Polytypic species and complexes of closely related species provide unusual opportunities to study the linkage between micro and macro evolutionary processes directly in nature because they are composed of taxa that persist at various stages of divergence, from genetically differentiated populations to ecologically divergent taxa. Of particular importance are ring species [1
], or circular overlaps [2
], in which populations at intermediate stages of divergence are distributed around a geographic barrier and reconnect at a terminus as reproductively isolated taxa. By preserving genetic interactions that are typical of species at the ring terminus, as well as interactions typical of populations around the ring distribution, these systems provide a natural demonstration of how micro-evolutionary processes (that is, colonization, genetic drift, gene flow, and local adaptation) result in a continuum of divergence, linking taxa that are generally recognized as species. Although prized as examples of evolutionary clarity, ring species also present a pattern of taxonomic irresolution in which, facing continuous levels of differentiation, different taxonomists recognize a varying number of species, depending on their criteria. Most previous studies of ring species have focused on the local geographical and ecological factors enabling species formation. Here, we develop a generalized model of geographic barriers and use the known examples of ring species to evaluate the number and distribution of other barriers from around the world that are topographically similar and thus may be promoting ring speciation processes in equivalent taxa.
Geographic species formation is intrinsically dependent on the spatial scale at which organisms interact with the landscape, encompassing both biological and historical factors that affect divergence (for example, age of the clade, generation time), and others that affect homogenization through gene flow (for example, degree of philopatry, rate and distance of successful migration, home range size) (see [3
]). Theoretically, ring species can arise frequently when the spatial scale of a geographic barrier matches the biological and historical 'scales' that are necessary for species-level divergence [4
]. Whether because that ratio is rarely met in nature or because of historical contingencies associated with the barrier or the organism, few polytypic taxa are in fact recognized by modern taxonomy as ring species [6
] and ring diversification is considered to be the exceptional mode of geographic diversification [7
]. Mayr [8
] stated that "circular overlaps can obviously develop only under highly exceptional constellations of geographical factors", so that the continuous levels of population divergence result from restrictions to gene flow within a species' range imposed by a central and long-standing geographic barrier. Despite their apparent rarity, ring species were extremely influential to the Evolutionary Synthesis [2
] and remain a cornerstone to our understanding of how geography influences species formation. These few examples seem to indicate that - even though species formation is clearly a continuous process [10
] - the geographic conditions that promote ring speciation are extremely rare. Perhaps there is a taxonomic impediment, in which discovery of parts of rings and their naming as species precedes (as in the case of the history of the Ensatina
ring prior to its recognition as a ring [11
]) or, perhaps more commonly, impedes recognition of the ring. In this paper, we release ourselves from existing taxonomic classifications, and possible related artifacts, in order to consider the processes that have enabled ring-distributed taxa ('ring taxa') to diversify in a continuous sense around geographic barriers, irrespective of whether the terminal forms are above or below species-level divergence.
Long-term research programs on ring species complexes, such as the plethodontid salamander Ensatina eschscholtzii
and the greenish warbler Phylloscopus trochiloide
s, provide empirical insights into the processes that can drive ring species formation: (i) conditioned by a long-standing geographic barrier, an ancestor expands around the barrier to form a ring distribution, (ii) restrictions to dispersal imposed by the barrier are such that contiguous populations become increasingly more divergent, and (iii) this divergence continues to the point where - at the ring terminus - the reconnecting terminal taxa are reproductively isolated or hybridize infrequently (that is, without an opportunity for gene flow). The persistence of the central geographic barrier is fundamental for ring diversification because it restricts movement of individuals to the ring distribution, thus promoting non-adaptive divergence through the initial colonization of available habitat, genetic drift of each local population, and limiting gene flow among continuous populations around the ring. Adaptive divergence may further affect neighboring populations around the ring distribution through such processes as local adaptation of anti-predatory strategies (for example, coloration in E. eschscholtzii
]) or the development of assortative mating (for example, song and coloration in P. trochiloide
]). While taxon-based studies have contributed to our understanding of the evolutionary processes that result in ring species, they are not easily generalized and thus cannot be used to evaluate the number and distribution of other geographic barriers around the world that may also favor continuous divergence in ring distributed taxa, so that terminal overlapping forms are near species-level divergence.
Here, we advance a new modeling framework to address the general question of which geographic barriers provide the topographic 'canvas' necessary for the establishment of ring species (Figure ). Rather than modeling ring distributions of species, our predictive model targets geographic barriers that, according to biologically relevant summary statistics (Table ), are topographically similar to barriers associated with ring species, or taxa with a similar diversification process (that is, ring taxa that express continuous levels of differentiation, with terminal forms being above or below species level divergence). By removing any subjective and ill-defined considerations of what constitutes a valid biogeographic barrier for species, our model simplifies environmental complexity so that barrier similarities may be quantified and evaluated consistently across taxa and environments. While 'environment' in our model can be defined according to a number of different variables, here we parameterize it using elevation because it is a major topographic variable leading to the formation of prominent ecotones and defined ecoregions [13
], which in turn are broad-scale determinants of species' distributions [14
]. First, we analyze a multivariate 'barrier-space' to evaluate whether barriers associated with ring taxa share topographic features, and whether those features are in fact rare when considered relative to all other barriers on the planet. Second, we use our model to identify candidate barriers with equivalent topographic features to those associated with ring taxa, and for taxa with comparable population biologies and histories provide spatially explicit hypotheses of where ring diversification might be occurring in nature.
Figure 1 Conceptual overview of the four-step modeling framework for quantifying geographic barriers formed by environmental gradients. A: Our generalized model is parameterized for both marine and terrestrial environments using elevation. B: We then compute slope, (more ...)
Summary statistics used in the topographic ring model, along with a brief description of biological relevance.