Drift drives the evolution of chromosome number I: The impact of trait transitions on genome evolution in Coleoptera

Abstract Chromosomal mutations such as fusions and fissions are often thought to be deleterious, especially in heterozygotes (underdominant), and consequently are unlikely to become fixed. Yet, many models of chromosomal speciation ascribe an important role to chromosomal mutations. When the effective population size (Ne) is small, the efficacy of selection is weakened, and the likelihood of fixing underdominant mutations by genetic drift is greater. Thus, it is possible that ecological and phenotypic transitions that modulate Ne facilitate the fixation of chromosome changes, increasing the rate of karyotype evolution. We synthesize all available chromosome number data in Coleoptera and estimate the impact of traits expected to change Ne on the rate of karyotype evolution in the family Carabidae and 12 disparate clades from across Coleoptera. Our analysis indicates that in Carabidae, wingless clades have faster rates of chromosome number increase. Additionally, our analysis indicates clades exhibiting multiple traits expected to reduce Ne, including strict inbreeding, oligophagy, winglessness, and island endemism, have high rates of karyotype evolution. Our results suggest that chromosome number changes are likely fixed by genetic drift despite an initial fitness cost and that chromosomal speciation models may be important to consider in clades with very small Ne.


Introduction
For any given trait, variation within and among species is a function of mutation, drift, selection, fidelity of trait expression, and isolation among lineages.Chromosome number is perhaps one of the simplest characteristics of a genome.Despite this simplicity, the relative importance of mutation, drift, and selection in generating patterns of chromosome number evolution across the tree of life has been poorly understood.Understanding the evolutionary forces that underlie strong karyotype conservation in some groups (Boyes and Shewell 1975;White 1978) while others are more labile (Kandul et al. 2007;Carbone et al. 2014) has remained elusive despite over 50 yr of work (but see Blackmon and Demuth 2014;Ross et al. 2015;Blackmon et al. 2019;Ruckman et al. 2020;Sylvester et al. 2020).
Hypotheses that propose an important role for positive selection to change chromosome number are easily allied with arguments for the costs and benefits of recombination (Muller 1932(Muller , 1964;;Fisher 1958;Hill and Robertson 1966;Nei 1967;Lewontin 1971;Felsenstein 1974).When recombination is limited to one crossover per chromosome or chromosomal arm per meiosis, selection for increased or decreased recombination is expected to propel corresponding changes in chromosome number (Otto and Payseur 2019).Selection is argued to favor increased chromosome number in social insects because having more chromosomes could decrease the average relatedness within a colony-limiting the opportunity for kin-recognition-based cheating (Sherman 1979;Templeton 1979).Increased chromosome number simultaneously allows for high genotypic diversity among sibs which has been shown to benefit colony growth, efficiency, and pathogen resistance (Tarpy 2003).However, analyses comparing solitary and social Hymenoptera show that the strength of this selection on chromosome number is likely weak (Ross et al. 2015).Positive selection may also be particularly important in decreasing the number of autosomes through selection for fusions between autosomes and sex chromosomes to resolve sexual antagonism (Charlesworth and Charlesworth 1980;Anderson et al. 2020;Sylvester et al. 2020).
Counter to the general applicability of positive selection's role as an agent of karyotype evolution (King 1995), empirical observations suggest that most changes in karyotype are either neutral or deleterious, with many being underdominant (i.e.deleterious when heterozygous).Underdominance of karyotype changes can result from difficulties in meiosis, where mismatched chromosomal types do not segregate properly.Such underdominant mutations are only expected to fix when natural selection is overcome by random genetic drift in small populations (Wright 1941;Lande 1979Lande , 1985)).It is also important to note that in a small population, an underdominant mutation has a higher frequency when it first occurs than in a large population with the initial frequency being the reciprocal of two times the population size.This means that it can reach a higher frequency through drift more quickly, and once it is the major allele in the population, it ceases to have a negative selection coefficient.Despite the difficulties of fixing underdominant mutations, attempts to ascribe a causal role to karyotype evolution in the speciation process have been abundant (Lewis 1966;White 1978;Bickham 1979;Grant 1981;Templeton 1981;Baker and Bickham 1986;Rieseberg 2001).Some models assume karyotype changes are neutral but facilitate diverging local adaptation by sheltering some genome regions from the homogenizing effects of gene flow and recombination (Guerrero and Kirkpatrick 2014).Chromosomal changes could even function under a Bateson-Dobzhansky-Mueller incompatibility model where two isolated populations fix neutral changes that, when combined into a single genome, lead to segregation defects and function as an isolating barrier upon secondary contact (Baker and Bickham 1986).
It is important to note that most information on the fitness effects of chromosomal mutations may not be representative of the changes that produce extant diversity.For instance, many examples have relied on crosses between divergent strains assessing fitness in offspring (Ratomponirina 1988;King 1995).However, because the parental strains or species have often been isolated for millions of years, fitness effects may be compounded by genic incompatibility (Bayes and Malik 2009).Other evidence comes from induced chromosomal changes using mutagenic techniques that produce changes that may be fundamentally different from naturally occurring chromosomal mutations (Roberts 1967(Roberts , 1970)).By leveraging phylogenetic comparative methods to analyze extant diversity, we believe we can more directly characterize the relative importance of mutation, selection, and drift in karyotype evolution and estimate the typical fitness effect of mutations that have led to observed divergence in chromosome number.
Given that effective population size (N e ) governs the efficacy of natural selection in relation to random genetic drift, one way to distinguish between these two evolutionary forces is to see whether factors associated with differences in N e are also associated with differences in the rate of karyotype evolution and or the direction of change in chromosome number.If karyotype changes are neutral, their fixation rate should be unrelated to N e .However, if karyotype changes are deleterious, then species with small N e should have higher rates of chromosome number evolution as more changes are fixed by drift.In contrast, if selection plays a broad role, we expect species with larger N e to have higher rates.Ultimately rates of karyotype evolution will be determined by the interplay of mutation, selection, and drift.Some empirical examples have illustrated the importance of mutation rate and selection (Carbone et al. 2014;Ross et al. 2015).What remains unclear is whether these are the exception or the rule.
Efforts to relate N e to karyotype evolution typically use ecological and phenotypic traits as proxies for expected differences in N e .For instance, all else being equal, winged species should have larger N e than wingless species because flight increases dispersal distances (N e = 4πσ 2 δ), where σ 2 is a measure of dispersal distance and δ is the density of adults per unit area (Wright 1946).Mating system has also been used where species classified as inbreeding are assumed to have lower N e than outbreeding species (Charlesworth 2003).Geographic distribution can be divided into continental and island endemics, with island endemics being assumed to have lower N e .Finally, the degree of diet specialization can be used with mono or oligophagous species having lower N e than polyphagous species (Li et al. 2014).
The distribution of these traits has then been compared with the rate of karyotype change as estimated by scaling the variance in chromosome number to a fossil date for the taxonomic group of interest (Wilson et al. 1975;Bush et al. 1977;Bengtsson 1980;Imai et al. 1983;Larson et al. 1984;Petitpierre 1987;Olmo 2005).These earlier studies suggest that taxa inferred to have highly structured populations also have faster rates of karyotype evolution.There is also a negative correlation between the estimated rate of karyotype evolution and allozyme heterozygosity levels in some cases (Coyne 1984).These studies have generally supported a hypothesis of random genetic drift in small populations driving increased rates of chromosome change.However, previous work has been limited by not incorporating phylogenies or evolutionary models for chromosome change and using comparisons between highly divergent clades where the underlying mutation rates and accuracy of fossil ages may differ dramatically (i.e.across all vertebrates).
The present study expands previous efforts to understand karyotype evolution in two ways.First, we incorporate ecological and phenotypic proxies for N e with a comprehensive database of Coleoptera karyotypes (Blackmon and Demuth 2014).Second, we employ a modern statistical phylogenetic framework to model the relationship between N e and chromosome evolution (Blackmon et al. 2019).Coleoptera is an excellent group to study the effect of N e on chromosome evolution because they exhibit variation in all proxies for N e (Crowson 1981), have a good phylogenetic scaffold, and contain an extensive database of karyotypes (4,957 species).We show that lineages with multiple traits associated with reduced N e (loss of wings, inbreeding, island endemism, restricted feeding) also have faster rates of karyotype evolution.Our findings suggest that random genetic drift is the predominant driver of fast karyotype evolution, as predicted if changes in chromosome number are typically underdominant or mildly deleterious.

Data collection
We compiled all available karyotypes from the Coleoptera Karyotype Database (www.karyotype.org)(Blackmon and Demuth 2015).Coleoptera karyotypes rarely include banding data and are typically reported as the meioformula, consisting of the number of autosomes plus the sex chromosome complement of the male.For this reason, we use male haploid autosome count as a surrogate for karyotype, and for the remainder of the paper, refer to this as the chromosome number.In 19 cases where multiple values were reported for a species, each value was retained, and these distributions were sampled in downstream analyses to account for tip state uncertainty.
Lack of overlap in the available data for karyotype, phylogeny, and N e -related traits resulted in our analysis being subdivided into a family-level analysis of Carabidae using the presence or absence of wings and a sparser but more phylogenetically diverse analysis of 12 clades using multiple N e -influencing traits.Data for the presence of wings in Carabidae were taken from a previous compilation of natural history data (Larochelle and Larivière 2003).Species reported as being polymorphic for wings were scored as having an equal probability of being either winged or wingless.To maximize the amount of data that could be analyzed, if wing data were not present for a species in the karyotype and phylogenetic datasets, but other species in the genus were reported, the species was assigned a probability reflecting available data for the genus.For instance, in the genus Calathus, 64% of species were reported as wingless; therefore, all Calathus species not in the trait dataset were also assigned a 64% probability of being wingless and 36% probability of being winged.
For each of the 12 clades included in our clade-level rate estimates, we performed literature searches to score the included species for the following traits: winged vs. wingless, inbreeding vs. outbreeding, island vs. continental distributions, and mono/oligophagy vs. polyphagy.If any species included in a clade dataset had a low N e version of a trait, the clade was scored as having this trait.This process led to categorizing clades into those with 0 to 2 low N e traits.We use this number of low N e traits occurring in a clade to classify them into high, medium, or low expected N e classes (Table 1).To account for phylogenetic history in our comparative analysis, we used 100 trees from the posterior distribution produced in an earlier study (Blackmon and Demuth 2014).Briefly, these trees are based on an analysis of seven genes (16s, 18s, 28s, COI, elongation factor 1, arginine kinase, and wingless) across 1,042 taxa in BEAST (v1.7.5;Drummond and Rambaut 2007;Suchard and Rambaut 2009).We assumed a lognormal relaxed clock and used normal distributions to place priors on the age of seven nodes where ages were based on previous estimates (McKenna and Farrell 2009).

Inferring rates of chromosome evolution
We used the R package ChromePlus to construct a Markov model of chromosome evolution (Fig. 1) that allows transitions in a binary character (i.e.wing presence or absence) and three mechanisms of chromosome number change: fusions (δ), fissions (γ), and whole-genome duplication (ρ) that can vary depending on the state of the binary character (Blackmon et al. 2019(Blackmon et al. , 2023;;Ruckman et al. 2020).Because the evidence for whole-genome duplication is limited, we also fit a model where the rate of whole-genome duplication was set to zero (Li et al. 2018).This model was fit in a Bayesian framework using the R package diversitree on each of the 100 phylogenies from the posterior distribution of phylogenies (FitzJohn 2012).Each Markov Chain Monte Carlo (MCMC) run was initialized with parameter values drawn from a uniform distribution from 0 to 10.We applied a broad exponential prior with a shape parameter of 2 to avoid sampling unrealistically high rates.We repeated the MCMC on all 100 trees for 200 generations.All runs converged within the first 25 steps.However, we conservatively discarded the first 100 generations as burnin for each MCMC run.Posterior distributions for rate parameters were compared with the prior distribution to ensure that the prior was not unduly influencing the inference of the posterior distribution.In this model, all rates reported are lambda parameters for exponential distributions that describe the expected waiting time for a transition to occur.To allow for easy interpretation of rates during the fitting process, we scaled trees to unit length; however, all rates reported here have been rescaled to convert to units of millions of years.
To determine whether wingless clades have higher fusion, fission, and whole-genome duplication rates, we report our results in terms of a mean rate difference statistic, ΔR x , where x is the model parameter of interest.For instance, for the rate of fusions (δ) for each post-burnin sample, we calculated ΔR δ as: We then examine the 95% credible interval of ΔR δ .In cases where the credible interval of ΔR δ is above zero, there is strong support for higher fusion rates in wingless lineages.If the credible interval of ΔR δ is below zero, there is strong support for higher fusion rates in winged lineages.In cases where the credible interval of ΔR δ overlaps zero, our interpretation is that there is limited or no support for differences in the rate of fusion between wingless or winged lineages.
For our clade-level analyses, we used two simplified chromosome evolution models, one with only fissions (γ) and fusions (δ) and one with fissions (γ), fusions (δ), and wholegenome duplication (ρ).These models were fit separately for each clade in our analysis.Model fitting and MCMC approaches were identical to those for the wingless analysis.In all analyses, if a tip had multiple chromosome numbers reported, we randomly sampled among possible values each time the model was fit on one of the 100 trees from the posterior distribution.Using this approach, we incorporate both uncertainties in phylogeny and tip states.All analyses were completed in R version 4.1.1(R Core Team 2021).Since previous work has shown that different rates of chromosome evolution may occur in the two major suborders of beetles (Blackmon and Demuth 2014), we analyzed the clades in each suborder separately.

Scaled variance estimates
Since the lack of overlap between species trait data and existing phylogenetic information causes a considerable reduction in the number of data points in our analysis, we also investigated whether estimating the rate of karyotype evolution without incorporating phylogenies (as many past studies have done) is consistent with the phylogenetic model-based approach above.We calculated time-scaled coefficients of variation by first locating the oldest available fossil record for each clade of interest in the Paleobiology Database (PaleoDB) (http://paleodb.org).We then used the fossil ages to scale the coefficients of variation for chromosome number in each taxon.To assess consistency between these "scaled variance" estimates and the phylogenetic model-based rate estimates, we calculated a mean rate of chromosome evolution in each taxon by taking the mean of the fission, fusion, and whole-genome duplication rates in each generation of the MCMC and then taking the means of these to arrive at a single value for each taxon.We then used a nonparametric correlation analysis (Kendall's τ).All tests were considered significant at P-value <0.05.Scripts for all analyses are available in a GitHub repository (https://github.com/coleoguy/coleochroms).

Data collection
We downloaded 4,957 records from the Coleoptera Karyotype Database (karyotype.org).Our karyotype dataset included data for all four extant suborders of Coleoptera.Two of these suborders (Myxophaga and Archostemata) are represented by only one and two karyotypes; therefore, we focused our analysis on the larger suborders of Adephaga and Polyphaga.These two suborders accounted for 1,285 and 3,669 karyotypes, respectively.In Adephaga, the number of autosomes ranged from 3 to 34 (mean = 15.57± 0.14), while in Polyphaga, the range was from 1 to 35 (mean = 10.63 ± 0.06).Polyphaga exhibits a single mode of nine autosomes, accounting for 952 species or 29% of all Polyphaga records.Conversely, Adephaga is bimodal, with concentrations at 11 and 18 autosomes accounting for 276 and 242 species or 23% and 20%, respectively (Fig. 2).

Phylogenetic model-based rate estimates
Karyotypes for 1,065 Carabidae species were available, and 136 of these were used in our comparative analysis because they were included in our phylogenetic tree and had data available on flight ability.These data were used to fit the two models (with and without whole-genome duplication).We evaluated results for more complex models that would allow wing gain and loss, but this has little support biologically and produced results that were qualitatively the same.All results below are for a model where wings can be lost but not regained.In the simplest model with only fusions and fissions, we estimate a mean ΔR fusion of −0.009 and a mean ΔR fission of 0.025.For ΔR fusion , the credible interval spanned zero.In contrast, the credible interval for ΔR fission was entirely positive (0.005 to 0.044; Fig. 3A).In our more complex model that includes whole-genome duplication, we estimate a mean ΔR fusion of 0.003 and a mean ΔR fission of 0.002.For both ΔR fusion and ΔR fission , the credible interval spanned zero.The mean estimate for ΔR wgd was 0.010, and the low end of the credible interval was just above zero (2.3 × 10 −5 ; Fig. 3B).In examining the posterior distribution, we found that just 1.3% of the 10,000 samples from the posterior distribution sampled regions with a negative ΔR wgd .Taken together, these results suggest that wingless Carabidae have higher rates of increases in chromosome number (Fig. 3).Model for the evolution of chromosome number in wingless and winged clades.At an instance in time, a lineage will have i chromosomes and be in a wingless or winged state.A lineage can make three transitions in chromosome number: fusion (δ), fission (γ), whole-genome duplication (ρ), and if currently winged, can transition to wingless (q winged→wingless ).Rates of fusion, fission, and whole-genome duplication are allowed to differ between winged and wingless lineages.
For the analysis of clade level, we scored each clade for the presence or absence of traits thought to reduce N e .This allowed us to assign each clade to a class based on expected N e .Four clades possess no N e -reducing traits, and we classify these as the high N e class.Three possess only one of these traits and form the medium N e class.Five clades (Calathus, Chrysolina, Cytronus, Dendroctonus, and Timarcha) possess two of the N e -reducing traits, which form the low N e class (Table 1).
For our clade-level analysis, we selected all clades where the phylogeny and karyotype data overlap included at least 12 species.This led to 12 clade-level analyses (five in the suborder Adephaga and seven in the suborder Polyphaga).One of these was the genus Cicindela (tiger beetles).More broadly, Cicindela and tiger beetles have been the focus of intense taxonomic studies and changes (Gough et al. 2019(Gough et al. , 2020)).In light of the taxonomic instability, we chose to include all species in the family Cicindelidae in our analysis of this clade (Duran and Gough 2020).
In our analysis of Polyphaga clades, we found that all four clades that we placed in the low N e size class had a higher mean rate than the three clades placed in the medium and high N e classes.Three low N e clades had credible intervals that did not overlap with the medium and high N e classes (Fig. 4).In our analysis of Adephaga clades, we found a similar pattern.The one genus (Calathus) that we scored as being in the low N e class had a higher mean rate and credible interval than all medium and high N e clades.We interpret this as strong evidence that traits expected to have low N e are associated with increased rates of chromosome number evolution.

Estimates based on scaled variance
For each of the 12 clades included in our rate estimate inference, we searched PaleoDB for fossil records.Nine of our target clades had fossil data available; if multiple dates were available, we recorded the age of the oldest available record.One taxon, Ips, was included based on a fossil that reflects the family rather than the genus.For this reason, we substituted an age for this genus that reflects the median age estimate based on a time tree analysis that used several fossils as priors on nodes (Gohli et al. 2017).These ages ranged from a low  of 7.24 million yr for Chrysolina to 150.8 million yr for Cicindelidae (Table 2).We calculated the scaled variance of chromosome number for each of the nine clades by dividing the coefficient of variation for chromosome number by the fossil-based age estimates (Table 2).These scaled variances ranged from 0.0005 in Diabrotica to 0.32 in Dendroctonus.Notably, we find no correlation between the scaled variancebased estimates of karyotype evolution and the phylogenetic model-based rate estimates for the nine clades with overlapping analyses (τ = 0.11, P-value = 0.76).

Discussion
Our analyses clearly show that traits that are expected to reduce N e are associated with increased karyotype evolution rates, and this pattern holds independently of potential differences in mutation rate between lineages.The most likely explanation for this pattern is that chromosome number changes are predominantly deleterious while segregating and become fixed by random genetic drift.
In our analysis of Carabidae, we fit two models.The first was a complex model that allowed fusion, fission, and wholegenome duplication.Under this model, only the rate of wholegenome duplication was higher in wingless lineages than in winged lineages.However, when we fit a simpler model with fusions and fissions we find that the rate of fission is higher in wingless lineages, but the rate of fusion was similar in all lineages.So in this case regardless of the model increases in chromosome number occur more frequently in lineages that have lost wings.
In our analysis of the Polyphaga and Adephaga clades, the difference between the low N e clades and the medium and high N e clades is striking.In Polyphaga, the mean rate of fusions in low N e clades ranges from 0.05 to 0.11.In contrast in medium and high N e clades mean rates were all below 0.025.In Adephaga, only one clade is classified as low N e (Calathus).However, Calathus exhibits strikingly high rates compared with the other four clades.All rates for Calathus were more than ten times higher than the average of the other Adephaga clades.
A few notable examples serve to highlight this overall pattern in beetles.First, within the Polyphaga family Curculionidae, our study includes the closely related scolytid genera Ips and Dendroctonus.Our estimate for the mean rate of karyotype evolution in Dendroctonus 0.025 was three times higher than the mean rate in Ips 0.0083.This marked difference matches expectations based on breeding behavior.Dendroctonus is an inbreeding genus producing biased sex ratios and practicing predispersal sibmating (Grégoire 1988).Meanwhile, Ips is an outbreeding genus where both males and females disperse, and neither sibmating nor biased sex ratios have been documented (Kirkendall 1993).These characteristics should lead to smaller N e in Dendroctonus and allow changes in karyotype to be fixed more easily even if they are underdominant, as theory predicts.Second, the three highest rates of karyotype evolution in Polyphaga were observed in the Chrysomelidae genera Cyrtonus, Chrysolina, and Timarcha, all of which have wingless, oligophagous species.In all three genera, the mean of the posterior distribution for the rates of karyotype evolution was higher than in Diabrotica, a chrysomelid genus lacking any of the small N e traits.
One potentially confounding factor in our analysis is the inclusion of pest species that experience periodic outbreaks that can lead to orders of magnitude increase in census population size (Kunegel-Lion and Lewis 2020).If outbreaks were frequent or lasted many generations this could lead to species with high effective population size despite exhibiting traits that we hypothesize to be associated with low effective population size.However, studies in locust suggest that effective population size is often quite similar in comparisons between populations experiencing outbreaks and those that are not (Chapuis et al. 2009).Outbreaking populations do typically exhibit higher levels of gene flow which can homogenize long-term effective population size across a species (Chapuis et al. 2008(Chapuis et al. , 2009)).The degree to which this result would be similar for strict sibmating species is unclear.
Finally, the genus Calathus provides the best example of the compound effects of phenotype and ecological history on the tempo of karyotype evolution.First, many species in Calathus are wingless and thus may be characterized by populations composed of small demes where fixation of karyotype changes should be more likely.However, the exceptionally high rate estimate in this genus is likely driven by just two taxa in our dataset.Calathus abaxoides and C. ascendens, these species

The role of mutation
Little is known about mutation rate variation in beetles; however, we recently hypothesized that differences in the mechanisms of meiosis might provide a mutational basis for differences in the rate of sex chromosome turnover between the two main beetle suborders, Polyphaga and Adephaga (Blackmon and Demuth 2014).The present analysis demonstrates that the two suborders also have very different overall rates of chromosome evolution (note the difference in scales between the left and right vertical axes of Fig. 4) that are consistent with our findings on sex chromosome rates.It is noteworthy, however, that despite this difference in the "background" rate of karyotype evolution, the pattern where small N e is associated with relatively rapid karyotype evolution holds within both suborders.Thus, while mutation rate may be a major factor driving the baseline rate of karyotype evolution, our analysis suggests that within a given mutational context, most changes are at least mildly deleterious and become fixed by random genetic drift.

Comparison with previous work
While our findings accord with earlier studies relating N e to variation in chromosome number, our phylogenetic modelbased rate estimates are not correlated with time-scaled variance estimates derived similarly to previous work.This inconsistency is worth noting because the scarcity of reliable phylogenies limits analyses in other groups.The lack of consistency between approaches highlights the risk inherent in ignoring the pattern of chromosome evolution over the phylogeny.Theoretically, a scaled variance method could work.However, its accuracy will be limited by the extent to which the ages estimated for the groups are accurate and correlated with the total phylogenetic branch lengths relating to the focal taxa.These requirements are unlikely to be met, particularly in groups with relatively incomplete and highly heterogeneous fossil records, such as insects.Methods not using a phylogeny will also be misled when the number of records is insufficient to capture the true variance of the groups being studied.This sampling issue is less of a problem when phylogenetic methods are used because the observed phenotypic divergence is accounted for within the context of the divergence times among the sampled species.In contrast, without a phylogeny, variance among sampled clades must be assumed to be a true measure of variance for the focal clade.The variance in chromosome number across families of Coleoptera can be partly explained by the number of records available (Pearson's correlation coefficient between family variance and the number of records = 0.41, P-value = 0.008).This suggests that some families have not been sampled sufficiently to capture the true variance of extant species.Applying an evolutionary model for karyotype evolution using a time-scaled phylogeny eliminates these issues.

Conclusion
Our results, in concert with previous work, suggest that chromosome number evolution is primarily governed by random genetic drift in small populations and that mutations that change chromosome number are deleterious (at least while segregating).Despite this finding there are almost certainly many individual cases where selection has driven a change in the karyotype (Kitano et al. 2009;Blackmon et al. 2019).
However, the association we find between factors influencing N e and evolutionary rate also puts bounds on the selection coefficient of mutations that change chromosome number and go on to be fixed, suggesting that many changes are likely to be only mildly deleterious; otherwise, reduced N e due to ecological and phenotypic transitions in Coleoptera would not be sufficient to drive significant increases in the number of chromosome changes that are fixed by random genetic drift.More broadly, our work suggests that when species evolve traits or inhabit locations that restrict population size, the rate of change in chromosome number often increases by orders of magnitude relative to closely related species.Increasing the fixation rate of karyotype changes makes speciation mechanisms requiring genome rearrangements more likely.This should be true for models that assume underdominance of karyotype mutations, such as those described by White (1978), and more recent models that assume karyotype changes to be neutral such as those described by Rieseberg (2001).Traditionally, chromosomal rearrangements are thought to be more likely to contribute to speciation in plants than animals, possibly due to gene expression in pollen or lack of differentiated sex chromosomes in most plants (reviewed in Rieseberg 2001).Chromosomal speciation has also been suggested to be more likely in mammals than invertebrates due to differences in meiosis (Coyne and Orr 2004).However, given that our results suggest most karyotype changes in beetles are deleterious while segregating, models that invoke karyotypic changes acting directly as reproductive barriers seem more widely plausible than they have been considered recently.Unfortunately, the coarse nature of karyotype data limits our analysis to mutations such as fusions and fissions that change the number of chromosomes.Future work incorporating genomic data would be helpful to determine whether other types of mutations, such as inversions and translocations, also reflect a similar pattern.

Fig
Fig.1.Model for the evolution of chromosome number in wingless and winged clades.At an instance in time, a lineage will have i chromosomes and be in a wingless or winged state.A lineage can make three transitions in chromosome number: fusion (δ), fission (γ), whole-genome duplication (ρ), and if currently winged, can transition to wingless (q winged→wingless ).Rates of fusion, fission, and whole-genome duplication are allowed to differ between winged and wingless lineages.

Fig. 2 .
Fig. 2. Haploid chromosome counts in Coleoptera.Each row represents a family of beetles, and each column indicates a male haploid autosome count.The shading of each cell represents the number of records with a given count with colors on a log scale.

Fig. 3 .
Fig. 3. Differences in rates of chromosome evolution in winged and wingless Carabidae.In each plot, we show the distribution of the differences in rates of wingless minus winged clades.The credible interval for each statistic is shown below the distribution.A) simple model with just fissions and fusions B) complex model with fission, fusions, and whole-genome duplication.

Fig. 4 .
Fig. 4. Mean rates of chromosome evolution in Coleoptera clades.For each clade, we plot 10,000 samples from the posterior distribution of mean rate estimates from each generation of the MCMC.The mean of the posterior distribution is indicated with a black circle, and the credible interval is indicated with a vertical black line.Rates for Polyphaga are plotted on the scale to the left, while rates for Adephaga are plotted on the scale to the right; the dashed line separates those clades plotted against different axes.The color of points indicates N e class.

Table 1 .
Distribution of traits likely to impact effective population size.
Traits were scored based only on species included in the analysis, and the majority state is reported.Expected N e is categorized by the number of N eimpacting traits in a clade.High, medium, and low N e categories were assigned if a clade had zero, one, or two N e -reducing traits, respectively.A (+) indicates the high N e version of a trait, and a (−) indicates the low N e version of a trait.After each clade name, we include the number of species in the analysis.

Table 2 .
(Emerson et al. 1999etic and scaled variance-based estimates of the rate of chromosome evolution.CV/age.have the highest and lowest chromosome numbers in the genus.Interestingly, C. abaxoides and C. ascendens are both endemic, wingless, Calathus species on the Canary archipelago.Both species occur on the island of Tenerife, which the genus has colonized in the last 12 million yr(Emerson et al. 1999).These species likely experienced an initial population bottleneck during colonization, and the continued restriction to an island has led to a sustained lower N e than species with continental distributions.While 17 to 19 autosomes are common for most species in this genus, C. abaxoides has increased to 27 autosomes, while C. ascendens has decreased to 10 autosomes.The observation that both the lowest and highest chromosome number are the product of a single recently colonized island further suggests that drift in small populations is responsible for rapid karyotype evolution.
d Coefficient of variation.e Scaled SCV =