Sequence mismatch analysis (MMA) and Bayesian skyline plots (BSP) are commonly used to reconstruct historical demography. A survey of 173 research articles (2009–2014), which included estimates of historical population sizes from mtDNA or cpDNA, shows a widespread genetic signature of demographic or spatial population expansion in species of all major taxonomic groups. Associating these expansions with climatic events can provide insights into the origins of lineage diversity, range expansions (or contractions), and speciation. However, several variables can introduce error into reconstructions of demographic history, including levels of sequence polymorphism, sampling scheme, sample size, natural selection, and estimates of mutation rate. Most researchers use substitution rates estimated from divergences in phylogenetic trees dated with fossils, or geological events. Recent studies show that molecular clocks calibrated with phylogenetic divergences can overestimate the timings of population-level events by an order of magnitude. Overestimates disconnect historical population reconstructions from climatic history and confound our understanding of the factors influencing genetic variability. If mismatch distributions and BSPs largely reflect demographic history, the widespread signature of population expansion in vertebrate, invertebrate, and plant populations appears to reflect responses to postglacial climate warming.

Coupling population history with climate change is essential for constructing evolutionary and biogeographic scenarios that illuminate the mechanisms shaping species’ diversity. Coalescence theory is a powerful means of extracting historical information from DNA sequences, because the pattern of coalescences in a genealogy reflects historical population sizes (Kingman 1982a, 1982b; Hudson 1990). The genealogies of most species coalesce in the Pleistocene Epoch (2.58–0.01 million years ago), a period whose climatic history is known with some accuracy from analyses of ancient glacial ice (Lisiecki and Raymo 2007) and ocean sediments (Bond et al. 1993). These records of climatic variability and the molecular clock hypothesis are commonly used to place historical population events into a time frame to clarify the environmental mechanisms that influence genetic variability within and among species.

The goal of this review is to examine the factors that subvert accurate demographic reconstructions with DNA sequence mismatch analysis (MMA; Rogers and Harpending 1992) and Bayesian skyline plots (BSP; Drummond et al. 2005). These 2 methods are commonly used in studies of natural populations with organellar DNA, but other approaches are available for making additional inferences (Kuhner 2009; Nikolic and Chevalet 2014). These methods generally employ coalescence theory and require a molecular clock calibration with a mutation rate, which directly influences the dating of population events (Ho et al. 2011). Sample design and natural selection can also influence the outcomes of these analyses. This review builds on the pioneering work of Hewitt (1996, 1999, 2000, 2004) in the use of genetic markers to understand the effects of Pleistocene climate shifts on evolutionary processes.

Climatic Variability and Demography

Climates oscillate on time scales ranging from decades to hundreds of thousands of years. Decadal climate changes can lead to shifts in distributions and abundance (Villalba 1994; Alheit and Hagen 1997; Gill et al. 2009), and Milankovitch glacial cycles lead to population extinctions in the terrestrial and marine realms, especially at high latitudes (e.g., Hewitt 1996; Fauvelot et al. 2003; Staubwasser et al. 2003). During glacial periods, large high-latitude areas were covered with ice, and nearshore marine habitats globally were radically changed by drops of tens-of-meters in sea level (Miller et al. 2005; Ludt et al. 2012). A wealth of phylogeographic studies of high-latitude species has provided insights into how these glaciations influenced genetic diversity through population extinctions and recolonizations.

Climate cycles also influenced populations in low-latitude areas through changes in rainfall patterns that were correlated with glacial cycles (Kershaw et al. 2003; Fujioka et al. 2009; Williams et al. 2009). Unglaciated continental areas of Eurasia, Africa, and North and South America experienced alternating humid and dry periods (van der Hammen and Absy 1994; deMenocal 1995; Ijmker et al. 2012) that greatly influenced the ecologies, distributions, and abundances of vegetation and fauna in these areas (Thompson et al. 1989; deMenocal 2004; Williams et al. 2011; Holm and Svenning 2014). The impacts on Austral-Asian ecosystems, for example, were as large as those in North America (Hope et al. 2004). Together, these results indicate that the last glacial maximum (LGM) had an overwhelming influence on population abundances that was not limited to particular taxa or ecoregions.

Inferences of Historical Demography

Tests of Neutrality

In the absence of natural selection and migration, a stable population is expected to show an equilibrium between the loss of genetic variation through random drift and the accumulation of diversity through mutation. A test for equilibrium conditions provides a basis for testing for neutrality, which can be influenced by both population history and natural selection. Most tests of neutrality in biogeographic studies are interpreted in terms of historical shifts in effective population size (Ne), rather than in terms of selection. Tests of neutrality are commonly used to support inferences from MMAs and BSPs (Ramos-Onsins and Rozas 2002; Ramírez-Soriano et al. 2008). One group of statistics compares different estimates of the diploid mutation parameter θ = 2N2µ (Nf2µ for mtDNA) based on the site frequency distribution, including DT (Tajima 1989), D, F, D*, F* (Fu and Li 1993), H (Fay and Wu 2000), and R2 (Ramos-Onsins and Rozas 2002). Another group examines haplotype-frequency distributions, including FS (Fu 1997). The results of these tests are usually used to support a conclusion of a demographic or spatial population expansion, or to justify proceeding with a MMA (Rogers and Harpending 1992) or constructing a BSP to depict historical population sizes (Drummond et al. 2005).

Nucleotide Mismatch Distributions

The analysis of a mismatch distribution to infer population history stems from the observation that episodes of growth and decline impart signatures on nucleotide-site differences between pairs of individuals. Simulations show that demographic population expansions produce a unimodal distribution that moves to larger mismatch values over time as mutations accumulate in a population (Rogers and Harpending 1992). A population in equilibrium shows a “ragged” multimodal distribution as deep divergences accumulate between lineages. Generally, a smooth unimodal distribution is taken as evidence of a recent population growth, but tests to detect raggedness have little power (Ramos-Onsins and Rozas 2002). When tests for raggedness are not rejected, the crest of the unimodal distribution yields an estimate of τ in units of mutational time in generations. The time in generations since expansion (t) is calculated with

 
(1)
t= τ/2u

where u = mµ is the mutation rate of the entire segment of m base pairs. Effective population size for uniparental inherited sequences is estimated with θ = 2Nµ, where θ is the expected mean pairwise difference among a set of mtDNA or cpDNA sequences (Rogers and Harpending 1992; Rogers 1995). MMA was used in a majority of the articles surveyed, even though the analysis of pairwise differences is less accurate for estimating effective population sizes than the analysis of genealogies (Felsenstein 1992).

Bayesian Skyline Plots

MMA and neutrality tests fail to make full use of historical demographic signals imprinted in DNA genealogies. Hence, BSP analysis is widely used to reconstruct historical population sizes with information contained in haplotype genealogies. Coalescence theory predicts the expected time (t) between coalescences in a genealogy from effective population size (Ni) and the number of lineages (ni) at the beginning of the ith interval between a coalescence as:

 
(2)
E(ti) =Nt/[ni(ni1)2]

Effective population size in the ith period between coalescences can then be estimated with

 
(3)
Ni=tini(ni1)2

(Strimmer and Pybus 2001). This equation produces the “skyline” silhouette plots of historical population size. A generalized BSP was developed to address the uncertainties in a single reconstructed genealogy by Markov chain Monte Carlo (MCMC) re-sampling of the genealogy (Drummond et al. 2005; Kuhner 2009). BSPs can be estimated with BEAST (Drummond and Rambaut 2007), a program requiring long MCMC chains and considerable computing time with large datasets, because the number of genealogies in a sample rises exponentially with the number of sequences. Estimates of Ne, or Nef for female genealogies estimated with mtDNA, are smoothed and used to define a trajectory of historical demography, extending back in time to the most recent common ancestor for a set of sequences (coalescence). The curve is defined by time in units of µg and by female population size for mtDNA in units of Nµg, where µ is the per-site mutation rate and g is generation length.

Survey of the Literature

A literature search was conducted with Google Scholar with the key words Bayesian skyline plot, mismatch analysis, mismatch distribution, historical demography, and mitochondrial DNA, molecular clock calibration, and time-dependent mutation rate. Since not all articles reporting the results of MMA or BSP included these words in the title or key words, reference lists provided further links to pertinent articles. A total of 173 primary research articles, published between 2009 and early 2014, were identified that included MMA, BSPs, or both (Supplementary Tables S1S8 online). This period post-dates the proposal of the time-dependent mutation rate (Ho et al. 2005). The survey was limited to studies using organellar DNA, mtDNA in plants and animals, or cpDNA in plants. These genomes have been embraced by phylogeographers, because their uniparental inheritance and lack of recombination (except for plant mtDNA) make them amenable to reconstructing haplotype genealogies (although nuclear DNA sequences may also be used to infer historical demography; Fahey et al. 2014). Several items reported in the surveyed articles were tabulated, including tests of neutrality (DT, D*, F*, R2, FS) and variables influencing the outcomes of MMA and BSP analyses (Supplementary Table S9 online). Outcomes are affected by estimates of mutation rate for a particular gene, sample sizes of individuals and nucleotides, and pooling of genetically heterogeneous samples.

Nearly all studies reported departures from neutrality, based on neutrality statistics, the mismatch distribution, or the shape of a BSP. Figure 1 shows typical results for uniparentally inherited mtDNA or cpDNA in a variety of taxonomic groups including vertebrates, invertebrates, and plants. Most species showed complex haplotype networks, often containing star-shaped subnetworks. Most of the studies depicted unimodal mismatch distributions or BSPs that were generally interpreted to indicate a sudden population expansion, a pattern not limited to a particular taxon or geographical region. The expansion was inevitably preceded by a flat demographic curve, commonly interpreted as a long period of population stability (all of the studies in Figure 1). In most studies, MMA, BSPs, or both were used to estimate the timing and magnitude of the expansion.

Figure 1.

Examples of MMA, BSP, and parsimony analyses of organellar sequence variability in plants, invertebrates, and vertebrates.

Figure 1.

Examples of MMA, BSP, and parsimony analyses of organellar sequence variability in plants, invertebrates, and vertebrates.

A majority of the articles proposed demographic or spatial population expansions in a species, a subgroup, or a phylogroup that predated the LGM (18–20 ka) (Supplementary Table S10 online). Among taxonomic groups, 52.9–94.4% of the MMAs were interpreted to indicate an episode of population growth, often reported as a “sudden population expansion” that preceded the LGM. BSPs were interpreted to indicate episodes of pre-LGM in 20.5–100% of the various groups. Many expansions were placed before 500 kyr, and even as early as 6 million years (e.g., Silva et al. 2014), or more (Chiang et al. 2009). Estimates of the timings of expansions in the MMA tended to be further in the past than those in the BSP analyses for birds, reptiles, amphibians, and fishes (Figures 2 and 3).

Figure 2.

Distribution of estimates from mismatch analyses of population or phylogroup expansion times in various groups of organisms. Values from all the articles surveyed were included. Vertical dashed line indicates the timing of the LGM.

Figure 2.

Distribution of estimates from mismatch analyses of population or phylogroup expansion times in various groups of organisms. Values from all the articles surveyed were included. Vertical dashed line indicates the timing of the LGM.

Figure 3.

Distribution of estimates from BSP analyses of population or phylogroup expansion times in various groups of organisms. Values from all the articles surveyed were included. Vertical dashed line indicates the timing of the LGM.

Figure 3.

Distribution of estimates from BSP analyses of population or phylogroup expansion times in various groups of organisms. Values from all the articles surveyed were included. Vertical dashed line indicates the timing of the LGM.

Possible Sources of Error

Several errors can influence the accuracies of a historical reconstruction of a population and can lead to a spurious population model. Some inference “errors” are beyond the control of a researcher. For example, each gene has a unique genealogical history because of randomness in genetic transmission and mutational history, so that the analyses of different genes may lead to apparently different population histories (Rosenberg and Nordborg 2002). Replicate genealogies stemming from the same population model can differ considerably from one another and might lead to different historical scenarios (Figure 4). It is tempting to attach too much importance to a particular outcome when testing a biogeographic hypothesis. The inclusion of several gene sequences can account for this randomness among loci (Heled and Drummond 2008). As noted by Avise (2000), genealogical concordance is a foundation for robust conclusions. Beyond random genealogical descent, 4 factors interact to influence the ability to detect population expansions: migration rate between populations, magnitude of expansion, time since expansion, and sampling design (Städler et al. 2009; Chikhi et al. 2010; Peter et al. 2010; Heller et al. 2013).

Figure 4.

The results of replicate coalescence simulations of the same population model of a sudden population expansion of 3 orders of magnitude from N = 103 to N = 106 at 0.075 mutation units (µg) in the past. Sample size n = 50. (a) The underlying gene genealogy. (b) The genealogy as recovered with mutations. (c) BSPs of the haplotype tree. (d) Mismatch distribution (solid line) with the expected distribution under a model of population expansion.

Figure 4.

The results of replicate coalescence simulations of the same population model of a sudden population expansion of 3 orders of magnitude from N = 103 to N = 106 at 0.075 mutation units (µg) in the past. Sample size n = 50. (a) The underlying gene genealogy. (b) The genealogy as recovered with mutations. (c) BSPs of the haplotype tree. (d) Mismatch distribution (solid line) with the expected distribution under a model of population expansion.

Sampling of Polymorphisms

The sampling of genes with low levels of polymorphism can substantially impede the successful reconstruction of a population’s history. A larger number of site polymorphisms, inherent in longer DNA sequences, provides greater phylogeographic resolution among weakly differentiated populations. For example, complete mtDNA sequences resolved 5 major lineages in brown bears, while shorter sequences indicated only a star-shaped haplotype genealogy (Keis et al. 2013). In Atlantic cod, long mtDNA sequences demonstrated a more complex phylogeographic structure (Carr and Marshall 2008; Johansen et al. 2009) than the shallow structure depicted by shorter sequences (Árneson 2004).

A particularly serious flaw in sample design is the use of only unique haplotypes in an analysis (Kuhner 2009), an error that appears to have occurred in at least 2 studies reviewed here. An analysis based on only unique haplotypes greatly overestimates values of Ne and pushes an apparent population expansion back hundreds of thousands of years before it actually occurred. Both MMA and BSPs assume a random sample of haplotypes from a population.

Sampling Scheme

Three sampling schemes have been used to make demographic inferences, each providing different views of population history. Coalescence analysis assumes that a sample has been drawn from a panmictic population with a unique population history. However, since most natural populations are subdivided to some degree, the assumption of panmixia can lead to misleading results. Two schemes, the sampling of a local population and the pooling of population samples, are most commonly used. When populations are subdivided by low levels of gene flow, the analysis of local populations may not detect species-wide expansions. Simulations show that the analyses of nucleotide-site frequency distributions in local samples reveal species-wide events at only high levels of gene flow approaching panmixia (Städler et al. 2009). The pooling of samples may overcome this problem, under some conditions. A third scheme, scattered sampling, consists of sampling a few randomly selected individuals from populations throughout a species’ distribution. This scheme is sometimes used for practical reasons when individuals are scarce, or are difficult, or costly to sample (e.g., Mattoccia et al. 2011; Fernandes et al. 2012; Myers et al. 2013). However, simulations show that under some combinations of gene flow, population size and population history scattered sampling may improve inferences of population history.

The use of these 3 sampling schemes depends on the research question and on the level of population subdivision, population size, and metapopulation structure. Simulations show that under some circumstances, pooling samples may better reflect a species’ history (Städler et al. 2009), but not under others (Chikhi et al. 2010). The effect of pooling on BSPs is complex and depends on the site-frequency spectra in the pooled samples. Genealogies may coalesce rapidly in some subpopulations, but not in others, depending on the historical sizes of the populations (Städler et al. 2009) and on the history of population subdivision (Peter et al. 2010). The pooling of local samples, often to increase sample size, tends to increase the occurrence of low-frequency polymorphisms relative to local samples (Ptak and Przeworski 2002) and, hence, produces more negative values of neutrality statistics such as DT and D*. Alternatively, population subdivision obscures a species-wide expansion by the loss of low-frequency alleles in local populations, rather than creating an excess of low-frequency alleles in pooled samples (Arunyawat et al. 2007). In any case, pooled samples tend to show a greater number of departures from neutrality than unpooled samples and may produce misleading signals in BSPs.

Pooling of samples from genetically divergent populations can produce a polyphyletic genealogy (Wakeley 2001; Wakeley and Aliacar 2001), which leads to inaccurate historical reconstructions by producing steps in a BSP curve that have been interpreted as punctuated episodes of population growth. For example, Kitchen et al. (2008) proposed multiple stages of human dispersal across the Bering land bridge, based on a stepped BSP curve. However, Fagundes et al. (2008) found that the curve was spurious, because nonnative DNA sequences representing a different lineage had been included in the BSP reconstruction.

Inappropriate sampling schemes can lead to other misinterpretations. For example, simulations of Wright-Fisher populations in mutation and migration-drift equilibrium showed that population subdivision with gene flow produced a false population bottleneck signal with some sampling schemes (Chikhi et al. 2010; Heller et al. 2013). When gene flow is high, a group of populations may act as a single panmictic population. However, when populations are genetically isolated from one another, genealogies tend to coalesce within a population, and gene flow introduces divergent genotypes that produce genealogies typical of a bottlenecked population. Under these circumstances, scattered sampling over many populations may counter a false signal of a population bottleneck (Städler et al. 2009; Chikhi et al. 2010).

Sample Size

Sample sizes of individuals greatly affect the power to reconstruct historical demographies. Small sample sizes do not appear to diminish the usefulness of MMA to the extent they affect BSP analysis. A sample of only a few individuals is likely to detect deep partitions in a population (Felsenstein 2006) but is insufficient to detect the effects of recent population shifts imprinted in the outer branches of a haplotype tree. To demonstrate the effect of sample size on BSPs, a simulated population expanding 3 orders of magnitude from an effective size of N = 105 to N = 108 was analyzed with samples ranging from n = 12 to n = 400 (Figure 5; Supplementary Table S11 online). The parameters for these BSPs were based on mtDNA variability in North Pacific walleye pollock, a marine fish that experienced a post-LGM expansion of at least 3 orders of magnitude (Grant et al. 2010). These simulations show 2 underappreciated effects of sample size. First, BSPs based on a population sample of fewer than 50 individuals often fail to capture a population expansion when it has occurred. A flat BSP is generally interpreted to indicate population stability, but when sample sizes are small, a flat BSP may be due to a lack of power to detect an expansion. Second, sample sizes less than 100 individuals may not capture the full extent of a population expansion. Even sample sizes of 400 individuals recovered only 57%, on average, of the size of the expansion in these simulations.

Figure 5.

The relationship between sample size and estimates of initial (N0) and contemporary (N1) population size of a population experiencing a sudden expansion in size from N0 = 105 to N1 = 108 at 0.075 mutation units (µg) in the past. Closed circles represent the mean of 10 replicates, the dashed lines represent the initial and ending population sizes in the model, boxes represent 95% confidence intervals, and the vertical bars represent the range of values around a mean. Simulated sequences were based on summary statistics for walleye pollock (Grant et al. 2010) (see Supplementary Table S11 online for additional information).

Figure 5.

The relationship between sample size and estimates of initial (N0) and contemporary (N1) population size of a population experiencing a sudden expansion in size from N0 = 105 to N1 = 108 at 0.075 mutation units (µg) in the past. Closed circles represent the mean of 10 replicates, the dashed lines represent the initial and ending population sizes in the model, boxes represent 95% confidence intervals, and the vertical bars represent the range of values around a mean. Simulated sequences were based on summary statistics for walleye pollock (Grant et al. 2010) (see Supplementary Table S11 online for additional information).

The reason that small population samples fail to provide the power needed to detect a population expansion is apparent in the fundamental equation (Equation 3) used to generate the skyline plots. Small sample sizes capture mid-frequency polymorphisms, but not the extent of mutation diversity in a recently expanded population. Large samples elevate estimates of diversity by including more low-frequency and singleton haplotypes. However, when samples sizes approach or exceed the effective size of a population, an excess of singleton haplotypes from mutations in the previous generation may produce an incorrect demographic reconstruction (Wakeley and Takahashi 2003).

Sample sizes in the studies surveyed here generally fell well below 50 individuals and were frequently as small as 15–20 individuals. Sample sizes of subgroups or lineages used to estimate mismatch distributions, or to construct BSPs, were often not reported in the surveyed literature, or were buried in Supplementary Material online. The reporting of sample size is an important prerequisite for readers to evaluate the accuracies of historical reconstructions. Small sample sizes may explain some of the flat, or shallow, BSP curves reported in the literature.

Deep Coalescences

How should complex datasets encompassing deep coalescences be analyzed? In populations with long, stable histories, progressively deeper coalescences are expected to appear and lead to equilibrium conditions typical of neutrality (Rogers and Harpending 1992). In many species, the imprint of a recent population expansion is superimposed on a genealogy with deep partitions. In MMA, the accumulation of lineages tends to push the crest of a mismatch distribution to the right, distorting the timing of a recent population expansion. This may account for the generally earlier population expansions estimated with MMA, than with BSPs, for the same dataset. Recent expansions in a BSP are not affected by deep coalescences, because a population expansion leads to an abundance of branches in the upper part of a genealogical tree. Deeper coalescences do not confound recent estimates of population size in a BSP.

Deep coalescences can appear in a population for 2 reasons. In a large population with a long stable demographic history, divergent lineages can appear because of lineage sorting (Ballard and Whitlock 2004). Alternatively, deep coalescences can appear in a population because of mixing between differentiated populations. In terrestrial species, genetic lineages are usually geographically isolated, so that a sample includes shallow diversity from only one lineage. In high gene flow marine species, however, divergent lineages can appear in a population because of the mixing of lineages with allopatric origins and unique histories.

In some studies, divergent lineages have been analyzed separately by pooling individuals in a lineage, regardless of sample origins, into a single sample (Ravago-Gotanco and Juinio-Meñez 2010; Peng and Zhang 2011; Borrell et al. 2012; Han et al. 2012). However, this procedure likely violates the assumption of panmixia. The analysis of sublineages in a genealogy might be justified to reconstruct the separate histories of lineages arising in allopatry. For example, Saillard et al. (2000) limited inferences of Eskimo population history to star-shaped subgroups, because the analysis of several star-like subgroups together would have produced a temporal estimate of colonization and population expansion that was not consistent with archeological dating of migration. In any case, the analysis of sequence datasets with deep coalescences can be problematic and requires some thought in formulating a statistical design.

Overinterpretation of Skyline Plots

The shape of a BSP is often interpreted to reflect subtleties of population history. For example, a small up- or downturn in the BSP curve near the present is sometimes interpreted to indicate a very recent shift in population size. However, small shifts often appear in BSPs of simulated populations that did not experience a sudden recent change in size (Grant WS, unpublished). These shifts in both empirical and simulated BSPs usually do not exceed the 95% credibility interval and appear to reflect random sampling of the MCMC haplotype trees. Hence, they cannot be interpreted to reflect changes in population size.

A nearly universal feature of the BSPs examined here was a flat curve preceding an upward deflection toward the present (Figure 1). This flat portion of the BSP was often interpreted to indicate a long period of population stasis before conducive conditions prompted a population expansion. The supposed period of population stability usually reached back to the deepest coalescence. Simulations, however, indicate that this interpretation is misleading. To test whether genetic imprints of pre-LGM population changes were present in contemporary datasets, Grant and Cheng (2012) and Grant et al. (2012) simulated DNA sequences generated with historical population sizes that followed the large global temperature swings over the last 4 glacial cycles, reaching back 350–450 k years. These sequences produced BSPs showing a single post-LGM population expansion, indicating that the contemporary sequences do not bear imprints of ancient population history. Population contractions during each global glacial maximum promote extinctions of haplotype lineages (the ns in Equation 3) and, hence, information about earlier population history is lost. This loss of genetic information does not necessarily imply strong population bottlenecks. Most species consist of populations that experience local extinctions and colonizations, so that even though total census numbers may remain large, the genetic signal can be lost because of metapopulation dynamics (Pannell 2003).

Natural Selection

Molecular markers used in phylogeographic and historical reconstructions are assumed to be largely “neutral” to the effects of selection, so that patterns detected with mismatch distributions and BSPs are interpreted in terms of genetic drift and migration. Even though the effects of natural selection on a molecular marker can invalidate neutral interpretations, they are generally dismissed by phylogeographers, in part, because attributing particular genetic patterns to one of the many forms of selection is a daunting task (Karl et al. 2012).

Natural selection can produce site- or haplotype-frequency distributions that resemble frequency distributions in an expanding population. Harmful mutations are generally rapidly eliminated by purifying selection and are unlikely to be seen in a sample. However, slightly deleterious mutations are eliminated more slowly by background selection, which prevents low-frequency mutations from moving to higher frequencies (Charlesworth et al. 1993). Site-frequency distributions shaped by selection are difficult to distinguish from distributions produced by a population expansion, especially if the 2 operate on similar time scales.

Comparisons of neutrality statistics may help to distinguish the effects of history demography from background selection, as D*, which is based on the distributions of singletons, is more sensitive to background selection than DT or FS (Fu and Li 1993). Using this approach, Crandall et al. (2012) concluded that the unimodal mismatch distributions and L-shaped BSPs were due to postglacial spatial expansions on the recently submerged Sunda Shelf and not to selection. However, tests of site- or haplotype-frequency distributions do not take into account the underlying genealogy.

Branching patterns in molecular genealogies reconstructed without enforcing contemporary tips may also help to detect background selection. Slightly deleterious mutations appearing as low-frequency, or singleton, mutations should be scattered in a genealogy with new mutations at the tips of the genealogy and older, less frequent mutations occurring on short branches buried in the genealogy. Selection prevents older, slightly deleterious mutations from becoming progenitors of new lineages.

Genetic hitchhiking (Maynard-Smith and Haigh 1974; Charlesworth 2012) of polymorphisms linked to a gene under positive selection may also produce a site-frequency distribution resembling a population expansion (Fu 1997). Both genetic hitchhiking and population expansions potentially produce high-frequency haplotypes with recent neutral and slightly deleterious mutations emanating from them, producing a star-shaped genealogy. Ballard and Whitlock (2004) discussed the occurrence of selective sweeps in animals, and, although they found a few clear examples, they concluded that sweeps were not common (see Karl et al. 2012 for further discussion). Even though positive selection can skew site-frequency distributions from neutrality, it is unlikely to be responsible for the prevalence of unimodal mismatch distributions and L-shaped BSPs. Adaptive mutations are unlikely to appear simultaneously among species.

Even though numerous studies show that sequences in natural populations persistently depart from neutrality (Hahn 2008; Wares 2010), neutral models are attractive to phylogeographers, because they are easy to parameterize and provide clear null hypotheses. However, the continued use of neutral theory to formulate expectations without considering the effects of selection may retard progress in understanding evolutionary processes. Unfortunately, incorporating selection into an analysis is difficult because no single model can explain all forms of selection. None of the articles reviewed here invoked selection to solely explain departures from neutrality, and only a few considered selection at all. While nuclear genes under selection can be identified by nucleotide and amino acid substitution patterns (McDonald and Kreitman 1991), or as outliers in genomic scans (Foll and Gaggiotti 2008; Lamichhaney et al. 2012; Limborg et al. 2012), these approaches are limited for mtDNA because of linkage between genes.

Mutation Rate Estimation

Choosing a mutation rate to place a historical reconstruction of a population into a timeframe is perhaps the greatest source of error in MMA and BSP inferences. Molecular clock rates can be estimated in several ways, including the dating of nodes in a phylogeny with geological events or fossils, the analysis of ancient DNA (aDNA) in dated samples, or the appearance of mutations in a pedigree. Methods for estimating a mutation rate for a particular set of sequences are not always straightforward for nonmodel species, and appropriate estimates of mutation rates for population analyses have been much debated (Ho et al. 2005; Emerson 2007; Ho et al. 2011; Emerson and Hickerson 2015).

The most common method of calibration is based on a dateable geological event. A widely used approach estimates substitution rates from divergences of sister taxa separated by the formation of a barrier, such as an isthmus between land masses that severed gene flow between ancestral populations of marine organisms, or a strait or an island that severed gene flow between terrestrial populations. The survey indicated that mutation rate (µ) was most often estimated from divergences between sister taxa, most often a sister species, but, in a few cases, a higher level group (e.g., rat-mouse split, Macholán et al. 2012) with the equation

 
(4)
µ unit-time1=dunit-time1/2,

where d is a measure of sequence divergence. Sometimes, µ is mistakenly derived from d without accounting for the accumulation of mutations along both lineages. The choice of a particular measure of divergence (corrected or uncorrected for multiple mutations) substantially influences estimates of d.

The survey of the literature indicated that the time since divergence began between 2 taxa was generally estimated by the formation of a geographical barrier to dispersal separating the taxa (Table 1). Many authors used the date of the final closure the Isthmus of Panama about 3.1–3.5 myr (Knowlton and Weigt 1998; Lessios 2008) to mark divergences between Pacific and Atlantic marine sister species, but also for North and South American terrestrial species (Stehli and Webb 1985). The gradual formation of this and other geological barriers to dispersal introduces uncertainty into estimates of divergence and, hence, into mutation-rate estimates. For example, the connections between ancestral tropical populations of deepwater organisms across the Isthmus of Panama may have been severed before the connections between shallow-water organisms were cut (Marko 2002). Additionally, dates of geologic events estimated by ocean sedimentology and isotope decay have uncertainties on the order of hundreds to thousands of years, depending on the time scale of interest (Martinson et al. 1987; Taylor 1997).

Table 1.

Methods for estimating substitution and mutation rates

Method Comment Examples 
Geology: Calibration of substitution rate by dating nodes in phylogenetic tree with dated geological events Stable isotope and stratigraphic dates have been published for many geological events that lead to the isolation and genetic divergence between ancestral populations of present-day species. Estimates of molecular divergence between sister taxa have been used most often to provide estimates of substitution rates. Isthmus of Panama: The appearance of this narrow land mass about 2.8 myr ago divided ancestral Atlantic and Pacific populations of tropical marine organisms (Knowlton and Weigt 1998; Marko 2002) and provided a corridor for the dispersal of North American terrestrial species into South America (Stehli and Webb 1985). 
Sardinia-Corsica: Ketmaier et al. 2003; Mattoccia et al. 2011  
Strait of Gibraltar: Marino et al. 2011; Dong et al. 2012; Yu et al. 2013  
Aegean Sea: Beerli et al. 1996; Papadopoulou et al. 2010  
Volcanic island: Croucher et al. 2012; Mello and Schrago 2012  
Japan Archipelago land bridges: Hope et al. 2010  
Fossils: Calibration of nodes in phylogenetic tree with the first appearance of a taxon in the fossil record The first appearance of a taxon in the fossil record establishes the latest date for the origin of the taxon. These anchor points in phylogeny may underestimate the timing of a node. These calibrations have been based on fossils tens of millions of years old. Insects: Gaunt and Miles 2002; Resende et al. 2010  
Reptiles: Shepard and Burbrink 2009; Lu et al. 2012; Myers et al. 2013  
Mammals: Chavez and Kenagy 2010  
Archeology: Estimate mutation rates by aligning expansions with archeological evidence of introduction As with fossils, these alignments may underestimate the timing of a demographic event but are likely to provide better mutation-rate estimates than more ancient fossil dates. Archeological evidence associated with humans usually extends to 10–15 kyr. Mammals: Förster et al. 2009  
Climate history: Estimate mutation rates by tying MMA or BSP estimates of population size to a climatic event Estimate mutation rate in newly colonized populations in previously glaciated areas. For cold- adapted species, a peak in population size can be anchored to the LGM (~18–21 kyr). A lag in the in the response to a climate shift may produce an underestimation of mutation rates. Insects: Schoville and Roderick 2009; Todisco et al. 2012  
Birds: Gratton et al. 2008  
Fishes: Grant et al. 2012  
Mammals: Galbreath et al. 2009; Luly et al. 2010  
Sea level history: Dated appearance of barriers to dispersal Estimate mutation rates from divergences initiated by dispersal barriers formed by lower sea levels. For example, lower sea levels across Torres Strait. Marine mammal: Blair et al. 2014  
Postglacial marine flooding: Estimate mutation rates in marine populations inhabiting areas previously drained by lower sea levels during the LGM As with the use of recently unglaciated areas, postglacial marine flooding after post-LGM sea level rise provides the maximum age of a population expansion. Organisms inhabiting flooded areas may be part of broader populations. Marine invertebrates: Crandall et al. 2012  
Population size: Match estimates of contemporary population size and generation time with Nf estimated by BSP analysis The estimate of Nf in a BSP is an evolutionary value integrated over long periods of time and may not realistically reflect contemporary NfBirds: Horreo et al. 2013  
Transferring rates from one locus to another: The ratio of divergences between samples for a locus is used to adjust the mutation rate for an uncalibrated locus Mutation rates for a particular study still depend on the validity of the mutation rate of the reference gene. Generally rates are very similar between genes used for this kind of adjustment and do not influence results to a great extent. Birds: Song et al. 2009; Qu et al. 2011  
aDNA: Estimate mutation rates in serial samples of aDNA Provides estimate of mutation rate for recent demographic events. These estimates tend to be much larger—often an order of magnitude larger—than phylogenetically derived mutation- rate estimates. Mammals: de Bruyn et al. 2009; Prost et al. 2010; Rosvold et al. 2012  
Pedigree analysis: Estimate mutation rates with molecular pedigrees over several generations  Humans: Howell et al. 2003; Santos et al. 2005  
Method Comment Examples 
Geology: Calibration of substitution rate by dating nodes in phylogenetic tree with dated geological events Stable isotope and stratigraphic dates have been published for many geological events that lead to the isolation and genetic divergence between ancestral populations of present-day species. Estimates of molecular divergence between sister taxa have been used most often to provide estimates of substitution rates. Isthmus of Panama: The appearance of this narrow land mass about 2.8 myr ago divided ancestral Atlantic and Pacific populations of tropical marine organisms (Knowlton and Weigt 1998; Marko 2002) and provided a corridor for the dispersal of North American terrestrial species into South America (Stehli and Webb 1985). 
Sardinia-Corsica: Ketmaier et al. 2003; Mattoccia et al. 2011  
Strait of Gibraltar: Marino et al. 2011; Dong et al. 2012; Yu et al. 2013  
Aegean Sea: Beerli et al. 1996; Papadopoulou et al. 2010  
Volcanic island: Croucher et al. 2012; Mello and Schrago 2012  
Japan Archipelago land bridges: Hope et al. 2010  
Fossils: Calibration of nodes in phylogenetic tree with the first appearance of a taxon in the fossil record The first appearance of a taxon in the fossil record establishes the latest date for the origin of the taxon. These anchor points in phylogeny may underestimate the timing of a node. These calibrations have been based on fossils tens of millions of years old. Insects: Gaunt and Miles 2002; Resende et al. 2010  
Reptiles: Shepard and Burbrink 2009; Lu et al. 2012; Myers et al. 2013  
Mammals: Chavez and Kenagy 2010  
Archeology: Estimate mutation rates by aligning expansions with archeological evidence of introduction As with fossils, these alignments may underestimate the timing of a demographic event but are likely to provide better mutation-rate estimates than more ancient fossil dates. Archeological evidence associated with humans usually extends to 10–15 kyr. Mammals: Förster et al. 2009  
Climate history: Estimate mutation rates by tying MMA or BSP estimates of population size to a climatic event Estimate mutation rate in newly colonized populations in previously glaciated areas. For cold- adapted species, a peak in population size can be anchored to the LGM (~18–21 kyr). A lag in the in the response to a climate shift may produce an underestimation of mutation rates. Insects: Schoville and Roderick 2009; Todisco et al. 2012  
Birds: Gratton et al. 2008  
Fishes: Grant et al. 2012  
Mammals: Galbreath et al. 2009; Luly et al. 2010  
Sea level history: Dated appearance of barriers to dispersal Estimate mutation rates from divergences initiated by dispersal barriers formed by lower sea levels. For example, lower sea levels across Torres Strait. Marine mammal: Blair et al. 2014  
Postglacial marine flooding: Estimate mutation rates in marine populations inhabiting areas previously drained by lower sea levels during the LGM As with the use of recently unglaciated areas, postglacial marine flooding after post-LGM sea level rise provides the maximum age of a population expansion. Organisms inhabiting flooded areas may be part of broader populations. Marine invertebrates: Crandall et al. 2012  
Population size: Match estimates of contemporary population size and generation time with Nf estimated by BSP analysis The estimate of Nf in a BSP is an evolutionary value integrated over long periods of time and may not realistically reflect contemporary NfBirds: Horreo et al. 2013  
Transferring rates from one locus to another: The ratio of divergences between samples for a locus is used to adjust the mutation rate for an uncalibrated locus Mutation rates for a particular study still depend on the validity of the mutation rate of the reference gene. Generally rates are very similar between genes used for this kind of adjustment and do not influence results to a great extent. Birds: Song et al. 2009; Qu et al. 2011  
aDNA: Estimate mutation rates in serial samples of aDNA Provides estimate of mutation rate for recent demographic events. These estimates tend to be much larger—often an order of magnitude larger—than phylogenetically derived mutation- rate estimates. Mammals: de Bruyn et al. 2009; Prost et al. 2010; Rosvold et al. 2012  
Pedigree analysis: Estimate mutation rates with molecular pedigrees over several generations  Humans: Howell et al. 2003; Santos et al. 2005  

Other calibration points were used for terrestrial species, including the separation of Europe from Africa across the Strait of Gibraltar (Marino et al. 2011; Dong et al. 2012; Yu et al. 2013), the separation of Sardinia from Corsica in the Mediterranean (Ketmaier et al. 2003), the appearance of the Aegean Sea (Beerli et al. 1996; Papadopoulou et al. 2010), and the appearance of volcanic islands (Hope et al. 2010; Croucher et al. 2012; Mello and Schrago 2012). Earlier geological events, such as the Mesozoic separation of Europe and Africa from the Americas, may have driven divergences between high-level taxa, but they are too ancient to estimate mutation rates from between-species divergences.

Several other approaches have been used to calibrate taxon-specific molecular clocks. Some calibrations were based on fossils that constrained the dates of nodes in a phylogenetic tree (Gaunt and Miles 2002; Shepard and Burbrink 2009; Chavez and Kenagy 2010; Resende et al. 2010; Lu et al. 2012; Myers et al. 2013). In the absence of geological or fossil calibrations, other approaches were used to calibrate a molecular clock, including dated archeological artifacts (Förster et al. 2009), climate history (Galbreath et al. 2009; Schoville and Roderick 2009; among others), appearance of postglacial marine habitats in southeast Asia (Crandall et al. 2012), separation across the Torres Strait by lower sea level (Blair et al. 2014), and match of contemporary population size and generation time (Horreo et al. 2013). The use of shifts in climate to calibrate a molecular clock assumes a close relationship between temperature, or other environmental variable, and population size. However, not all species were influenced by the same events in the same way (e.g., Shapiro et al. 2004; Galbreath et al. 2009; Prost et al. 2010).

Serial samples of aDNA have also been used (de Bruyn et al. 2009; Korsten et al. 2009; Prost et al. 2010; Rosvold et al. 2012). However, the use of aDNA to estimate µ may show an upward bias, because aDNA usually consists of short sequences targeted for their polymorphisms (Debruyne and Poinar 2009), may contain errors due to DNA degradation (Stiller et al. 2006), or may violate model assumptions (Navascués and Emerson 2009). Nevertheless, aDNA provides an alternative opportunity to estimate time-dependent mutation rates and can provide reasonably accurate estimates when the temporal spread of samples is large (Ho et al. 2007a; Molak et al. 2013).

Contemporary mutation rates have been estimated with the appearance of variants in pedigrees (Howell et al. 2003). In contrast to phylogenetic calibrations on scales of millions of years, these analyses provide molecular clock calibrations on time scales of generations to, at most, hundreds of years. Pedigree clock rates tend to be much faster than those derived from phylogenetic trees (e.g., Sigurğardóttir et al. 2000; Howell et al. 2003) and lend support to the time-dependent hypothesis. However, pedigree mutation rates for the control region in a human population were at the upper end of estimates from phylogenetic analysis after corrections for gender and the probability of fixation in individuals (Santos et al. 2005).

In some studies, molecular clock calibrations were made with mutation rates estimated for phylogenetically related or ecologically similar taxa (Bilgin et al. 2009; Galbreath et al. 2009), or for other genes in the same species (Song et al. 2009; Qu et al. 2011). When mutation rates were transferred from one gene to another, relative levels of polymorphism in the 2 genes were used to adjust the mutation rate of the target by assuming that higher levels of polymorphism indicated higher rates of mutation. However, this practice reduces the apparent variance in coalescence among genes and may lead to bias or overconfidence in the conclusions. For many species, none of these calibration methods are available, and authors often resort to the use of a “universal” mutation rate, which, for mtDNA protein encoding genes, is judged to be higher in vertebrates (Brown et al. 1979; Avise 2000) than in plants (Wolfe et al. 1987).

Patterns of Mutation Among Tissues and Genes

Various classes of genes expressed in different tissues appear to evolve at different rates. In mammals, frequently translated genes expressed in a wide range of tissues tend to evolve more slowly at nonsynonymous nucleotide sites than genes expressed during development or in a limited number of tissues (Duret and Mouchiroud 2000; Zhang and Li 2004). The slower accumulation of mutations in frequently translated genes is likely due to the greater intensity of selection on translated products. Differences among studies could therefore arise because of the sampling of different tissues. For example, Santos et al. (2005) found that almost half of the point mutations found in a human pedigree were in somatic tissues. However, there is no apparent relationship between gene expression patterns among tissues and the pattern of substitution at synonymous sites (Duret and Mouchiroud 2000). These results indicate that singleton mutations in a genealogy can arise in the current generation, but are not inherited.

Even various segments of mtDNA and cpDNA show different levels of variability, likely reflecting selective constraints. For example, the control region of mtDNA is well known to evolve more rapidly than protein coding genes, or tRNAs. Hence, the larger mutation rate of the control region provides a small window into the past, making the control region the sequence of choice for resolving recent demographic events for most species. Mutation rates among coding genes can also differ, so that inaccuracies can be introduced by the use of a “universal” mutation rate, or the use of a mutation rate estimated for one locus for another locus. Mutation rate greatly influences the placement of a reconstructed historical demography into a temporal framework, but does not affect the shape of a mismatch distribution, or BSP.

“Time-Dependent” Mutation Rates

Among the research articles surveyed, mutation rates were most often estimated by substitution rates derived from molecular divergences between related taxa. Under the theory of neutral molecular evolution, the substitution rate in a lineage is expected to equal the mutation rate (Kimura 1983). Hence, a phylogenetic substitution rate should provide an accurate estimate of mutation rate, but only in the absence of selection and changes in population size. However, recent mutation rates appear to be larger, often much larger, than substitution rates (Ho et al. 2005, 2007b, 2008, 2011), and this departure from expectations greatly affects the calibration of a molecular clock for historical reconstructions.

Several mechanisms may account for this departure from neutrality, including natural selection (Ho et al. 2007b), temporal shifts in population size, ancestral population structure (Miller et al. 2009), and ancestral polymorphisms (Peterson and Masel 2009; Charlesworth 2010). Natural selection and shifts in population size can hasten or retard the fixation of an allele by countering, or accelerating, drift. The presence of ancestral alleles in a taxon can also lead to an apparent elevation of recent mutation rates, so that estimates of mutation rates from recently diverged species may be greater than those between ancient species (Charlesworth 2010). These factors produce “time-dependent” mutation rates that decline exponentially to reach substitution rates estimated from divergences dating to about 106 years (Ho et al. 2005; Crandall et al. 2012). Apparent mutation rates change rapidly, making it difficult to accurately estimate time-dependent mutation rates at particular times during this transition. Nevertheless, a consideration of time-dependent-rate concept is most important for placing historical reconstructions on a time scale.

Pre-LGM Population Expansions

Over half of the spatial or demographic population expansions inferred with MMA and BSPs in the surveyed articles were estimated to have occurred during or before the LGM. Most of these estimates were taken at face value by authors without considering the potential effects of subsequent climate shifts on the genetic imprints of an earlier population expansion. Some researchers argued that high-latitude glaciations and climate shifts did not influence populations in some low-latitude regions. While low-latitude regions were not directly affected by glaciations, drops in temperature, and shifts in rainfall greatly influenced low-latitude habitats and the associated faunas and floras. Glacial maxima generally led to substantial reductions in rainfall in tropical area of Austral-Asia (Hope et al. 2004; Williams et al. 2009), Africa (Anhuf et al. 2006; Tierney et al. 2008), and South America (Anhuf et al. 2006). For example, high rainfall forests were reduced during the LGM by 84% in Africa and by 54% in Amazonia from their present-day extents (Anhuf et al. 2006). Species behaving counter to expected climate trends have been identified, but examples are limited to high-latitude, high-altitude, cold-adapted small mammals that flourish during periods of cooling when snow cover is extensive (Galbreath et al. 2009; Hope et al. 2010; Prost et al. 2010).

Conclusions

Climate variability has an overwhelming influence on population abundance, directly by physical environmental influences, such as temperature, and indirectly by biological interactions, such as the abundances of prey and predators. Shifts in population abundances driven by climate variability in the Pleistocene and Holocene have sculpted patterns of genetic diversity within and among species. The challenge to biologists is to elucidate evolutionary mechanisms through the analysis of DNA polymorphisms. However, pitfalls at every step of this analysis await phylogeographers and can produce erroneous biogeographic conclusions that are often repeated in the literature.

The sampling of polymorphisms, numbers of populations, and numbers of individuals strongly influences the outcome of a study. Molecular markers with low levels of polymorphism are unable to resolve recent phylogeographic events, because of a mismatch in the time scales of population events and mutation rates. Geographic sampling strategies can also influence the outcome of a study, depending on the levels of gene flow between populations and the geographic extend of the sampling. When gene flow is limited, the sampling of local populations may not provide insights into species-wide events. Beyond geographical sampling schemes, sample sizes also control the power of a study to reconstruct historical population demographies. The use of small sample sizes has likely led to widespread underestimates of the magnitude of population expansions in many species, or to the conclusion of long-term population stability. Samples are often pooled, especially when specimens are difficult or costly to collect, or when “scattered” sampling is an intentional survey strategy. Samples are also often pooled within a lineage for analysis to reconstruct the evolutionary history of the lineage. Pooling, however, can alter the site- or haplotype-frequency spectrum, especially when samples are genetically heterogeneous, and produce genetic reconstructions that are disconnected with climate history.

Other potential challenges in the use of MMA and BSPs to reconstruct historical demographies include the presence of deep coalescences in a species. The origins of large divergences between lineages are not always apparent but are important for experimental design and interpretation of the results. Another persistent pitfall in the MCMC sampling of genealogies to reconstruct historical population sizes is the overinterpretation of BSP curves. BSPs generally have large, credible intervals around point estimates of historical population size so that small shifts in population size are unlikely to be meaningful. Another common overinterpretation is that the commonly observed flat curve preceding a population expansion depicts population stability. In fact, this flat portion of the curve reflects the loss of information during population fluctuations.

MMA and BSPs are used chiefly to estimate historical population parameters by assuming that the molecular markers used in a study are not influenced by natural selection. However, background selection and genetic hitchhiking of genes linked to a gene under positive selection can produce site- and allele-frequency spectra that resemble those produced by rapid population expansions. The extent to which selection shapes genetic diversity is a topic currently being addressed by breakthroughs in genomic sequencing and statistical analyses designed to detect loci under selection.

A persistent problem is the estimation of mutation rates to calibrate the molecular clocks used to date historical population events. A common practice for estimating mutation rates is to use substitution rates derived from divergences between species, which often occurred a few million years ago in the early Pleistocene, Pliocene, or late Miocene. If the widespread signal of population expansion in MMAs and BSPs of especially high-latitude species is due to a postglacial warming, then phylogenetic estimates of mutation can greatly overestimate the timings of population events. In some studies, putative demographic or spatial population expansions were postulated to have occurred during or prior to the LGM and likely reflect poor choices of a mutation rate to set a molecular clock. However, climate cycles may not influence populations in the same way. Local populations of some high-latitude species may thrive during periods of cooling and decline during warm periods because of ecological and biotic interactions. The widespread signal of a sudden population expansion among terrestrial and marine species, when calibrated with a time-dependent mutation rate, most likely reflects post-LGM population growth following the availability of new habitat space.

Supplementary Material

Supplementary material can be found at http://www.jhered.oxfordjournals.org/.

Acknowledgments

F. Allendorf, Y. Borrell, B. Bowen, E. Crandall, S. Francisco M. Grant, H. Laakkonen, S. Karl, E. Myers, J. Robalo, B. Templin, and J. Viñas provided comments on a draft of the manuscript that improved ideas and presentation. My acknowledgement of their contributions does not necessarily imply agreement with the final conclusions. I thank the review editor Fred Allendorf for the opportunity to expound on an important topic and 2 reviewers for insightful comments. I also thank B. Templin for encouraging me to write this review. This is Professional Publication number PP-of the Commercial Fisheries Division of the Alaska Department of Fish and Game, Anchorage Alaska.

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Author notes

Corresponding Editor: Fred Allendorf