A two-dimensional reanalysis of the breeding ranges of 3,839 New World bird species (Hawkins & Diniz-Filho, 2006) showed that mean range size per grid cell is smallest in the tropical Andes, varies little with latitude in the lowlands, and is dominated by an interaction between topographic relief and climate — consistent with climate constraining ranges indirectly through habitat size rather than directly through species' thermal tolerances. The best regression model, using elevation range, coldest-month temperature, their interaction, continental width and biome area, explained only 51% of the variation in mean range size and left substantial spatially autocorrelated residual variation, indicating missing spatially structured drivers; the authors named biotic interactions (competition, predation) and historical processes such as Pleistocene glaciation as candidates but could not evaluate them with available data, and left the pattern's generality to other taxa and biogeographic regions untested. Later work has partitioned species-level range-size variation among environment, phylogeny and space, tested glacial-history and climate-stability drivers in plants and amphibians with opposing outcomes, and extended driver analyses to terrestrial vertebrates globally, but no study has identified and quantified the drivers of the residual, spatially structured variation in the assemblage-level New World bird pattern, and syntheses as recent as 2025 show the mechanism question remains unsettled. The problem is to operationalize and test the candidate missing drivers — biotic interactions and Quaternary historical processes in particular — for the New World avifauna, and to establish how far the two-dimensional pattern and its habitat-size explanation generalize across taxonomic groups and regions.

Background

Rapoport's rule is the observation, formalized by Stevens (1989) and named for earlier observations by Eduardo Rapoport, that the geographic ranges of species tend to be broader at higher latitudes; Stevens proposed it as one explanation for the latitudinal gradient in species richness. The mechanism usually invoked is the climatic variability hypothesis: species living where climates fluctuate strongly across the year (at high latitudes) evolve broader environmental tolerances, which allow them to occupy longer climate gradients and hence larger ranges than species from climatically stable tropical environments. Most early tests were one-dimensional, relating range size to latitude through latitudinal bands or midpoints, and produced mixed support: a meta-analysis of 49 studies (Ruggiero & Werenkraut, 2007) found the pattern strong in Eurasia and North America but weak or non-significant at global scale and in South America, Australia and the New World as a whole, and showed that the analytical method used strongly affects the estimated strength. A separate theoretical input is Janzen's (1967) argument that 'mountain passes are higher in the tropics': because seasonal temperature variation is small in the tropics, the climates at the base and the top of a tropical mountain never overlap, so a tropical mountain is a sharper climatic barrier than a temperate one; this predicts that tropical montane species should have unusually small ranges while high-latitude montane species should not.

Hawkins and Diniz-Filho (2006) moved this question into two-dimensional geographic space for the breeding avifauna of the New World. From digitized range maps of 3,839 bird species they computed, for each cell of 27.5 km and 110 km grids spanning the Americas, the mean breeding range size of all species present in that cell — an assemblage-level (community-level) summary rather than a per-species measurement. They related this response to the range of elevation within each cell (a measure of topographic relief), the mean temperature of the coldest month, the interaction between the two, the area of the biome (a large-scale vegetation-climate zone) containing the cell, and the width of the continent, using correlation, analysis of variance and multiple regression. Because nearby grid cells share most species and environments, the response is spatially autocorrelated — statistically, values in neighboring cells are not independent, which inflates apparent sample sizes and significance; the authors therefore first removed the dominant spatial trend with a simultaneous autoregressive model (a regression that includes a weighted average of neighboring cell values as an extra predictor) and fitted environmental models to what remained, checking residuals with Moran's I, a standard statistic that measures correlation between values at neighboring locations.

The results rejected the classical picture: mean range size varies minimally with latitude in the lowlands, so Rapoport's rule in its usual one-dimensional form is not what the map shows; instead the smallest mean ranges concentrate in the tropical Andes, and the dominant signal is the interaction between topography and climate, consistent with Janzen's mechanism in which climate acts indirectly, by generating sharp mesoscale habitat gradients on tropical mountains, rather than by widening species' thermal tolerances. The best-supported regression model (elevation range, coldest-month temperature, their interaction, continental width and biome area) explained 51% of the variation in mean range size, and its residuals retained substantial spatial autocorrelation — meaning that whatever else shapes range sizes is itself spatially structured and not captured by any included variable. The authors explicitly left open which variables are missing, naming biotic interactions such as competition and predation and historical processes such as Pleistocene glaciation (the alternating ice ages of the last 2.6 million years, which repeatedly eliminated and reassembled temperate habitats and may leave lasting signatures on range sizes through speciation, extinction and post-glacial expansion) as candidates that available data could not evaluate, and left the generality of the two-dimensional pattern and its explanation to other taxa and regions untested. A later methodological result qualifies the whole framework: aggregated, assemblage-level variables such as mean range size per cell carry structural bias, because species occurring in many cells drag their attributes across the map, so that even biologically meaningless 'random' species attributes can show strong spatial structure (Hawkins et al., 2017) — a methodological caveat that is relevant, alongside error in expert-drawn range maps, to interpreting residual spatially structured variation in such analyses.

Problem Statement

For the breeding avifauna of the New World, as mapped by Hawkins & Diniz-Filho (2006): (1) operationalize and empirically evaluate the two candidate classes of spatially structured variables missing from their climate–topography–area model — biotic interactions (such as competition and predation) and Quaternary historical processes (such as Pleistocene glaciation and its legacy on habitat availability, speciation, extinction and post-glacial expansion) — testing, for each class, whether it accounts for a substantive share of the roughly half of the variation in grid-cell mean breeding range size that the model leaves unexplained, and for its residual spatial autocorrelation; the identification of missing variables is bounded to these two candidate classes, so that unnamed or additional drivers are optional extensions rather than required deliverables; and (2) establish how far the two-dimensional pattern — smallest ranges in tropical mountains, weak latitudinal gradients in lowlands, dominance of the topography × climate interaction and the indirect, habitat-size-mediated action of climate — and its explanation generalize beyond the New World avifauna, by re-testing them in at least one additional taxonomic group and at least one additional biogeographic region. In testing the proposed drivers, the solver must quantify the marginal contribution of each driver with data measured independently of the response variable, and must assess how much of the previously unexplained spatially structured variation (and of the residual autocorrelation) the added drivers remove. A contribution counts as a substantive share only when it is so quantified, is estimated from data independent of the response variable, and remains distinguishable from zero once residual spatial autocorrelation is accounted for. The empirical evaluation and quantification of both candidate classes, together with the re-test in an additional taxonomic group and an additional biogeographic region, are the mandatory elements that resolve the task; evaluating only one candidate class, or omitting the additional taxonomic group or the additional biogeographic region, leaves it incomplete. The inputs required to re-run the analysis are standard, publicly recoverable data rather than materials supplied with the task: digitized New World breeding-range maps (e.g. BirdLife/IUCN range maps), a global elevation model (e.g. GTOPO30 or SRTM), a coldest-month temperature climatology (e.g. WorldClim), a terrestrial biome or ecoregion layer (e.g. the WWF biomes), a continental-outline layer for continental width, and a published Last Glacial Maximum climate reconstruction for the Quaternary-historical predictors; the biotic-interaction class has no off-the-shelf continental-scale predictor and must be operationalized from available occurrence or interaction data. The two components share one objective: a mechanistically identified account of broad-scale spatial variation in species range sizes, of which the New World bird map is the type case.

References

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