~. Theoret. BioL (1962) 2, 69-7x

The Generation of Self-Incompatibility Alleles

D. LEwis

Department of Botany, University College, London, England

The several hundreds of different incompatibility alleles in many species of plants, each producing a characteristic protein in the pollen and style, present problems in population genetics and in gene organization which have not been solved. One of the main problems is the origin of the different alleles. A mathematical treatment of the population equilibrium requires the generation of alleles with "new", i.e. with non-parental characteristics, at a rate of lO .4 (cf. S. Wright, I939, 196o; Fisher, 196o ). For the consideration of the population equilibrium it is immaterial whether the non-parental alleles arise by recombination or by mutation. Experiments using a method of self-pollination capable of detecting rare mutational and recombinational events have not revealed the production of new alleles, indicating a rate of origin of less than IO -s (Lewis, I95I ). To explain this discrepancy between experiment and theory, Fisher has proposed a system of origin of new alleles, or more correctly incompatibility gene complexes, which would not be detected by the screening method of self-pollination used in my experiments. There are, however, some difficulties in accepting Fisher's model both on the grounds of the known biochemical action of the system of pollen inhibition controlled by the incompatibility gene and on disagreement with the facts of extensive breeding experiments. Breeding experiments with many species of plants having the type of incompatibility system under consideration have revealed certain rules which have had a high predictive value. These a re : - - i. Plants are incompatible to two genotypes of pollen only: all other pollen

genotypes are compatible. 2. The reciprocal crosses, i.e. A ~ × B d ~ and B ~ × A d ~ give identical

results, incompatible, or half compatible or fully compatible. There are rare exceptions to both these rules but they are in families pro- duced by self-fertilization which can occur occasionally in certain plants. These are exceptions which prove the rule because some plants on selfing produce progenies which are homozygotes for the incompatibility allele. As expected, these are incompatible with only one type of pollen and can give a reciprocal difference with some heterozygotes.

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7 ° D. L E W I S

Because both of these rules would be violated by Fisher's model it is important to re-examine the published data in order to find how well these rules are established, and to find what frequency of exceptions to the rules could have remained undetected with the breeding data available. An objective survey of all the published data is not possible because, owing to the early acceptance of these two rules, the reciprocal crosses have either not always been made or if they have been made they are not recorded. For this reason, attention has been confined to two extensive and well- recorded studies, in Prunus avium (Crane & Brown, i937) and in Oenothera organensis (Emerson, i938 ). These data have an additional significance in that they are in species which have been used in mutational experiments and in population studies.

In Prunus avium, crosses involving sixty-five different varieties and more than 35 ° different pairs of reciprocal crosses have been made. No excep- tions to the reciprocal rules were found. In Oenothera organensis, xo 9 pairs of reciprocal crosses are recorded with no exceptions. In Prunus, the probability of not detecting a frequency of x.3 % of reciprocal differences is .02. In Oenothera, the data could have detected 5% with the same probability. In the pooled data, the detectable frequency at the .02 level would be about I%. It seems reasonable to exclude any scheme which would generate reciprocal differences in excess of these values.

The simple scheme of three genes A, B and C, in which X is a recom- binant from A and B, is not intended by Fisher to apply without elaboration to the incompatibility system under consideration, but it must be examined in the light of the rules before the more elaborate schemes with xo to 2o antigenic sites can be examined.

The three genes A, B and C have two interpretations: x. A, B and C are active and produce three different antigens in pollen

and style, their alleles a, b and c are inactive and do not produce antigens. In this case:

A = A b c , B = a B c , X = A B c

The recombinant A B c (X) would, as postulated, be incompatible on an A B style, but contrary to Fisher's scheme, when X is in the style it would be incompatible to A and B pollen. 2. There are two active allelic forms of A, B and C:

al, a~; bl, b2, etc., each of which produces a different antigen. In this c a s e :

A might be a t b 1 c 1 B might be a 2 b2 cl C might be a I bl c2 X might be a 1 b2 cl

THE G E N E R A T I O N OF S E L F - I N C O M P A T I B I L I T Y ALLELES 7 I

The genotype al bl cl - - as a female parent would be incompatible with a S b~ c 1

a 1 ba c 1 pollen, but a t b, c 1 in a female parent would be compatible with a 1 b t c 1 (A) and a S bz c 1 (B) pollen. This fits Fisher's system in all respects.

This system of three sites with two alternatives at each will generate by recombination eight different haploid pollen genotypes and 28 different diploid plant genotypes. I f these plants are inter-crossed in all pairwise combinations, approximately 35~/o of the crosses will have reciprocal differences of the type:

al bl el + a l b l c l ~ × - - c ~ compatible a 1 b~ c 1 a x b~ c 2

reciprocal incompatible

I f the number of sites is increased to four, i.e. a, b, c, d, then 49% of the crosses will differ in the reciprocal combination. Fur ther increase in the number of sites to IO or zo will not reduce this frequency of reciprocal differences. The scheme, therefore, does not fit the facts, and any scheme which assumes that a new allele in pollen is incompatible on its own parental mother plant will encounter this type of difficulty.

Unti l a scheme is devised for generating new alleles which would not be detected by self-pollination, and which obeys the basic rules, there is no profit in discussing it in relation to the biochemistry of incompatibility.

The self-pollination sieve has detected mutational changes to self- compatibility and it should detect changes to new alleles by mutat ion or recombination which have a qualitatively different antigen from the two parental alleles. But it will not, as Fisher points out, detect an allele which produces a mixture of the two parental antigens such as gene X.

REFERENCES CRANE, M. B. & BROWN, A. G. (I937)..7. Pomol. x5, 86. EMERSON, S. (1938)- Genetics, 23, 19 o. FISHER, R. A. (*96o). Aust..7. biol. Sci. x4, 76. FISHER, R. A. (1961)..7. theoret. Biol. x, ¢xI. LEwis, D. (I95I). Heredity, 5, 399- WRIGHT, S. (I939). Genetics, z4, 538. WRIGHT, S. (196o). Biometrics, x6, 6i.