Burdon, 0. H. Frankel, R. H. Groves, D. R.Marshall, G. F. Mo- ran, R. N. Oram, and J. G. West forcomments on the manuscript. D.J.S. acknowledges support from ...
Proc. Natl. Acad. Sci. USA Vol. 88, pp. 4494-4497, May 1991 Population Biology
Intraspecific variation in population gene diversity and effective population size correlates with the mating system in plants (inbreeding species/genetic conservation/neutral model/maximnum likelihood/isozyme)
DANIEL J. SCHOEN* AND ANTHONY H. D. BROWN Commonwealth Science and Industry Research Organization, Division of Plant Industry, GPO Box 1600, Canberra, ACT 2601, Australia
Communicated by Michael T. Clegg, February 19, 1991 (received for review August 20, 1990)
ABSTRACT Published data on allele frequencies at isozyme loci in inbreeding and outbreeding plant species were analyzed to examine intraspecific variation in gene diversity and effective population size (Ne). Compared with outbreeders, inbreeding species showed markedly greater variation among populations in average values of Nei's gene diversity statistic. Effective population size was estimated by assuming that the variation observed at isozyme loci is selectively neutral. Inbieeding species showed greater levels of variation in Ne than did outbreoders, although the upper range of Ne was similar in the two classes of species. The results suggest that there may be considerable genetic variation and potential for evolutionary change in some but not all populations of inbreeders. Moreover, these findings are important with respect to the conservation of genetic resources. In particular, that the amount of intraspecific variation in population genetic diversity and Ne differs between inbreeding and outbreeding species should be taken into account in sampling efforts designed to optimize the diversity of germplasm collections.
the species in question was known either through progeny testing of open-pollinated seed parents (5), from analysis of genotype frequencies (6), or based on the observation of self-incompatibility-furthermore, to preserve an extreme contrast in the mating system of the taxa compared, we included only those species shown to be either predominant selfers or outcrossers; (ii) there were no apparent problems in the genetic interpretation of the isozyme phenotypes (e.g., we excluded from consideration species having polysomic inheritance where no formal Mendelian analysis had been conducted); and (iii) isozyme data were available for a minimum of seven populations, allowing a representative range of intraspecific variation in gene diversity and Ne to be sampled. The species studied are listed in Table 1, together with information on their mating system and the numbers of populations and loci surveyed in the allozyme studies. We noted the existence of additional studies of outcrossing plant species, particularly of forest trees, but the results from analyses of these data are not included below for two reasons. First, as much as possible, we wished to balance our overall comparison by considering data from species with a wide variety of different growth habits and ecologies. Second, data from additional forest tree species gave results very similar to those for the three tree species presented below. Data on allele frequencies and numbers of individuals sampled, obtained from the references listed in Table 1, were used to calculate the average population value of Nei's gene diversity statistic for each population (hj) according to the formula
Studies of genetic variation in plants have typically used Nei's genetic diversity statistics or Wright's F statistics as tools for describing the extent of differentiation among populations (1-3). While informative, these statistics do not provide direct information about the amount of among-population variation in levels of polymorphism and gene diversity, a feature that can be of key importance in efforts to conserve the genetic resources of a species. In this regard, a survey of isozyme variation in several plant populations conducted by Brown (4) suggested that inbreeding species will tend to show greater variation among populations in the level of genetic diversity compared with outbreeding ones. Brown (4) proposed that, in inbreeders, among-population variation in the average value of Nei's gene diversity statistic will often exhibit an L-shaped or bimodal distribution. Published data for the predominantly self-pollinating plants Hordeum spontaneum and Lycopersicon pimpinellifolium supported this view (4). In this investigation, we analyze additional published isozyme data from inbreeding and outbreeding plant species in order to explore in detail the nature and implications of variation in genetic diversity among populations of inbreeding and outbreeding species. This is done by examining the level of among-population variation in gene diversity. We have also asked what the observed patterns of variation in diversity imply about the amount of variation in effective population size in species with contrasting breeding systems. MATERIALS AND METHODS Published tables of allozyme frequency data were used in all analyses described below. These data sets were selected according to the following criteria: (i) the mating system of
h.j EA EaP2VI Ei hifl, =
=
[1]
where Pa. is the frequency of the ath allele at the ith locus (i = 1, .. ., I) in the jth population (j = 1,... , J) (1). The distribution of these hj values was compared for each inbreeding and outbreeding species after angular transformation. To estimate effective population size (Ne), we used Chakraborty and Neel's (29) procedure based on Kimura and Crow's model of selectively neutral variation (30). For this model, Ewens (31) has shown that when a population is at equilibrium under mutation-drift balance, the likelihood (L) of observing k alleles in a sample of n genes from a given locus and population is
ikln.ok r(6) r(n + 0)
[2]
where the coefficient l(k) is the Stirling number of the first kind (32) corresponding to k and n, 6 = 4UNe, u is the mutation rate at the locus in question, and J7( ) is the gamma function (33). With I loci and J populations, there are I + J parameters
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Abbreviation: MLE, maximum likelihood estimate. *Present address: Department of Biology, McGill University, 1205 Avenue Dr. Penfield, Montreal, Quebec H3A IB1, Canada. 4494
Proc. Natl. Acad. Sci. USA 88 (1991)
Population Biology: Schoen and Brown
4495
Table 1. Mating systems, numbers of populations, and numbers of loci for species used to estimate Ne Outcrossing rate Allozyme data or compatibility from I loci, J reaction Species populations Ref(s). Self-fertilizing species 0* Arabidopsis thaliana 7 7, 16 0.02* 8-10 Avena barbata (California) 7, 14 0.02* Avena barbata (Spain) 8, 12 8, 9, 11 Ot 12 Avena canariensis 8, 19 0.02* H. spontaneum 25, 28 13, 14 15 0.14* L. pimpinellifolium 13, 41 0.22* 16 Phlox cuspidata 5, 43 0.17t 17 Plantago major 7, 7 0.13t 18 Polygala vulgaris 10, 53 Outcrossing species 0.97* Echium plantagineum 16, 8 19, 20 21 Helianthus debilis Self-incompatible 5, 17 16 Phlox drummondii Self-incompatible 5, 73 Phlox roemariana 16 Self-incompatible 4, 15 0.89* Picea abies 4, 8 22, 23 0.90* Pinus sylvestris 10, 8 24, 25 17 Plantago lanceolata Self-incompatible 14, 7 0.90* Pseudotsuga menziesii 18, 11 26, 27 28 Stephanomeria exigua Self-incompatible 8, 11 *Outcrossing rate estimated by progeny-testing parents. tOutcrossing rate estimated from genotype frequency data in population.
(u... ,u1, Nei... Ne,). Using only those loci that segregate in at least one of the J populations, Chakraborty and .
..
.
Neel (29) have shown that the appropriate joint-likelihood function is I
L=
(k
+,J)k.( Hi.(
[ i
j
nij+Oj (nj 1)'!61ijF(6ij) Ht(1 Hl r(+8[3]
I'
J
Maximum likelihood estimates (MLEs) of the model parameters were found by iterating the set of normal equations for
the ui and Nej (obtained through partial differentiation of Eq. 3 with respect to the ui and Nej and subject to the constraint that Oij = 4ui Nej) (29). For simplicity, we assumed that the number of genes sampled, n, in outcrossing populations equals 2-Z, where Z is the number of individuals sampled from the population (29). With inbreeding populations, we assumed n = Z; i.e., to account for the high probability that the two genes sampled from single individuals are identical by descent (2), as expected, given the high levels of inbreeding characteristics of most of the selfing species in our study (Table 1). Because the ui and Nej appear only in product form, it is not possible to obtain estimates ofthem without first assuming an overall mean value for either one of these two sets of parameters. In our work, we assume that _u = 10-5 (31). This allows for estimation of the absolute values of the Nej. Importantly, while the estimates of the absolute values of the Nej are dependent on the choice of u, the pattern of variability of the Nej is not.
RESULTS Table 2 summarizes several characteristics on the distributions of population gene diversity in eight inbreeding and nine outbreeding plant species. Gene diversity in the inbreeders is
lower (mean = 0.12) than in the outbreeders (mean = 0.26), that is in accord with the larger survey conducted by Hamrick and Godt (3). Moreover, apparent from this table is the greater range and variability of h*j in the inbreeders. The average range of h.1 in the inbreeding species is 0.29, compared with 0.15 for the outbreeding species. The average coefficient of variation of h.1 is 64% in the inbreeding species and 12% in the outbreeding species. All but one of the a result
Table 2. Summary of variation in average population values of Nei's diversity statistic (h.) Mean Min Max Range CV of Species hj of hi h.j,* % hi hi
Self-fertilizing species A. thaliana A. barbata
(California) A. barbata (Spain) H. spontaneum L. pimpinellifoliumt P. cuspidata P. major P. vulgaris Mean
0.137
0
0.385
0.385
53
0.041 0.068 0.110 0.137 0.050 0.165 0.145 0.125 0.024
0 0 0 0 0 0.056 0 0.008 0.008
0.268 0.228 0.197 0.271 0.252 0.336 0.264 0.294 0.026
0.268 0.228 0.197 0.271 0.252 0.280 0.264
162 94 35 38 95 55 36
0.286 0.021
64 15
0.399 0.228 0.390 0.372 0.363 0.343 0.373 0.218 0.268 0.328 0.024
0.118 0.206 0.367 0.264 0.066 0.074 0.083 0.054 0.153 0.154 0.035
SE Outcrossing species E. plantagineum 0.337 0.281 H. debilis 0.130 0.022 P. drummondii 0.178 0.023 P. roemariana 0.275 0.108 P. abies 0.336 0.297 P. sylvestris 0.320 0.269 P. lanceolata 0.355 0.290 P. menziesii 0.193 0.164 S. exigua 0.187 0.115 Mean 0.257 0.174 SE 0.028 0.038 Min, minimum; Max, maximum. *Angular transform of data. tPopulations of fewer than 20 plants not
included.
6 25 30 16 4 4 5 5 14 12 3
4496
Population Biology: Schoen and Brown
inbreeding species had some populations that were monomorphic at all loci tested, and, therefore, the minimum h values in these species were 0. On the other hand, the maximum hj values in the inbreeding species were only slightly lower than those in the outbreeding species. Estimates of Nej are shown in Fig. 1 for inbreeders and in Fig. 2 for outbreeders. The mean values of Nej for inbreeding and outbreeding species were 3557 and 6990, respectively. Apparent from the two figures is the generally greater range of Nej values for the inbreeding versus outbreeding species. On average, the range of Nej in the inbreeding species was 8530 (SE = 1277), while in the outbreeding species it was 4444 (SE = 782). The coefficient of variation of Nej in the inbreeding species was 84%, on average, while in the outbreeding species it was 24%. The average minimum Nej in the inbreeding species was 86 (SE = 86), while in the outbreeding species it was 4668 (SE = 1119). The average maximum Nej in the inbreeding species was 8721 (SE = 1331), while in the outbreeding species it was 9143 (SE = 1354). Significant variation among the Nej values of the selfing species, but not those of the outcrossing species, is further indicated by examination of the confidence intervals of the MLEs obtained from the large sample variance formula (29, 31) (where Nej values of 0 have been set equal to 1). For all outcrossing species, the 95% confidence limit around any single estimate of relative Nej includes all other estimates, whereas for all selfing species the 95% confidence limits of the largest and smallest Nej values do not overlap. The estimation of Ne via allele counts (29) is sensitive to sampling effects when populations have low levels of polymorphism, as occurs in some populations of inbreeding species. In particular, if a population is scored as monomorphic for all loci tested, but is in fact polymorphic for one or Araboh)psi5tiIXixahll 4
Ai 'l bur/'i hiena VO Wharfala Ca
-
i i; iforn11
8
. (I thl Ca 'tIt At 7 (V 'IN.\
SpI il11
4ni
1
I.
I L l 111 }tt{ e t ./ [eO i II IM,~ W
s Iiuu vqler( uis )p 'e 'u
pllif7ilIII/ IfiIi!Ift? -.
C-r J
I
0 2468 4 6 8 11012 0 12 02
Phiox cuspidali
0 0123456789 1 23 45 6 7 8 9O
ir
nll/f Plantago
Ne
x
l
i. j .
Proc. Natl. Acad. Sci. USA 88 (1991) 1irununiJ.
}{(1/ii1t1[/l|s.t elf Fiji;
;-
4.,'E
or/
A
r
4
;: gX _
^
f ;;
--l
C
In
;.
"-.
) . Li . 1 1 . ? It ?
"t
')
