Genomic inference accurately predicts the timing and severity of a recent bottleneck in a non-model insect population

Abstract

The analysis of molecular data from natural populations has allowed researchers to answer diverse ecological questions that were previously intractable. In particular, ecologists are often interested in the demographic history of populations, information that is rarely available from historical records. Methods have been developed to infer demographic parameters from genomic data, but it is not well understood how inferred parameters compare to true population history or depend on aspects of experimental design. Here we present and evaluate a method of SNP discovery using RNA-sequencing and demographic inference using the program δaδi, which uses a diffusion approximation to the allele frequency spectrum to fit demographic models. We test these methods in a population of the checkerspot butterfly Euphydryas gillettii. This population was intentionally introduced to Gothic, Colorado in 1977 and has since experienced extreme fluctuations including bottlenecks of fewer than 25 adults, as documented by nearly annual field surveys. Using RNA-sequencing of eight individuals from Colorado and eight individuals from a native population in Wyoming, we generate the first genomic resources for this system. While demographic inference is commonly used to examine ancient demography, our study demonstrates that our inexpensive, all-in-one approach to marker discovery and genotyping provides sufficient data to accurately infer the timing of a recent bottleneck. This demographic scenario is relevant for many species of conservation concern, few of which have sequenced genomes. Our results are remarkably insensitive to sample size or number of genomic markers, which has important implications for applying this method to other non-model systems.

Introduction

Demographic history shapes patterns of genetic variation within and between populations (Wright, 1931). Recent methods take advantage of these patterns to infer past demographic events from genomic data sampled from natural populations (Adams & Hudson, 2004; Gutenkunst et al, 2009; Lopes et al, 2009; Lukić & Hey, 2012; Lohmueller et al, 2009; Pool et al, 2010; Li & Durbin, 2011; Cornuet et al, 2008; Beaumont, 1999). Inferences from genomic data supplement paleontological records to reveal ancient events in populations’ history, including expansions, crashes, and migration events. While these approaches have proven invaluable, most methods of demographic inference have been empirically validated in systems where demographic history is known only by indirect means (e.g. alternative genetic methods or fossil evidence) and by comparing inferences to known parameters from simulated datasets. Meanwhile, all evolutionary simulations rely on particular simplifying assumptions (e.g. neutrality or absence of linked selection) that are often violated in nature and can potentially lead to inaccurate estimates of demographic parameters 30 (Messer & Petrov, 2013). It is therefore important to test methods on positive controls from natural systems with known demographic history to examine under what circumstances inferences are sensitive or robust to these violations. Similarly unexplored are issues of experimental design for generating the genomic data upon which these methods rely. A reference genome and other genomic resources are not available for many non-model species in which knowledge of demographic history may be desired. An approach that can inexpensively and universally survey genetic variation at the scale necessary for demographic inference can help reveal important aspects of population history in diverse study systems.

An introduced population of Gillette’s checkerspot butterfly, Euphydryas gillettii (Nymphalidae), which has experienced recent and severe bottlenecks, offers an ideal system to examine whether demographic inference can be accurately applied to events occurring on an ecological timescale. This univoltine butterfly species inhabits meadows on eastern facing slopes of the northern Rocky Mountains. Adults fly during a four week period from June through mid-August with females laying clusters of more than one hundred eggs on leaves of the larval hostplant, Lonicera involucrata (Williams et al, 1984). Eggs hatch in July through September, with pre-diapause larvae forming communal feeding webs. The larvae then overwinter in diapause within these webs until they emerge in May and June, experiencing high mortality during diapause. Post-diapause larvae move out of the web for feeding and pupate away from their host plants near the ground.

The E. gillettii native range spans from western Wyoming through Idaho and Montana into Alberta and British Columbia. In 1977 (33 years prior to sampling for this study), the species was intentionally introduced to a field site at the Rocky Mountain Biological Laboratory in Gothic, Colorado (CO) (Holdren & Ehrlich, 1981) (Figure 1A). Founder individuals were obtained from a population at Granite Creek, Wyoming (WY), which has since been extirpated (McCoy & Boggs, personal observation). The CO and WY habitats were intentionally matched as closely as possible, including an increase in elevation in CO accounting for the difference in latitude between the two sites. As a poor disperser with narrow habitat requirements, the introduced population of E. gillettii has been completely isolated from the native range by the arid Great Divide Basin, eliminating gene flow as a potentially confounding factor in our demographic analyses (Williams, 1988; Boggs et al, 2006). Demographic data were recorded throughout these 34 generations with the exceptions of 1990–1997 and 1999–2001, during which the population was unlikely to have reached large numbers. The population established at the introduction site, persisting at 200 or fewer adult individuals for over a decade, including two separate observed bottlenecks of fewer than 25 adult butterflies (Figure 1B). Over the past decade, the population experienced drastic fluctuations, with mark-release-recapture estimates ranging from 100 to nearly 10,000 adult individuals (Boggs et al, 2006, Boggs, unpublished data).

Figure 1.

Documented history of the E. gillettii introduction. A: In 1977, E. gillettii were intentionally introduced to Rocky Mountain Biological Laboratory, Gothic, CO from propagules obtained from Granite Creek, WY. Contemporary samples were obtained from Gothic as well as a site at Togwotee Pass, WY, a proxy for the now-extirpated Granite Creek source population. B: Mark-release-recapture (MRR) estimates of adult population size in the Colorado population. The y-axis is depicted on a log scale to show fluctuations at very small population sizes.

Using this unique ecological system, our study demonstrates that multiplex cDNA-sequencing (RNA-seq) can inexpensively generate sufficient polymorphism data to perform demographic inference in an ecological model species with no pre-existing genomic resources. We used the program δaδi (Gutenkunst et al, 2009) to infer parameters of demographic models that best fit the genomic data. The program uses a numerical solution of a multipopulation diffusion equation to calculate the expected allele frequency spectrum for a specified demographic model, then performs optimization to find the values of the parameters which maximize the likelihood of the data given the model. This numerical approach is fast and overcomes the need for computationally-demanding coalescent simulations as implemented by other approaches such as approximate Bayesian computation (ABC) (e.g. Beaumont et al, 2002) and Markov chain Monte Carlo (MCMC) methods (e.g. Drummond et al, 2012). We chose to use the δaδi software for our analyses because 1) frequency spectra can be generated from any class of polymorphic marker and the method can thereby be generalized to any large-scale genomic dataset, 2) as models are fit to the frequency spectra alone, results can be more easily interpreted as compared to more complex methods relying on many summary statistics and 3) the δaδi’s application programming interface facilitates performance analyses to help understand how inference depends on various aspects of experimental design. Future work may compare results from different approaches to demographic inference using the same data, but such an analysis is beyond the scope of this study which is focused on the demonstration that the frequency spectrum generated from a single dataset contains sufficient information to reveal recent demographic history in a non-model species. The program δaδi has been widely applied, including investigation of the demographic history of humans (Gutenkunst et al, 2009), rice (Molina et al, 2011), orangutans (Locke et al, 2011), and other species.

Our study leverages detailed knowledge of ecology and population history of the unique E. gillettii system to evaluate parameter estimates and provide an important positive control in the case of recent bottlenecks, a demographic scenario that applies to many non-model species of conservation concern. We outline a widely-applicable method for marker discovery and genotyping as well as discuss experimental considerations for studying recent bottlenecks in other non-model systems.

Materials and Methods

Population sampling and library preparation

Eight third instar larvae were sampled from each of two field sites in September 2010: Togwotee Pass, Teton County, WY and Rocky Mountain Biological Laboratory, Gunnison County, CO. The Togwotee Pass population serves as a proxy for the now-extirpated population from Granite Creek, Teton County, WY, which is located approximately 40 km southwest of the Togwotee Pass site. The Granite Creek population, from which the CO population is derived, presumably maintained some connectivity with the Togwotee Pass population and with the rest of the E. gillettii metapopulation scattered throughout the Gros Ventre Wilderness. Larvae were collected and shipped alive in refrigerated containers, allowing them to clear their guts before freezing at −80°C.

Population genomic studies encounter a common tradeoff between the number of genomic markers covered at sufficient depth and the number of individuals genotyped. Faced with this tradeoff, we decided to use RNA-seq of pooled, barcoded samples as a method to capture a reduced representation of the genome. This method allowed us to build a reference transcriptome and to discover variants from a single dataset. In contrast to restriction site associated DNA sequencing (RAD-seq) or other methods of reduced representation, RNA-seq is biased toward discovery of variation in coding regions (Davey et al, 2011). By contrasting results of demographic inference using synonymous versus nonsynonymous SNPs, we also sought to understand the impact of selection on demographic inference, which may be a confounding factor for certain experimental designs.

Total RNA was extracted from each of 16 whole larvae using a standard Trizol RNA isolation protocol. Samples were treated with the TURBO DNA-free kit (Ambion) according to manufacturer’s protocol to remove DNA contamination. Samples with the highest quality (i.e., the least evidence of small RNA fragments on Bioanalyzer (Agilent) traces) were used for downstream library preparation. RNA Integrity Number (RIN) is not a reliable metric for this species as E. gillettii ribosomal RNA apparently harbors a hidden break that causes the 28S rRNA to fragment and co-migrate with the 18S rRNA (Winnebeck et al, 2010).

To prepare cDNA libraries for the selected 16 samples, we used the TruSeq RNA Sample Preparation Kit (Illumina). This protocol includes poly-A mRNA selection, enzymatic fragmentation, first and second strand cDNA synthesis, end-repair, 3′ adenylation, adapter ligation, and PCR amplification. Sample preparation proceeded according to the manufacturer’s protocol, except for the adapter ligation step during which we incorporated custom adapters (synthesized by IDT) with 8 bp barcodes unique to each of the 16 libraries. Libraries were pooled and sequenced on a single lane of the Illumina HiSeq 117 2000 platform at the Stanford Center for Genomics and Personalized Medicine. Over 100 million 2 × 100 bp paired-end reads passed quality filtering and were utilized in downstream analyses.

Transcriptome assembly and annotation

We sought to assemble the E. gillettii transcriptome de novo as a reference to which to map individual sample data to discover population variation. We first de-multiplexed individual sample data in silico according to the unique 8 bp barcodes, then trimmed these barcode sequences along with adenine-overhangs (9 bp total) from the beginning of reads. We used the FastQC quality control tool <http://www.bioinformatics.bbsrc.ac.uk/projects/fastqc> to evaluate the processed reads’ qualities. Based on these metrics, we performed dynamic read trimming, removing ambiguous base calls at the end of FASTQ reads with the FASTX-Toolkit <http://hannonlab.cshl.edu/fastx_toolkit/index.html>. We discarded reads containing adapter and primer contamination using TagDust (Lassmann et al, 2009) and any remaining orphan reads were discarded.

In preparation for de novo transcriptome assembly, we pooled reads from all 16 libraries, then input these data to the de Bruijn graph-based assembler Trinity (Grabherr et al, 2011). The Inchworm module of Trinity generates a kmer catalog and performs greedy extension based on kmer overlap. Using a range of kmer lengths during assembly can potentially improve sensitivity and allow reconstruction of transcripts with a wider range of expression levels (Schulz et al, 2012). We therefore modified the Trinity (version r2012-10-05) source code (Wheat, personal communication) to perform six separate assemblies with six kmer lengths (odd values from k=21 to k=31). We limited assembly to odd kmer lengths because even kmers may be palindromic reverse complements of themselves and introduce ambiguity to the de Bruijn graph. Assemblies were conducted on the Stanford SCG3 computing cluster with 120G of RAM. We calculated standard assembly metrics (contig number, assembly length, N50) for each of these assemblies, and used blastx (Altschul et al, 1997) to search for homology between our contigs and a custom database of lepidopteran peptides downloaded from Insecta Central (Papanicolaou et al, 2008). We assessed the degree of overlap among assemblies by comparing composition of blastx hits to the InsectaCentral lepidopteran protein database with e-value < 1e-05 and alignments covering >80% of the targets’ length. Based on the apparent similarity in length and content for assemblies using different kmer lengths, we selected the k=31 assembly for downstream analysis to reduce the possibility that repetitive regions would produce spurious SNPs. In our case, the challenge of removing redundancy outweighed the possible gain in sensitivity of combining multiple kmer assemblies.

As quality control, we evaluated the k=31 assembly based on homology to protein databases of three lepidopteran species. We first selected the longest contig sequences from each Trinity subcomponent, since multiple contigs deriving from a single subcomponent can share exons and may therefore be partially redundant. We used reciprocal blast searches to compare the E. gillettii transcriptome assembly to protein databases from the silkmoth (Bombyx mori), monarch (Danaus plexippus), and postman butterfly (Heli conius melpomene). We used blastx to search E. gillettii transcripts against these databases and tblastn (Altschul et al, 1997) to reciprocally search the protein databases against the E. gillettii transcriptome. Here we report the number of unique hits with e-value < 1e-03, as well as the fraction of each reference database hit by the query database (Table S2). We then limited these assessments to the small subset of contigs that harbored SNPs that we discovered downstream in our pipeline and used for demographic inference. For these contigs, we report the number of unique hits with e-value < 1e-03 and the number of these hits that cover greater than 80% of reference proteins or 50% of reference contigs (Table S3). Shorter alignment length is expected for focal species to E. gillettii because UTRs will not be aligned when blasting protein sequences to mRNA transcripts. We also used blastx (Altschul et al, 1997) to search SNP-containing contigs against the NCBI nr database, assessing the top species hits (e-value < 1e-03) for all contigs as a quality control.

SNP discovery

In order to identify SNPs for the generation of site frequency spectra, each sample’s preprocessed reads were mapped to the newly-generated Trinity reference using BWA (version 0.6.2) (Li & Durbin, 2009). We used SAMtools (version 0.1.18) to extract only uniquely-aligned reads (Li et al, 2009). SNPs were discovered in the filtered multi-sample alignments using the GATK (version 2.3) UnifiedGenotyper algorithm with default parameters. We found that many called variants exhibited an extreme excess of heterozygote genotypes as well as deviation from the expected 50:50 allele balance (i.e., proportion of reads supporting the reference versus alternative allele). In some cases, several linked variants exhibited these patterns. We suspected that these observations were due to an abundance of closely-related paralogs or other repetitive sequences. In the case that one member of a paralog family is expressed at a low level, it may not be represented in the reference sequence, and reads derived from this gene will map to its highly-expressed, assembled paralog. Recent work supports the conclusion that a large proportion of called SNPs from RNA-seq data are indeed false positives due to hidden paralogy (Gayral et al, 2013).

To therefore reduce potential false positives, we modified our pipeline to allow only one mismatch per aligned read. We then used a hard filter to extract potential false SNPs with at least one sample sequenced to ≥10× coverage with reads supporting both alleles and >75% of reads supporting the reference allele. We likewise extracted putative true SNPs for which all samples were sequenced to ≥10× coverage and any individual with non-zero counts of each allele had an allele balance between 30 and 70%. The resulting sets of 965 putative false SNPs and 6834 putative true SNPs were used to train the GATK Variant Quality Score Recalibration (VQSR) tool (Depristo et al, 2011) and classify all 42620 raw SNP calls as true or false at various sensitivity thresholds. The VQSR procedure, as implemented here, uses a Gaussian mixture model to distinguish true and false variants based on allele balance, the inbreeding coefficient (a measure of deviation from Hardy-Weinberg equilibrium), and mapping quality. We then extracted a final variant set consisting of SNPs that passed VQSR at a truth sensitivity threshold of 0.90 and had at least 6× coverage per sample in at least 12 of the 16 samples.

We annotated SNPs as synonymous, non-synonymous, or untranslated by identifying open reading frames (ORFs) with the program OrfPredictor (version 2.3) (Min et al, 2005). OrfPredictor uses homology information from blastx (to the InsectaCentral lepidopteran peptide database, in our case) as well as de novo prediction based on intrinsic signals in the absence of blastx results. Using ORF predictions, we translated sequences after substituting the alternative SNP, classifying variants as nonsynonymous if the substitution altered the amino acid sequence.

In order to limit the potentially confounding effects of selection on demographic inference, we first confined analyses to high-confidence synonymous SNPs discovered by our pipeline. These SNPs were used to generate a joint site frequency spectrum for input to δaδi (version 1.6.3). In order to incorporate information from all markers and deal with instances of missing data, we projected the frequency spectrum down to six samples (12 alleles) per population. The projection method of δaδi uses a hypergeometric distribution to effectively average over all possible results of sampling 6 alleles per population from the total number of genotype calls at each SNP (Gutenkunst et al, 2009).

For visualization of the genetic data used for demographic reconstruction, we generated a heatmap of the folded (i.e. unpolarized) joint frequency spectrum of all SNPs using the package ggplot2 within the R statistical environment (Figure 3A) (Wickham, 2009; R Core Team, 2013). We also performed Q-mode principal component analysis on the genotype matrix using the ade4 package (Figure 3B) (Dray & Dufour, 2007). Genotypes were encoded as 0, 1, and 2, representing homozygous for the major allele, heterozygous, and homozygous for the minor allele, respectively.

Figure 3.

Representations of the genetic data. A: Joint allele frequency spectrum composed of all SNPs segregating in WY, CO, or both populations. The frequency spectrum illustrates the loss of ancestral genetic variation in the CO population due to genetic drift during the bottleneck. Frequencies range from 0 to 16 chromosomes per population. The spectrum, displayed as a heatmap, is folded (i.e. unpolarized), as the state of the ancestral allele is unknown. B: Individual samples plotted according to the first two principal components of the genotype matrix of all SNPs. Populations are indicated with different plotting symbols. Upon stratifying data by SNP class (synonymous, nonsynonymous, UTR), results were qualitatively similar and are not depicted. Principal component 1 separates samples according to population membership, while principal component 2 separates individuals within the WY population (within which the CO samples are nested, but tightly clustered).

Demographic inference

For each of these three models, best fit parameter estimates were inferred using synonymous SNPs conforming to our aforementioned filtering criteria (Table 1). We then simulated Poisson sampling from the frequency spectrum with the built-in sampling method in δaδi to generate 1000 bootstrap samples per model. Confidence intervals were constructed using empirical quantiles of the bootstrap distribution. All model parameters were positive by definition, so in cases where greater than 2.5% of bootstrap results fell at the lower boundary of the parameter space, the lower end of the confidence interval is reported as zero. We specified three simple demographic models in δaδi, the first and last of which reflect known demographic history.

Table 1.

Best fit parameter estimates for alternative demographic models fit to various portions of the data. Models correspond to Figure 2. Fixed parameters are indicated in bold, and 95% confidence intervals are indicated in brackets. Effective population sizes are reported with respect to an ancestral population arbitrarily set at η_ANC=1, times are reported in units of τ, where τ×2N _ANC =T generations, and migration rates in units of M _i→j, where M _i→j/2N _ANC =m_i→j, the proportion of individuals in population j who are new migrants from population i every generation. Likelihoods and AIC are directly comparable for models A, B1, and B2, which represent nested models fit with the same data.

Data	Model	ηWY	ηCO	M WY→CO	M CO→WY	τSPLIT	Log likelihood	AIC
WY & CO syn.	A	0.922 [0.673 1.253]	0.104 [0.076 0.137]	NA	NA	0.066 [0.047 0.087]	−211.86	429.72
WY & CO syn.	B1	0.884 [0.671 1.166]	0.119 [0.082 0.171]	0.080 [0.051 0.121]	NA	0.887 [0 2.056]	−211.01	430.02
WY & CO syn.	B2	0.893 [0.649 1.190]	0.121 [0.083 0.167]	0.081 [0.051 0.122]	0.906 [0 1.911]	0.002*	−211.00	432.00
CO syn.	C	NA	0.104	NA	NA	0.048 [0.029 0.143]	−21.65	NA
WY & CO syn., nonsyn., & UTR	A	1.320 [0.936 1.838]	0.173 [0.121 0.230]	NA	NA	0.117 [0.083 0.156]	−284.17	NA

^*In model B2, bootstrap estimates of τ_SPLIT were highly erratic and non-normally distributed, so the confidence interval is not reported.

Model A

Model A, a two population model (Figure 2A), was fit using data from both the WY and CO populations. In this model, we inferred the parameters τ_SPLIT, η_WY, and η_CO, which specify the timing of the CO population establishment (or alternatively, the bottleneck duration), the effective size of the WY population, and the effective size of the CO population, respectively.

Figure 2.

Demographic models specified in δaδi. A: Two-dimensional model fit with WY and CO data. An ancestral population in WY gives rise to a derived CO population through a founding event at time τ_SPLIT in the past. The resulting populations in WY and CO have sizes η_WY and η_CO, respectively. B1: Model A is extended to include possible unidirectional migration from WY to CO. B2: Model A is extended to include possible bidirectional migration, both from WY to CO and from CO to WY. C: Single population model fit with CO data. An ancestral population experiences a bottleneck at time τ_SPLIT in the past, reducing its size to η_CO.

Population sizes were inferred in units relative to an ancestral effective population size arbitrarily set at one, while time was inferred in coalescent units of τ, where τ · 2N_ANC = T generations. To therefore compare τ_SPLIT to the timing of the introduction known from the demographic record, we estimated the effective population size of the CO population (N_CO). We derived annual population estimates from mark release-recapture estimates of census N or counts of egg clusters, as detailed in Boggs et al (2006) (Table S4). For years during which mark-release-recapture was not performed, we used a regression model incorporating significant weather variables to estimate adult population size (Table S5). We accounted for deviations from 1:1 sex ratios with the equation N_e = 4N_mN_f/(N_m + N_f), where N_m and N_f are the annual census estimates of adult males and females, respectively (Hedrick, 2011). For years during which mark release-recapture data were insufficient to generate separate counts of males and females, we applied the average reduction in N_e due to deviation from 1:1 sex ratio of 0.94N. The multigeneration estimate of N_e is then the harmonic mean of these sex-ratio-corrected single-generation estimates (N_i) across t generations: $1/N_e=\frac{1}{t}{\displaystyle {\sum }_{i=1}^t(1/N_i)}$ (Hedrick, 2011). We then incorporated a literature-derived estimate of variance in reproductive success based on cage experiments in Bicyclus anynana (Nymphalidae), further reducing N_e to 0.60N (Brakefield et al, 2001). This reduction is consistent with data from several species within Nymphalidae that suggest that nearly half of males do not mate (Boggs, 1979; Oberhauser, 1989, Boggs, in preparation). Upon incorporating each of these factors, we generated a rough estimate of N_CO = 34. This estimate was used to calculate an estimate of N_ANC = N_CO/η_CO and scale all inferred demographic parameters to units of individuals (for population size parameters) and generations (for time parameters).

We wish to emphasize that there are many sources of uncertainty that affect our estimate of N_CO, including several factors for which we did not account in interest of simplicity. Variance due to sampling of the frequency spectrum and error in the regression models are easily quantified and are reported here (Table 1, Table S4, Table S5). Countless other potential sources of error, including factors such as the effect of early male emergence (protandry), fine scale population structure, and assortative mating are not quantified here. The final scaling factor should therefore be regarded as a rough estimate to demonstrate that the frequency spectrum generated from expressed SNPs contains sufficient information to perform such inference. Nevertheless, the estimate of N_CO is independent of the genetic data and based on intensive field survey over several decades, a rare advantage of this ecological system.

Model B

In models B1 and B2 we extended model A to infer recent migration between the WY and CO populations (Figure 2B). Though we know that no such migration actually occurred, we were interested in inferring migration because in many systems researchers will not have pre-existing knowledge that precludes gene flow. In these cases, inferences of gene flow may confound inference of other demographic parameters. In model B1, we inferred the rate of unidirectional migration from WY to CO (Figure 2B1). If barriers to migration were absent, this scenario would be plausible since the native range populations could act as a source to the smaller CO sink population. In model B2, we inferred separate migration rates in each direction (Figure 2B2). In each case, inferred migration rates are reported in units of M_i→j, where M_i→j = 2N _ANC m_i→j and m_i→j is defined as the proportion of individuals in population j that are new migrants from population i every generation. We then performed model selection by calculating the Akaike information criterion (AIC) for each of the migration models as well as the model with no migration, preferring the model with the minimum AIC value (Akaike, 1974).

Model C

Model C (Figure 2C) was fit using data from only the CO population. Inferring demographic history from only one population allowed us to understand how the addition of data from the second (proxy ancestral) population affected precision in demographic inference. In this model, an ancestral population experiences a bottleneck starting at time τ_SPLIT in the past and extending to the time of sampling. This bottleneck is modeled by a change in the effective population size from η_ANC to η_CO at time τ_SPLIT. Because τ_SPLIT and η_CO are confounding variables, we fixed η_CO to the best fit estimate from the two-dimensional model and inferred τ_SPLIT.

Nonsynonymous SNPs

In order to test the effect of selection on parameter estimates, we repeated the demographic inference procedure for model A (Figure 2A), this time fitting our model to the full dataset of 6349 high-confidence synonymous, nonsynonymous, and untranslated SNPs with genotype calls in at least six samples per population. We contrasted parameters estimated from this larger dataset to those inferred from the smaller set of synonymous markers alone. To verify that any differences were not an artifact of the larger number of markers, we randomly subsampled the frequency spectrum to the same size as the synonymous dataset (1881 SNPs), repeating this procedure 1000 times and estimating 95% confidence intervals.

Performance analyses

We were interested in the sensitivity of parameter estimates to the number of SNPs included in our analysis. We used the program ms (Hudson, 2002) to sample varying numbers of SNP markers from eight individuals per population, simulating the frequency spectrum under the best fit parameters of model A (Figure 2A). Given that the relative genomic locations of SNP markers were unknown, we elected to simulate a single locus with a high recombination rate (ρ = 2000 = 4N_refr, where r is the per-generation probability of recombination between the ends of the locus and N_ref is the effective size of the ancestral population). We then scaled the resulting frequency spectrum to a given number of segregating sites using the frequency spectrum manipulation functions in δaδi. We also tested a range of recombination rates, finding that they did not qualitatively alter our results. Our approach represents a balance between speed of simulation and a desire to account for additional variance in the frequency spectrum due to physical linkage among markers. An alternative to this approach would be to independently simulate unlinked loci, but our approach is conservative in that it accounts for correlations in coalescent history arising from physical linkage of among markers. We repeated the simulations 1000 times for each number of sampled markers and used δaδi to infer the best fit parameter estimates for each simulated dataset. This procedure allowed us to examine how the variance in estimates as well as the proportion of non-converging estimates changed as a function of sample size of SNP markers (Figure 4A).

Figure 4.

Performance analysis to test the effect of number of samples and number of SNPs on demographic inference results. We removed results where estimates hit the upper or lower bounds of the set parameter range, but report the proportion of these non-converging estimates on the top axes. Simulated parameter values are indicated by the horizontal line and correspond to the best-fit estimates from model A. A: Best fit parameter estimates when fitting the model with varying numbers of SNPs, demonstrating that variance in estimates is relatively stable with 300 or fewer markers. Sample number is fixed at 8 per population, and simulation and model fitting are performed 1000 times for each size SNP set. B: Best fit parameter estimates when fitting the model with varying numbers of samples per population, demonstrating that variance in estimates is relatively stable with as few as two samples (four alleles) per population. SNP number is fixed at 1881, and simulation and model fitting are performed 1000 times for each number of samples.

We were similarly interested in the sensitivity of parameter estimates to the number of sampled individuals per population. We again simulated model A (Figure 2A) using ms, but incremented the number of sampled individuals from one to 10 per population, with the number of SNPs fixed at 1881. We repeated the simulations 1000 times under the best fit parameters of model A (Figure 2A) and again used δaδi to infer the best fit parameters estimates for each simulated dataset. We then examined how variance in parameter estimates and the proportion of non-converging estimates changed as a function of the number of individuals sampled per population (Figure 4B).

Results

Transcriptome assembly, annotation, and SNP discovery

Combining sequence data from all 16 individuals, we used Trinity to perform de novo assembly of the E. gillettii larval transcriptome. We performed separate assemblies using a range of kmer lengths for the first Trinity module called Inchworm. Each assembly produced greater than 50,000 subcomponents which contain one or more isoforms of putative transcripts. When selecting the longest contig per subcomponent, N50 length ranged from 812 to 1320 for different kmer choices (Table S1). Greater kmer lengths are better for distinguishing among short repetitive sequences, but may lead to a more convoluted de Bruijn graph. Based on our goal of variant discovery, we were less concerned with assembly contiguity than the presence of false positive SNPs, so we selected the k=31 assembly for all downstream analyses.

We compared the E. gillettii transcriptome to protein sequence data available from three other lepi dopteran species using reciprocal blast searches. Our transcriptome assembly covered a large proportion (69.6–76.5%) of the proteomes of these related species (Table S2). We observed a comparable number of matches when searching these species’ proteomes against the E. gillettii transcriptome. The lower fraction of hits to the target database reflects differences in the sizes of the transcriptome and proteome databases, divergence among orthologs, genes that are unique to individual species, as well as possible contamination or spurious transcripts within each database.

All downstream analyses were biased, however, toward transcripts that were sufficiently highly expressed in enough individuals to make high-confidence genotype calls. As a result, only 2757 of the 56536 unique contigs harbored high-confidence SNPs ultimately used for demographic inference. Higher expression levels facilitate the faithful reconstruction of mRNA transcripts, and highly-expressed genes tend to be more evolutionarily conserved (Subramanian, 2004). We consequently observed a higher proportion of reciprocal blast hits between this subset of E. gillettii transcripts and protein databases of related species (Table S3). Of 2408 SNP-containing contigs with significant (e-value < 1e-03) hits to 322 the NCBI nr database, 15 had top matches to plants, 99 had top matches to bacteria, and only one had a top match to humans, which together represent the most likely sources of contamination in this experiment. Meanwhile, 2009 sequences had top matches to lepidopteran species. The remainder likely reflects genes that are either species-specific, highly conserved, or highly diverged and therefore do not match to lepidopteran reference proteins. We therefore opted against filtering SNPs based on these results, as such filtering could introduce new biases that could confound downstream demographic analyses. Together, our results suggested that spurious transcripts and contamination are rare in the portion of our assembly utilized for demographic inference.

We incorporated homology information from blast searches to all available lepidopteran protein data to identify likely ORFs using the program OrfPredictor. This allowed us to classify 2277 synonymous, 1396 nonsynonymous, and 2675 UTR SNPs with at least 6× coverage per sample in at least six samples per population. As expected under purifying selection, the synonymous and nonsynonymous frequency spectra differed in shape in both the WY (χ²[6, N=1276]=16.79, p=0.010) and CO (χ²[6, N=531]=12.63, p=0.049) populations, with an excess of nonsynonymous SNPs at low frequency (WY synonymous Tajima’s D=−0.0494, WY nonsynonymous Tajima’s D=−0.385, CO synonymous Tajima’s D=0.692, CO nonsynonymous Tajima’s D=0.505). Of the 2277 synonymous SNPs, 1991 and 959 were segregating in the WY and CO populations, respectively. While we identified 71% of CO SNPs segregating in WY, we only identified 34% of WY SNPs segregating in CO. The asymmetry in the number and overlap of segregating sites is consistent with the founder event and subsequent bottlenecks causing substantial allelic extinction in the derived population.

Demographic inference

Model A

The demographic model in which an ancestral population from WY splits to form the introduced CO population (Figure 2A), reflects our knowledge of the true population history. Upon fitting this model using data from both the contemporary WY and CO populations, we recovered converging estimates of all demographic parameters (Table 1). Our model underestimated the number of low frequency SNPs that were lost in the CO population, but provided a good fit to the data overall as the model and data frequency spectra were not significantly different (χ²[86, N =1881.4]=50.09, p=0.999) (Figure S1). While the effective size of the WY population (η_WY) was inferred to be approximately the same as the ancestral population (95% CI [0.673 1.253]), δaδi inferred a severe bottleneck (95% CI [0.076 0.137]) in the CO population (η_CO). These population sizes are reported with respect to an ancestral population arbitrarily set at η_ANC=1. In addition, δaδi detected that the bottleneck timing (τ_SPLIT) was recent (95% CI [0.047 0.087]), with time reported in units of 2N _ANC generations.

Upon scaling the inferred parameters to units of individuals and generations (for population sizes and times, respectively), we found that inferred parameters were consistent with the documented history of the population. Our census-based estimate of N_CO = 34 placed the scaled estimate of τ_SPLIT based on best-fit parameters of model A between 40 and 47 generations in the past (95% CI), calculated as 2τ_SPLIT (N_CO/η_CO). We note, however, that this confidence interval accounts only for uncertainty in τ_SPLIT and η_CO. Uncertainty in the crude estimate of N_CO also contributes to uncertainty in the scaled parameter estimate, which would inflate the confidence interval beyond the reported limits. Nevertheless, our estimate of bottleneck onset is close to the known population establishment 33 generations prior to sampling, with one generation per year in this system. This result demonstrates that the joint frequency spectrum generated from RNA-seq data contains sufficient information to infer parameters of demographic scenarios occurring in the recent past.

Model B

Further analyses focused on considering the robustness of the above results to different treatments of the data and different specifications of the demographic model. First, we extended the two dimensional demographic model to infer recent migration between the WY and CO populations (Figure 2B), although we are confident that no such migration occurred. In many systems, however, researchers will not be able to exclude this possibility, and inferences of migration may be confounded with inferences of other demographic parameters. We therefore incorporated migration by modeling unidirectional gene flow from WY to CO (M_{WY →CO}, Figure 2B1) as well as bidirectional gene flow of potentially different magnitudes between WY and CO (M_WY→CO and M_CO→WY, Figure 2B2).

For model B1, we found that δaδi inferred a low migration rate (95% CI [0.051 0.121]), but that uncertainty in the estimate of τ_SPLIT (95% CI [0 2.056]) dramatically increased to the point that the confidence interval included the parameter boundary of zero (Table 1). This result is not unexpected, given that migration and drift have contrasting effects on the allele frequency spectrum (Gutenkunst et al, 2009). In order to observe the same amount of drift in the joint frequency spectrum in the face of non-zero migration, bottleneck duration must be greater. However, these effects cannot be disentangled from the frequency spectrum alone, which generates uncertainty in the estimates. Estimation of τ_SPLIT became erratic upon adding the free parameter M_CO→WY in model B2, likely due to overfitting of our limited sample.

We evaluated the improvement in likelihood given the increase in model complexity by calculating the AIC for each migration model as well as the model with no migration (Akaike, 1974). The model with no migration had the minimum AIC and was therefore preferred over the more complex migration models, consistent with the known demographic history of population isolation (Table 1). As models A, B1, and B2 represent nested models, we similarly applied the likelihood ratio test, finding that the model fit was not significantly improved when allowing for unidirectional (χ²[1]=1.70, p=0.192) or bidirectional migration (χ²[2]=1.72, p=0.423) as compared to the null model with no migration. Finally, Gutenkunst et al (2009) showed that fitting data including migration with a no-migration model results in correlated residuals. Our residuals plot for model A shows no evidence of this phenomenon (Figure S1C). In summary, our results demonstrated that while inference of migration may confound inference of other demographic parameters, model selection procedures may help indicate whether such migration actually occurred.

Model C

When we fit a simple bottleneck model to data from only the CO population (Figure 2C), our model predictions fit the data relatively well (χ²[3, N=803.6]=3.15, p=0.370). Nevertheless, bottleneck magnitude (η_CO) and timing (τ_SPLIT) have confounding effects on the site frequency spectrum and cannot be disentangled using data from a single population. We were interested, however, in the effect of the additional information from the WY population on inference of τ_SPLIT. We therefore fixed η_CO to 0.104, its best fit estimate from the model fit using data from both populations and repeated demographic inference on the CO site frequency spectrum. With η_CO fixed, δaδi infers a τ_SPLIT of 0.048. The confidence interval of τ_SPLIT inferred from this single-population spectrum (95% CI [0.029 0.143]) entirely includes that estimated from the joint-population spectrum in model A (95% CI [0.047 0.087]) demonstrating that we gained precision with multiple-population inference.

Nonsynonymous SNPs

We initially fit all models using only synonymous SNP data, which we presumed was important because selection can alter the frequency spectrum, confounding signatures of neutral demographic history. We examined whether this is the case for RNA-seq data by comparing inferences using only synonymous SNPs to the full dataset of 6349 synonymous, nonsynonymous, and UTR SNPs. In this case, best fit estimates of η_WY, η_CO, and τ_SPLIT significantly exceeded those inferred when fitting the model using synonymous SNP data alone (Table 1). This difference is not an artifact of the larger number of SNP markers, as randomly resampling to the same size as the synonymous dataset (1881 SNPs) produced confidence intervals for η_W (95% CI [0.936 1.838]), η_CO (95% CI [0.121 0.230]), and τ_SPLIT (411 95% CI [0.083 0.156]) that included the estimates from the full dataset, but exceeded the estimates from the synonymous data alone. These results suggest that natural selection indeed distorted the frequency spectrum and changed our inferences of demographic parameters. Parameter overestimation is caused by the skew of the nonsynonymous frequency spectrum toward rare variants in both populations (Figure S2). The distortion of the CO frequency spectrum for nonsynonymous SNPs is likely a carryover of purifying selection in the ancestral population, since N_CO was too small for selective differences to generate observable frequency differences within CO.

Performance analyses

In order to better understand how parameter estimates were sensitive to the number of SNP markers and the number of sampled individuals per population, we simulated frequency spectra under the best fit parameters of demographic model A (Figure 2A), then used δaδi to infer these parameters from the simulated data. We subsampled the simulated frequency spectra for different numbers of SNP markers and different numbers of individuals. While median parameter estimates were robust even for very small marker sets (as few as 50 SNPs), variance in inferred parameters increased substantially below approximately 400 SNPs (Figure 4A). Increasing marker sets above 400 SNPs only marginally decreased the variance in estimates and the proportion of non-converging estimates. We likewise found that δaδi performed remarkably well even with sample sizes as low as 3 individuals per population (Figure 4B). Given our particular demographic scenario, sampling more than 4 individuals per population did not appreciably reduce variance in estimates or the proportion of non-converging estimates.

Discussion

Our study generated the first genomic resources for Gillette’s checkerspot butterfly, Euphydryas gillettii, using a single dataset to assemble the reference transcriptome and discover genetic variation in two populations. We leveraged these population genomic data to perform demographic inference in this rare isolated system with a well-known history of recent bottlenecks. This demographic scenario is relevant to many ecological systems, including species introductions from a small number of propagules and populations of conservation concern that have experienced recent declines. We used the program δaδi to accurately infer the timing of the population’s introduction (and accompanying reduction in population size), providing a unique positive control given this particular demographic history. Our study complements a large body of previous work using checkerspot butterflies as model systems in conservation and metapopulation biology (Ehrlich & Hanski, 2004). Within this context, this work demonstrates how genomic studies of ecological model systems can provide valuable tests of population genetic theory and methods.

SNP discovery in RNA-seq data without pre-existing genomic resources is challenging. Well-developed methods such as the GATK framework (Depristo et al, 2011) are designed for detecting variants in genomic DNA-derived sequence data. However, high coverage whole-genome resequencing is currently prohibitively expensive in most eukaryotic systems, and sequence capture methods depend on a priori knowledge of the genome sequence to be targeted. Restriction-site-associated DNA sequencing (RAD-seq) offers one reduced representation alternative by sequencing restriction-site flanking regions in multiple individuals. For the purpose of demographic inference, RAD-seq may in fact be preferable to RNA-seq in that highly expressed genes do not account for a large proportion of overall sequence data (although normalization methods have been devised to address this problem (Christodoulou et al, 2011)), purifying selection is less likely to affect these randomly dispersed genomic regions, and gene paralogy is less likely to confound marker discovery. For systems with no pre-existing genomic resources, however, researchers may desire a method that can discover neutral genomic markers for demographic inference as well as surveying functional regions. RNA-seq may be preferable in such cases because it requires no a priori knowledge of the genome sequence and preferentially targets transcribed regions of the genome that are more likely to be functional. As we demonstrated, this allows researchers to address not only questions about neutral effects of demographic history, but also the interplay of selection and demography in non-model systems. With the appropriate experimental design, the same data may also be leveraged for gene expression analysis or comparative transcriptomics between populations or between species.

Careful curation of the reference assembly, tuning of mapping parameters, and stringent filtering are however necessary to extract a high-quality SNP set from RNA-seq data. Hidden paralogy generates many spurious SNP calls which can have negative effects on downstream analyses (Gayral et al, 2013). Here, we used heuristic SNP filtering to conservatively identify putative false positives and true positives, using these sets to train a Gaussian mixture model and classify variants. Filtering should be performed with care, as certain filtering strategies (e.g. allele frequency thresholds) could distort the resulting frequency spectrum and confound demographic inference.

We specified three basic demographic models, the first of which reflected the known demographic history and included both the WY and CO populations (Figure 2A). We fit this model using the synonymous joint frequency spectrum, then scaled the inferred bottleneck duration (τ_SPLIT) based on our estimate of the effective size of the CO population. This estimate was derived from mark-release-recapture estimates of adult population size and sex ratios in E. gillettii (Boggs et al, 2006, Boggs, unpublished data) as well as a correction for high variance in reproductive success as reported in other lepidopteran species (Boggs, 1979; Oberhauser, 1989; Brakefield et al, 2001). The resulting estimate of bottleneck duration of between 40 and 47 generations (95% CI) compares favorably to the documented introduction 33 generations ago. We note that the scaled values of demographic parameters carry uncertainty from both the inference procedure (due to sampling of the frequency spectrum, for which we account using the bootstrap procedure) and from uncertainty in the estimate of the scaling factor N_CO, for which we do not account, but discuss here. Crude methods of estimating effective population size tend to overestimate N_e, as most biological factors reduce N_e relative to census N. In particular, our consideration of how variance in reproductive success reduces N_CO likely underestimates the true reduction because variance in survival among egg clusters from individual females would introduce additional variability among parents. Likewise, E. gillettii, like many checkerspots, is highly sedentary, and population structure could further reduce N_e relative to census N (Boggs et al, 2006; Williams, 1988). It is also likely that there is additional error in δaδi’s estimate due to complex evolutionary forces including genetic hitchhiking distorting the frequency spectrum relative to assumed neutrality. Nevertheless, the fact that we recover estimates of demographic parameters consistent with known demographic history suggests that these assumptions are not consequential for demographic inference, at least in this particular case.

In many cases, researchers will not have pre-existing knowledge of demographic history, yet will be interested in absolute estimates of demographic parameters rather than coalescent units relative to N_e. In such cases, estimates of N_e are often obtained from the population genetic data by estimating the parameter θ=4N_eμ (Watterson, 1975) and using literature-derived estimates of the mutation rate μ. Many estimates of θ, however, make the assumption of stable demographic history and can be strongly biased under certain demographic scenarios, including bottlenecks. A better approach involves inferring θ under a specified demographic model, as implemented by δaδi and other methods. Mutation rate can also be estimated by performing sequence alignment between the study species and a closely related species: μ = D/2T, where D is the pairwise sequence divergence and T is the divergence time in units of generations.

Our study highlights the importance of fitting multiple demographic models to test diverse demographic scenarios. We found that the model likelihood was not significantly improved by the addition of migration parameters when we extended the population split model to incorporate possible migration between WY and CO (Figure 2B). In all other cases, however, our reported model likelihoods were not directly comparable because they were fitted with different data sets. We evaluated our models with 501 χ² goodness-of-fit tests, examining whether the frequency spectrum predicted under our optimized demographic models were significantly different than the data frequency spectrum. In each case, we failed to reject the demographic models fit with synonymous data, suggesting that these demographic models captured important aspects of the true demographic history.

In the third demographic model, we performed demographic inference using only the CO frequency spectrum, finding that uncertainty in estimates of demographic parameters was significantly greater than when including data from the WY population. Because of correlated effects on the allele frequency spectrum, bottleneck magnitude and duration could not be disentangled from these data. The addition of the WY dataset (described above) added sufficient information to simultaneously infer these parameters. Upon fixing η_CO at its optimized value from two-dimensional demographic inference, we estimated τ_SPLIT similar to the two-dimensional inference. Uncertainty in the estimate increased, however, demonstrating that the addition of data from the proxy ancestral population improved precision. This result is not unexpected, as the joint frequency spectrum contains dramatically more information than the frequency spectrum of individual populations. For example, analysis of the joint frequency spectrum revealed that of 984 total SNPs (discovered in either population and successfully genotyped in all 16 individuals) 866 were segregating in WY while only 392 were segregating in CO. Without addition of the WY data, the zero frequency class would be excluded, and limiting inference to the CO frequency spectrum comprised of fewer markers. The joint frequency spectrum likewise contains information about the magnitude of genetic drift by capturing the change in allele frequencies since the populations’ divergence.

By contrasting inferences using synonymous data with inferences using the entire joint frequency spectrum of synonymous, nonsynonymous, and UTR SNPs, we show that natural selection distorts the frequency spectrum and leads to inaccurate parameter estimates. The fact that δaδi overestimates parameters upon inclusion of nonsynonymous and UTR SNPs is consistent with the skew of these markers toward rare variants compared to synonymous SNPs (Figure S2). Signal in the frequency spectrum is thereby confounded because the excess of rare variants is a signature of population expansion, but also purifying selection. We should note that excluding nonsynonymous and untranslated SNPs from our analysis would not entirely resolve this issue, as purifying selection on synonymous sites as well draft due to background and/or positive selection would be reflected in the synonymous frequency spectrum. One alternative to selecting only putative neutral sites is to specify the distribution of selective effects and incorporate purifying selection in the demographic model itself (Gutenkunst et al, 2009) (although, see Messer & Petrov (2013) for how this approach does not resolve the issue in the case of linked selection).

We demonstrate that inferences of demographic parameters are remarkably robust to both sample number and number of genetic markers. However, our results are particular to the demographic history of this system. For other systems with different demographic histories, simulations like those that we present can be useful during the planning stages of an experiment. By simulating frequency spectra for a range of demographic scenarios, researchers can evaluate the necessary number of samples and markers to achieve a given level of confidence in parameter estimates.

The δaδi approach is one of many approaches for reconstructing demographic history using population genomic data. We tested this approach on our dataset as it fits demographic models using the frequency spectrum alone, which simplifies the interpretation of inference results. The flexibility of the software also facilitates various performance analyses. We remain agnostic, however, to the question of whether alternative methods would give consistent or potentially superior results. For example, Gutenkunst et al (2009) point out that diffusion approximation assumes that N is large and that frequency changes are small per generation, an assumption that may be violated by an extreme bottleneck. The fact that we recover parameter estimates consistent with known demographic history, however, suggests that the approach is robust to this assumption in this particular case. The demographic history of our study population may be particularly easy to resolve due to dramatic effects on the allele frequency spectrum, whereas for other demographic scenarios that require information about the distribution of rare alleles, larger sample sizes will be required. Alternative approaches may be more appropriate for inferring parameters of different demographic scenarios on different time scales. For larger populations, the frequency spectrum contains information about substantially older events, allowing reconstruction of events occurring hundreds to thousands of generations in the past (e.g. Molina et al, 2011). Extreme bottlenecks introduce noise to the frequency spectrum, erasing signatures of ancient events.

Positive controls are important for understanding the circumstances under which demographic inference from genomic data is sensitive to unrealistic model assumptions and simplifications as well as particular methods of data generation. Our study provides one such positive control in a particularly well-studied system, demonstrating that it is possible to recover estimates of demographic parameters numerically consistent with known demographic history. The ability to recover information about past bottlenecks from patterns in genetic data is particularly important since bottlenecks increase the risk of population extinction (Whitlock, 2000). Our RNA-seq-based approach provides a means to simultaneously perform marker discover and multisample genotyping in systems with no existing genomic resources. We advocate more positive controls in diverse ecological model systems, leveraging detailed knowledge of species’ life 563 history for demographic modeling. Meanwhile, application of this multiplex RNA-seq approach in non-model species permits the study of transcribed gene sequence and expression levels while also generating polymorphism data to accurately infer recent bottlenecks. Together, these analyses from genomic data can elucidate important aspects of species’ ecology and conservation status.

Supplementary Material

Figure S1: Results of fitting model A with synonymous SNP data. A: Data joint frequency spectrum with minor allele frequencies ranging from 0 to 12 alleles per population. B: Model frequency spectrum after parameter optimization. C: Anscombe residuals between the model and the data. Red indicates that the model predicted too many alleles for that cell, while blue indicates that the model predicts fewer alleles than observed. D: Histogram of Anscombe residuals.

Figure S2: Allele frequency spectra normalized to number of total SNPs of each class (synonymous and nonsynonymous). Spectra are folded (i.e. unpolarized), as the state of the ancestral allele is unknown. A: Normalized frequency spectrum only depicting frequencies of SNPs segregating within WY. B: Normalized frequency spectrum only depicting frequencies of SNPs segregating within CO.