Some features of the site may not work correctly. DOI: Kalinowski Published Biology, Medicine Heredity As more microsatellite loci become available for use in genetic surveys of population structure, population geneticists are able to select loci to use in population structure surveys. This study used computer simulations to investigate how the number of alleles at loci affects the precision of estimates of four common genetic distances. This showed that equivalent results could be achieved by examining either a few loci with many alleles or many loci with a few alleles.
More specifically, the… Expand. View on Nature. Save to Library Save. Create Alert Alert. Share This Paper. Background Citations. Methods Citations. Results Citations. The number of migrants required for allelic richness maintenance, at least when founding events are considered, depends on the specific parameters of the scenario e.
This analysis points out, once again, that the OMPG rule has limitations for limitations from other perspectives, see [21] , [55]. More specifically, its application should be reserved for cases in which low heterozygosity is a concern.
Maintenance of heterozygosity might be achieved with one migrant per generation, but this can be too low a migration rate for allelic richness maintenance.
Following a founder effect, heterozygosity should be a concern for the period immediately following the event, but allelic richness should be more important for the long-term evolutionary potential of the population [2] , [12] , and the OMPG rule should be used with this distinction in mind. Allelic richness and heterozygosity form the basis of the two most commonly used measures of genetic diversity, but heterozygosity is applied much more regularly.
While a third group of locus-level diversity measures, based on Shannon's index, has been suggested and has recently seen some development [56] , the evolutionary interpretation of these measures is still unclear [57] , and they are not yet in common use. Allelic richness measures are essential to our understanding of the aspect of a population's genetic diversity pertaining to the long term evolutionary potential of the population [2] , [13] — [15] , [17].
The differences between the measures, in regards to treatment of rare and common alleles, are perhaps more apparent when considering them as two diversity indices. Allelic richness is a diversity measure where a is the number of alleles and are the allele frequencies , and heterozygosity is the Geni-Simpson index, which has a diversity [58] , [59].
The order of the diversity index, q , indicates the sensitivity of the measure to common and rare alleles, where a diversity is completely insensitive to allele frequencies and, therefore, favors rare alleles, and diversity favors common alleles with a diversity, Shannon's index, rare and common alleles are proportionally weighted [56] , [58]. The presence of alleles is indicative of the potential of selection to act upon an allele and, thus, relates directly to the evolutionary potential of the population [13].
This genetic goal can be used in analysis of stochastic models and in combination with an allele frequency spectrum to provide predictions for allelic richness under different ecological scenarios, as shown in the model presented here. While F-statistics provide a framework for analyzing heterozygosity dynamics, our understanding of allelic richness dynamics is limited. Allelic richness, which emphasizes the number of alleles over their frequencies, is affected by various parameters, such as migration rates, allele frequency and demographic parameters, as demonstrated by the model results.
However, heterozygosity, which focuses on allele frequencies and thus is insensitive to rare alleles, is affected differently by different parameters in similar systems [2] , [16] , [18] , [41] , [62].
Thus, an allelic richness evaluation requires different considerations than that of an F-statistics framework, as demonstrated by the comparison of the OMPG rule with the simulation results. With the ecological and evolutionary consequences of heterozygosity versus allelic richness in mind, both measures should be considered in conservation and management efforts aiming at maintaining genetic diversity.
Generalization of the framework to include a simple one-generation founder event. Mean allele frequencies at equilibrium as a function of the number of migrants per generation M. Solid lines indicate the estimation of the mean allele frequency equation 4. Dashed lines indicate thresholds. Dashed-dotted lines indicate regression analysis results for the model ; details in S3 Table. Proportion of allelic richness recovered by gene flow and cut-off frequencies Q c for deterministic migration pattern.
Fitted regression models for for mean allele frequency at equilibrium. Curves shown in S1 - S9 Figs. We wish to thank the anonymous reviewers for very constructive comments. Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field. Abstract Allelic richness number of alleles is a measure of genetic diversity indicative of a population's long-term potential for adaptability and persistence.
Introduction Genetic diversity is an important aspect of the dynamics of populations, as it is directly related to the evolutionary potential of the population and the deleterious effects of inbreeding [1].
Methods 2. Model The model consists of a source population and a newly founded population. Simulations Simulations were carried out for different scenarios with the following parameter values: initial population size ; carrying capacity ; population growth rate.
Simulation analysis Probability measures can be broken into a discrete part and a continuous part Jordan's decomposition theorem [46].
Download: PPT. Figure 1. Cumulative density functions for the allele frequency at the equilibrium phase. Source population allele frequency spectrum In order to assess the model's implications for a polymorphic locus and not just a single allele, the allele frequency spectrum of the source population is compared with results for simulations with different Q values. Results In all simulated scenarios, the mean allele frequency in the founded population increased over time, showing eventual stabilization.
Figure 3. Mean allele frequencies at equilibrium as a function of the number of migrants per generation. Table 1. Figure 4. Allele frequency spectrum Performing an analysis on polymorphic loci requires attention to different alleles with different frequencies, and not just a single allele. Figure 5. Probability of allele presence for different Q values allele frequencies in source population. Table 2. Proportion of allelic richness recovered by gene flow and cut-off frequencies Q c.
Discussion The model follows a single allele that is subject to two evolutionary forces: gene flow and genetic drift. Allele frequency spectrum analysis Typically, it is not that the presence of a specific allele is of concern, but rather the presence of many alleles across many loci [51]. The OMPG rule and allelic richness Conservation and management programs increasingly address genetic issues, as small, vulnerable populations are susceptible to genetic diversity loss, which might negatively impact their status [1].
Allelic richness vs. Supporting Information. S1 Appendix. Migration patterns and allelic diversity. S2 Appendix. Code for the simulations. S3 Appendix. S1 Fig. S2 Fig. S3 Fig. S4 Fig. S5 Fig. S6 Fig. S7 Fig.
S8 Fig. S9 Fig. S1 Table. S2 Table. S3 Table. Acknowledgments We wish to thank the anonymous reviewers for very constructive comments. References 1. Ecol Lett — View Article Google Scholar 2. Allendorf FW Genetic drift and the loss of alleles versus heterozygosity. Zoo Biol — View Article Google Scholar 3. First we must appreciate that genes do not act in isolation. The genome in which a genotype is found can affect the expression of that genotype, and the environment can affect the phenotype.
An allele can be dominant over one allele but recessive to another allele. Model of dominance from enzyme activity: no copies produce no phenotype, one copy produces x amount of product and two copies produces 2x then the alleles are additive and there is no dominance intermediate inheritance. If one copy of the allele produces as much product or has as high a rate of flux as a homozygote then there is dominance.
There are cases where the heterozygote is greater in phenotypic value than either homozygote: called overdominance. Single genes do not always work as simply as indicated by a dominance and recessive relationship. Other genes can affect the phenotypic expression of a given gene. One example is epistasis "standing on" where one locus can mask the expression of another. Classic example is a synthetic pathway of a pigment. Mutations at loci controlling the early steps in the pathway gene 1 can be epistatic on the expression of genes later in the pathway gene 3 by failing to produce pigment precursors e.
Genes can also be pleitropic when they affect more than one trait. The single base pair mutation that lead to sickle cell anemia is a classic example. Mutations in cartilage are another example since cartilage makes up many different structures the effects of the mutation are evident in many different phenotypic characters.
The number of loci in the samples was varied from 2 to All combinations of these four parameters was examined number of loci, number of alleles, N e , t. The coefficients of variation for each of these genetic distances were estimated from the data by dividing the standard deviation of the estimates by the average estimate.
Contour plots showing the coefficient of variation for data sets with different numbers of loci and varying numbers of alleles per locus were created with SigmaPlot Simulated data showed that highly polymorphic loci provided better estimates of genetic distances than less polymorphic loci Figure 1. For example, 16 loci each having two independent alleles had approximately the same coefficient of variation for each of the genetic distances as two loci having 16 independent alleles each.
For example, the coefficient of variation of genetic distances for populations of individuals separated for 50 generations was identical to the coefficient of variation of estimates of genetic distances between populations of individuals separated for generations.
Results for loci with infinite alleles mutation a and stepwise mutation b are shown. These results are in good agreement with an analysis of the Sanghvi genetic distance made by Foulley and Hill The Sanghvi distance is not used often for describing population structure, but it has tractable mathematical properties and has been shown to estimate phylogenies effectively Takezaki and Nei, Foulley and Hill showed analytically that the coefficient of variation of the Sanghvi distance is approximately proportional to the sum of the number of independent alleles at each locus in the sample.
This is not especially problematic, for the utility of these genetic distances to quantify genetic differences between highly differentiated populations is limited.
Keep in mind that both genetic drift and mutation lead to differentiation. Both D A and D C approach their maximum value of 1. This results in these statistics having a low coefficient of variation when divergence time and polymorphism are high Figure 1 , but decreases their ability to describe the length of population separation. D S loses its utility when polymorphism is high, divergence time is long, and few loci are scored.
In this case, samples from each population often share no alleles and D S is undefined. For example, about half of the loci having 33 alleles had no alleles in common in populations of individuals after generations. It asymptotically approaches a maximum value, and this value is inversely proportional to the amount of polymorphism present in the populations eg, Hedrick, Of the four distances examined, D A and D C exhibited the strongest equivalence of alleles within and between loci Figure 1.
For both of these distance measures, adding more loci decreased the coefficient of variation faster than increasing the number of alleles per locus. For example, eight loci with two independent alleles produced better estimates of D S than two loci with eight independent alleles.
Mutation mechanism did not appear to have a strong affect upon the coefficient of variation when divergence time was short. However, for both mutation mechanisms, the equivalence of alleles observed at low divergence times broke down at loci with high mutation rates ie, those with greater than eight alleles but not at loci with lower mutation rates. Increasing allele number was associated with decreased coefficients of variation for each of the four genetic distances studied.
The standard error of these statistics, however, behaved differently. The coefficient of variation of these statistics decreased only because the average value of these genetic distances increased faster than the standard error Figure 2.
Distributions of estimates of D A between two populations of individuals separated for generations. Each estimate is based on eight simulated loci. A log-uniform distribution of mutation rates was used to simulate mutation rates and each mutation was assumed to create a new allele.
Each line is a spline curve of the proportions of estimates that fell into a bin with width of 0. The equivalent utility of alleles within and across loci for estimating genetic distances described here is significant because it demonstrates that study design for estimating genetic distances is flexible as long as the amount of divergence is not great. There is no requirement to examine either highly polymorphic loci or large numbers of loci. The only requirement is that a sufficient number of alleles be examined.
Phylogenetic analysis: models and estimation procedures. Evolution , 21 : —
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