One size fits all? Direct evidence for the heterogeneity of genetic drift throughout the genome

Abstract

Effective population size (N_e) is a central parameter in population and conservation genetics. It measures the magnitude of genetic drift, rates of accumulation of inbreeding in a population, and it conditions the efficacy of selection. It is often assumed that a single N_e can account for the evolution of genomes. However, recent work provides indirect evidence for heterogeneity in N_e throughout the genome. We study this by examining genome-wide diversity in the Danish Holstein cattle breed. Using the differences in allele frequencies over a single generation, we directly estimated N_e among autosomes and smaller windows within autosomes. We found statistically significant variation in N_e at both scales. However, no correlation was found between the detected regional variability in N_e, and proxies for the intensity of linked selection (local recombination rate, gene density), or the presence of either past strong selection or current artificial selection on traits of economic value. Our findings call for further caution regarding the wide applicability of the N_e concept for understanding quantitatively processes such as genetic drift and accumulation of consanguinity in both natural and managed populations.

1. Introduction

The effective population size (N_e) measures the magnitude of genetic drift in a population. It determines expected levels of polymorphism, the efficacy of selection and the potential for accumulation of consanguinity in a population. Given its widespread use in population and conservation genetics, it is important to know whether a single N_e can account for the observed patterns of evolution in a population. Theory predicts that selection acting at linked sites can modulate the amount of genetic drift and hence the N_e experienced by a given site. The intensity of linked selection is expected to vary throughout the genome and thereby generate heterogeneity in N_e [1,2].

Empirical evidence for the heterogeneity of N_e has been indirect, relying almost exclusively on joint patterns of polymorphism and divergence [3]. It has been difficult to prove directly that N_e is heterogeneous throughout the genome and that heterogeneity observed in polymorphism is not merely reflecting variation in mutation rates [3,4].

Here, we use a method for directly estimating N_e based on temporal variation in allele frequencies. We test for heterogeneity of estimated N_e by genotyping a total of more than 1000 individuals representing three successive generations in a population from the Danish Holstein cattle breed. We find statistical evidence for substantial variation in N_e throughout the genome. We find that proxies commonly used for the expected intensity of linked selection cannot account for the variation observed.

2. Material and methods

(a). Sampling of individuals and genotyping

We studied the Danish Holstein population [5]. We selected three cohorts of individuals born in 1995, 2000 and 2005 (268, 295 and 579 individuals, respectively), genotyped using the 54 K SNP chip. Marker positions refer to the UMD3.1 assembly of the Bos taurus genome [6]. We only included SNPs with less than 10% missing data and genotyped in all cohorts, leaving a total of 46 268 SNPs. See the electronic supplementary material for further details.

(b). Estimation of N_e from temporal variation in allele frequency

For each autosome, SNPs were grouped in non-overlapping windows containing 100 SNPs (n = 447 windows). We used two N_e estimators based on the temporal variance in allele frequency, which have complementary statistical properties of variance and bias [7,8]. These estimators do not rely on pedigree information and provide direct estimates of N_e over a time interval in each window. We calculated the standard error (s.e.) of the N_e estimates within each window using 10 000 bootstrap samples (see the electronic supplementary material).

(c). Genomic covariates

For each window, we obtained data on the local recombination rate (centiMorgan per megabase), the density of genes (fraction of window in coding regions), the presence of quantitative trait loci (QTL) for three economically important traits selected in the population for the time period considered here (milk production, fat and protein content) and footprints of past selection in the Holstein breed (see the electronic supplementary material).

(d). Statistical analysis

We used linear models with N_e estimated in each window as the dependent variable, and genomic covariates, the chromosome of origin and physical length of each window as explanatory variables. Analyses were carried out in R [9] and are available as the electronic supplementary material. To account for the heterogeneity of standard errors around N_e estimates, models were fitted by weighted least squares using the function lm() and each window in the analysis was weighted by 1/s.e.

3. Results

We estimated N_e over one generation in two time intervals (1995–2000 and 2000–2005) and, unless stated otherwise, results reported here use the time interval 1995–2000 where roughly equal numbers of individuals were available. All results use estimator [8], as the alternative method [7] yielded similar N_e estimates (electronic supplementary material, figure S1).

We found that the estimated N_e of each autosome varied by a factor of almost two (mean: 48, median: 45, min: 36 ± 2.6 on chromosome 25, max: 72 ± 6.4 on chromosome 23, electronic supplementary material, figure S1). We then estimated N_e within 447 autosomal windows of 100 SNPs, spanning on average 5 Mb (range: 3–10 Mb). This revealed considerable heterogeneity between windows in the estimated N_e (median: 50.83, s.d.: 37.4; figure 1a). Although some of the variation observed is due to sampling error, genuine variation remains among windows (p < 0.0001).

Figure 1.

Heterogeneity of estimated N_e in genomic windows. (a) Distribution of N_e over one generation (1995–2000) in 447 windows. Histogram: empirical distribution of N_e estimates. Dashed line: distribution expected under homogeneous N_e and incorporating standard errors on estimated N_e (electronic supplementary material, figure S5). Solid line: expected distribution for the estimated N_e under a model accounting for standard errors as above and further assuming lognormally distributed parametric variation in N_e among windows (see the electronic supplementary material). (b) Example of within-chromosome heterogeneity in estimated N_e. Each dot represents the N_e estimated per window. Errors bars indicate 1 s.e. (estimated by bootstrapping).

Genetic diversity is reduced in regions of low recombination rates and/or regions with high gene density [1,10], because they are expected to experience more background selection and are more likely to be affected by neighbouring selective sweeps. Therefore, we tested whether a number of genomic variables used as proxies for linked selection could explain the observed variation in estimated N_e. Although chromosome of origin significantly affected the estimated N_e of a window, neither local recombination rates nor gene density explained the variation in estimated N_e (table 1; electronic supplementary material, figures S2 and S3).

Table 1.

Effect of genomic covariates on log (N_e) in autosomal windows.

explaining variables	estimatea	s.e.a	F-test	p-valueb
chromosome	n.a.	n.a.	3.56	<0.00001
physical window length	−3.31 × 10−8	2.006 × 10−8	1.09	0.297
local gene density	−0.134	0.169	0.006	0.94
local recombination	−0.087	0.049	3.49	0.06
past selective sweeps	0.0872	0.037	4.46	0.035
number of QTLs	−0.0346	0.054	0.197	0.657

^aEstimates of regression coefficients and associated standard errors are only provided for regressing/continuous explanatory variables.

^bSignificance was tested using an F-test in a linear model accounting for heterogeneity of variance around N_e estimates.

Episodes of strong natural or artificial selection are expected to affect the evolutionary trajectory of linked regions. Although a single N_e cannot rigorously account for the effect of directional selection on the diversity of neighbouring regions, we expect regions currently affected by a sweep to exhibit reduced estimated N_e. Using information on past selective sweeps in Holstein [11], we found no differences among N_e estimated in windows with no selective sweep (n = 378 windows) or 1, 2 or more than 2 selective sweeps (respectively n= 49, 13 and 7 windows; Wilcoxon rank sum test, p = 0.56; electronic supplementary material, figure S4). We found an effect of the presence of past selective sweep but this effect is very small (table 1; electronic supplementary material, table S2). We also used three traits of major economic value in the breed and currently under artificial selection in this population. No difference in estimated N_e among windows containing either no QTL (n = 375 windows) or QTLs for 1, 2 or 3 traits (respectively, n = 64, 7 and 1 windows) was found (Wilcoxon test, bins with QTL versus no QTL, p = 0.49; figure 2). N_e estimated in the vicinity of the 7 QTLs with the largest phenotypic effect was not markedly reduced relative to the remaining windows (p = 0.33; electronic supplementary material, table S1).

Figure 2.

Boxplot of log (N_e) among windows with either no QTL or harbouring QTLs coding for 1, 2 or 3 traits under artificial selection.

To guard against heterogeneity spuriously created by physical window size, we estimated N_e in 433 windows spanning 5 Mb (and thus variable number of SNPs). Irrespective of the window type used (fixed number of SNPs versus fixed length), we uncover very similar patterns of variation in estimated N_e and effect of chromosomes (electronic supplementary material, figure S6 and table S2). We still reveal significant heterogeneity among chromosomes (p < 0.0001) and no effect of other covariates.

We also estimated N_e over two generations (1995–2005) and found low correlations with estimates for the same window obtained for one-generation intervals (1995–2000 and 2000–2005). There was a weak and non-significant tendency for chromosomes with the highest N_e estimates in 1995–2000 to have the lowest N_e estimates in 2000–2005 (electronic supplementary material, figure S7).

4. Discussion

We provide direct evidence that the intensity of genetic drift varies throughout the genome. Our finding is robust to the choice of estimator for inferring N_e, potential effect of linkage decreasing effective sample size (electronic supplementary material, figure S1), time interval considered and type of window used (electronic supplementary material, figure S6). Overlapping generations and some non-random mating can bias N_e estimates based on temporal variance [12], but this bias will apply with equal forces throughout the genome and not create heterogeneity per se. Scale of analysis is ultimately limited by the sampling variance around N_e estimates and 100 SNPs per window was the minimum needed to get reliable N_e estimates.

Genome-wide average N_e estimated for the interval 1995–2000 (48) and for individual chromosomes (35–72; electronic supplementary material, figure S1) are within the range of values reported for this breed. N_e was estimated to be 49 for the Danish Holstein population for the period 1993–2003 using rates of inbreeding inferred from the pedigree [5]. Similarly, N_e for the US Holstein has been estimated to be 39 by the same method [13]. The magnitude of the heterogeneity we detected for N_e throughout the genome (figure 1a) was comparable, albeit in the lower range, of what was recently estimated indirectly in 10 species [3].

No effect of either local recombination rate, gene density or the presence of QTLs for traits under artificial selection was detected on estimated N_e (table 1; electronic supplementary material, table S2). Local recombination rates and gene density are commonly used proxies for the long-term effect of linked selection on nucleotide diversity throughout genomes [2,10,14]. We detect no correlation between these variables and the estimated N_e (table 1; electronic supplementary material, table S2). One possibility is that recombination rates and gene density do affect the intensity of selection at linked sites, but at a scale of about 100 kb [14]. The windows we used were typically 50 times larger. Linked selection is also likely to act in an episodic fashion and most regions may not currently be experiencing linked selection. Another possibility is that the effect of linked selection acts cumulatively over timescales larger than the few generations examined here.

Interestingly, we detected no effect of the presence of QTL on estimated N_e over the 1995–2000 or 2000–2005 time intervals, but when estimating N_e over the 1995–2005 interval, we detect a modest effect of the presence of QTLs on N_e estimated in 5-Mb windows (electronic supplementary material, table S2). We expect that cumulative effects of selection on QTLs will be easier to detect in studies using longer time intervals. Summing up, although we present strong evidence for heterogeneity in N_e, the processes underlying this heterogeneity and that could account for the lack of correlation in N_e over successive generations (electronic supplementary material, figure S7) remain unknown.

5. Conclusion

Several studies report pervasive effects of selection throughout the genome of Drosophila [3,10,14]. A review on N_e and its applicability concludes: ‘ (…) no nucleotide in the compact genome of D. melanogaster is evolving entirely free of the effects of selection on its effective population size; it will be of great interest to see whether this applies to species with much larger genomes’ [1, p. 203]. Here, we provide direct evidence for extensive variation in N_e in a much less compact genome.

N_e plays a prominent role in conservation genetics to assess the status of populations, predict the rate of accumulation of consanguinity and forecast adverse consequences of inbreeding depression. If the variation in N_e we uncover is typical, caution should be used when interpreting mean values of N_e, as genomic regions can drift and accumulate consanguinity at a much higher rate than would be predicted if N_e was homogeneous (see [15] for a review in the topic).

Pervasive variation in N_e throughout the genome also raises concern for the uncritical use of genome-wide scans for footprints of selection. A popular strategy consists of deriving a null distribution for a test statistic, such as level of subdivision, length of homozygosity tracts, etc., expected under selective neutrality. Genomic regions exhibiting discrepant values for these statistics are then flagged as ‘candidates for selection’. However, null distributions for selective neutrality used so far rely on the implicit assumption that all regions undergo a common N_e. The true null distribution might actually contain substantially more variance than expected, and ignoring such variation will invariably yield inflated rates of false positives.

Data accessibility

Supporting data, metadata and R script are available as the electronic supplementary material.

Authors' contributions

B.J.M. and T.B. designed and wrote the study with input from all co-authors. B.G., R.B. and G.S. obtained SNP and analysed QTL data. B.J.M., P.T. and T.B. analysed SNP data. All authors agree to be held accountable for the content therein and approve the final version of the manuscript.

Competing interests

The authors have no competing interests.

Funding

B.J.M. benefitted from a grant from Erasmus-Mundus PhD School ‘EGS-ABG’ and INRA Animal Genetics. The data for QTL are funded by the project ‘Genomic selection—from function to efficient utilization in cattle breeding’ (grant no. 3405-10-0137).