Data collection

DNA samples of 200 individuals participating in the 1000 Genomes Project [68] were acquired from Coriell Cell Laboratories (Camden, NJ). Individuals belonged to eight 1000 Genomes Project populations: 25 CEPH/Utah (CEU), 27 Han Chinese in Beijing, China (CHB), 30 Finnish in Finland (FIN), 25 Gujarati Indian in Houston, TX (GIH), 25 Luhya in Webuye, Kenya (LWK), 18 Mexican ancestry in Los Angeles (MXL), 25 Toscani in Italy (TSI), and 25 Yoruba in Ibadan, Nigeria (YRI). Of these populations, two are native African (LWK, YRI), two are native European (FIN, TSI), and one is native Asian (CHB). The remaining three populations consisted of dispersed individuals whose ancestry is European (CEU), Asian (GIH), and an admixture of European and Native American (MXL).

Genotypes of 146 microsatellite loci were determined for all 200 individuals at Prevention Genetics (Marshfield, WI) using fluorescent fragment-length analysis. Sanger sequencing was used to corroborate the genotypes of individuals at ten randomly chosen loci. In all cases, sequences agreed with the genotype calls derived from fragment-length analysis. None of the sequenced microsatellites at these loci harbored point or indel imperfections to the microsatellite sequences. Two of the 146 loci harbored point imperfections in the human genome reference sequence.

Genotyped loci comprised mostly dinucleotide and trinucleotide repeats, although several mononucleotide, tetranucleotide, and pentanucleotide loci were included. Loci were further classified as: (1) potentially targeted by natural selection, (2) intergenic, or (3) closely linked to known targets of selection on SNPs. We chose members of the first category based on information in the literature and genomic databases, including potential for mutation to affect protein sequence as well as functional and suggestive evidence of regulatory activity [39, 69, 70]. Microsatellites that were not chosen based on findings in the literature were instead chosen based on the inherent hazard their mutation presents (e.g., coding dinucleotides) or their proximity to indicators of gene regulatory activity such as DNAseI hypersensitivity marks and putative cis-regulatory elements. We also included four trinucleotide loci previously identified as having anomalously low variance for their allele size in the human genome (Jim Weber, personal communication). Finally, we included loci implicated in trinucleotide repeat disorders. Although sampled variation at these loci was largely non-pathogenic, we were interested in testing whether non-pathogenic distributions are shaped by selection. Intergenic loci were restricted to microsatellites >250kbp away from the closest RefSeq gene based on RefSeq Release 47 released immediately prior to genotyping. Although our results suggest otherwise in several cases (see Results), we chose these loci assuming they had a greater chance of evolving neutrally and therefore providing points of comparison to loci we suspected might be targeted by selection. In this manuscript, we report results for loci suspected to be targeted by selection as well as putatively neutral, intergenic loci. Results for loci linked to known targets of selection will be reported elsewhere.

Conversion of fragment-length genotypes (in base pairs) to repeat-length genotypes was made possible by comparing fragment-length genotypes to previously predicted genotype calls (in repeat-length) for 1000 Genomes individuals using LOBSTR [71,72]. Although LOBSTR-based calls of the very same loci as we genotyped allowed the desired conversion, it also revealed that publicly available microsatellite genotype data [72] are enriched for false identification of heterozygotes as homozygotes. This issue is likely due to the difficulties associated with calling microsatellites based on short-read DNA sequence data, particularly the tendency of next-generation sequencing technologies to miss evidence of the second allele in a heterozygote [73] (S1 Text provides an illustrative example).

Evolutionary modeling

Simulation models of molecular evolution capture necessary details of the evolutionary process by including parameters related to mutation, migration, neutral/non-neutral evolution, etc. When simulations of the model are run, parameter values are drawn from prior distributions. We used uniform priors whose minimum and maximum represent the bounds of reasonable values a parameter can take (see subsection Natural Selection below).

Approximate Bayesian computation (ABC) methods require a large pool of simulated results because the unifying core of these methods is a comparison of the one empirical dataset to many simulated datasets. Following simulation, both empirical and simulated data sets are summarized using summary statistics–e.g., allele frequencies, observed and expected heterozygosity, number of private alleles, etc. Posterior probability densities on model parameters are approximated using the parameters from those simulations whose summary statistics best match those of the empirical data.

Mutation

Direct, empirical estimates of human mutation rate as a function of allele size were obtained from [11] for dinucleotide microsatellites. Dinucleotide mutation rate was μ_di = (0.08+0.002a+0.0002a²)/1000, where a is allele size. To our knowledge, the literature does not provide similarly informative estimates of mutation rates specific to allele size for mono-, tri-, tetra-, and penta-nucleotide microsatellites in human. To address uncertainty in microsatellite mutation rates, we used several mutation curves in simulations of each motif size to integrate over this uncertainty (S1 Fig). However, we caution that loci that depart considerably from mean rates of microsatellite mutation for a given motif may provide results that are less robust than those presented here. Mutation rates at microsatellites with allele sizes <8 tend to be quite low and, to our knowledge, have not been estimated for microsatellites of any motif size. Therefore, we assumed mutation rates of alleles of size <8 to be between 10⁻⁸ and 10⁻⁶ (S1 Table).

Demography

Because demographic models specifying the split times of 1000 Genomes populations are not available, we devised a general demographic model based on recent literature. The timing and order of population splits is shown in S2 Fig. We assumed a generation time of 20 years and that all populations had an equilibrium effective population size of N_e = 10,000. The initial population sizes of descendant populations in our model are expressed as proportions of the parent population. For example, descendant populations B and C might start at 0.99 and 0.01 the size of ancestral population A; this represents a peripatric split. In other cases, both descendant populations were established as small samples of their ancestral population. For example, both CEU and TSI begin at 0.01 the size of their ancestral population, WECA (S2 Fig). These low proportions reflect the fact that CEU and TSI are not truly sister populations descended from a single population split. All descendant populations grew linearly, adding 100 individuals per generation until they reached the equilibrium N_e of 10,000.

Natural selection

We devised five models of microsatellite evolution derived from our earlier work on the topic [58]. In addition to a neutral model, four models of natural selection were used. Under the neutral model, all genotypes were assigned a relative fitness of 1.0. The models of natural selection hinge on key allele size, α, which is the allele with the greatest marginal fitness (= 1.0). Two of the four models of selection are single-optimum models because the genotypic fitness surface includes a single genotype (α/α) with maximum relative fitness of 1.0. The other two models of selection are periodic-optima models, in which all alleles with a size that is a multiple of α have a marginal fitness of 1.0. Thus, genotypes α/α, α/2α, 2α/2α, 2α/3α, and so forth all have a relative fitness of 1.0 under the periodic optima models.

We set the bounds of the uniform prior for s to (0, 0.02]. The lower limit on the prior for s excluded zero to ensure some selective pressure. The upper limit of 0.02 was based on preliminary simulations and early analyses. Although we initially simulated greater values of s, we set the upper limit on s to 0.02 when running our final analyses. This decision was based on the prior knowledge that values of s > 0.02 were never recovered in 95% highest posterior densities, making simulations with values of s this high unnecessary for consideration with our data set. Bounds on the uniform prior distribution of key allele size α were set to [2, 50]. Here, the upper bound was set to 50 because the greatest mean allele size at any of the loci studied was ~36 repeats long. We therefore reasoned that any locus in our data set targeted by selection would not have a key allele size greater than 50.

The periodic-optima models were motivated by the frequent occurrence of bimodal allele frequency distributions and the occasional occurrence of trimodal frequency distributions among the loci we sampled and genotyped. We note that fitness landscapes inferred under the periodic-optima models imply fitness peaks at genotypes far from the empirical distribution of genotypes in our sample. We advise that this subset of fitness peaks should be treated with caution.

The marginal fitness of an allele of size a under the two single-optimum models was calculated using a Gaussian fitness function [74]: , where s is the strength of selection. Thus, two parameters– α and s–defined marginal fitness (Fig 1A). Under the two periodic-optima models, we defined the marginal fitness of an allele of size a as: , where ⌊ ⌋ and ⌈ ⌉ are the floor and ceiling operators, respectively (Fig 1B). Again, the same two parameters defined the models of marginal fitness.

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Fig 1. Marginal fitness vs. allele size.

(A) Single-optimum, with key allele size of α = 12 and s = 0.005 (black circles) or s = 0.0005 (blue circles). (B) Periodic-optima using the same parameter values, with marginal fitness of 1.0 for multiples of the key allele size– 12, 24, 36, 48, etc.

https://doi.org/10.1371/journal.pgen.1011524.g001

In addition to the marginal fitness of each component allele, the relative fitness of a genotype depended on whether the model was additive or dominant. Under the additive single-optimum (ASO) and periodic-optima (APO) models, the relative fitness of a genotype was set to the average marginal fitness of the two component alleles. Thus, under the ASO model, genotype α/α would have a relative fitness of 1.0 while any other genotype would have a lower relative fitness.

Under the dominant single-optimum (DSO) and periodic-optima (DPO) models, the relative fitness of a genotype was set to the maximum marginal fitness of the two component alleles–i.e., genotypes α/α, α/(α−2), α/(α+3), and any other genotype with at least one allele of size α would be assigned a relative fitness of 1.0. Fig 2 shows representative genotypic fitness surfaces for the four selection models.

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Fig 2. Genotypic fitness surfaces for the four models of natural selection simulated.

Parameter values used to generate these graphs were α = 12 and s = 0.005. (A) additive, single-optimum (ASO) with a single, most-fit genotype of 12/12. (B) dominant, single-optimum (DSO) where all genotypes 12/_ have a relative fitness of 1.0. (C) additive, periodic-optima (APO). (D) dominant, periodic-optima (DPO). Compare the relative fitness scales of the ASO (A) and DSO (B) models to those of APO (C) and DPO (D); the relative fitness of the least-fit genotype on the surface is substantially lower under the single-optimum models.

https://doi.org/10.1371/journal.pgen.1011524.g002

Simulation

ABC-random forests analysis

Like all approximate Bayesian computation (ABC) methods, the ABC using random forests (ABC-RF) approach provides likelihood-free approximations to posterior distributions of competing models or parameter values by comparing simulated and empirical data. ABC-RF differs from traditional ABC methods by using the machine learning RF algorithm to learn the connection between summary statistics and a model or parameter. This approach contrasts with the simple ABC rejection algorithm [78, 79], which requires calculation of the distance δ between each simulated data set and the empirical data set. The level of approximation is then controlled by setting a tolerance level ϵ, and only simulations where δ≤ϵ are retained for approximation of the posterior density. We used both the regression and classification variants of random forests in ABC-RF for parameter estimation and model choice, respectively.

Because ABC-RF uses all training examples (i.e., the collection of simulated data referred to as a reference table), the method makes efficient use of simulation effort and eliminates the need for selecting only those simulations that match based on a semi-arbitrary tolerance. Moreover, the out-of-bag error calculated as a standard procedure in random forests analysis may be used as a good estimate of test error [80]. This eliminates the need to produce extra simulations in the service of cross-validation. Nevertheless, ABC-RF remains an ABC method because the observations used to train the RF model are summaries of simulated data, which substitute for explicit likelihood calculation.

ABC-RF in practice.

A separate RF model was trained for each microsatellite motif size. We tuned three hyperparameters of known importance to RF performance: (1) number of trees in each forest (ntree), (2) the number of randomly selected features to use at each split in a tree (nfeat), and (3) the minimum number of simulated observations required to perform another split (minobs) when constructing a decision tree component of the random forests algorithm. Hyperparameter tuning for a particular motif size was performed using five-fold cross-validation and a reference table of results from simulations of the relevant motif size. In this way, we identified the combination of hyperparameters that provided the smallest test error for a particular motif size. For all motif types, tuned hyperparameters were found to be ntree = 200 and minobs = 15. Depending on motif type, the tuned value of nfeat was either 20 or 30.

To train an RF model for a particular motif size, we passed the tuned hyperparameter values to an RF classification algorithm and trained the RF model using a reference table of 500,000 observations derived from simulations in which the relevant motif size was assumed (Fig 3A). Empirical data from each locus of the same motif size were input to the trained RF model, which returned the posterior probabilities of each evolutionary model. If a locus received a plurality or majority of support for one of the four models of natural selection, we then approximated the posterior distributions of the two selection parameters: key allele size α and strength of selection s.

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Fig 3.

(A) Model choice using the ABC-RF classification algorithm. A separate RF model was trained for each motif size based on 500,000 simulations. Output for a single locus is an array of posterior probabilities for each evolutionary model. We chose the model with the greatest posterior probability. (B) Parameter estimation using the ABC-RF regression algorithm. A separate RF model was trained for each motif size and each model of natural selection based on 100,000 simulations. The output for a single locus is the approximated posterior density of the parameters.

https://doi.org/10.1371/journal.pgen.1011524.g003

We assessed RF model performance using out-of-bag (OOB) error estimation. Random forests are a collection of decision trees, each trained on a bootstrap replicate of the original data. We followed the common practice of setting aside roughly one-third of the bootstrap replicates (the OOB data) to assess performance. The other two-thirds of bootstrap replicates were used to train the model. Model performance was assessed by measuring how well the trained model predicted the model and parameters used to simulate the data set in question.

We used the R package abcrf [80] to estimate parameters α and s. We trained a regression RF model for each combination of motif size and evolutionary model; these regression RF models were trained on a reference table of 100,000 results from simulations in which the relevant combination of motif size and evolutionary model were assumed (Fig 3B). Before training each model, hyperparameter tuning was performed as above for model choice. Each empirical locus was input to the appropriate trained RF model, returning the approximated posterior distribution of the parameter of interest. Per [80], each parameter was estimated separately (Fig 3B).

Raw and calibrated microsatellite genotypes, simulation code, and R scripts used for computational analyses are available in a Dryad Digital Repository [82].

Microsatellites are multifaceted genetic variants

To visualize patterns of variation in our sample, we began by comparing mean allele size (M_AS) with variance in allele size (V_AS) for a class of microsatellites suspected a priori to evolve neutrally: 54 intergenic dinucleotide loci. Most of these microsatellites were CA repeats, while 10 were TA repeats. We found that V_AS generally increased with allele size (Fig 4A), most likely due to the increased mutability of longer microsatellites [11–13]. Indeed, we have previously used this well-known characteristic of microsatellites to show that a simple summary of variation such as the number of alleles at a locus assumed to evolve neutrally does well at estimating the population mutation rate ፀ [83].

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Fig 4.

(A) Sample-wide variance in allele size (V_AS) vs. mean allele size (M_AS) for 54 intergenic dinucleotide microsatellites. In general, genetic variance at microsatellites increases with allele size, despite clear outliers with anomalously high variance. (B) Mean allele size of the same 54 intergenic dinucleotide microsatellites. Loci, from left to right along the x-axis, are ordered by increasing variance in allele size. Each locus is represented by eight dots, which are the means of each sampled population for that locus.

https://doi.org/10.1371/journal.pgen.1011524.g004

Yet, even in this modest sample of intergenic dinucleotides we found conspicuous outliers, where V_AS was much greater than the general increasing trend. In most cases, these outliers bore inflated V_AS due to bimodal allele size distributions. This includes the locus with the greatest V_AS in this dinucleotide set, located on chromosome 4, with a striking bimodal allele frequency distribution, and one which our method classified as evolving under natural selection (see final case study below). Using a different visualization of the data, Fig 4B shows that while there was a general trend of increasing variation with allele size, many loci defied the trend. Many of the intergenic dinucleotide microsatellites with relatively large V_AS had surprisingly small mean allele sizes. Furthermore, some loci showed substantial variation in mean allele size among populations, while others showed little or none.

Therefore, our carefully chosen sampling of microsatellite variation demonstrates the unpredictability of the microsatellite diversity landscape, and how little we know about the numerous factors shaping these multifaceted allele frequency distributions. Even when we grouped microsatellites by motif size, the microsatellites in these groupings were difficult to justify as identically distributed. This suggests more formal stochastic models of natural selection of microsatellite alleles would likely require a hierarchical modeling approach.

Method performance

Identifying and characterizing selection on microsatellites

Microsatellites in different genomic and functional contexts show evidence of natural selection.

We applied our method to a carefully chosen set of 94 microsatellites genotyped in 200 humans from a diverse collection of eight populations. Microsatellites were chosen based on established or predicted effects on disease, gene expression, or protein sequences. We also included microsatellites with previous indications of aberrant patterns of variation and intergenic microsatellites not suspected to be functional.

Our results for different categories of microsatellites again emphasize the multifaceted nature of microsatellites and point to causes of distinct patterns of variation among loci. Genomic context provides certain expectations for how a microsatellite should evolve and thereby influences the need to invoke natural selection as an explanatory factor of the variation observed at a given locus. For example, exonic dinucleotides are clear hazards, as one-step and two-step mutations to these microsatellites are also frameshift mutations. Here, the genomic context would seem to necessitate a role for purifying natural selection, which is supported by the near-total lack of variation at these loci in our sample (Table 1) [84]. As a counterexample, the genomic context of an ATG-trinucleotide microsatellite in GRIN2B is an intron of the gene, suggesting evolution of the locus should be largely unrestricted by selective pressures. Yet, as shown below, this microsatellite harbored nearly no variation. Here, the lack of variation at a site suggests the influence of natural selection because genomic context leads to the expectation of appreciable variation.

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Table 1. Microsatellites analyzed and posterior probabilities assigned to each evolutionary model.

Locus categories include causative of a known trinucleotide repeat disorder (triDisorder), other trinucleotide with low variance and relatively large mean allele size (triOther), Rockman and Wray (2002) site (RW), DNase I hypersensitivity site (DNaseI), intergenic dinucleotide (InterDi), and coding dinucleotide (CodingDi). Observed variance in allele size (V_AS) and mean allele size (M_AS) are global–i.e., calculated using genotypes pooled from all eight populations sampled. N = neutral; ASO = additive, single-optimum; DSO = dominant, single-optimum; APO = additive, periodic-optima; DPO = dominant, periodic-optima. The evolutionary model with the greatest posterior support is bold-faced for each locus, and loci receiving greatest support from a model of selection are backshaded. Loci are ordered by motif size, then by category, and finally by V_AS.

https://doi.org/10.1371/journal.pgen.1011524.t001

To determine which microsatellites are targets of selection, empirical summary statistics for each locus were input to RF models trained on simulations of the appropriate motif size. 43 of the 94 loci (45.7%) tested received greatest posterior support for a selection model over the neutral model (Table 1).

Three of the four trinucleotide microsatellites implicated in triplet expansion disorders—located in ATN1, DMPK, and ATXN3—were inferred to evolve neutrally (Table 1). The TBP microsatellite showed evidence of selection, with support spread among different models and favoring a role for dominance (Table 1). Across these four microsatellites, our sample contained only one allele of known pathogenic size (43x) at the TBP locus.

All four trinucleotide microsatellites previously identified as having anomalously low variance for their allele size were found to be targets of selection, with additive models combining to receive majorities of support (Table 1). Three of these four microsatellites are in genes that fulfill a range of functions. One microsatellite is found in GRIN2B, which codes for a subunit of a postsynaptic receptor for the neurotransmitter glutamate and is implicated in learning, memory, and neuronal development [85]. The second microsatellite is found in the intron of an alternative transcript of the gene DPT, whose protein dermatopontin is part of the extracellular matrix [86] and postulated to modulate the activity of the cytokine TGF-β [87]. The third intragenic microsatellite is found in the gene HRC whose protein helps facilitate skeletal muscle contraction and has been connected to heart disease [88]. The last of the four trinucleotides is intergenic but found in an interesting location. Namely, this TTA-repeat sits at the midpoint of a ~15 kbp intergenic sequence separating tightly linked genes ARRDC1 and ZYMND19, which are transcribed in opposite directions away from the microsatellite. In this location, the microsatellite is bracketed by the promoters of both genes, suggesting a possible co-regulatory role for the microsatellite.

All exonic dinucleotides were identified as evolving under a model of selection (Table 1). The additive, single-optimum model received overwhelming support for 13 of 18 of these loci (Table 1). Dinucleotides in two genes—FGFRL1 and RBM5—were judged to have periodic optima. The microsatellite in SLTM was inferred to follow a dominant, single-optimum model (Table 1). The C3ORF27 microsatellite is only a partial exonic dinucleotide and was supported as neutral (Table 1). Only the first of its GA repeats belongs to an exon–albeit, as the open reading frame’s UGA stop codon–while the remaining GA repeats belong to its 3’ UTR.

The group of microsatellites known or suspected to regulate gene expression in humans displayed variable evidence of selection. Two of the eleven loci we chose from the set compiled by Rockman and Wray [39]–found in genes COL1A2 and SLC11A1 –showed strong signs of selection (Table 1). The COL1A2 microsatellite is located in the first intron roughly 1 kbp downstream of exon 1; it overlaps with both a candidate cis-regulatory sequence (ENCODE; proximal-enhancer-like signature) and a strong H3K27Ac mark. The SLC11A1 microsatellite, on the other hand, is located in the gene’s promoter, approximately 330 bp upstream of the gene’s transcription start site. The allele frequency distributions of these two loci are intriguing for different reasons. While the COL1A2 microsatellite showed a strong bimodal distribution of allele frequencies (favoring the existence of periodic optima), the microsatellite in SLC11A1 is notable for its near lack of variation (global V_AS = 0.2). The neutral model received the greatest support for the other nine microsatellites chosen from the set in [39]. In addition, two long dinucleotides associated with signals of transcription factor binding in the form of strong DNaseI marks were both overwhelmingly resolved as neutral and associated with large V_AS (Table 1).

One-third of intergenic dinucleotides chosen without regard to function (18 of 54) were identified as evolving under selection (Table 1). Intergenic dinucleotides possessed zero or low V_AS in all 18 cases. Yet, each of the four selective models was favored by a subset of these microsatellites, suggesting variation in the fitness landscape among loci.

Strength of selection spans a wide range across microsatellites.

To characterize the strength of selection on microsatellites, a separate RF regression model was trained for each combination of motif size and model of selection (e.g., dinucleotide mutation model + additive, single-optimum). For each locus inferred to fit a model of selection, the appropriate RF model was used to estimate the strength of selection (s), as well as its 95% Highest Posterior Density (HPD). Like RF models trained for classification of evolutionary models, the variables of greatest importance to training regression RF models for estimating s were the observed heterozygosities of all eight simulated populations. For loci where V_AS was zero or negligible, s was non-identifiable because any value of s above some threshold was sufficient to eliminate all genetic variation at the locus. In these cases, we ran 1,000 simulations to identify the minimum s needed to consistently obtain no variation.

The greatest point estimate of s = 0.013 was obtained for three loci evolving by an additive selection model: two coding dinucleotides (located in C3ORF27 and RBM5) and an intronic trinucleotide (Table 2; bold-faced). Three of the four trinucleotide loci sampled for their coupling of low variance and relatively large mean allele size returned noticeably large point estimates of s (Table 2; triOther). Point estimates of s for intergenic dinucleotides identified as targets of selection ranged from 0.0013 to 0.008 (Table 2). The trinucleotide microsatellite in exon 3 of TBP, which codes for a poly-glutamine tract of the protein, is notable for obtaining a relatively high point estimate of s = 0.006 despite its reasonably high V_AS. Our results indicate substantial variation in the strength of selection targeting microsatellites.

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Table 2. Estimates of evolutionary model parameters s (strength of selection) and α (key allele size) for microsatellites receiving a plurality of support for one of the four selection models.

For loci with zero or negligible variance in allele size (V_AS), we note the minimum s required to maintain zero variance at a locus of the same motif size, under the identified model of selection, and using an assumed value of α.

https://doi.org/10.1371/journal.pgen.1011524.t002

Microsatellite alleles navigate complex fitness surfaces

For each microsatellite determined to evolve according to one of the four selection models, point estimates of s and α were used to reconstruct the diploid genotypic fitness surface. Fig 5A–5H shows the estimated fitness surfaces for the seven intragenic microsatellites identified as targets of natural selection. These genotype-to-fitness maps are substantially more complex than the same mapping for a diallelic SNP under an additive or dominant selective regime (Fig 5I). Our results illuminate the diversity of selective dynamics that shape microsatellite variation in humans.

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Fig 5.

Inferred fitness surfaces for six genic microsatellites and one intergenic microsatellite in human (A-H). Note that each locus has a different scale of relative fitness (w_i,j). Examples of loci following the additive single-optimum (B, gene GRIN2B; E, gene SLC11A1), dominant periodic-optima (A, gene TBP; C, gene COL1A2; H, intergenic locus on chromosome 4), and additive periodic-optima (D, gene RBM5; F, gene DPT; G, gene HRC) models are shown. Panel I shows a simpler mapping of genotypes to fitness for a hypothetical A/G SNP in which the adaptive A allele is either additive or dominant. White, gray, and black colors represent high, middle, and low relative fitness, respectively.

https://doi.org/10.1371/journal.pgen.1011524.g005

Case studies in microsatellite selection

The fitness surface for a microsatellite in a gene that encodes collagen reflects strong dominance of two separate allele sizes.

COL1A2 encodes one chain of type I collagen and is found in most connective tissues [95]. Mutations in this gene are associated with osteogenesis imperfecta and various subtypes of Ehlers-Danlos syndrome [96, 97]. The TG-repeat in intron 1 of COL1A2 is coincident with a strong H3K27Ac mark and is imperfect, with 2–3 TC rather than TG dinucleotides. In the reference sequence, the longest uninterrupted TG-repeat is 14x. The COL1A2 microsatellite received a plurality of support for the dominant periodic-optima model. Parameter estimates were s = 0.005 and α = 5 (Table 2 and Fig 5C). Enrichment for genotypes with at least one allele of size 20 or 25 is evident in the fitness surfaces visualized in Fig 6, providing a good example of dominant, periodic optima with most genotypes lying along ridges of this surface that correspond to a maximum relative fitness of 1. Genotypes lacking a 20x and a 25x allele were primarily found in African populations (Fig 6).

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Fig 6. Estimated dominant, periodic-optima fitness surface for a dinucleotide microsatellite in the first intron of gene COL1A2.

Most genotypes contain a 20x or 25x allele in accordance with the estimated α = 5 in a periodic optimum model. The most prominent exceptions to this pattern are in the African YRI and LWK populations.

https://doi.org/10.1371/journal.pgen.1011524.g006

A microsatellite known to affect expression of a gene important to human health appears subject to modest selection.

Protein SLC11A1 is a transmembrane transporter of iron and manganese. Various polymorphisms located in this gene, including the microsatellite in question, have been tied to human disease and immune response, including early-onset type 1 diabetes [102], type 2 diabetes mellitus [103], reduced immune response in tuberculosis patients [104], as well as susceptibility to tuberculosis [105]. The microsatellite in question is roughly 325bp upstream of the transcription start site of the gene and has been shown to influence the expression of SLC11A1 [106]. Both single-optimum models received equal posterior support in model selection (Table 1). We estimated an additive, single-optimum fitness surface, in which the ubiquitous 22x allele sits atop the peak of a shallow-sloped hill (Fig 7).

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Fig 7. Estimated additive, single-optimum fitness surface for a dinucleotide microsatellite in the basal promoter of SLC11A1.

Note the large allele sizes (22x, 23x, and 24x), which would suggest high mutability and predict a wider distribution of allele sizes than observed.

https://doi.org/10.1371/journal.pgen.1011524.g007

Themes and lessons

Despite confirmed functional capacity of microsatellites, model-based inferences about the role of natural selection at these loci are only beginning to appear [12, 24]. The selection models reported here are applicable to different modalities of natural selection acting on microsatellites, including both positive and purifying selection. The simple equations underlying our models of selection (see Materials and Methods) provide the relative fitness of any possible genotype. These models thereby lead naturally to fitness landscapes that are easily visualized and provide an intuitive readout of selective dynamics. Moreover, because we focus on individual loci, the common concern regarding the fitness landscape metaphor that the x and y axes are undefined and unitless is irrelevant here. The axes are well-defined as the two alleles of the genotype in units of allele size. Our portrait of microsatellite fitness surfaces reveals several themes and lessons.

Fitness landscapes of microsatellites are remarkably diverse. Each of our four selection models was favored for a subset of microsatellites. Estimated strength of selection ranged from 0.002 to 0.013 and optimum allele size ranged from 5 to 22 repeats across loci. Although our general models capture essential parameters of selection on microsatellites, specific microsatellites’ genomic context or functional role may require more heavily parameterized models with the potential to produce an even greater diversity of microsatellite fitness landscapes.

Dominance is an important component of selection targeting microsatellites. Dominant models received a plurality or majority of support for several loci. Our models made the simplifying assumption that dominance is determined by the most-fit allele of a genotype. Our results—along with the potential for microsatellites to harbor many alleles—suggest that models featuring a spectrum of dominance relations among different pairs of alleles are worth considering in the future.

Another striking implication of our results is that microsatellite allele frequency distributions and, by implication, fitness landscapes, can be conserved across human populations. This conservation is surprising, given the diversity of environmental conditions experienced by members of our sampled populations and the potential for mutation to rapidly generate new, adaptive allele sizes. Although our results differed between African and non-African populations at a handful of loci (see below for one example), most of the microsatellites for which we found evidence of selection showed similar patterns of variation among the eight populations in our dataset. Perhaps this finding partly reflects biases in our procedure for choosing microsatellites. Still, among the loci we analyzed, selective optima appear to have been established early in human evolution and maintained for long periods of time.

The constancy of key allele size across human populations at loci inferred to be under selection contradicts the expected outcome of microsatellites acting as tuning knobs of gene expression. The rapid evolutionary response promised by microsatellites’ high mutation rates is decidedly absent from most of our dataset; instead of shifting allele frequency distributions in human populations across the globe, we note distributional conservation. We found one notable exception. Key allele size of the promoter microsatellite in TBP has apparently shifted from around 34 to 36 between African and non-African populations. This finding was affirmed by ABC-RF model choice of (1) advanced models of selection in which African and non-African populations were allowed to take different values of s and α over (2) the models of worldwide selection covered here (S2 Text).

Finally, the rate of deleterious mutation across microsatellites in the human genome is probably high. In general, low observed heterozygosity (i.e., variation) in the sampled populations was the primary determinant of whether a model of selection was chosen. Maintenance of low variation at loci with high mutation rates requires constant purging of less-fit alleles that are continuously reintroduced by mutation–a significant mutational burden. In fact, it was recently predicted that the genome-wide burden of deleterious mutations imposed by microsatellites resembles the burden generated by SNPs [24]. As previously noted [58], these details suggest analytical investigation of microsatellites may benefit from drawing an analogy between traditional models of mutation-selection balance and microsatellite evolution by natural selection.

Microsatellites that cause disease

We considered four loci implicated in neurological disorders resulting from pathogenic expansion of a trinucleotide repeat and uncovered evidence for selection at one: the microsatellite in TATA-box binding protein (TBP). Expansion of the CAG/CAA repeat located in exon 3 of TBP causes spinocerebellar ataxia type 17 (SCA17) [89, 109], typically when allele size falls in the range of 46-55x [109]. The maximum allele size we observed was 44x. The TBP microsatellite is likely subject to selective pressures beyond avoidance of allele sizes prone to pathogenic expansion. As one of six general transcription factors involved in eukaryotic transcription initiation, wild-type functioning of TBP is of existential importance to a cell. The poly-glutamine (polyQ) tract encoded by the TBP microsatellite is involved in multiple protein-protein interactions including its essential binding to another general transcription factor, TFIID [110, 111]. Collectively, these details suggest that selection acting on the TBP microsatellite is driven by maintenance of its role in facilitating a physical connection to TFIID rather than its association with disease.

We inferred neutral evolution for the three other microsatellites causative of the trinucleotide expansion disorders SCA3 (ATXN3) [112], dentatorubral-pallidoluysian atrophy (DRPLA) (ATN1) [113], and myotonic dystrophy type 1 (DM1) (DMPK) [114]. Maximum allele sizes sampled at these three loci were well below the range of pathogenic allele sizes: 32x at ATXN3 compared to allele sizes causative of SCA3 that range from 56x to 87x [112]; 26x at ATN1 compared to alleles causative of DRPLA that range from 49x to 88x [115]; 27x at DMPK compared to causative alleles of DM1 that range from 50x to 6500x [114]. Our results suggest that wild-type alleles at these microsatellites are not subject to selective constraint.

In addition to weighing the evidence for selection on microsatellites with established connections to disease, our findings point to microsatellites that deserve to be examined in the context of disease. One of the most striking patterns we documented is the near absence of variation at an ATG microsatellite located in intron 3 of GRIN2B. Mutations in this gene cause GRIN2B-related neurodevelopmental disorder, and variants are associated with risk for schizophrenia, autism spectrum disorder, and attention-deficit/hyperactivity disorder [92–94, 116]. GRIN2B encodes the GluN2B subunit of the N-methyl D-aspartate (NMDA) receptor involved in learning and memory [91]. Functional studies of variants in mice indicate that GRIN2B affects neuronal differentiation, dendrite morphogenesis, synaptogenesis, circuit refinement, and synaptic plasticity [116].

Intriguingly, GRIN2B is predicted to be among the genes least tolerant to mutation in humans [117]. Our results suggest this status should be extended to intolerance even of microsatellite mutations in non-coding sequence. Although point mutations in introns 2 and 11 are implicated in GRIN2B-related disorders [91], potential functional importance of the intronic GRIN2B microsatellite is unclear. The microsatellite does not overlap with known CREs or alternative splice sites. Nevertheless, selective strength at the GRIN2B locus is among the strongest estimated in our study, suggesting studies of pathogenesis involving GRIN2B should add alleles at this microsatellite to the list of variants that deserve consideration.

Microsatellites connected to gene expression

We examined patterns of variation at 13 microsatellites for which a cis-regulatory role in modulating gene expression was established or suspected [39]. Two of these loci showed evidence for selection, with contrasting fitness landscapes.

The microsatellite located in the promoter of SLC11A1 plays a key role in immunity. It is associated with susceptibility to tuberculosis, inflammatory bowel disease, and rheumatoid arthritis. In mice, transcription factor HIF-1 regulates allelic variation in SLC11A1 expression by binding directly to the microsatellite during macrophage activation by infection or inflammation [118]. SLC11A1 encodes a macrophage protein that induces expression of MHC Class II molecules, cytokines, and chemokines. The fitness surface for the SLC11A1 microsatellite shows evidence of weak selection, with slow declines in fitness away from the key allele size of 22x.

We also uncovered evidence for selection targeting the microsatellite found in the first intron of COL1A2. The length of this microsatellite is connected to differences in expression levels of the linked gene [39], a collagen gene for which mutations are associated with osteogenesis imperfecta and Ehlers-Danlos syndrome [96, 97]. Our estimated fitness surface for this microsatellite is of interest for two reasons. First, we devised the periodic-optima models based on the idea that multiples of a locus-specific, key allele size would optimize physical distance between CREs, thereby leading to a specific level of gene expression. Therefore, inference of a periodic-optima model is compelling because it confirms a pattern expected under this hypothesis that a relationship exists between microsatellite allele size, CRE spacing, and gene expression. Second, the dominant model was best supported by the data for this locus. The estimated fitness surface for the COL1A2 microsatellite overlain with observed genotype frequencies in our sample shows that most sampled genotypes bear at least one of the two observed optimal allele sizes (20x or 25x; α estimated as 5) and therefore line up along the ridges of the fitness surface (Fig 6).

Eleven of the thirteen loci connected to gene expression appear to evolve neutrally, suggesting that differences in expression mediated by variation at these microsatellites do not affect fitness. In addition, correlations between microsatellite length and levels of expression are identified in a variety of ways. Support for these correlations depends on the method used to detect them. For example, we might place more trust in direct functional evidence of a microsatellite’s effect on gene expression than correlative signals such as DNase I sensitivity.

Microsatellites with no known or suspected function

It seems reasonable to expect that randomly chosen microsatellites located far from genes would evolve without selective constraint. Surprisingly, 18 of 54 intergenic dinucleotides were identified as targets of selection by our analysis. Our results for this set of 18 intergenic loci include inference of all four selective models and a range of selection coefficients. Like the identification of highly conserved sequences in genomic regions lacking functional annotations [119], our inference of selection targeting intergenic microsatellites paves the way for discovering new functions of non-coding DNA. The prevalence of inferred selection among our essentially random sample of intergenic microsatellites suggests microsatellites may be more frequent targets of selection than previously thought.

Caveats and prospects

Several caveats accompany our conclusions about the fitness landscapes of microsatellites. First, although our analyses incorporated major characteristics of microsatellite mutation, we ignored some features of this process. The ratio of contraction and expansion mutations is known to skew towards contraction mutations as allele size increases [11]. We did not include this detail in simulations because empirical estimates of this characteristic are lacking. In addition, we did not account for potential decreases in mutation rate for the few microsatellites we surveyed that contain imperfect repeats. Furthermore, though we incorporated direct estimates of dinucleotide mutation rate and step size probabilities from Sun et al.[11], trinucleotide mutation rate curves were less certain. For all motif sizes, we integrated over uncertainty by drawing one of many mutation rate curves at the start of each simulation (S1 Fig).

Second, the populations we surveyed were assumed to follow a demographic history previously inferred from genome-wide patterns of sequence variation. We recognize that reconstructing the history of eight populations is challenging, even in humans. True elements of human demographic history that we did not incorporate in our demographic model (S2 Fig) presumably reduced the accuracy of our conclusions. Concerns regarding this shortcoming are somewhat allayed by the fact that allele frequency distributions tended to be consistent across the sampled populations.

Third, it is possible that the signatures of selection we identified in patterns of microsatellite variation were generated by selection on linked SNPs instead of microsatellite alleles. We consider this an unlikely alternative hypothesis because microsatellite mutation occurs frequently enough to reduce linkage disequilibrium involving the microsatellite allele size to which a new, adaptive SNP allele is initially linked. Furthermore, all other alleles of this size will begin linked to the ancestral SNP allele. Therefore, the effects of linked selection on microsatellite variation should not mimic the patterns of direct selection on a microsatellite that we detect here. For example, we do not expect selection on a SNP allele to drastically reduce variation at a linked microsatellite–the very detail common to most microsatellites found to be under selection here. If there is variation at the microsatellite at the onset of linked selection, the adaptive SNP allele rising in frequency will become associated with many microsatellite allele sizes. If there is no initial variation at the microsatellite, it will remain so if under direct selection, but not because of selection for the linked, adaptive SNP allele.

Fourth, additional selective models may merit consideration. For example, our models presuppose symmetry in fitness declines moving away from the optimal allele size. For microsatellites implicated in expansion disorders, this assumption may be violated by a stark reduction in marginal fitness at the threshold between alleles in the normal range and alleles in the disease range. A mixture model of fitness landscapes for different ranges of allele sizes could be developed to better describe the dynamics of these loci.

Fifth, our results demonstrate the value of using forward-in-time (prospective) simulations, which require considerably greater computation time to perform than retrospective, coalescent simulations [75]. Among the more than 400 summary statistics used for model choice in ABC-RF, the observed heterozygosities of the eight sampled populations were identified as the summaries most informative about selection. Because coalescent simulations generally return allele frequencies, their output can only be used to calculate expected heterozygosity. Furthermore, because expected heterozygosity is a function of observed allele frequencies (all remaining summary statistics), it does not provide additional information for inference. Thus, prospective simulation not only allows us to model complex scenarios of mutation, demography, and selection; it also generates summary statistics of considerable inferential merit.

Finally, our portrait of the universe of fitness landscapes inhabited by human microsatellites is restricted to the set of loci we analyzed. In our approach, we favored careful and separate consideration of each microsatellite over the goal of describing general principles of microsatellite evolution. As advances in sequencing and bioinformatics improve the ability to genotype microsatellites from genome sequences [27, 63–66], model-based inferences of selection targeting microsatellites are beginning to be applied genome-wide [12, 24]. The insights emerging from these complementary perspectives will enable synergistic growth in our understanding of the importance of the microsatellite variant to evolution.