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• W1972112436 abstract "To the Editor: The controversial relationship between Neanderthals and modern humans recently received much attention, owing to the recovery of a Neanderthal mtDNA fragment, the analysis of which indicated that the most-recent common ancestor (MRCA) of Neanderthal and modern-human mitochondria was several times more ancient than that of modern humans only (Krings et al. Krings et al., 1997Krings M Stone A Schmitz RW Krainitzki H Stoneking M Pääbo S Neanderthal DNA sequences and the origin of modern humans.Cell. 1997; 90: 19-30Abstract Full Text Full Text PDF PubMed Scopus (878) Google Scholar; fig. 1). This finding was considered to be strong evidence that Neanderthals and anatomically modern humans are separate species, the latter having replaced the former without interbreeding (“In our genes?”In our genes?, 1997In our genes? (1997) The Economist 344(8025), July 12th, pp 71–72Google Scholar; Kahn and Gibbons Kahn and Gibbons, 1997Kahn P Gibbons A DNA from an extinct human.Science. 1997; 277: 176-178Crossref PubMed Scopus (18) Google Scholar; Lindahl Lindahl, 1997Lindahl T Facts and artifacts of ancient DNA.Cell. 1997; 90: 1-3Abstract Full Text Full Text PDF PubMed Scopus (49) Google Scholar; Wade Wade, 1997Wade N Neanderthal DNA sheds new light on human origins.New York Times. 1997; (July 11, sec A.)PubMed Google Scholar; Ward and Stringer Ward and Stringer, 1997Ward R Stringer C A molecular handle on the Neanderthals.Nature. 1997; 388: 225-226Crossref PubMed Scopus (31) Google Scholar). Here, I investigate the strength of this evidence by considering the probability of erroneous rejection of interbreeding (i.e., the probability of a type I error). I demonstrate that, although completely random mating clearly can be rejected, more-relevant models of interbreeding cannot. The question of whether Neanderthals and anatomically modern humans interbred is a question of ancient levels of gene flow. Thus, although the relevant features of the data can be conveniently summarized as in figure 1, this figure is not, a priori, a phylogenetic tree for Neanderthals and humans: indeed, the question is whether such a tree exists. Figure 1 is simply a genealogical tree representing the history of the sampled mtDNA. In the following discussion, I ignore the considerable uncertainty in the estimation of this history and focus on the question of whether, given perfect knowledge of mtDNA genealogy, we would be able to conclude that anatomically modern humans and Neanderthals did not interbreed. First, I consider whether Neanderthals and anatomically modern humans could have mated randomly. Two features of the data summarized in figure 1 provide evidence against such a scenario: The first is the topology, with the modern sample being monophyletic, and the second is the more than fourfold difference between Tr, the age of the MRCA of the modern humans and the Neaderthal, and Te, the age of the MRCA of the modern humans only. If anatomically modern humans and Neanderthals mated randomly, the probability of such a result can be calculated as follows. Let An(t)∈{1,…,n} be the random number of ancestors, at time t, of a sample of n mtDNAs at t=0; its distribution is known under a variety of neutral models (TavaréTavaré, 1984Tavaré S Line-of-descent and genealogical processes, and their applications in population genetic models.Theor Popul Biol. 1984; 26: 119-164Crossref PubMed Scopus (400) Google Scholar). Conditional on A986(ts)=k, the number of ancestors of the modern sample who are contemporary with the sampled Neanderthal, the probability sought can be written as the product of the probability that a compatible topology is observed and the probability that sufficiently extreme coalescence times are observed. The former probability is easily shown to be P[topology|A986(ts)=k]=2/[k(1+k)] (this also may be obtained as a special case of more-general results [Watterson Watterson, 1982Watterson GA Mutant substitutions at linked nucleotide sites.Adv Appl Prob. 1982; 14: 206-224Crossref Google Scholar; Saunders et al. Saunders et al., 1984Saunders IW Tavaré S Watterson GA On the genealogy of nested subsamples from a haploid population.Adv Appl Prob. 1984; 16: 471-491Crossref Google Scholar]). An exact expression for the latter probability also can be obtained (T. Nagylaki and M. Nordborg, unpublished data) but is cumbersome and in some cases difficult to evaluate numerically. Estimation of the probability through standard Monte Carlo–simulation techniques is more convenient (e.g., Marjoram and Donnelly Marjoram and Donnelly, 1997Marjoram P Donnelly P Human demography and the time since mitochondrial Eve.in: Donnelly P Tavaré S Progress in population genetics and human evolution. Springer-Verlag, New York1997: 107-131Crossref Google Scholar). Two simple scenarios for human demography were used—namely, constant population size and constant ancient-population size followed by exponential growth 50,000 years ago. For both cases, the effective number of females in the constant population was assumed to be 3,400, growing exponentially to 5×108 for the latter case. These parameters were chosen so that the probability would be high that Te lies within the range 100,000–200,000 years, when a generation time of 20 years is assumed. The age of the sampled Neanderthal, ts, was assumed to be 30,000–100,000 years (the recovery of DNA more ancient than 100,000 years seems highly doubtful [Krings et al. Krings et al., 1997Krings M Stone A Schmitz RW Krainitzki H Stoneking M Pääbo S Neanderthal DNA sequences and the origin of modern humans.Cell. 1997; 90: 19-30Abstract Full Text Full Text PDF PubMed Scopus (878) Google Scholar]). I argue below that the absolute values of all these parameters are of considerably lesser importance than their relative values. Table 1 gives the results for models of random mating. As expected, the probability that both a compatible topology and an extreme difference between Te and Tr would be observed is low, and, therefore, the hypothesis that modern humans and Neanderthals were a randomly mating population may be rejected. However, closer inspection reveals the more interesting fact that the topology alone may not be unlikely. The reason for this is that, unless the sampled Neanderthal lived long after human populations had started to grow exponentially, most of the modern mtDNA lineages would have coalesced at ts: if, for example, the modern sample only had two ancestors who were contemporary with the sampled Neanderthal, it would not be surprising if they were monophyletic (probability of 1/3). A large difference between Te and Tr, on the other hand, is always unlikely under random mating.Table 1Results for Models of Random MatingConstant Population Size andts(in Years) =Recent Population Growth andts(in years) =Parameter30,000100,00030,000100,000E[A986(ts)]4.861.757822.86P(topology).085.563.3 × 10−6.24P(topology and Tr⩾4Te).0063.0353.7×10−8.002Note.—E[A986(ts)] is the expected number of ancestors of the modern sample who are contemporary with the sampled Neanderthal. P(topology) is the probability that the topology in figure 1 would be observed, and P(topology and Tr⩾4Te) is the probability that both unlikely features of the data would be observed. All values were estimated through Monte Carlo simulation, as well as by calculation from the analytical results, except for those in the third column, for which the latter approach proved to be computationally too difficult. The 95% confidence intervals for the simulated values do not alter the decimals given. In the constant–population-size model, the expected Te was ∼136,000 years, with an SD of ∼70,000 years; for recent exponential growth, the expected Te was ∼180,000 years, with, again, an SD of ∼70,000 years. Open table in a new tab Note.— E[A986(ts)] is the expected number of ancestors of the modern sample who are contemporary with the sampled Neanderthal. P(topology) is the probability that the topology in figure 1 would be observed, and P(topology and Tr⩾4Te) is the probability that both unlikely features of the data would be observed. All values were estimated through Monte Carlo simulation, as well as by calculation from the analytical results, except for those in the third column, for which the latter approach proved to be computationally too difficult. The 95% confidence intervals for the simulated values do not alter the decimals given. In the constant–population-size model, the expected Te was ∼136,000 years, with an SD of ∼70,000 years; for recent exponential growth, the expected Te was ∼180,000 years, with, again, an SD of ∼70,000 years. Thus, the data constitute considerable evidence against the hypothesis that all sequences were drawn from a single population. This perhaps should not be surprising: the recovered Neanderthal sequence clearly was not sampled from a random individual at time ts but was sampled specifically from an individual who was morphologically distinct from anatomically modern humans. Furthermore, fossil data strongly suggest that Neanderthals and anatomically modern humans were not a randomly mating population. To ask questions about interbreeding, more-interesting null hypotheses are needed. One pleasingly simple scenario is the following. Assume that Neanderthals were an isolated population for a long time, until they encountered anatomically modern humans at time tm and merged with them to form a single, randomly mating population, with a fraction, c, of the population being Neanderthal. Then, the so-called replacement hypothesis is simply that c=0. The data in figure 1 are perfectly consistent with this scenario; that is, the probability of the data is 1, without interbreeding. However, this provides support for replacement only to the extent that alternative scenarios can be shown to have a much lower probability. Therefore, the probability of the data must be found for different values of c>0. Under the assumption that the sampled Neanderthal lived before tm (i.e., a “pure” Neanderthal), the probability sought is simply the probability that none of the ancestors at time tm came from the Neanderthal fraction of the population. This probability can be written as Σk=1986(1-c)kP[A986(tm)=k], which is the probability-generating function for A986(tm). Figure 2 shows a plot for the two demographic scenarios described above, with tm=30,000 or 100,000 years. Clearly, for the scenarios in which the expected number of ancestors at tm is low (table 1), the data tell us little about interbreeding, except perhaps that the Neanderthals did not make up the majority. The situation is completely different if the expected number of ancestors at tm is high. In this case, all but very small values of c may be rejected. In cases for which we expect few ancestors at tm, the probability that none of the 986 sampled mtDNAs came from the Neanderthal fraction of the population does not differ much from the probability that none of the currently existing mtDNAs did so. This latter probability is equal to the well-known probability that an allele starting at frequency c is lost, through drift, by time tm (Kimura Kimura, 1955Kimura M Solution of a process of random genetic drift with a continuous model.Proc Natl Acad Sci USA. 1955; 41: 144-150Crossref PubMed Google Scholar). Under this assumption, another question of interest can be addressed: Given that extant humans do not carry Neanderthal mtDNA, what does this suggest about the rest of the genome? For the constant–population-size model, for example, assume that Neanderthals and anatomically modern humans merged 1 coalescent-time unit ago (equivalent to tm=68,000 years, for the population size used above) and that Neanderthals composed 25% of the new population. Then, the probability that all Neanderthal mtDNA was lost through drift is .52 (the probability that Neanderthal mtDNA was not in the sample [calculated as above] is the same, to two decimal places). At the same time, each nuclear locus, for which the coalescence-time scale is four times slower, would have lost all Neanderthal alleles with probability .10 and would have become fixed for them with probability 9.8×10−5. Thus, 90% would still be segregating for Neanderthal alleles. In conclusion, data such as those shown in figure 1 shed little light on the issue of replacement versus interbreeding, unless the number of ancestors of the sample was large throughout the periods of interest. This is part of a general problem: in order to estimate gene flow, a large sample is needed, and, in order to estimate ancient-gene flow, a large ancient sample is needed. According to coalescent theory, large ancient samples usually cannot be obtained by the sampling of modern populations. The rate of coalescence is quadratic in the number of ancestors and linear in the inverse of the population size. Thus, the expected number of ancestors of a sample usually decreases rapidly as earlier time periods are studied. Exceptions include exponentially growing populations, in which the number of ancestors may be large shortly after the onset of growth (reviewed in Donnelly and TavaréDonnelly and Tavaré, 1995Donnelly P Tavaré S Coalescents and genealogical structure under neutrality.Annu Rev Genet. 1995; 29: 401-421Crossref PubMed Scopus (274) Google Scholar; Marjoram and Donnelly Marjoram and Donnelly, 1997Marjoram P Donnelly P Human demography and the time since mitochondrial Eve.in: Donnelly P Tavaré S Progress in population genetics and human evolution. Springer-Verlag, New York1997: 107-131Crossref Google Scholar). In the present case, it seems clear that the statistical power to detect interbreeding that took place before the human population started to grow exponentially is close to zero. I also have considered the mtDNA genealogy as known. The extreme uncertainty of the reconstruction of ancient DNA and the genealogy shown in figure 1 presumably suggests that conclusions from the data should be made with even more caution. Additional Neanderthal mtDNA sequence data would reduce these sources of uncertainty, but the main problem discussed above can be alleviated only by the study of data from several unlinked loci. The fact remains that an inference about population properties that is based on a single locus (or a nonrecombining genome) is an inference from a single data point. This does not mean that single loci contain no information: I have shown that random mating can be rejected, and the existence of a single Neanderthal mtDNA that differed little from modern mtDNA would allow rejection of the hypothesis that there was no interbreeding. Such an observation probably could never be made, however, since contamination would be impossible to rule out. Finally, the above analysis depends on the selective neutrality of mtDNA variation. It is well known that human mtDNA variation suggests a genealogy that is “star shaped”: this has been interpreted as the result of a historical population expansion (Di Rienzo and Wilson Di Rienzo and Wilson, 1991Di Rienzo A Wilson AC The pattern of mitochondrial DNA variation is consistent with an early expansion of the human population.Proc Natl Acad Sci USA. 1991; 88: 1597-1601Crossref PubMed Scopus (310) Google Scholar; Merriwether et al. Merriwether et al., 1991Merriwether DA Clark AG Ballinger SW Schurr TG Soodyall H Jenkins T Sherry ST et al.The structure of human mitochondrial DNA variation.J Mol Evol. 1991; 33: 543-555Crossref PubMed Scopus (175) Google Scholar; Vigilant et al. Vigilant et al., 1991Vigilant L Stoneking M Harpending H Hawkes K Wilson AC African populations and the evolution of human mitochondrial DNA.Science. 1991; 253: 1503-1507Crossref PubMed Scopus (930) Google Scholar; Rogers and Harpending Rogers and Harpending, 1992Rogers AR Harpending H Population growth makes waves in the distribution of pairwise genetic differences.Mol Biol Evol. 1992; 9: 552-569PubMed Google Scholar). However, data from several nuclear loci do not show this pattern (Harding et al. Harding et al., 1997Harding RM Fullerton SM Griffiths RC Bond J Cox MJ Schneider JA Moulin DS et al.Archaic African and Asian lineages in the genetic ancestry of modern humans.Am J Hum Genet. 1997; 60: 772-789PubMed Google Scholar; Hey Hey, 1997Hey J Mitochondrial and nuclear genes present conflicting portraits of human origins.Mol Biol Evol. 1997; 14: 166-172Crossref PubMed Scopus (105) Google Scholar). Together, these observations may constitute evidence against neutrality, with a plausible alternative being a recent selective sweep in human mtDNA (Hey Hey, 1997Hey J Mitochondrial and nuclear genes present conflicting portraits of human origins.Mol Biol Evol. 1997; 14: 166-172Crossref PubMed Scopus (105) Google Scholar). The conclusions in this paper clearly are not robust to this type of violation of assumptions: if there has been a recent selective sweep in human mtDNA, even random mating cannot be rejected. I thank B. Bengtsson, A. Di Rienzo, P. Donnelly, R. Harding, the reviewers, and especially T. Nagylaki, for their comments on the manuscript. This work was supported by the Erik Philip-Sörensen Foundation." @default.
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• W1972112436 title "On the Probability of Neanderthal Ancestry" @default.
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