data compiled from surveys with variable sampling. Our estimates of EDR averaged low in forest compared with non-forest habitats, and low in deciduous compared with conifer forests. Therefore, it may be important to account for habitat-based differences in detectability when estimating population sizes. Detectability of boreal birds appeared to be negatively related to the amount of foliage available to obscure birds and their vocalizations during surveys, with deciduous vegetation having a particularly negative influence on detectability. This is supported by an acoustic study that found that sounds attenuated at increasing rates from open habitats, to conifer forests, to deciduous forests, with the magnitude of the difference increasing between deciduous and conifer forests with increases in sound frequency (Date and Lemon 1993). Our findings are also supported by studies using recordings of bird songs that have found avian detectability to decrease in forests from before to after leafout, and from coniferous to mixed coniferous-deciduous to pure deciduous compositions (Schieck 1997, Pacifici et al. 2008).

We did not control for other factors known to affect avian detectability during surveys, such as observer ability, weather, and background noise (Alldredge et al. 2007a, b; Marques et al. 2007; Pacifici et al. 2008; Simons et al. 2009). Such information was not consistently recorded among the 54 studies from which we analyzed data. However, we used a combination of model averaging and a large, spatially extensive data set to estimate EDR. Thus, our estimates of EDR should be pooling-robust to such factors (Buckland et al. 2001:41–42, Marques et al. 2007) and, therefore, more suitable for broad application than EDRs derived from relatively small, localized studies that are more sensitive to heterogeneity in unmeasured factors.

Although EDR estimated from unlimited-distance data averaged 17% higher than EDR from survey data truncated at 100 m, resulting estimates of breeding densities were not sensitive to the truncation distance. This indicates that EDR should be estimated separately for surveys with different truncation distances, but that the resulting estimates of density will be similar. This supports the prediction that EDR will scale with truncation distance, such that estimates of density will remain stable given that (1) the survey data meet the assumptions of distance sampling and (2) the proper model of the detection function is used (Buckland et al. 2001:105). The binomial distance-sampling models we used may have performed well in this regard because we had relatively large sample sizes and used model averaging, both of which can improve estimation (Buckland et al. 2001, Burnham and Anderson 2002). The majority of species we examined (80%) also had low detection probabilities (<0.1) for observations beyond 100 m. The removal of data at large distances is generally understood to result in more robust estimates of density because of the smaller number of parameters needed to adjust the detection function for outlying observations (Buckland et al. 2001). Densities estimated from binomial distance-sampling models were not sensitive to outlying observations, possibly because the binomial models we used were restricted to a single parameter and were therefore not prone to overfitting like multinomial distance-sampling models (Buckland et al. 2001).

Our finding that estimates of EDR were not sensitive to the duration of point-count surveys was useful because it allowed us to pool data among surveys with different count durations and thereby maximize the data available to estimate habitat-specific EDRs. However, the raw survey counts increased with survey duration, causing our estimates of breeding density to increase, on average, by 19% from 3-min to 5-min surveys and by 25% from 5-min to 10-min surveys. This was similar to a 27% increase in estimated bird density from 5- to 10-min point-count surveys in temperate hardwood forests (Reidy et al. 2011). Estimates of breeding density appear to be quite sensitive to survey duration and, therefore, cannot be directly compared among studies using counts of different duration unless the survey counts are first adjusted for count duration. Several studies have shown that the number of species and the number of individual birds detected during surveys accumulate with the length of the recording time at each point-count station (see papers in Ralph and Scott 1981, Ralph et al. 1995b). However, it is unclear to what extent this accumulation results from movements of birds into the count area, double counting of birds, or increases in the availability of birds for detection during the longer-duration counts. All of these violate assumptions of distance sampling and may lead to biased estimates of detection probability or breeding density (Scott and Ramsey 1981). Violations of the assumptions that birds remain stationary or that birds are counted a single time during the survey will both result in a positive bias in density. This argues for a short-duration count or a snapshot approach when conducting point-count surveys (Buckland et al 2001:147, Buckland 2006). Violation of the assumption that -P_avail = 1 will result in density estimates that are biased low, particularly for counts of shorter duration (Buckland et al. 2001:172).

In reality, these assumptions in distance sampling are likely violated to varying degrees during omnibus surveys of birds (Simons et al. 2009), with the magnitude of the violations a function of temporal and species-specific factors. For example, the rate at which nesting passerines move between their nests and foraging sites varies among species and tends to increase from incubation to nestling periods (2–10 trips h^-1, n = 10 species; Martin et al. 2000). Similarly, P_avail estimated from June surveys tends to be higher among migrants (0.62–1.0, n = 36 species; Farnsworth et al. 2002, 2005; Thompson and La Sorte 2008; Handel et al. 2009; Reidy et al. 2011) than among resident species (0.44–0.85, n = 5 species; Handel et al. 2009). This likely results from surveys targeting the peak singing periods of migrant rather than resident species (Handel et al. 2009). Estimates of P_avail can also vary with time of day (Rosenberg and Blancher 2005) and time of year (Farnsworth et al. 2002).

Given variability in movement and singing probabilities among species, it may be best to record data during point-count surveys in multiple time intervals to maximize flexibility in how the data can be analyzed (Lee and Marsden 2008, Reidy et al. 2011). The EDR could be estimated using a full 10-min count, to maximize the data available to model detectability. For species with high P_avail, EDR could then be applied to the subset of data collected during the first 3 or 5 min of the count. This would minimize the effects of movement or double counting on estimates of density. For species with low rates of P_avail, data from the full 10-min count may be needed to estimate both detection probability and density. Alternatively, the data collected for multiple time and distance intervals could be analyzed using a combination of distance sampling and removal models to adjust the survey counts for both P_detect and P_avail (Burnham et al. 2004:352–356, Farnsworth et al. 2005, Handel et al. 2009). These hybrid models have not been widely applied to avian survey data but would be particularly useful if they were developed to account for important covariate effects on detectability, such as habitat on P_detect, or time-of-day and time-of-year on P_avail (Farnsworth et al. 2002, Marques et al. 2007). Such models would relax the distance-sampling assumption of perfect detectability at the point (Farnsworth et al. 2005) and address recent suggestions for improving future estimates of landbird population sizes by more fully accounting for detection bias in avian point-count surveys (Thogmartin et al. 2006, Thogmartin 2010). However, these models should be field tested to verify their accuracy in estimating avian abundance (Nichols et al. 2009, Simons et al. 2009, Reidy et al. 2011).

Acknowledgments

This publication is a contribution of the Boreal Avian Modelling (BAM) Project, an international research collaboration for the ecology, management, and conservation of boreal birds (www.borealbirds.ca). We acknowledge the BAM Project funders, data partners, and Technical Committee members who made this project possible. We thank the following institutions for providing data: Acadia University, Alberta Biodiversity Monitoring Institute, Alberta Pacific Forest Industries Inc., Alberta Innovates Technology Fund (formerly Alberta Research Council Inc.), AMEC Earth & Environmental, AREVA Resources Canada Inc., AXYS Environmental Consulting Ltd., Bighorn Wildlife Technologies Ltd., Bird Studies Canada, Canadian Natural Resources Ltd., Canfor Corporation, Daishowa Marubeni International Ltd., Ducks Unlimited Canada, Environment Canada's Canadian Wildlife Service, Forest Products Association of Canada, Global Landcover Facility, Golder Associates Ltd., Government of British Columbia, Government of Ontario, Government of Saskatchewan, Government of Yukon, Hinton Wood Products, Hydro-Québec Équipement, Kluane Ecosystem Monitoring Project, Komex International Ltd., Louisiana Pacific Canada Ltd., Manitoba Hydro, Manitoba Model Forest Inc., Manning Diversified Forest Products Ltd., Matrix Solutions Inc., MEG Energy Corp., Mirkwood Ecological Consultants Ltd., Natural Resources Canada (Canadian Forest Service and Canada Centre for Remote Sensing), Numerical Terradynamic Simulation Group, Ontario Ministry of Natural Resources, OPTI Canada Inc., PanCanadian Petroleum Limited, Parks Canada, Petro Canada, Principal Wildlife Resource Consulting, Regroupement Québec, Rio Alto Resources International Inc., Shell Canada Limited, Suncor Energy Inc., Tembec Industries Inc., Tolko Industries Ltd., Université de Moncton; Université du Québec à Montréal, Université du Québec en Abitibi-Témiscamingue, Université Laval, University of Alberta, University of British Columbia, University of Guelph, University of New Brunswick, University of Northern British Columbia, URSUS Ecosystem Management Ltd., West Fraser Timber Co. Ltd., Weyerhaeuser Company Ltd., and Wildlife Resource Consulting Services MB Inc. We thank the following individuals for providing data: J. Ball, P. Belagus, S. Bennett, R. Berger, M. Betts, J. Bielech, A. Bismanis, R. Brown, M. Cadman, D. Collister, M. Cranny, L. Darling, M. Darveau, C. De La Mare, A. Desrochers, T. Diamond, M. Donnelly, M. Drapeau, C. Duane, B. Dube, D. Dye, R. Eccles, P. Farrington, R. Fernandes, D. Fortin, K. Foster, M. Gill, R. Hall, S. Hannon, B. Harrison, J. Herbers, L. Imbeau, P. Johnstone, V. Keenan, S. Lapointe, R. Latifovic, R. Lauzon, M. Leblanc, L. Ledrew, J. Lemaitre, D. Lepage, B. MacCallum, P. MacDonell, C. Machtans, L. Margantini, S. Mason, M. McGovern, D. McKenney, T. Nudds, P. Papadopol, M. Phinney, D. Phoenix, D. Pinaud, D. Player, D. Price, R. Rempel, A. Rosaasen, S. Running, R. Russell, C. Savingnac, J. Schieck, P. Sinclair, A. Smith, C. Spytz, P. Taylor, S. Van Wilgenburg, P. Vernier, D. Whitaker, J. Witiw, S. Wyshynski, and M. Yaremko. We gratefully acknowledge the support and counsel of our Technical Committee: P. Blancher, M. Darveau, J.-L. DesGranges, A. Desrochers, A. de Vries, P. Drapeau, C. Francis, C. Handel, K. Hobson, C. Machtans, J. Morissette, R. Rempel, S. Slattery, P. Taylor, S. Van Wilgenburg, L. Venier, P. Vernier, and M.-A. Villard. We thank J. Campbell for compiling information on bird vocalizations from spectrographs; S. Buckland, E. Rexstad, and L. Thomas for advice on analyzing data using distance sampling; and R. Earles, C. Handel, C. Rostron, D. Stralberg, and two anonymous reviewers for improving the manuscript. This project was generously funded by Environment Canada, Université Laval, University of Alberta, and the U.S. Fish and Wildlife Service.

Appendix

Author notes

Associate Editor: C. M. Handel