Rare edges and abundant cores: range-wide variation in abundance in North American birds

Abstract

Understanding how the abundance of species varies across geographical ranges is central to ecology; however, few studies test hypotheses using detailed abundance estimates across the full ranges of species on a continental scale. Here, we use unprecedented, detailed estimates of breeding abundance for North American birds (eBird) to test two hypotheses for how abundance varies across species' ranges. We find widespread support for the rare-edge hypothesis—where the abundance of species declines near the range edge—reflecting both reduced occurrence and lower local abundance near range edges. By contrast, we find mixed support for the abundant-centre hypothesis—where the abundance of species peaks in the centre of the range and declines towards the edges—with limited support in conservative tests within species, but general support in among-species tests that control for unbalanced sampling and consider a broader definition of the range centre. Overall, results are consistent with a gradual decline in suitable conditions and increase in challenge towards the range edge that eventually limit the ability of populations to persist.

1. Introduction

Understanding the factors that facilitate and constrain the abundance and distribution of species is a central goal of ecology, and provides a foundation for understanding patterns of species coexistence and diversity [1–3]. Towards this end, ecologists have asked how the abundance of species varies consistently across their geographical ranges, potentially reflecting areas where ecological requirements of species peak and decline, eventually limiting the ranges of species [1,2,4,5]. The abundant-centre hypothesis suggests that species’ abundance peaks in the centre of the geographical range where ecological conditions should be ideal, and then declines from the range centre towards the edges as ecological conditions become less favourable [4–7]. Despite its broad appeal, evidence to support the abundant-centre hypothesis is mixed, with abundance peaking away from the range centre in many species [7–11].

One element of the abundant-centre hypothesis—the decline in abundance of species towards the range edge—is thought to be widespread [1], reflecting the decline in suitable ecological conditions, and increase in the intensity of challenges, that are thought to ultimately determine the range limits of species [1,4,5]. This idea, which we refer to here as the rare-edge hypothesis, does not require that species reach their peak abundance in the centre of the range; instead, abundance could peak anywhere away from the range edge. The decline in abundance towards the range edge could arise because species become less abundant (which we refer to as ‘local abundance’), or because the species' distribution becomes sparser towards the range edge (i.e. more locations with zero individuals; which we refer to as reduced ‘occurrence’; sometimes also called ‘population occupancy’; [12]); the contribution of these two mechanisms could reflect the ways in which ecological conditions limit the distributions of species [12].

Evidence consistent with the rare-edge hypothesis is much more widespread (e.g. [1]), but not universal [12,13], leading to the question of why some species show abrupt limits to their ranges, with consistently high abundance up to the range edge. The nature of the range edge, and specifically whether ecological conditions change abruptly (e.g. transition from land to ocean) or gradually (e.g. decline in temperature with latitude), could explain variation in the tendency of species to support the rare-edge hypothesis [4]. Similarly, ranges limited by dispersal, rather than the gradual change in ecological conditions, could lead to abrupt range limits where species maintain high abundance at the range edge that coincides with an abrupt change in environmental conditions that also act as a barrier to dispersal (e.g. a river; [4]). An alternative explanation for variation in the patterns of abundance across geographical ranges is biased or poor sampling [7,10]—we simply lack accurate estimates of abundance across the entire range of most species, particularly species with large geographical ranges. This sampling bias may be particularly acute at the range edges if species become rare and sparse, and thus more difficult to detect, but could also be important at the range centre because of fewer possible sampling points compared with the edge (see equal-distance sampling, figure 1).

Figure 1.

An example of range-wide abundance data and two different approaches to analysing them using the field sparrow (Spizella pusilla). Left panel shows the relative abundance of field sparrows across their entire geographical breeding range, estimated for the year 2018 using eBird data and an adaptive spatio-temporal modelling approach that controls for sampling bias [14] (data from [15]). A thin black line designates the breeding range limit; white signifies areas of zero abundance within the breeding range; colours (blue to orange) represent 20 quantile bins from lowest (non-zero) to highest relative abundance. Centre maps show two different approaches to estimating the relative percentile distance between the range centre and edge. Equal-distance percentiles (top) create percentiles of equivalent distance from the range centre to the edge, where the number of points in percentile bins (top right graph) increases towards the edge, creating poor and spatially restricted sampling towards the centre. Equal-area percentiles (bottom) create percentiles of equivalent numbers of points (bottom right graph), but increasing breadth (kilometre) of bin widths towards the centre. Centre maps show 10 percentile bins that alternate in colour (dark blue versus grey) from the centre to the edge. Histograms (right) show the number of data points in each percentile bin.

Here, we use what is perhaps the best data yet compiled on the relative abundance of diverse species across their entire geographical ranges on a continental scale to test predictions of both the rare-edge and abundant-centre hypotheses for how the abundance of species varies across their ranges. Specifically, we use detailed (2.8 km² grid) community-science-derived data (eBird; [16]) on the relative abundance of breeding birds in North America, based on millions of observations and an adaptive spatio-temporal modelling approach that controls for sampling bias [14]. These data allow us to overcome limitations of sampling, coverage, incomparable methodologies and inaccurate range delineations that have hindered previous tests of hypotheses [7,8,10,17,18]. We use these data to further test how abundance patterns vary with the nature of the range edge (terrestrial or oceanic), different definitions of edge and core (5 or 10 percentile bins), issues of unequal sampling from core to edge (equal-distance versus equal-area percentiles, figure 1), species occurrence versus local abundance (inclusion versus exclusion of zeros) and different analytical approaches (species tallies, comparative tests with bivariate predictors versus smooth functions). We find widespread support for the rare-edge hypothesis, with declines in abundance near the range edge caused by both reduced occurrence (more zeros) and reduced local abundance, and the strongest patterns evident for terrestrial range edges. By contrast, we find mixed support for the abundant-centre hypothesis, with limited support in conservative tests with narrow definitions of the range centre, but general support in tests that control for unbalanced sampling and consider a broader definition of the range centre.

2. Methods

(a) . Relative abundance data

We used high-resolution abundance data from the status and trends analysis of eBird data for the breeding ranges of North American birds [14,15]. These analyses (i) focused on a subset of high-quality eBird data with details of time, date and focused area or location, with all bird species and numbers reported (referred to as ‘complete checklists’), (ii) accounted for variation in detection rates and temporal scales, and (iii) modelled environmental descriptors to estimate associations between species' abundance with land cover, elevation and topography variables using ensembles of machine learning models, controlling for spatio-temporal variation in sampling [14]. The analyses produced a highly accurate estimate of range-wide relative abundance and occurrence (i.e. presence or absence) of North American birds at a scale of 2.8 km² grids, where accuracy was assessed using model validations [14], and is evident in comparisons with independent, geographically focused, intensive surveys (e.g. [19,20]). The modelling approach used to estimate relative abundance across each range was unbiased with respect to the hypotheses tested here, because it did not incorporate geographical location relative to range edges or centre [14]. See Fink et al. [14,15] and electronic supplementary material for more details.

(b) . Selection of species

From the species provided in the status and trends dataset, we selected a subset whose breeding ranges were entirely covered by well-sampled areas within Canada, the USA and extreme northern Mexico, and where the edges of the breeding ranges did not abut poorly sampled regions that had too little data to accurately estimate abundance for the species. See electronic supplementary material, methods for additional details on the selection of species. The subset of species (N = 109 species) that met our criteria for inclusion collectively provided the strongest dataset to assess geographical variation in the relative abundance of species across their full ranges, providing an ideal dataset to test the predictions of our hypotheses.

(c) . Data compilation

We acquired relative abundance estimates for the breeding ranges of our focal species for the year 2018 from the eBird status and trends products [15] using the R package ebirdst (v. 0.2.0; [21]). These estimates are the result of ensembles of local machine learning models, controlling for spatio-temporal variation in sampling described above (see electronic supplementary material, methods for further details). Data for 2018 show similar patterns of relative abundance and distribution to other years (https://science.ebird.org/en/status-and-trends), and appear to represent abundance-distribution patterns of our focal species more generally [22] (although they do not address shifting or expanding ranges over time). The eBird status and trends data provide continental measures of abundance for each species, including zeros that are within and outside of the breeding range of each species. Thus, we created a breeding range map for each species by recording presence (relative abundance > 0) or absence (relative abundance = 0) after modifying the resolution of maps by aggregating raster cells by a factor of 10 using the ‘aggregate’ function in the R package raster [23]; this aggregation reduced the resolution of the original dataset by 100 times (i.e. 2.8 km² to 28 km² resolution), allowing us to delineate smoothed breeding ranges for our analysis of geographical variation in abundance. Thus, the range edges were set by generalizing the limits of where each species was recorded (figure 1 for an example), and we define the breeding range as the generalized area where our focal species were predicted to occur during their species-specific breeding season in 2018 after data aggregation. We note that geographically isolated occurrences were insufficient to contribute to breeding ranges using our methods (cf. isolated points above the northern boundary of breeding range in figure 1). We chose to aggregate using a factor of 10 following Fanelli et al. [24], who found that this factor was large enough to avoid the removal of large urban areas from the breeding ranges of species, but still retain a high-resolution breeding distribution map. Once we had created breeding range maps for each focal species, we clipped each species' relative abundance dataset with the breeding range, creating a range-specific relative abundance dataset for each focal species at the original 2.8 km² resolution (figure 1 for an example).

(d) . Statistical analyses

We performed statistical analyses and plotting in R (v. 4.0.2; [25]). We used a shapefile of North America (all lakes removed; from naturalearthdata.com) and erased the breeding range of each focal species in ArcGIS 9.0 (ESRI, Redlands, California). For each species, we then measured the distance (kilometre) of each abundance data grid cell (converted to points) to the nearest (i) terrestrial edge of their breeding range (using the distance to North America with the breeding range erased), and (ii) nearest oceanic edge (using shapefiles for oceans from naturalearthdata.com), using the ‘join’ function in ArcGIS. We selected the smaller of the two values (terrestrial or oceanic range edge) as the minimum distance to the geographical range edge for each point and recorded whether this edge was terrestrial or oceanic for use in analyses. Lakes were not considered range edges in our analysis. We defined the centre of each species' breeding range as the points within the range that are furthest from the edge (either greater than 95th or greater than 90th percentile distance from the edge; figure 1). We did not define a single range centre for each species (e.g. using an area-weighted mean centroid), because such points can occur at the range edge or even outside of the range for some geographical range configurations, leading to inaccurate tests [10].

In R, we partitioned the data for each species into five percentile bins based on their relative distance to the range edge using both equal-distance and equal-area percentile bins (figure 1 for illustrations). The equal-distance percentiles create bins of equivalent distance breadths from the centre to the edge, but have fewer points and reduced area towards the centre of the range (figure 1). The equal-area percentiles create bins of equal sampling and area, but have narrower bin widths towards the edge of the range (figure 1). We created five percentile bins to (i) simplify each species’ dataset (which were initially almost 1 million datapoints for some species), (ii) easily control for differences in the number of points from the range centre to the edge, and (iii) minimize the influence of spatial autocorrelation while retaining detailed estimates of variation in relative abundance from the range centre to the edge.

For each 5th percentile bin, we calculated the mean relative abundance across points within the bin by taking the mean of 1000 bootstrapped estimates in the R package boot [26], and then calculating 95% confidence limits of these 1000 estimated means. We took a bootstrapping approach to estimating means and variances because the data are spatially autocorrelated and potentially skewed, and thus could bias standard calculations of means and (particularly) confidence limits. We calculated independent means and confidence limits for each bin for all combinations of the following: (i) all data included versus all zeros removed, (ii) equal-distance versus equal-area bins, (iii) all edges, terrestrial edges and oceanic edges, and (iv) range edges or centres defined as within the 5th or 10th percentiles of the range edge or centre, respectively. Terrestrial versus oceanic edge datasets were a subset of the full dataset that included only points that were closest to either a terrestrial or oceanic edge, respectively. We compared patterns among points closest to terrestrial versus oceanic edges because we expected oceanic edges to be more abrupt; beyond this comparison, we did not assume or estimate heterogeneity of environments (e.g. landscape, climate) within the ranges or at the edges of our focal species (although such heterogeneity might explain variation in our results within or among species).

Once we had our estimates for mean relative abundance and confidence limits for each 5th percentile bin for each species across the various datasets, we tested the predictions of the two hypotheses in two different ways. The first approach tallied the number of our focal species that showed evidence consistent with each hypothesis; the second approach combined data in a comparative test across species. For the first approach, we predicted that the mean relative abundance of each species (focal species tallies) should be lowest at the edge of its range compared with all other non-edge bins (rare-edge hypothesis) and highest at the centre of its range compared with all other non-centre bins (abundant-centre hypothesis). When the edge and centre were defined more broadly (5th and 10th percentile bins closest to the edge or centre, respectively), both bins had to meet the predictions of the hypothesis (i.e. bins were not combined). These tests are conservative; for example, even one non-edge bin with a mean abundance below that of the edge would lead to the rejection of the rare-edge hypothesis for a focal species. Because of the already conservative nature of these tests, we did not incorporate the confidence intervals for the means in our assessments, but plot the means and confidence limits for each bin for each species in electronic supplementary material, figures S1 and S2. We tested whether most species show patterns consistent with each hypothesis using a binomial test (binom.test in R), with the number of species showing evidence consistent with the pattern out of the total number of species with adequate data for the test.

We also plotted the proportion of species with their lowest and highest mean abundance in each percentile bin, from the centre to the edge of their ranges. These plots allowed us to broadly characterize where the lowest and highest abundances occur within species' ranges, rather than simply testing the predictions of each hypothesis, strictly interpreted.

For our second approach (comparative across species), we predicted that the relative abundance of species, on average, should be lower in the edge versus non-edge regions of their ranges (rare-edge hypothesis) and higher in the centre versus non-centre regions of their ranges (abundant-centre hypothesis). We tested these predictions using linear mixed-effects models, with species as a random effect and either edge/non-edge (rare-edge hypothesis) or centre/non-centre (abundant-centre hypothesis) as predictors, and mean relative abundance in each 5th percentile bin (20 bins per species) as the response variable. Non-edge and non-centre refer to every bin that was not characterized as edge or centre, respectively. See electronic supplementary material, methods for further details of models and checks of model fit.

We also examined the general pattern of variation in relative abundance from the centre to edge of the ranges of focal species using generalized additive models (GAMs) in the R package mgcv [27,28]. We fit models with all combinations of (i) all data versus zeros removed, and (ii) equal-distance versus equal-area percentiles, with transformed relative abundance for each five percentile bin (20 per species) as the response variable, and s(percentile bin, by = sqrt(maximum distance between the range centre and edge in kilometre)) as a fixed effect, and species as a random effect with a Gaussian distribution, where s represents the smooth function specified for different values of distance from range edge to centre using the ‘by’ command. Including the distance between the range centre and edge allowed us to test if geographical variation in relative abundance varied among species with different breeding range sizes.

3. Results

(a) . Rare-edge hypothesis

(i) . Tallies of species

Across focal species, 98% showed evidence in support of the rare-edge hypothesis in at least one of the 24 tests, with their lowest mean abundance in the 5th or 10th edge percentiles of their breeding ranges (binomial test, 107 of 109 species, 95% CI: 93.5–99.8%, p < 0.0001; electronic supplementary material, table S1 and figures S1 and S2). In our main tests (all range edges, all data), 78–83% of species showed their lowest abundance at the edges of their ranges (binomial test, average of 86 of 107 species, 95% CI: 71.5–87.4%, p < 0.0001; see electronic supplementary material, tables S2–S7 and figure S3a). With zeros removed, 46–53% of species showed their lowest relative abundance at the edge of their ranges (all range edges; electronic supplementary material, tables S2 and S5), though these numbers were higher (up to 79%) when oceanic range edges were excluded (electronic supplementary material, tables S3 and S6 and figure S3a). Results of tallies aligned with plots of where the lowest average abundance occurs for most species (figure 2a). The majority of species showed their lowest average abundances at the edge of their ranges (less than 5th percentiles), with 79–95% of species showing their lowest average abundance in the outer half of their ranges (figure 2a).

Figure 2.

The proportion of focal North American bird species showing their lowest average abundance (a) and highest average abundance (b) at different distances to the range edge, measured in 5 percentile bins. Left data panels show equal-distance percentiles; right data panels show equal-area percentiles (figure 1). Top data panels show patterns with all data; bottom data panels show patterns with all zeros removed. Inset summaries show the percentage of species with their lowest average abundances in the outer half of their range (0–50 percentile distance to the edge) (a), and their highest average abundances in the inner half of their range (50–100 percentile distance to the edge) (b). N = 105 species for bottom right panels of (a) and (b), N = 107 species for all other panels.

For points closest to terrestrial range edges, 90–93% of species showed their lowest relative abundances at the range edge for equal-distance percentiles (all data), with 67–68% showing the pattern when zeros were removed (electronic supplementary material, table S3 and figure S3a). For equal-area percentiles (terrestrial edges only), fewer species showed their lowest abundances at the range edge when zeros were included (66–75%) versus excluded (78–79%) (electronic supplementary material, table S6 and figure S3a). For points closest to oceanic range edges, most species also showed their lowest relative abundance at the extreme oceanic range edge (5th percentile: 55%, 88% of species, equal-distance, equal-area percentiles, respectively; electronic supplementary material, tables S4 and S7), but these percentages declined if the range edge was broadened to the 10th percentile (28%, 67% of species, equal-distance, equal-area percentiles, respectively; electronic supplementary material, tables S4 and S7 and figure S3a). A larger percentage of species showed their lowest relative abundance at the range edge for terrestrial compared with oceanic range edges with equal-distance percentiles; however, results were more similar for equal-area percentiles where the range edges were thinner (cf. figure 1) (electronic supplementary material, figure S3a).

(ii) . Comparative analyses (linear mixed-effects models)

Overall, species showed reduced abundances, on average, at the range edges compared with areas away from the range edges in all analyses (figures 3 and 4; electronic supplementary material, table S8). Support for the rare-edge hypothesis was evident when percentile distance to the range edge was defined as equal-distance or equal-area and as the outer 5th or 10th percentiles (figures 3 and 4; electronic supplementary material, table S8). Relative abundance at the edges of breeding ranges were 81–84% lower in the outer 5th percentiles of the range, and 74–81% lower in the outer 10th percentiles of the range, relative to non-edge regions (all data; equal-distance, equal-area percentiles; based on back-transformed model estimates) (figure 3). The difference in abundance was greatest when all data were included, but persisted when zeros were removed, consistent with both reduced occurrence (more zeros) and reduced local abundance of populations contributing to the lower abundance at the range edge (figures 3 and 4; electronic supplementary material, table S8). Differences in the per cent decline in abundance (non-edge to edge; based on back-transformed model estimates with/without zeros; figure 3) suggested that reduced occurrence accounted for about half (51%, 52%; 5th and 10th equal-distance percentiles, respectively) or most (59%, 67%; 5th and 10th equal-area percentiles, respectively) of the reduced abundance at the range edge (all edges). The reduction in abundance at the range edge was significant for points closest to terrestrial and oceanic range edges, but was much larger for points closest to terrestrial edges (figure 4; electronic supplementary material, table S8). With equal-distance percentiles, terrestrial range edges showed 91–95% lower abundance compared with non-edge, while oceanic range edges showed only 31–38% lower abundance compared with non-edge (5th and 10th percentiles) (figure 4). When the sampled edge was narrower (equal-area percentiles; figure 1), the differences between relative abundance in edge versus non-edge regions were reduced between terrestrial (96–97% lower than non-edge) and oceanic (54–66% lower than non-edge) range edges, suggesting that the decline in abundance at oceanic range edges is more abrupt.

Figure 3.

Predictions (top) of the rare-edge hypothesis for variation in abundance across geographical ranges, and data (bottom) testing the predictions in North American breeding birds (N = 105 species for bottom right panel, N = 107 species for all other panels). Left data panels show tests with equal-distance percentiles; right data panels show tests with equal-area percentiles (figure 1). Top data panels show tests with all data; bottom data panels show tests with all zeros removed. Edge percentiles (light or dark) correspond to the percentile breadth of the edge (less than 5th percentile or less than 10th percentile from the edge). p-values are from linear mixed effects models testing for differences in relative abundance between the edge and non-edge portions of species’ ranges (colour-coded for different edge percentile breadths). See electronic supplementary material, table S8 for detailed statistical results. See electronic supplementary material for details of relative abundance and units.

Figure 4.

Data testing the predictions of the rare-edge hypothesis for variation in abundance across geographical ranges using North American breeding birds, separated by whether the nearest range edge abutted land (terrestrial, left panels) or ocean (oceanic, right panels). See figure 3 for a graphical illustration of predictions and descriptions of panels, legend and p-values. See electronic supplementary material, table S8 for detailed statistical results. Sample sizes are: terrestrial range edges, equal-distance, all data (N = 107 species), zeros removed (N = 107 species); equal-area, all data (N = 105 species), zeros removed (N = 105 species); oceanic range edges, equal-distance, all data (N = 76 species), zeros removed (N = 73 species); equal-area, all data (N = 74 species), zeros removed (N = 73 species).

(b) . Abundant-centre hypothesis

(i) . Tallies of species

Overall, 65% of focal species showed evidence in support of the abundant-centre hypothesis in at least one of the 24 tests, with their highest mean abundance in the central 5th or 10th percentiles of their breeding ranges (binomial test, 71 of 109 species, 95% CI: 55.4–74.0%, p = 0.002; electronic supplementary material, table S1 and figures S1 and S2). In our main tests (all range edges, all data), 22–43% of species showed their highest abundance at the centre of their ranges (binomial test, average of 36 of 107 species, 95% CI: 24.8–43.4%, p = 0.0009; electronic supplementary material, tables S2 and S5 and figure S3b), revealing that most species do not show their highest abundance in the range centre. With zeros removed, 15–31% of species showed their highest relative abundance in the centre of their ranges (all range edges; electronic supplementary material, tables S2 and S5 and figure S3b). Plots of where the highest average abundance occurs for most species (figure 2b) revealed that most species (72–93%) showed their highest average abundances in the inner half of their ranges, even though the proportion of species with their highest average abundance in the central percentiles (greater than 90 percentile from the edge) varied (figure 2b).

For points closest to terrestrial range edges, 24–26% of species showed their highest relative abundances in the range centre for equal-distance percentiles (all data), with similar patterns (20–23%) when zeros were removed (electronic supplementary material, table S3 and figure S3b). For equal-area percentiles (terrestrial edges only), these numbers were higher: 41–47% (zeros included) and 31–38% (zeros excluded) (electronic supplementary material, table S6 and figure S3b). For points closest to oceanic range edges, few species showed their highest relative abundance in the centre (zeros included: 12–18%, zeros excluded: 9–12%), with similar results across equal-distance and equal-area percentile methods (electronic supplementary material, tables S4 and S7 and figure S3b).

(ii) . Comparative analyses (linear mixed-effects models)

Overall, species showed significantly higher abundances, on average, at the centre of their ranges when percentiles were defined as equal-area, but not when percentiles were defined as equal-distance (figure 5; electronic supplementary material, table S9). Relative abundance in the centres of breeding ranges were 21% higher, on average, in both the inner 5th and 10th equal-area percentiles of the range compared with non-centre regions (all data; based on back-transformed model estimates) (figure 5). For the equal-area percentiles, the difference in abundance was strongest when all data were included, but persisted when zeros were removed (figure 5; electronic supplementary material, table S9). Differences in the per cent increase in abundance (non-centre to centre; based on back-transformed model estimates with/without zeros; figure 5) suggested that increased occurrence accounted for about half of the increased abundance in the range centre (47%, 52%; all range edges; 5th, 10th percentiles, respectively). Points closest to terrestrial range edges showed similar patterns to the overall results (figures 5 and 6; electronic supplementary material, table S9). By contrast, we found no support for the abundant-centre hypothesis when points were closest to oceanic range edges (figure 6; electronic supplementary material, table S9), with some conditions (e.g. equal-distance, zeros removed) showing evidence for lower relative abundance at the range centre, opposite to the predictions of the abundant-centre hypothesis (figure 6; electronic supplementary material, table S9).

Figure 5.

Predictions (top) of the abundant-centre hypothesis for variation in abundance across geographical ranges, and data (bottom) testing the predictions in North American breeding birds (N = 105 species for bottom right panel, N = 107 species for all other panels). Left data panels show tests with equal-distance percentiles; right data panels show tests with equal-area percentiles (figure 1). Top data panels show tests with all data; bottom data panels show tests with all zeros removed. Centre percentiles (light or dark) correspond to the percentile breadth of the centre (less than 5th percentile or less than 10th percentile from the centre). p-values are from linear mixed effects models testing for differences in relative abundance between the centre and non-centre portions of species' ranges (colour-coded for different centre percentile breadths). See electronic supplementary material, table S9 for detailed statistical results. See electronic supplemental material for details of relative abundance and units.

Figure 6.

Data testing the predictions of the abundant-centre hypothesis for variation in abundance across geographical ranges using North American breeding birds, separated by whether the nearest range edge abutted land (terrestrial, left panels) or ocean (oceanic, right panels). See figure 5 for a graphical illustration of predictions and descriptions of panels, legend and p-values. See electronic supplementary material, table S9 for detailed statistical results. Sample sizes are: terrestrial range edges, equal-distance, all data (N = 107 species), zeros removed (N = 107 species); equal-area, all data (N = 105 species), zeros removed (N = 105 species); oceanic range edges, equal-distance, all data (N = 76 species), zeros removed (N = 73 species); equal-area, all data (N = 74 species), zeros removed (N = 73 species).

(c) . Variation in abundance across the range

We found general declines in the relative abundances of species from the cores of ranges near the range centres towards the edges for equal-distance and equal-area percentiles, and for cases with and without zeros (figure 7; electronic supplementary material, table S10). The best-performing model that included all data did not retain the maximum distance from the range centre to the edge (kilometre) as a predictor. When zeros were removed, however, the slope of the relationships between percentile distance and relative abundance varied with the maximum distance from the range centre to the edge (an estimate of range size), with lower abundances of smaller range species (shorter maximum distances to the range edge) in the cores of their ranges (electronic supplementary material, figure S4 and table S10). Equal-area percentiles that had equal sampling across the range showed more linear declines in abundance from the centres of species' ranges towards the edges (figure 7), consistent with both the rare-edge and abundant-centre hypotheses. Equal-distance percentiles, however, peaked in abundance away from the centre of species' ranges before declining at an accelerating rate towards the range edges (figure 7).

Figure 7.

Relationships between the relative distance to the range edge (percentiles) and the relative abundance of North American breeding birds (N = 105 species for bottom right panel, N = 107 species for all other panels). Graphs show model-predicted lines and 95% confidence limits (grey) from GAMs. Left data panels show tests with equal-distance percentiles; right data panels show tests with equal-area percentiles (figure 1). Top data panels show tests with all data; bottom data panels show tests with all zeros removed.

4. Discussion

We used some of the most detailed, geographically extensive data on the abundance of species—range-wide relative abundance estimates for North American breeding birds well-sampled by eBird [14,15]—to test two hypotheses for how abundance varies across geographical ranges. We find widespread support for the rare-edge hypothesis, where abundance is lower at the edge of species' ranges, with consistent support across species (figure 2a; electronic supplementary material, figure S3a and tables S1–S7), definitions of range edges (5th or 10th percentile bins; equal-distance or equal-area percentiles), nature of range edges (terrestrial, oceanic), and inclusion or exclusion of zeros (figures 3 and 4; electronic supplementary material, tables S8 and S10). By contrast, we find mixed support for the abundant-centre hypothesis, with most species reaching their peak abundance away from their narrowly defined geographical range centres (figure 2b, electronic supplementary material, figure S3b and tables S2–S7), and evidence consistent with the hypothesis for only terrestrial range edges using specific approaches (equal-area percentiles) (figures 4 and 5; electronic supplementary material, tables S9 and S10). Nonetheless, the average relative abundance across species showed patterns consistent with the abundant-centre hypothesis when sampling and area were evenly distributed from range centres to the edges (equal-area percentiles; figure 7, right panels). Furthermore, most species showed patterns consistent with the abundant-centre hypothesis when the centre of the range was broadly defined (e.g. inner half of the range; figure 2b).

(a) . Rare-edge hypothesis

Most species showed their lowest mean abundances at the range edge across measures, and comparative analyses showed significantly lower abundances, on average, in the range edges across tests. These results are consistent with previous work suggesting that most species decline in mean abundance at the edges of their geographical ranges (e.g. [1]). Points where the closest range edge was terrestrial showed the strongest decline towards the range edge across tests (figure 4; electronic supplementary material, table S8). Points where the closest range edge was oceanic still showed significant declines towards the range edges, but the decline appeared to be more abrupt, suggesting a rapid transition in ecological conditions over a shorter distance in oceanic compared with terrestrial range edges (figure 1 for an example; see also [4]). The decline in abundance towards the range edge resulted from both reduced occurrence (more zeros) and reduced local abundance at the range edge; the relative importance of these two components varied across species and approaches, with a higher contribution of reduced occurrence to the overall pattern in equal-area percentiles that have a narrower edge (cf. figure 1). With broader range edges (equal-distance percentiles), reduced occurrence and reduced local abundance contributed similarly to the overall decline in relative abundance at the range edge, suggesting a higher contribution of reduced local abundance than reported in previous reviews [12].

Our methods for defining the range edge could increase the likelihood of support for the rare-edge hypothesis by generalizing peripheral occurrences to form a range edge with a large component of zero occurrences (cf. figure 1). Nonetheless, most species showed their lowest abundances in both the outer 0–5th and 5–10th percentiles, with the latter region separated from the defined edge. Similarly, GAM analyses revealed a steady decline in the average abundance of species across the outer half of their ranges (figure 7), illustrating that the pattern is not driven solely by the range edge itself.

Only two species showed no evidence for the rare-edge hypothesis across tests—wrentit (Chamaea fasciata) and seaside sparrow (Ammospiza maritima) (electronic supplementary material, table S1)—both of which show peak abundances in coastal habitats [22]. Other species known to flourish in coastal habitats also showed patterns opposite to the predictions of the rare-edge hypothesis for some analyses (e.g. fish crow, Corvus ossifragus, and piping plover, Charadrius melodus, which use coastal shoreline; chestnut-backed chickadee, Poecile rufescens and pacific wren, Troglodytes pacificus, which use coastal coniferous forest; electronic supplementary material, figures S1 and S2; [22]). These coastal species join previous examples from coastal dune plants [13] that collectively suggest that species associated with habitats that rapidly transition between land and ocean may provide consistent exceptions to the rare-edge hypothesis, or may show more abrupt declines in abundance towards their range edges (e.g. below the resolution of our analysis here) [4].

(b) . Abundant-centre hypothesis

The mixed support for the abundant-centre hypothesis is consistent with previous work ([7–11] and references therein) and probably reflects both biological causes and unbalanced sampling. Considering sampling, equal-distance percentile bins, where each bin had the same width (kilometre), led to reduced sampling of the centre of species' ranges (figure 1). Most of our focal species show relatively few points and regions of extremely high abundance across their ranges (see also [5]) and thus reduced sampling (both of area and number of points) reduces the likelihood of capturing these high abundance points, reducing the mean abundance towards the range centre (figure 7). Controlling for sampling using equal-area percentiles led to equal numbers of points and area from the range edge to the centre, and expanded the geographical definition of range centre to include a broader region (figure 1), increasing the likelihood that the centre would encompass points or regions of high abundance. The result was a somewhat monotonic decline in mean relative abundance from the range centre to the edge across species (figure 7) and greater support for the abundant-centre hypothesis overall (figure 5; electronic supplementary material, table S9). Unequal sampling is likely to have influenced many previous tests of the abundant-centre hypothesis that use distance from the edge or centre as a predictor (e.g. [9,10]), and thus sampling bias could help to explain the inconsistent results across studies.

Our mixed support for the abundant-centre hypothesis probably also reflects biological variation in the location of peak abundance of species within their geographical ranges. While range edges had lower relative abundance overall, we might expect optimal conditions for a species to occur anywhere in its geographical range away from the range edge, rather than specifically in the range centre [10]. These ideas align more with an abundant-core distribution pattern [11], with the added stipulation that the core region (with peak mean abundance) occurs away from the range edge for most species. This constrained abundant-core distribution pattern is consistent with the patterns of individual species in our dataset, where most species did not reach their highest mean relative abundance in the centre of their ranges in our main tests, but nonetheless peaked in abundance somewhere in the inner half of their ranges (figure 2b). When these patterns were averaged across species and sampling was balanced from centre to edge, the overall pattern revealed the highest abundance in the range centre and lowest at the range edge, entirely consistent with the abundant-centre hypothesis (figure 7, right panels). This support for the abundant-centre hypothesis appears to be restricted to points closest to terrestrial range edges; points closest to oceanic range edges showed no evidence to support the pattern in any of our analyses (figure 6). The conflicting evidence that depended on methods and definitions of the range centre could explain some of the conflicting conclusions from previous studies that differed in their methodologies and data (e.g. birds: [9,10] compared with [11]; see also [17,18]). Nonetheless, the support for the abundant-centre hypothesis that we found in this study aligns with recent studies with stronger sampling [11,18], and could be more consistent with the initial ideas that motivated the hypothesis (cf. [1]; e.g. higher abundance in the core of the range, rather than at the narrowly defined centre).

(c) . Understanding patterns of abundance across ranges

Our analyses of patterns of abundance across range-wide distributions of 109 North American bird species suggest that most species reach their highest mean abundances in a core region of their breeding ranges away from the range edge, with abundance declining closer to the range edge as populations become sparser and as the relative abundance within local populations declines. These patterns are consistent with a decline in suitable conditions and increase in challenge towards the range edges of species that eventually set the limits of their geographical ranges directly, or limit further dispersal and expansion [4,29], but do not exclude other ideas for the causes of geographical range limits [30]. Our tests of the predictions of the rare-edge and abundant-centre hypotheses provide a more comprehensive and nuanced understanding of patterns of abundance than previous tests. Analyses of patterns across ranges are frequently unbalanced, never estimate abundance across the full range of a species, and often include ‘peripheral’ populations that are not truly peripheral or are selected because they are large and workable and thus not representative (see [12] for a review). Previous work also lumps patterns at the range edge with less-supported predictions for the range centre, obscuring distinct patterns and processes acting in the core versus edge of species' ranges that have different levels of support. Our analysis suggests that these details matter, and that community science approaches to broad-scale mapping can be an important way to improve our understanding of broad biogeographical patterns.

Ethics

This work did not require ethical approval from a human subject or animal welfare committee.

Data accessibility

R code and data for analysis are available from: https://osf.io/prsgz/?view_only=dcd7d20cf190406881c9d4bce9e82e7d; eBird data that we used in this paper are available from: https://science.ebird.org/en/status-and-trends/download-data.

Supplementary material is available online [31].

Declaration of AI use

We have not used AI-assisted technologies in creating this article.

Authors' contributions

P.R.M.: conceptualization, data curation, formal analysis, writing—original draft; O.J.R.: data curation, formal analysis, writing—review and editing; F.B.: conceptualization, data curation, writing—original draft, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

This work was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).