Topology of syngameons

Abstract Syngameons are sets of species linked by interspecific hybridization. Common observations regarding the structure of syngameons are that hybridization propensity is not uniform across species and that patterns of hybridization are dominated by a few species. I use computer simulations to test these claims in naturally occurring syngameons selected from the literature and from personal observation. Natural syngameons, especially those involving plants, typically exhibit nonrandom structure: The first three order statistics for the number of hybrid partners and the variance in the number of hybrid partners are larger than chance alone would predict. The structure of two insect syngameons examined is not significantly different from random. To test a hypothesis that variation in hybridization propensity across species in natural syngameons is simply an artifact of hybridization opportunity, I examine the structure of four artificial syngameons (fertility relationships) produced by full diallel crosses. Three of four artificial syngameons exhibit nonrandom structure, as the observed variation in number of successful crosses is larger than chance alone would predict. In general, there are no significant results involving the order statistics. Finally, I discuss biogeographic, ecological, and phylogenetic hypotheses for variation in hybridization propensity across species in natural syngameons.


Patterns of interspecific hybridization exhibit several emergent
properties. For animals, the probability of hybridization between species may be inversely related to their phylogenetic distances (Coyne & Orr, 1989;Tubaro & Lijtmaer, 2002). For plants, the probability of homoploid versus polyploid hybrid speciation appears to be positively associated with the extent of genetic divergence of hybridizing species (Buggs, Soltis, & Soltis, 2011;Chapman & Burke, 2007;Paun, Forest, Fay, & Chase, 2009). In addition, the occurrence of hybrids varies by taxonomic group, with approximately 25% of plant species and 10% animal species producing natural hybrids (Mallet, 2005;Rieseberg, 1997). Lastly, there may be a strong phylogenetic signal to hybridization propensity, as natural hybrids are not equally distributed among families and genera of vascular plants (Ellstrand, Whitkus, & Rieseberg, 1996;Whitney et al., 2010).
A syngameon is produced when a group of closely related species forms a complex set of hybrid combinations (Lotsy, 1925). Classic examples include irises of the California Pacific Coast (Lenz, 1959), white oaks of the Eastern United States (Hardin, 1975), and British species of Potamogeton (Clapham, Tutin, & Warburg, 1962). Syngameons also exhibit emergent properties; a common observation is that hybridization events are not equally distributed among species and that a few species dominate the pattern of hybridization. Consider the pattern of hybridization between southwestern white oaks as depicted by a network graph (Figure 1) -the set of hybridizations is dominated by three species: Quercus gambelli, Q. arizonica, and Q. grisea; and the number of hybrid partners ranges from 8 (Q. grisea) to 1 (Q. striatula).
Variation between species within a syngameon in hybridization propensity may be due to a number of factors related to biogeography, ecology, phylogeny, reproductive biology, and genetics. Alternatively, the pattern may be due to chance alone. The appearance of a structured pattern of hybridization within a given syngameon may simply be an artifact of the number of species involved and the number of hybrid combinations. Nonrandom structure in the pattern of interspecific hybridization among closely related species addresses a fundamental question in interspecific hybridization, namely "Why do some species readily hybridize, while others do not." The first step in answering this question is to demonstrate that there are, in fact, nonrandom patterns of hybridization. To date, this has not been done.
To reject chance in favor of more biologically interesting mechanisms producing patterns of hybridization within syngameons, it is necessary to enumerate all possible network graphs constrained by the observed number of species and hybrid combinations. The observed structure of a given syngameon can then be compared to the sample space of possible network graphs. I use computer simulations to determine whether syngameons, as represented by network graphs, exhibit nonrandom structure. In particular, I examine order statistics and variation in the number of hybridization partners to determine whether hybridizations events are significantly concentrated in a few species and whether the variation in hybrid propensity is greater than chance alone would predict. The objective was to place observations regarding the structure of syngameons on a sound probabilistic foundation.
To test a hypothesis that structure in natural syngameons is simply a function of variation among species in the opportunity to hybridize, I conducted two separate analyses. First, I examined four artificial syngameons (fertility diagrams) selected from the literature and produced by full diallel crosses. Because each species was mated to all other species, hybridization opportunity was equal for all species. The structure of these artificial syngameons was analyzed as described below. Second, I examined the relationship between geographic range and hybridization propensity in the Boechera syngameon. I assumed, all other things being equal, that geographic range is related to the opportunity to hybridize. I examined county-level species occurrences for Boechera species throughout the Southwestern United States F I G U R E 1 Pattern of hybridization between white oaks of the Southwestern United States and Northern Mexico T A B L E 1 Natural and artificial syngameons examined for nonrandom structure based on order statistics and standard deviations of observed numbers of hybrid combinations

| RESULTS
There was considerable variation in the structure of natural syngame- Oak syngameon (Figure 1). The first several order statistics for the number of hybrid combinations by species were significantly larger than were those expected by chance alone (Figure 2). This pattern held for all but one of the natural plant syngameons (California Iris syngameon).
Observed values of the order statistics and observed values of the standard deviations in number of hybrid partners were significantly larger than chance alone would predict (Table 1). (The first two order statistics for the Potamogeton syngameon were weakly significant, while the standard deviation in number of hybrid partners was highly significant.) The two insect syngameons did not exhibit nonrandom structure; none of the order statistics or standard deviations in the number of hybrid partners were significantly different from that expected by chance alone. Adding artificial hybrids to the Heliconius Butterflies, syngameon did not produce significant nonrandom structure.
As expected, the four artificial syngameons exhibited higher hybridization rates than did the natural syngameons. However, in no F I G U R E 2 Observed and expected order statistics for the number of hybrid combinations between species in the Southwestern White Oak syngameon Computer simulations indicated significant nonrandom structure in three of the four artificial syngameons. While the order statistics generally were not significantly different from that expected by chance alone, the standard deviations in the number of hybrid partners were. Only the Allium syngameon did not exhibit nonrandom structure (Table 1).
Nonparametric regression indicated a marginally significant relationship (p = .052) between the number of hybrid partners and number of counties occupied for species in the Boechera syngameon.
Geographic distribution explained roughly 26% of the variation in hybridization propensity.

| DISCUSSION
I have demonstrated that artificial and natural syngameons, at least for those involving plants, exhibit nonrandom structure with respect to variation in hybridization propensity. I also have demonstrated that patterns of hybridization within these syngameons are typically dominated by a few species. I found no evidence that syngameons involving animals, in this case insects, exhibited patterns of hybridization that differed from those that chance alone would predict. Of course, the sample size for animal syngameons was quite small, and an adequate determination of nonrandom structure in animal syngameons must await a larger compendium of case studies.
Unresolved is the mechanism that produces nonrandom structure in syngameons. For natural syngameons, differences in the geographic distributions of species are a compelling candidate mechanism.
Geographically widespread species simply have more opportunities for hybridization than do geographically restricted species. I found partial support for this hypothesis in the Boechera syngameon, as there was a marginally significant positive relationship between a species' geographic range and number of hybrid-producing mating combinations. I recognize that the measure of geographic range, the number of counties occupied, is not optimal. A rigorous test regarding the relationship between geographic range and hybridization propensity must await a more thorough analysis. This list is not exhaustive, nor is it mutually exclusive. Of course, the opportunity hypothesis and the intrinsic-factors hypothesis are not mutually exclusive either.
One potential intrinsic factor that deserves greater investigation is phylogenetic position. It is known at a gross level that there is a phylogenetic signature to hybridization propensities. Plants produce natural hybrids more readily than do animals (Mallet, 2005), and production of natural hybrids is not equally distributed across orders of vascular plants (Ellstrand et al., 1996;Whitney et al., 2010). At a finer level, the probability of interspecific hybridization may be related to genetic distance (Chapman & Burke, 2007;Coyne & Orr, 1989). Avid hybridizers may be those species with many close neighbors in genetic space, or they may typically occupy basal or distal positions within their respective clades. A robust test of this hypothesis will require a large compendium of case studies with detailed phylogenies that include all members of a syngameon.

I thank Donovan Bailey and two anonymous reviewers for comments
and suggestions on a previous version of the manuscript. I thank D. Bailey for data on the Boechera syngameon, and I thank Patrick Alexander for data on the geographic ranges of Boechera species. This work was supported, in part, by NSF Grants to W. Boecklen (DUE 1141320) and to D. Bailey (DEB 0817033).