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Matters Arising---...:.7=55 ~NA~TU~R~E__:_:VO~L::_::.3=04-"'25:....:A=U=GU=ST~1=98:::._3 -----MATTERS ARISING-----------.....:.7=55 Heterozygosity and In addition, the correlation between the between heterozygosity (H) and genetic heterozygosity and the evolutionary rate distance (D) with D = 0 when H = 0 and genetic distance of proteins of proteins may be due to differences in with the slope set by the values of the IN a statistical study of the relationship the mutation rate for different proteins. parameters' divergence time (t) and between genetic distance1 (D) and Examining only those mutants that are effective population size (N.). However, avera~e heterozygosity (H), Skibinski and neutral, a protein with relatively high our observed linear regression of D on H Ward '3 observed that D increased with mutation rate should have both a higher calculated for a sample of 31 different increasing H but D > 0 when H = 0. heterozygosity and a greater genetic dist­ proteins had a significant intercept on the Arguing that D should be 0 when H is ance between species than a protein with genetic distance axis. Because our method 0, they concluded that their observation a lower mutation rate. More specifically, was designed with the aim of controlling is inconsistent with the neutral mutation the ratio of the genetic distances for two for variation in t and N. among proteins, hypothesis. This conclusion is not justified proteins with different mutation rates is we argued that, regardless of the values for the following reasons. -lid ll2 and the ratio of their hetero­ of its parameters, neutral theory could not First, the fact that D > 0 when H = 0 zygosities is nearly li1(4N.ll2 +1)/ explain this result. indicates that gene substitution has li2(4Nellt + 1) where ll 1 and ll2 are the Chakraborty and Hedrick first point out occurred in the evolutionary process for mutation rates for two different proteins that, as a result of sampling error, the the protein loci involved, and this in turn and N. is the effective population size. If observed heterozygosity at a neutral locus means that mutation occurs occasionally there is a 10-fold difference in mutation may be' below its expected value while at these loci. In other words, the mutation rates (lit= l0ll2), the genetic distance genetic distance for the locus may be high. rate for these loci is not zero, and thus would differ by almost a factor of 10 and Such situations are common in practice, the expectation of H is not really zero, the heterozygosity would differ by almost for example when two related species are unlike Skibinski and Ward's assumption. a factor of 10 (assuming 4N.ll1 is not too fixed for different alleles. In our study, In practice, however, His subject to large large). The cited genetic distances given however, both H and D were estimated stochastic and sampling errors when it is in Fig. 1 of ref. 3 range from about 0.1 for each protein using a minimum of 30 estimated from a relatively small number to 1.0 and the heterozygosities from 0.02 loci from 30 pairs of species (most sample 4 of individuals • Indeed, when n genes are to 0.2. Although there is little direct infor­ sizes are much greater). The estimates will sampled from a population, the probabil­ mation of appropriate mutation rates, a therefore be much closer to the expected ity (P) that no variant alleles are found at 10-fold difference among molecules values than in the single locus example of 4 a neutral locus is (1/n) N", where N and seems possible due to several factors. Chakraborty and Hedrick. Moreover, if ll are the effective population size and Thus we conclude that the careful and sampling variation in H (estimated from 5 2 3 mutation rate, respectively • Thus, if elegant analysis of Skibinski and Ward • the standard error of heterozygosity for 4Nll = 0.02 (yielding an average does not provide any evidence against the each protein) is taken into account in our heterozygosity, H, of -0.02) and n = 100, neutral mutation hypothesis of molecular analysis, the regression constant is P = 0.91. The probability that this locus evolution. reduced by only a negligible amount (from is monomorphic in two independent 0.16 to 0.15). Thus the argument of Chak­ 2 RANAJIT CHAKRABORTY species is P = 0.83. Therefore, the esti­ raborty and Hedrick exaggerates the mate of H can easily become zero even Center for Demographic effect of sampling in relation to our study. if the expectation of H is not zero. On and Population Genetics, It is true that D for an individual pro­ the other hand, D increases with Graduate School of tein can be high if the time since diver­ evolutionary time, and if the time since Biomedical Sciences, gence is great even if neutral mutation University of Texas, divergence between two species is long, rate (ll) and thus the expectation of H is D can be large even if ll or the expectation Houston, Texas 77025, USA low. However, for the same time period, of His small. In other words, the observa­ relatively larger D values would accumu­ tion of D > 0 when H = 0 is perfectly late, according to neutral theory, for pro­ compatible with the neutral theory. PHILIP W. HEDRICK teins with higher ll and H. The true Second, Skibinski and Ward3 used a Department of Genetics, relationship between H and D for a steady-state model on the supposition University of California at Berkeley, sample of proteins with different ll is then that average heterozygosities in related Berkeley, California 94720, USA expected, according to neutral theory, to species are more or less similar. While no be approximately linear and to pass a priori information regarding hetero­ through the origin. This is the crux of our I. Nei, M. Am. Nat. 106, 283-292 (1972). zygosity at different points of time are 2. Skibinski, D. 0. F. & Ward, R. D. G<n<t. Rts. 38,71-92 argument, not the distances accumulated available, this assumption is not guaran­ (1981). by individual proteins considered in iso­ 3. Skibinski, D. 0. F. & Ward, R. D. Naturt 298, 49()-492 teed as many natural populations have (1982). lation. probably experienced bottlenecks of 4. Nei, M. & Roychoudhury, A. K. Gtn<tics 76, 379-390 Second, Chakraborty and Hedrick pro­ population size in the past. The effects of (1974). 5. Kimura, M. Thtor. Popular. Bioi. 2, 174-208 (1971). pose a non-equilibrium model which bottlenecks of population size are quite 6. Chakraborty, R. & Nei, M. Evolution 31,347-356 (1977). allows for the possibility that heterozygos­ long-lasting, and furthermore in such a ity changes with time and which they say case the initial rate of accumulation of is consistent with our findings. Although genetic distance is much faster due to bottlenecks may affect locus heterozygos­ larger effects of random drift on D than ity within a population or species, the H (ref. 6). This distorts the relationship SKIBINSKI AND WARD REPLY-Chak­ protein heterozygosity values in our study between D and H, particularly when raborty and Hedrick disagree with our were averages for many loci and many heterozygosity is low. Actually, under a conclusion 1 that neutral mutation theory species from different vertebrate groups, non-equilibrium infinite allele model, the cannot completely account for the ob­ and there are no a priori reasons to believe relationship between D, (distance at a served relationship between protein that these global average heterozygosity time t) and H, (heterozygosity at time t) genetic distance and heterozygosity. We values are very different now from those may be written are not convinced, however, that their in the past. Furthermore, we do not see criticisms are justified. how this non-equilibrium model can D, = 2llt -In [(1-Ho)/(1-H,)] (1) The basis of our argument was that account for the non-zero intercept on the which would also make D, non-zero even steady-state neutral theory predicts genetic distance axis. Deviations from if H, is zero. an approximately linear relationship equilibrium could arise either from a 0028-0836/83/340755-02$01.00 © 1983 Macmillan Journals Ltd .
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