Fig 1.
Schematic representation of the theoretical behavior of spatial congruence with respect to range similarity, threshold values, depth of direct and indirect congruences, and gradient recognition.
All figures are spatial representations; darker tones indicate overlapped (shared) ranges. (A) The CS index (y-axis) compares position, extent, and shape between two species ranges. For identical size and shape, position determines the amount of overlap; when shape and position (e.g., centroids) are the same, one area will reside entirely in the other and difference in area alone will determine their congruence; and, finally, if area and position are the same, shape will be determinant. (B) The congruence threshold (CT) is the reference for spatial relationships. Range R1 is directly congruent with R2 when their CS (calculated from their area of overlap–hashed area) is greater than or equal to CT. Indirect relationships occur when ranges are linked by congruence in a concatenated chain of CS ≥ CT. R1 is indirectly congruent with R3 because R2 is as congruent (same CS) to R3 as it is to R1. At relaxed threshold requirements (i.e., CT < CS, R1R3), R2 and R3 are both directly related to R1. (C) Indirect links allow the recognition of many types of syndromes of shared distributions potentially associated with distinct historical or ecological range drivers. Links may, at least theoretically, lead to nuclear regions of congruence (example1), congruence zones following patches of favorable habitat (e.g. mountain slopes, or riverine habitats; ex. 2), gradients of expansion or contraction (ex. 3), or linear gradients (ex. 4). Indirect congruence (depth) at very low congruence thresholds may also lead to scalar distortions (ex. 5,6).
Fig 2.
Schematic representation of the hypothetical gradient of thirty species ranges proposed by Kreft & Jetz [45].
Two well delimited biogeographical centers of diversity, a northern (pale gray) and a southern (medium gray), have species extending their ranges through a zone of transition. Each vertical bar represents the latitudinal extent of the range of a particular species (named S1-15 and N16-30). The longitudinal ranges (bar widths and position) of all species are assumed to be identical, such that they all overlap spatially. The original symmetric scheme [45] included a few small exceptions (small arrows) to the otherwise uniformly graded range differences. To further examine the influence of non-uniform gradations on detection of congruence patterns, we reduced the range differences among N28-30 relative to the others, which adds a single slightly larger range discontinuity (large arrow).
Fig 3.
Partial chorotypes (closed lists) detected in a simulated gradient of ranges.
Like colors indicate species ranges (bars) grouped into partial chorotypes recovered at particular congruence thresholds (minimum CT values are shown at the base and top of each closed group). White bars indicate “biogeographically uninformative” species that did not give rise to and were not included in any closed list, at each corresponding maximum depth setting. Four examples are shown (see S1 Table for full details). A) Small but highly congruent partial chorotypes (closed groups) were located next to zones of range discontinuity and favored larger ranges, with smaller proportional area differences. The extended discontinuity only at the northern extreme allowed the recognition of one pattern composed of small-range species. B) At lower congruence thresholds (e.g., from 0.94 to 0.88, or 0.89 to 0.88, or 0.76 to 0.55; compare Fig 3A and 3B), partial chorotypes included adjacent species with smaller ranges. C) Increasing depth (allowing more levels of indirect congruences) increased the size of partial chorotypes at relatively high congruence thresholds. D) At lower congruence thresholds, the entire northern and southern groups were recovered as a whole. Allowing for extensive indirect range comparisons (maximum depth of 10, not shown), most reference species led to convergence on a single chorotype. Note that all recovered partial chorotypes can be nested in others and there was no non-nested overlap nor recovery of the transition zone as an independent chorotype.
Fig 4.
Congruence diagrams illustrating the whole set of partial chorotypes of Icterus nigrogularis and Amazilia tobaci bird species.
A didactic representation of spatial congruence relationships depicts congruence threshold (CT, y-axis, free scale) and depth (x-axis). (A) Icterus nigrogularis (Yellow Oriole) and (B) Amazilia tobaci (Copper-rumped Hummingbird). For each CT and depth, ranges (light-green) are overlaid; number of species in each group are shown for each round at each depth. Circles depict the closed lists (partial chorotypes) at the end of each round of threshold analysis. The common area is shown in dark-blue. South America insets show reference species ranges as black. Grouped species and synonymous patterns are listed in S3 and S4 Tables, respectively. Geographic scales differ because maps are zoomed out to accommodate successively larger lists. Credit: images of I. nigrogularis and A. tobaci adapted from Wikimedia Commons under Attribution-Share Alike 2.0 Generic license (creativecommons.org/licenses/by/2.0/deed.en).
Fig 5.
Partial chorotypes of Heliodoxa hummingbirds in lowland Amazonia and pre-Andes.
Brilliant hummingbirds include a large diversity of species with distinctive biogeographical characteristics. Widespread lowland species: (A) H. aurescens (Gould’s Jewelfront) composes a two species chorotype, and (B) H. schreibersii (Black-throated Brilliant) is not biogeographically informative (does not gives rise to closed lists). Highland species show spatially localized patterns. In the east, the Pantepui chorotype (C) H. xanthogonys (Velvet-browed Brilliant). In the west, the pre-Andean region: (D) H. gularis (Pink-throated Brilliant); (E) H. branickii (Rufous-webbed Brilliant); (F) H. whitelyana (Black-breasted Brilliant). These summarized views of chorotypes present the range of congruence thresholds, depth (in parentheses), and number of species as descriptive parameters. Grouped species are listed in S3 Table. Ranges of individual species leading to partial chorotypes are shown in yellow; the common area for all species is in blue.