Heredity 63(1989) 135—141 The Genetical Society of Great Britain Received 17 February 1989

Geneticanalysis of isoenzyme using single tree progenies

Elizabeth Gillet and Abteilung für Forstgenetik und Forstpflanzenzüchtung, Hans H. Hattemer Georg-August-Universität Göttingen, Büsgenweg 2, 3400 Göttingen, Federal Republic of Germany

A methodof genetic analysis is proposed for determination of the mode of inheritance of environmentally and ontogenetically stable isoenzyme phenotypes as expressed in angiospermous forest trees. This method also applies to higher plant and animal species characterized by multiple matings of single female parents. The modes of inheritance considered are codominance in the absence and the presence of a (recessive) null . The analyzed material coRsists of zymograms of single maternal trees and their progenies (as seeds or seedlings) from open pollination. Such data is more easily obtained than controlled crosses and can represent the total variation in the population. The genetic analysis requires only the basic assumptions of classical Mendelian analysis, which make use only of the elementary mechanisms of meiosis and fertilization. Additional assumptions on the mating system, such as those required by the mixed mating model, are not needed. The results confirm the need for explicit genetic analysis of zymograms.

THE NECESSITY OF GENETIC ANALYSIS OF Therefore, it is not clear from the zymogram ENZYME PHENOTYPES alone whether or not the presence of double bands can be interpreted as heterozygosity. (c) The differences in electrophoretic mobility of Complexitiescan arise in the interpretation of the products of multiple loci controlling enzyme phenotypes, some of which are not at all an enzyme system are not always greater than visible in the zymograms alone. The following are differences among allozymes (Stuber and of importance: Goodman, 1984, for 6-PGDH in maize). Thus (a) Null may exist which code for an the "zones" of a zymogram can overlap, caus- enzyme of reduced or no activity in vivo, in ing problems in assigning the variation in one vitro, or both. All types of null alleles are zone to the genetic variation at one gene . operationally recessive under routine pro- This is particularly true if the enzymes are cedures of laboratory analysis. Thus, if the monomers. modes of extraction and staining are not sensi- (d) Intergenic (or interlocus) heterodimers among tive to the amount of active enzyme in the multiple gene loci make it difficult to discrimi- zymogram bands, an individual heterozygous nate between zones of a given zymogram and for the null allele will appear to be homo- thus between possible modes of transmission zygous for its active allele, and thus its null involving differing numbers of gene loci. MDH allele will not be detected. Furthermore, homo- in pine seeds (O'Malley et aL, 1979; El- for a null allele can be a lethal con- Kassaby, 1981; Müller-Starck, 1985a) and in dition. Since only viable genotypes can be spruce seeds (Cheliak et a!., 1985; Pitel et a!., observed, analysis of the zymogram patterns 1987) may serve as an example. If intergenic alone can never reveal the existence of the heterodimers occur together with null alleles, null allele in such cases. as is the case with MDH in maize (Goodman (b) Some alleles of gene loci controlling et a!., 1980) and Douglas-fir (El-Kassaby, monomers code for double bands even in 1981) as well as 6-PGDH in maize (Stuber and haploid tissue, as is known from both acid Goodman, 1984) and beech (Müller-Starck, phosphatase and leucine aminopeptidase in personal communication), the zymograms conifer endosperm (Bergmann, 1973, 1974). may be uninterpretable. 136 E. GILLET AND H. H. HATTEMER These complexities exist in only a few enzyme cite here (cf. Rudin, 1986), deal with the mode systems (cf. Shields et al., 1983). In most systems, of inheritance of enzyme phenotypes in conifers. information on the structure of the enzyme In contrast, comparatively few studies have molecule helps to avoid ambiguities of genetic been published on the mode of inheritance of interpretation. For instance, appropriate bio- enzyme phenotypes in angiospermous tree species. chemical methods consisting of inhibition of enzy- For one, analysis of their tissue usually requires mes migrating into one of two different zones might special extraction techniques (Torres, 1983; be applied to prove that a certain enzyme system Arulsekar et a!., 1983). Furthermore, analysis of is controlled by two gene loci. Nevertheless, such the triploid endosperm depends upon the detect- complexities do arise, sometimes coinciding with ability of allele dosage differences (Schoen, 1979, post-translational modification of the isoenzyme 1980). Most existing studies have used progeny . If they go unnoticed and thus are not from controlled crossings. Among these are the incorporated into the postulated mode of inherit- investigations by Feret and Stairs (1971) and Feret ance, all further interpretations based on the (1972) on Ulmus species, Guzina (1978) and erroneous mode of inheritance, such as charac- Rajora (1986) on Populus species, Kim (1979, terization of the mating system, population 1980), Thiebaut et a!. (1982), and Müller-Starck differentiation, genetic distance between popula- (1985b) on Fagus sylvatica, Wendel and Parks tions, or degree of heterozygosity, can be worthless. (1982) on Camellia japonica, Linares-Bensimón For this reason, genetic analysis of zymograms is (1984) on Alnus glutinosa, and Arulsekar et a!. essential. (1985) on Juglans species. Genetic analysis of enzyme phenotypes in various fruit trees using controlled crossings was reviewed by Torres GENETICANALYSIS OF ENZYME PHENOTYPES (1983). Several investigators utilized single tree IN TREE SPECIES offspring from open pollination but postulated the mode of inheritance on the basis of comparison Inmost tree species, classical Mendelian analysis, with other species as well as comparison of total which requires offspring from controlled crosses progeny and maternal gene frequencies (Brown et as well as parental and offspring tissue of the same a!. (1975) and Phillips and Brown (1980) on type and ontogenetic stage, is problematical. Con- Eucalyptus species; reviewed in Moran and Bell trolled crosses in trees are often technically difficult (1983)) or comparison of the genotypic distribu- to perform, and the numbers of offspring obtain- tions within population samples with Hardy- able from controlled crosses ae often too small Weinberg-proportions (Saidman and Naranjo for statistical testing. Yet even if controlled crosses (1982) in the leguminous tree Prosopis ruscifolia, succeed, the long generation intervals in trees O'Malley eta!. (1988) in Bertholletis exce!sa). Brot- imply that tissue of a particular type and schol (1983) also used the former method in her ontogenetic stage can rarely be sampled from both investigation of Liriodendron tulipifera, addi- parents and offspring. Nevertheless, since the tionally testing hypotheses against a 1: 1 segrega- expression of a number of enzymes has been tion ratio of the maternal alleles in offspring found to be ontogenetically and environmentally possessing an allele not found in the maternal tree, stable, comparison of different ontogenetic stages wherever possible. Finkeldey (1988) investigated in successive generations is often possible. Analy- single-tree offspring from open pollination of sis of offspring at the earliest possible ontogenetic Quercus petraea, basing choice of mode of inherit- stage has the additional advantage of eliminating ance in cases of doubt on the results of a paternity possible distortive effects of differential selection analysis. during later stages. New methods of genetic analysis are needed In coniferous tree species, segregation analysis that comply with the reproductive biology of of the haploid endosperm, which genetically rep- angiospermous tree species in that they allow the resents the maternal gamete, allows observation of inference of genotypes without requiring sexually ordered genotypes in seed from open pollination differentiated tissue and consider the necessity of single trees (Bartels, 1971; Bergmann, 1973). for comparison of different ontogenetic stages in This of course requires that the enzyme expression successive generations. Such methods must use can be shown to be under complete genetic control, unordered genotypes and be based on a combina- but controlled crossings are not necessary and tion of genealogical and population data as com- ontogenetic stability of expression is not a pre- pensation for the generally limited opportunities requisite. Numerous investigations, too many to for performing controlled crosses. Such a method, GENETIC ANALYSIS OF ENZYME PHENOTYPES 137 utilizing zymograms of maternal trees and their contribut:ion Am will also have seed offspring from open pollination, will be pres- maternal allelic contribution ented below. A,, In this connection, the paper of Brown et a!. =P(AA)/P(A),where (1975) on the estimation of the mating system in P(A) =probabilitythat an egg cell will a Eucalyptus species using single tree progenies be fertilized by a pollen grain must be mentioned. These authors are sometimes having the allele Am to form a cited as having presented a method of genetic zygote, and analysis. Instead, based on the mixed mating P(AA) =probabilitythat a zyote have model, they infer the unknown maternal genotype ordered genotype A,A, i.e. using the "known" genotypes of a progeny sample. maternal allelic contribution A, The progeny genotypes had been previously infer- and paternal allelic contribu. red from the zymograms, apparently without con- tion Am, sideration of the proportions of different = phenotypes within each progeny set. Due to the (ii) implies P(A,?A) IA)P(A)for all alleles incorporation of numerous prior estimates stem- A. and Ak. The most important consequence of (i) ming from the mixed mating model, it is question- and (ii) on which all further considerations will able whether an incorrect hypothesis on the mode be based is that, for maternal genotype AA3, of inheritance would be revealed in the course of P(AA) =P(AAIA).P(A) analysis. = P(A).P(A) =P(AJ).I'(A) AMETHOD OF GENETIC ANALYSIS USING SINGLE TREE PROGENIES = P(AAIA) .P(A) Basic requirements = P(AA). Assumethat the enzyme system under study is In words, this means that any allele Ak contained under complete genetic control and that the in the local pollen pool will have equal chances expression is ontogenetically stable (e.g. observ- of fertilizing egg cells with either of the two mater• able in both leaf and seed tissue). In cases where nal alleles. the genetic control has not yet been established, it will often become apparent or be disproven in the Material course of the investigation. Furthermore, suppose that an hypothesis on the mode of inheritance of Leafor bud tissue and seed samples from single enzyme phenotypes involving a single gene locus trees, ideally belonging to a single population, are has been inferred from zymograms. collected and the zymograms obtained by elec- A regularly segregating gene locis is assumed trophoresis. Previously obtained zymograms of to fulfill the following three requirements, sub- prospective maternal trees can give an indication sequently referred to as "requirements> ",which of the variability present in the population and also underlie classical Mendelian analysis: thus aid in selection of those trees which can be (i) regular meiotic segregation during egg pro- expected to yield the most information. duction; (ii) random fertilization of the eggs by each pollen Method (haplo) type; (iii) absence of differential viability selection in Themethod consists in the formulation of the offspring prior to the investigation. necessary conditions which must be fulfilled in Denoting each progeny set under P(A) :=probabilitythat an egg cell has —a given hypothesis as to the mode of inheritance the allele A,, of an isoenzyme phenotype, formaternal —the postulated maternal genotype, and (i) implies P(A) =P(A)=. —the fulfilment of the requirements>. genotype A•A1 (ij).Interms of the conditional probabilities Due to the differing genotype-to-phenotype relationships implied by different modes of gene P(AA, A) =(conditional)probability that action, the conditions will depend upon the postu- a zygote having paternal allelic lated relationships between alleles. 138 E. GILLET AND H. H. HA1TEMER

Here the two variants most commonly encountered Table 1Genetic analysis using single tree progenies. Single- in the single-locus inheritance of enzyme locus codominant mode of inheritance phenotypes will be considered, namely Proposed Possible Expected relationship codominance between all alleles; and maternal genotypes between observed numbers the presence of a recessive null allele and genotype of offspring of offspring phenotypes codominance between active alleles. A,A, A,A1 Following the patterns laid out below, analogous A,Ak(ki) conditions for more complex modes of gene action, AA A,A, such as mixtures of dominance and codominance AA3 N=N1+N in an allelic series, should not be difficult to derive. A,A AAk NIk =NJk(k i,j) A1A (ki,j)

Single-locuscodominant mode of inheritance null allele, which is present only in a heterozygous Thenecessary conditions are as follows, where state in the population. If a phenotypically "homozygous" maternal tree were actually P(A,A,,) —probabilitythat a zygote have heterozygous for a null allele, then offspring could unordered genotype A,A,,. be found which seem to be homozygous for a ={P(AA)+ P(AA)] .(2— non-maternal allele. On the other hand, a null where&m —1ifI =mand 8,,,, =0otherwise allele among the paternal trees would cause an (Kronecker delta), and excess of offspring phenotypically "homozygous" for a maternal allele. N,, =observednumber of offspring with The inclusion of a recessive null allele in the phenotype A1Am hypothesis on the mode of inheritance therefore If a maternal tree is requires a more involved method of analysis. (Cl) homozygous AA,, then each offspring must Nevertheless, the above-mentioned consequence have the allele A,; of the requirements for a regularly segregating gene locus, namely that for heterozygous maternal (C2) heterozygous AA(i theneach offspring must have the allele A, or A, and it holds that genotype AA1 any allele Ak contained in the local pollen pooi will have equal chances of fertilizing P(AA) = egg cells with either of the two maternal alleles, is P(AJ?A-P(A.A.) still valid in the presence of a null allele. The P(AA)=P(AA)J necessary conditions are as follows, where -P(A1A,)+P(AA) P(A, —)= probabilitythat a zygote have phenotype P(AA) = -+P(AAk) A, —,i.e.genotype A,A, or A,A0 P(AA) N, —= observednumber of offspring with =P(AJAk) phenotype A, —,respectively: This formal approach was suggested by H.-R. If a maternal tree is Gregorius. Obviously, a seed must contain one (C 1°) homozygous A0A0 for a null allele A0, then of the maternal alleles. However, since only un- each offspring must have the allele A0; ordered genotypes can be inferred, the above prob- (C2°) homozygous ALA, for an active allele A, abilities for ordered genotypes among the offspring (i0), then each offspring must have the of a heterozygous maternal tree must be combined, allele A,; as indicated by the brackets. These probabilities (C3°) heterozygous A.A0 for a null allele A0 and can then be used to test the observed numbers of an active allele A (I0), then each offspring possessing each of the unordered offspring must have the allele A0 or A, and genotypes with the expectation, as is summarized it holds that in table 1. P(AA) =P(AA)1 P(AA) =P(AA)1 Single-locuswith recessive null allele and codominance between active alleles P(A0A0)P(A-) P(AA)=P(AA) -* Rejectionof an hypothesis of codominance by the above method could be caused by an undetected P(Ak—)=P(AIAk) i); GENETIC ANALYSIS OF ENZYME PHENOTYPES 139

(C4°) heterozygous AA for two active alleles A, reduced viability of carriers of null alleles will not and A3 (0i 0), then (a) each lead to rejection of the null allele hypothesis by offspring must have the allele A, or A3, and the above method, as long as the viability of the it holds that null allele homozygote does not exceed the viabil- ity of any of the null allele heterozygotes. P(AAg) =P(AYAOd) P(AA) =P(AA) P(AA) =P(AA) GENERALPROCEDURE OF GENETIC ANALYSIS P( AA,) P(AI —) +P(A3 —) Theresults of the previous section suggest the P(AA)=P(AA)- following procedure for the genetic analysis of P( AA ) =P(AJAk)(k 0, i,j). zymograms in populations of angiospermous trees: (i) Trees in the population are chosen by some A maternal allele must, of course, be present. plan (not necessarily randomly) in the hopes However, if the maternal tree contains a null allele, that they will represent as much genetic varia- then all "homozygous" phenotypes can appear bility as possible (for example, if neighboring within the progeny. The probabilities for ordered trees are expected to be closely related, then genotypes must now be combined not only accord- the chosen trees should be widely scattered ing to the proposed unordered genotypes but also throughout the population); to the phenotypes. The observed numbers of (ii) tissue (e.g. buds or leaves) of each of the offspring with each of the phenotypes can be tested chosen trees is analyzed electrophoretically for conformity to these probabilities, as is summar- for the enzyme system under study; ized in table 2. (iii) hypotheses as to the mode of inheritance of the observed phenotypes are constructed on Table 2 Genetic analysis using single tree progenies. Single- the basis of these zymograms; locus mode of inheritance with a recessive null allele and (iv) representatives of each of the proposed codominance between active alleles genotypes are selected, and their respective seed progenies from open pollination are col.. Proposed Possible Expected relationship maternal phenotypes between observed numbers lected; genotype of offspring of offspring phenotypes (v) genetic analysis of the individual progeny sets is performed according to the method in the A0A0 A0A0 previous section. Ak— This procedure has been applied to Castanea sativa AA1 A,- (Fineschi et aL, submitted).

A,A0 A0A0 N00 J A1 EXAMPLES Ak_ A Single-treeharvesting of offspring from open polli- N1N+N1_ nation or, in other species, analogous collection A1A of a single maternal individual's offspring cohort AAk Nk=NJk i,j) with father(s) of unknown phenotype presents few i,j) technical problems as compared to the perform- ance of controlled crosses. It therefore seems sur- prising that the phenotypic distributions within Null alleles have in some cases been shown to such offspring sets have, judging from the difficulty be sublethal or even lethal in a homozygous state. in finding published data, rarely been used in For example, for mitochondrial MDH in maize, genetic analysis. (An exception is found in species homozygosity for a null allele at all of the three possessing haploid tissue at some ontogenetic controlling loci is lethal, while a single active allele stage, e.g., the maternally-inherited haploid endo- at any one of the loci suffices for viability (Good- sperm in conifer seeds, as discussed above. man et al., 1981). Thus at any one of the three loci the number of offspring homozygous for the respective null allele will be reduced by the number Example 1 of non-viable offspring homozygous for the null One exception is a study by Thiebaut et a!. (1982) allele at all three loci. It is interesting to note that on beech. They support their hypothesis on the 140 E. GILLET AND H. H. HATTEMER existence of a null allele at a peroxidase locus by Acknowledgement The authors are indebted to S. Fineschi and examination of offspring from open pollination of M. E. Malvolti, whose enzyme investigation of bud tissue of single chestnut trees (of the angiospermous species Caslanea a single tree. Renaming alleles, the postulated sativa Mill.) and their seed from open pollination motivated maternal genotype is A2A0 (case (C3°) in previous these considerations and to H.-R. Gregorius for suggesting the section), and the numbers of the offspring formal approach to the genetic analysis. phenotypes are: N00 =0,N2 =2,N. =12,and N12 =11(their table 5). (C3°) holds, since N00 < N2_ and the ratio N1_: N12 of 12:11 is as close as possible to 1: 1. These results give no reason to reject the hypothesized mode of inheritance nor REFERENCES to doubt the fulfilment of requirements>. ARULSEKARS., PARFITT, D. F. AND MCGRANAHAN, G H. 1985.lsozymegene markers in Juglans species. J.Hered., 76,103-106. Example 2 BARTELS. H. 1971. Genetic control of multiple esterases from needles and macrogametophytes of Picea abies. Planta, 99, Christiansen et al. 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