Allopatric speciation across rivers is a major hypothesis to explain present-day allopatric distributions and regional endemism in the Amazon (see Rull and Carnaval, 2020). Sister species or phylogenetic lineages occurring on opposite banks of large rivers and the boundaries of the distribution of species coinciding with large rivers can be used as evidence that the river subdivided a population to the point of preventing gene flow among individuals and promoted allopatric speciation (Ribas et al., 2012). However, extrapolation of this process based only on present-day species distributions should be done with caution. There is evidence that many species distributions have shifted over time (e.g. Elias, 1992; Graham et al., 1996; Kaustuv et al., 2001), and even sympatric species or lineages could have speciated in allopatry and expanded their ranges into sympatry (Losos and Glor, 2003). More importantly, sympatric speciation followed by dispersal, could result in present-day allopatric distributions (e.g. Graham and Lundelius, 1984), overestimating the importance of allopatric speciation for many taxonomic groups. Haffer (1997a,b) attributed the abutting distributions of many species to secondary contact rather than vicariance speciation owing to the formation of a river.

Recent studies have called into question the frequency with which river-related vicariance events explain allopatry in Amazonia. Several studies have found examples of similar species, sister species or not, which are separated by large rivers, but the evidence indicates that many of these species were not formed by the process of vicariance resulting from the division of a species by the formation of a river (e.g. Byrne et al., 2018; Lynch Alfaro et al., 2015; Hayes and Sewlal, 2004; Moraes et al., 2016). Studies of several morphologically similar and closely related species have failed to support allopatric speciation owing to the formation of a river (e.g. Naka and Brumfield, 2018). Many currently allopatric species separated by rivers have divergence times inconsistent with a river vicariance event (Naka and Brumfield, 2018). In these cases, the river could have been a physical barrier that limited the expansion of species that diverged elsewhere (see Haffer, 1997a,b, 2008), as has been suggested for the robust capuchin monkey Sapajus spp. (Boubli et al., 2015).

The occurrence of sister species or phylogenetic lineages on opposite banks of large rivers without evidence for a vicariance barrier implies that ecological interactions between species could maintain allopatry (Haffer, 1969, 1985). When the river is not an absolute physical barrier, ecologically similar species on an opposite river bank could exclude each other geographically in areas where they come into contact and this pattern might explain what has been described for species in nature. For example, a species of squirrel monkey, Saimiri sciureus, is widely distributed only on the north bank of the Amazon River, but one individual was recorded on the south bank (Mercês et al., 2015). Another squirrel-monkey species, Saimiri collinsi, is widely distributed only on the south bank of the Amazon River, but two individuals were recorded on the northern margin (Mercês et al., 2015). Similarly, the lizard Norops trachyderma is abundant and normally restricted to the right bank of the Tapajós River, but an individual was recorded on the left bank of the river; where the congeneric species, Norops tandai, is abundant and restricted (Moraes et al., 2016).

The species pairs described in the previous paragraph are morphologically similar, and it is uncommon to have morphologically similar congeneric species in sympatry (Darwin, 1859), though competition may be asymmetrical (Twomey et al., 2008). The trumpeter species used to propose endemism areas in the Amazon (Ribas et al., 2012) differ principally in color pattern, which is more important for intra- than inter-species competition, and would presumably compete strongly if in sympatry. Therefore, barriers to dispersal are presumed to be important in generating and maintaining species diversity in the Amazon.

These empirical studies indicate that some individuals of similar species can cross rivers (or could be living in the “wrong” side of the river for many generations at very low densities), but apparently this has not yet resulted in successful invasion and displacement of resident species on that bank. Therefore, the river can be a zone of secondary contact for species that diverged elsewhere. This raises the question of why the individuals of similar species crossing the river did not result in the competitive exclusion of one of the species?

Under the neutral theory of biodiversity (Hubbell, 2001), low dispersal rates can result in some species becoming more abundant by ecological drift and locally dominant due to the low rate of species substitution that is caused by decreased dispersal of individuals. Under neutral theory, the probability of an individual being replaced is given by the relative abundance of the individuals of that species, and this simple process can make a species competitively superior despite the entry of ecologically identical colonizers from places with low dispersal rates. This can result in long-term maintenance of species that are competitively similar. Thus, a large river only reducing the dispersal of a species across the river and not eliminating dispersal, could maintain these species allopatrically distributed over many generations, since the extinction probability of a species is predicted to be a function of population size, resulting in recent colonizers being weaker competitors and more prone to extinction.

To illustrate this process, we developed a two-dimensional cellular-automata model for two allopatrically-distributed species (the expected distribution pattern when the river is a geographical barrier for species dispersal) under neutral-theory dynamics (Hubbell, 2001) and we show that two competitively-identical species may remain allopatrically distributed for hundreds of generations when the chance of a species crossing a large river is reduced. In our simulations, individuals crossed the river but did not spread to the point of eliminating the species occupying the opposite bank in patterns similar to what has been described for species in the nature. This illustrates how rivers can maintain species boundaries, even when the process that generated the species was not a river-related vicariance event.

Our results show that simple processes expected under neutral theory (Hubbell, 2001) can result in a large river maintaining two species allopatrically distributed on secondary contact even though the river is not an absolute barrier to dispersal. In a neutral model (Hubbell, 2001), the probability of an individual being replaced is given by the relative abundance of individuals of a particular species, and this simple process makes a species competitively stronger relative to new colonizers simply by the effect of density on competition. Thus, the inclusion of a large river that only reduced the chance of individuals crossing from one bank to another (reducing the entry of new colonizers) was sufficient to maintain two allopatrically-distributed species for hundreds of generations. The process described in our simulation provides a potential mechanism for the maintenance of Amazonian biodiversity, as it allows competitively-similar species to coexist for many generations even though one species would quickly eliminate the other in the absence of the river (Hubbell, 2001).

The discrepancy between the local and regional-scale results highlights the effect of density on competition and how it can maintain two competitively-identical species allopatrically distributed for hundreds of generations when rivers are not absolute barriers. The general pattern was similar to what has been described for species in the Amazon, with dominance of one species on each bank, but with few individuals frequently colonizing small areas on the opposite bank and subsequent extinction of the colonizers on that bank. This is consistent with the proposal of Haffer (1969, 1985, 1997a, 1997b), who discussed the role of Amazonian rivers as secondary barriers for species distributions based on competitive exclusion, rather than complete inability of a species to cross the river, though Haffer (1969, 1985, 1997a, 1997b) did not consider the species to be competitively identical, as in neutral-theory dynamics.

We argue that occurrence of allopatrically-distributed species on either side of a large river need not always be explained by simple stationary process (Case et al., 2005; Holt and Keitt, 2005; Holt et al., 2005) that assume that species are allopatrically-distributed because (i) habitat is not available (e.g. non-flooded flooded areas), and/or (ii) the habitat available is lower-quality (reduced niche limits). The alternative explanation is that the habitat available is separated by physical or biotic factors that weaken colonization rates. Our simulation suggests that when the river reduces the chance of either species crossing, the inability of individuals that cross the river to persist below a critical threshold density makes the immigrant population more vulnerable to extinction and could reduce invasion speeds or even reverse invasions, generating a stable range limit and resulting in large numbers of allopatrically-distributed individuals. Many mechanisms have been proposed for such patterns (see Courchamp et al., 2008) in the absence of adaptive evolution (e.g. see Andrade-Restrepo et al., 2019; Kanarek and Webb, 2010), but our analyses cannot distinguish between them.

The present simulation shows how rivers may act as effective secondary barriers as suggested by Haffer (1969, 1985, 1997a, 1997b). It is likely that sister species or phylogenetic lineages have originated on opposite banks of large rivers without river-related vicariance events, then spread rapidly by chance (Hubbell, 2001), either due to the absence of a competitor (Case et al., 2005) or predator-prey interactions (Kubisch et al., 2014) within an area bounded by rivers (often called endemism centers) until they meet somewhere near the river. When they meet, both species would remain allopatrically distributed because it is difficult for new immigrants to establish themselves and to reproduce (e.g. Gascoigne et al., 2009) within the interfluve occupied by another species. This mechanism does not assume that the species have accumulated sufficient divergence to exploit different niches. The absence of divergence makes the species ecologically similar, but they remain allopatrically distributed for long periods because of competitive exclusion and dispersal limitation (e.g. Gutiérrez et al., 2014; Pigot and Tobias, 2013, 2015; Weir and Price, 2011). This process could maintain competitively-identical species allopatrically distributed for hundreds of generations, giving opportunity for genetic drift or adaptation to different environments resulting in evolutionary differences that prevent fertile crosses between species (Luzuriaga-Aveiga and Weir, 2019; Nosil, 2012).

A number of studies (e.g. Fecchio et al., 2017; Ferreira et al., 2017; Naka et al., 2012) have concluded that large Amazonian rivers increase Amazonian biodiversity throughout vicariant speciation without refuting plausible alternative conclusions. Models based on vicariant speciation, where rivers are assumed to have divided previously continuous populations, have been used to justify interfluves between major rivers as endemism areas that can be used in conservation planning when detailed information about most taxa is lacking (Caro and O’Doherty, 1999; Da Silva et al., 2005). However, several studies indicate that the large rivers are insufficient to explain the spatial-distribution limits of species and to indicate endemism areas for most phylogenetic lineages (Santorelli et al., 2018). The effectiveness of rivers as dispersal barriers also varies longitudinally, being greater near the mouth than in the upper reaches (Godinho and da Silva, 2018). The role of large rivers as geographical barriers works for some taxa better than others (e.g. Paula Lima et al., 2020) and in some rivers more than others (Nazareno et al., 2019), and does not work well for highly-dynamic rivers, as there are several cases in which river-capture processes (e.g. Ruokolainen et al., 2019; Albert et al., 2018) could have resulted in species with small populations on the side of the river occupied by a congeneric species.

Models based on vicariance work well for some organisms, especially large birds (Ribas et al., 2012), but less so for others (Santorelli et al., 2018). To improve conservation models, it will be necessary to have more complex models that include dispersal modes, rates of evolution of different taxa, the potential for competitive exclusion and differences in the degree of sexual selection. All these focus on deterministic differences among taxa, but our simulations show that neutral processes based on relative abundances may be important to maintain and possibly generate diversity across rivers. Reduction in the amount of habitat available to taxa through deforestation will affect relative abundances and the processes that we have described, with implications for conservation planning well beyond the identification of vicariance speciation.

In conclusion, our simulation study shows that neutral processes and reduced dispersal across Amazonian rivers present another mechanism by which present-day allopatric distributions of similar species may arise without invoking a river-related vicariance event. To differentiate among hypotheses to explain allopatric distributions, we strongly recommend the use of the protocol proposed by Naka and Pil (2020). However, there is a need for more understanding of the dispersal characteristics of organisms and factors that limit river crossing, especially under scenarios of climate change that may reduce river flows, alter dispersal patterns, and change relative densities of species on opposite banks.

Data are available on the PPBio site <https://ppbio.inpa.gov.br/> and Data ONE (Brazilian Program for Biodiversity Research - PPBio - Western Amazon & Center for Integrated Studies of Biodiversity in the Amazon - CENBAM).

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.