Estimating Relatedness in the Presence of Null Alleles

Studies of genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. However, with the presence of null alleles, an observed genotype can represent one of several possible true genotypes. This results in biased estimates of relatedness. As the numbers of marker loci are often limited, loci with null alleles cannot be abandoned without substantial loss of statistical power. Here, we show how loci with null alleles can be incorporated into six estimators of relatedness (two novel). We evaluate the performance of various estimators before and after correction for null alleles. If the frequency of a null allele is <0.1, some estimators can be used directly without adjustment; if it is >0.5, the potency of estimation is too low and such a locus should be excluded. We make available a software package entitled PolyRelatedness v1.6, which enables researchers to optimize these estimators to best fit a particular data set.     

Analysis of population genetic structure with RAPD markers

Recent advances in the application of the polymerase chain reaction make it possible to score individuals at a large number of loci. The RAPD (random amplified polymorphic DNA) method is one such technique that has attracted widespread interest. The analysis of population structure with RAPD data is hampered by the lack of complete genotypic information resulting from dominance, since this enhances the sampling variance associated with single loci as well as induces bias in parameter estimation. We present estimators for several population-genetic parameters (gene and genotype frequencies, within- and between-population heterozygosities, degree of inbreeding and population subdivision, and degree of individual relatedness) along with expressions for their sampling variances. Although completely unbiased estimators do not appear to be possible with RAPDs, several steps are suggested that will insure that the bias in parameter estimates is negligible. To achieve the same degree of statistical power, on the order of 2 to 10 times more individuals need to be sampled per locus when dominant markers are relied upon, as compared to codominant (RFLP, isozyme) markers. Moreover, to avoid bias in parameter estimation, the marker alleles for most of these loci should be in relatively low frequency. Due to the need for pruning loci with low-frequency null alleles, more loci also need to be sampled with RAPDs than with more conventional markers, and some problems of bias cannot be completely eliminated.     

Reliability assessment of null allele detection: inconsistencies between and within different methods

Microsatellite loci are widely used in population genetic studies, but the presence of null alleles may lead to biased results. Here, we assessed five methods that indirectly detect null alleles and found large inconsistencies among them. Our analysis was based on 20 microsatellite loci genotyped in a natural population of Microtus oeconomus sampled during 8 years, together with 1200 simulated populations without null alleles, but experiencing bottlenecks of varying duration and intensity, and 120 simulated populations with known null alleles. In the natural population, 29% of positive results were consistent between the methods in pairwise comparisons, and in the simulated data set, this proportion was 14%. The positive results were also inconsistent between different years in the natural population. In the null‐allele‐free simulated data set, the number of false positives increased with increased bottleneck intensity and duration. We also found a low concordance in null allele detection between the original simulated populations and their 20% random subsets. In the populations simulated to include null alleles, between 22% and 42% of true null alleles remained undetected, which highlighted that detection errors are not restricted to false positives. None of the evaluated methods clearly outperformed the others when both false‐positive and false‐negative rates were considered. Accepting only the positive results consistent between at least two methods should considerably reduce the false‐positive rate, but this approach may increase the false‐negative rate. Our study demonstrates the need for novel null allele detection methods that could be reliably applied to natural populations.     

An estimator for pairwise relatedness using molecular markers

I propose a new estimator for jointly estimating two-gene and four-gene coefficients of relatedness between individuals from an outbreeding population with data on codominant genetic markers and compare it, by Monte Carlo simulations, to previous ones in precision and accuracy for different distributions of population allele frequencies, numbers of alleles per locus, actual relationships, sample sizes, and proportions of relatives included in samples. In contrast to several previous estimators, the new estimator is well behaved and applies to any number of alleles per locus and any allele frequency distribution. The estimates for two- and four-gene coefficients of relatedness from the new estimator are unbiased irrespective of the sample size and have sampling variances decreasing consistently with an increasing number of alleles per locus to the minimum asymptotic values determined by the variation in identity-by-descent among loci per se, regardless of the actual relationship. The new estimator is also robust for small sample sizes and for unknown relatives being included in samples for estimating allele frequencies. Compared to previous estimators, the new one is generally advantageous, especially for highly polymorphic loci and/or small sample sizes.     

Nondetectability of restriction fragments and independence of DNA fragment sizes within and between loci in RFLP typing of DNA.

We provide experimental evidence showing that, during the restriction-enzyme digestion of DNA samples, some of the HaeIII-digested DNA fragments are small enough to prevent their reliable sizing on a Southern gel. As a result of such nondetectability of DNA fragments, individuals who show a single-band DNA profile at a VNTR locus may not necessarily be true homozygotes. In a population database, when the presence of such nondetectable alleles is ignored, we show that a pseudodependence of alleles within as well as across loci may occur. Using a known statistical method, under the hypothesis of independence of alleles within loci, we derive an efficient estimate of null allele frequency, which may be subsequently used for testing allelic independence within and across loci. The estimates of null allele frequencies, thus derived, are shown to agree with direct experimental data on the frequencies of HaeIII-null alleles. Incorporation of null alleles into the analysis of the forensic VNTR database suggests that the assumptions of allelic independence within and between loci are appropriate. In contrast, a failure to incorporate the occurrence of null alleles would provide a wrong inference regarding the independence of alleles within and between loci.     

‘True’ null allele detection in microsatellite loci: a comparison of methods,assessment of difficulties and survey of possible improvements

Null alleles are alleles that for various reasons fail to amplify in a PCR assay. The presence of null alleles in microsatellite data is known to bias the genetic parameter estimates. Thus, efficient detection of null alleles is crucial, but the methods available for indirect null allele detection return inconsistent results. Here, our aim was to compare different methods for null allele detection, to explain their respective performance and to provide improvements. We applied several approaches to identify the ‘true’ null alleles based on the predictions made by five different methods, used either individually or in combination. First, we introduced simulated ‘true’ null alleles into 240 population data sets and applied the methods to measure their success in detecting the simulated null alleles. The single best‐performing method was ML‐NullFreq_frequency. Furthermore, we applied different noise reduction approaches to improve the results. For instance, by combining the results of several methods, we obtained more reliable results than using a single one. Rule‐based classification was applied to identify population properties linked to the false discovery rate. Rules obtained from the classifier described which population genetic estimates and loci characteristics were linked to the success of each method. We have shown that by simulating ‘true’ null alleles into a population data set, we may define a null allele frequency threshold, related to a desired true or false discovery rate. Moreover, using such simulated data sets, the expected null allele homozygote frequency may be estimated independently of the equilibrium state of the population.     

A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.     

Assigning alleles to different loci in amplifications of duplicated loci

Duplicated loci, for example those associated with major histocompatibility complex (MHC) genes, often have similar DNA sequences that can be coamplified with a pair of primers. This results in genotyping difficulties and inaccurate analyses. Here, we present a method to assign alleles to different loci in amplifications of duplicated loci. This method simultaneously considers several factors that may each affect correct allele assignment. These are the sharing of identical alleles among loci, null alleles, copy number variation, negative amplification, heterozygote excess or heterozygote deficiency, and linkage disequilibrium. The possible multilocus genotypes are extracted from the alleles for each individual and weighted to estimate the allele frequencies. The likelihood of an allele configuration is calculated and is optimized with a heuristic algorithm. Monte‐Carlo simulations and three empirical MHC data sets are used as examples to evaluate the efficacy of our method under different conditions. Our new software, mhc‐typer V1.1, is freely available at https://github.com/huangkang1987/mhc-typer .     

The Exact Test for Cytonuclear Disequilibria

We extend the analysis of the statistical properties of cytonuclear disequilibria in two major ways. First, we develop the asymptotic sampling theory for the nonrandom associations between the alleles at a haploid cytoplasmic locus and the alleles and genotypes at a diploid nuclear locus, when there are an arbitrary number of alleles at each marker. This includes the derivation of the maximum likelihood estimators and their sampling variances for each disequilibrium measure, together with simple tests of the null hypothesis of no disequilibrium. In addition to these new asymptotic tests, we provide the first implementation of Fisher's exact test for the genotypic cytonuclear disequilibria and some approximations of the exact test. We also outline an exact test for allelic cytonuclear disequilibria in multiallelic systems. An exact test should be used for data sets when either the marginal frequencies are extreme or the sample size is small. The utility of this new sampling theory is illustrated through applications to recent nuclear-mtDNA and nuclear-cpDNA data sets. The results also apply to population surveys of nuclear loci in conjunction with markers in cytoplasmically inherited microorganisms.     

Characterization of 11 microsatellite loci derived from genomic sequences of polychaete Capitella capitata complex

Eleven microsatellite loci derived from the genomic sequence data of Capitella capitata were characterized using 30 samples. The observed number of alleles per locus ranged from four to 36. The levels of observed and expected heterozygosities for polymorphic loci were from 0.10 to 0.87 and from 0.37 to 0.98, averaging 0.52 and 0.77, respectively. Analyses of Hardy–Weinberg equilibrium and genotypic linkage disequilibrium suggest the possible presence of both null alleles and Wahlund effect. One of the 11 loci was difficult to amplify for genotyping. Therefore, the rest 10 loci are good molecular markers for population genetic analysis.     

Characterization of dinucleotide microsatellite markers in the parthenogenetic mourning gecko (Lepidodactylus lugubris)

We present 16 variable dinucleotide microsatellite markers to quantify genetic variation in the parthenogenetic gecko, Lepidodactylus lugubris. Genetic diversity at these loci was unusually high for an asexual species. Subsets of individuals produced identical genotypes across all loci. Individual loci revealed evidence of polyploidy and marked differences between observed and expected heterozygosity, indicating the presence of null alleles. These patterns conform to prior expectations based on the distant genetic relationships between the presumed sexual progenitors of L. lugubris. Comparisons with sexual relatives will be required to determine the sources of the observed genetic variation.     

A comparison of microsatellite-based pairwise relatedness estimators

Studies of inbreeding depression or kin selection require knowledge of relatedness between individuals. If pedigree information is lacking, one has to rely on genotypic information to infer relatedness. In this study we investigated the performance (absolute and relative) of 10 marker-based relatedness estimators using allele frequencies at microsatellite loci obtained from natural populations of two bird species and one mammal species. Using Monte Carlo simulations we show that many factors affect the performance of estimators and that different sets of loci promote the use of different estimators: in general, there is no single best-performing estimator. The use of locus-specific weights turns out to greatly improve the performance of estimators when marker loci are used that differ strongly in allele frequency distribution. Microsatellite-based estimates are expected to explain between 25 and 79% of variation in true relatedness depending on the microsatellite dataset and on the population composition (i.e. the frequency distribution of relationship in the population). We recommend performing Monte Carlo simulations to decide which estimator to use in studies of pairwise relatedness.     

identix,a software to test for relatedness in a population using permutation methods

The computer program identix estimates relatedness in natural populations using multilocus genotypic data. Queller & Goodnight's (1989) and Lynch & Ritland's (1999) estimators of pairwise relatedness are implemented, as well as the identity index of Mathieu et al. (1990). Estimates of the confidence intervals around these pairwise values are also provided. The null hypothesis of no relatedness (multilocus genotypes are independent draws from a panmictic population) is tested using a permutation method that compares the observed distribution of the moments of pairwise relatedness coefficients to that expected in unstructured population.     

The genetics of speciation: are complex incompatibilities easier to evolve?

Reproductive isolation can evolve readily when genotypes containing incompatible alleles are connected by chains of fit intermediates. Experimental crosses show that such Dobzhansky–Muller incompatibilities (DMIs) are often complex (involving alleles at three or more loci) and asymmetrical (such that reciprocal introgressions have very different effects on fitness). One possible explanation is that asymmetrical and complex DMIs are ‘easier to evolve’, because they block fewer of the possible evolutionary paths between the parental genotypes. To assess this argument, we model evolutionary divergence in allopatry and calculate the delays to divergence caused by DMIs of different kinds. We find that the number of paths is sometimes, though not always, a reliable predictor of the time to divergence. In particular, we find limited support for the idea that symmetrical DMIs take longer to evolve, but this applies largely to two‐locus symmetrical DMIs (which leave no path of fit intermediates). Symmetrical complex DMIs can also delay divergence, but only in a limited region of parameter space. In most other cases, the presence and form of DMIs have little influence on times to divergence, and so we argue that ease of evolution is unlikely to be important in explaining the experimental data.     

Estimation of relatedness by DNA fingerprinting

The recent discovery of hypervariable VNTR (variable number of tandem repeat) loci has led to much excitement among population biologists regarding the feasibility of deriving individual estimates of relatedness in field populations by DNA fingerprinting. It is shown that unbiased estimates of relatedness cannot be obtained at the individual level without knowledge of the allelic distributions in both the individuals of interest and the base population unless the proportion of shared marker alleles between unrelated individuals is essentially zero. Since the latter is usually on the order of 0.1-0.5 and since there are enormous practical difficulties in obtaining the former, only an approximate estimator for the relatedness can be given. The bias of this estimator is individual specific and inversely related to the number of marker loci and frequencies of marker alleles. Substantial sampling variance in estimates of relatedness arises from variation in identity by descent within and between loci and, with finite numbers of alleles, from variation in identity in state between genes that are not identical by descent. In the extreme case of 25 assayed loci, each with an effectively infinite number of alleles, the standard error of a relatedness estimate is no less than 14%, 20%, 35%, and 53% of the expectation for full sibs and second-, third-, and fourth-order relationships, respectively. Attempts to ascertain relatedness by means of DNA fingerprinting should proceed with caution.      

Estimating effective paternity number in social insects and the effective number of alleles in a population

Estimating paternity and genetic relatedness is central to many empirical and theoretical studies of social insects. The two important measures of a queen's mating number are her actual number of mates and her effective number of mates. Estimating the effective number of mates is mathematically identical to the problem of estimating the effective number of alleles in population genetics, a common measure of genetic variability introduced by Kimura & Crow (1964). We derive a new bias-corrected estimator of effective number of types (mates or alleles) and compare this new method to previous methods for estimating true and effective numbers of types using Monte Carlo simulations. Our simulation results suggest that the examined estimators of the true number of types have very similar statistical properties, whereas the estimators of effective number of types have quite different statistical properties. Moreover, our new proposed estimator of effective number of types is approximately unbiased, and has considerably lower variance than the original estimator. Our new method will help researchers more accurately estimate intracolony genetic relatedness of social insects, which is an important measure in understanding their ecology and social behaviour. It should also be of use in population genetic studies in which the effective number of alleles is of interest.     

Population estimators or progeny tests: what is the best method to assess null allele frequencies at SSR loci?

Nuclear SSRs are notorious for having relatively high frequencies of null alleles, i.e. alleles that fail to amplify and are thus recessive and undetected in heterozygotes. In this paper, we compare two kinds of approaches for estimating null allele frequencies at seven nuclear microsatellite markers in three French Fagus sylvatica populations: (1) maximum likelihood methods that compare observed and expected homozygote frequencies in the population under the assumption of Hardy-Weinberg equilibrium and (2) direct null allele frequency estimates from progeny where parent genotypes are known. We show that null allele frequencies are high in F. sylvatica (7.0% on average with the population method, 5.1% with the progeny method), and that estimates are consistent between the two approaches, especially when the number of sampled maternal half-sib progeny arrays is large. With null allele frequencies ranging between 5% and 8% on average across loci, population genetic parameters such as genetic differentiation (F _ST) may be mostly unbiased. However, using markers with such average prevalence of null alleles (up to 15% for some loci) can be seriously misleading in fine scale population studies and parentage analysis.     

Do malaria parasites mate non-randomly in the mosquito midgut?

Polymerase chain reaction (PCR)-based genotyping of oocysts dissected from mosquito midguts has previously been used to investigate overall levels of inbreeding within malaria parasite populations. We present a re-analysis of the population structure of Plasmodium falciparum malaria using diploid genotypes at three antigen-encoding loci in 118 oocysts dissected from 34 mosquitoes. We use these data to ask whether mating is occurring at random within the mosquito midgut, as is generally assumed. We observe a highly significant deficit of heterozygous oocysts within mosquitoes at all three loci, suggesting that fusion of gametes occurs non-randomly in the mosquito gut. A variety of biological explanations, such as interrupted feeding of mosquitoes, positive assortative mating and outcrossing depression, could account for this observation. However, an alternative artefactual explanation--the presence of non-amplifying or null alleles--can account for the observed data equally well, without the need to invoke non-random mating. To evaluate this explanation further, we estimate the frequencies of null alleles within the oocyst population using maximum likelihood, by making the assumption that non-amplifying oocysts at any of the three loci are homozygous for null alleles. Observed levels of visible heterozygotes fit closely with those expected under random mating when non-amplifying oocysts are accounted for. Other lines of evidence also support the artefactual explanation. Overall inbreeding coefficients have been recalculated in the light of this analysis, and may be considerably lower than those estimated previously. In conclusion, we suggest that the deficit of heterozygotes observed is unlikely to indicate non-random mating within the mosquito gut and is better explained by misscoring of heterozygotes as homozygotes.     

SSR-based assessment of genetic diversity in South American Vitis vinifera varieties

Six SSR loci, previously developed for grapevine, were analyzed to evaluate the genetic variability and cultivar relatedness in a collection of 25 autochthonous Vitis vinifera varieties from Perú and Argentina.

The number of alleles per locus ranged from 6 to 13, while the number of microsatellites genotypes varied between 9 and 16. The expected heterozygosity varied between 0.71 and 0.89 and the polymorphism information content ranged from 0.70 to 0.88 indicating that the SSRs were highly informative. It was possible to identify 76 different genotypes, with all accessions showing-at least one-specific combination of alleles. Triallelic loci were observed with some SSR. Sequence analysis revealed that variation in the number of repeats and insertion/deletions (InDels) accounted for the polymorphisms observed. Clustering analysis resulted in four separate groups of varieties sharing at least 75% of the markers. A few cases of synonymies were found within the Peruvian accessions. Varieties were clustered following a general pattern of shared morphological and enological traits, rather than geographical origin.     

Simultaneous estimation of null alleles and inbreeding coefficients

Although microsatellites are a very efficient tool for many population genetics applications, they may occasionally produce "null" alleles, which, when present in high proportion, may affect estimates of key parameters such as inbreeding and relatedness coefficients or measures of genetic differentiation. In order to account for the presence of null alleles, it is first necessary to estimate their frequency within studied populations. However, the commonly used null allele frequency estimators are not of general applicability because they can produce upwardly biased estimates when a population under study experiences some inbreeding. In such a case, 2 formerly described approaches, population inbreeding model and individual inbreeding model, can be applied for simultaneous estimation of null allele frequencies and of the inbreeding coefficient. In this study, we demonstrate the properties and utility of these 2 methods and show that they outperform the commonly used approaches in the estimation of null allele frequencies based on genotypic data. The methods are applied to empirical data from a natural population of European beech (Fagus sylvatica L.), and results are briefly discussed. The methods presented in this paper are implemented in the Windows-based user-friendly INEST computer program (available free of charge at http://genetyka.ukw.edu.pl/INEst10_setup.exe).