The population genetics of the self-incompatibility polymorphism in Papaver rhoeas. IV. The estimation of the number of alleles in a population

Abstract

SUMMARYThree methods of estimating the number of S-alleles in a population have been proposed in the literature (Bateman, 1947;Whitehouse, 1949;Paxman, 1963). These methods, all of which assume that genotype frequencies in the population are equal, are described briefly and are used to estimate the number of alleles in populations of Trifolium pratense (Williams and Williams, 1947), Oenothera organensis (Emerson, 1939) and Papaver rhoeas (Campbell and Lawrence, 1981 b;Lawrence and O'Donnell, 1981). The estimates yielded by Bateman's and Whitehouse's methods are similar to those given by Paxman's maximum likelihood method with the Trifolium and Oenothera data where there is little reason to suppose that the allele frequencies are other than equal. Bateman's method, however, breaks down when used on the Papaver data in which the S-allele frequencies are known to be unequal; and Whitehouse's and the maximum likelihood methods yield estimates which are biased downwards when used on these data.An attempt has been made, therefore, to devise two new estimators of the number of S-alleles in a population which do not assume that their frequencies are equal. The properties of these estimators has been investigated with data from eight populations generated on the computer in which the numbers and frequencies of alleles are known. One of these new estimators (E2) yields estimates which are less biased downwards than those given by Paxman's method when allele frequencies are unequal, but gives estimates which are biased upwards when these frequencies are equal. The other estimator (E1) is generally less satisfactory than the first, particularly when the number of alleles in the population is large. Though neither of these new estimators are wholly satisfactory, there is some justification for using E2 when allele frequencies are known to be unequal. Estimates given by E2 when used on the Papaver data range from 34 to 42 alleles which, bearing in mind that these estimates are still likely to be biased downwards, suggests that the number of alleles in natural populations of this species is likely to be between 40 and 45.A new procedure for calculating confidence intervals for maximum likelihood estimates, assuming equal allele frequencies, is also described and applied to the Oenothera and Papaver data.

The population genetics of the self-incompatibility polymorphism in Papaver rhoeas. VI. Estimation of the overlap between the allelelic complements of a pair of populations

“…There are two reasons for doubting whether this notion is true. Firstly, while the number of alleles in populations of Trifolium pratense (Williams & Williams, 1947;O'Donnell & Lawrence, 1984) and T repens (Atwood, 1944) appear to be large, this number appears to be much smaller in the two most thoroughly investigated species with a one-locus, multi-allelic, gametophytic system of self-incompatibility. Thus Emerson (1940) found 45 different S-alleles in Oenothera organensis and we have found, quite coincidentally, the same number in P. rhoeas.…”

The population genetics of the self-incompatibility polymorphism in Papaver rhoeas. V. Cross-classification of the S-alleles of samples from three natural populations

“…Previous values and estimates are shown in parentheses and revised values in bold. The entries in rows 1-5 for R102 and R104 replace those given in Table 5 of Lawrence and O'Donnell (1981) and those in the last row replace the corresponding entries shown in Table 3 of O'Donnell and Lawrence (1984). The estimates of N for the poppy populations are those obtained from the E2 estimator of O'Donnell and Lawrence (1981); that for the Oenoihera organensis population (Emerson, 1939 mates derived from the R102 and R104 data; the revised values are shown in Table 3.…”

Allelic diversity of S-RNase at the self-incompatibility locus in natural flowering cherry populations (Prunus lannesiana var. speciosa)

“…Tests of the hypothesis of the equality of allele frequencies, expected under GSI, revealed that the allele frequencies in flowering cherry are significantly uneven, unlike other GSI species, for example, Oenothera organensis where the data fit expectations of equal frequencies (O'Donnell and Lawrence, 1984). We sampled all of the individuals growing in each plot area.…”