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GENETIC DIVERSITY^ AND^ DIVERSITY
OF ENVIRONMENTS
THEODOSIUS DOBZHANSKY
THE ROCKEFELLER UNIVERSITY, NEW YORK CITY
- Introduction
Like many ignorants, I have my deep respect for mathematics tinged with
a kind of superstitious awe. Using their recondite, and to me inscrutable methods,
mathematicians reach conclusions about problems of genetics and evolution,
which I must humbly accept as following inexorably from the premises and the
assumptions made. I^ hope, however, I am not being impertinent if I say that
not all of these conclusions are always convincing. The difficulty stems from
the premises and the assumptions. Most exasperating is the habit of certain
mathematical geneticists who make their assumptions implicit rather than ex-
plicit, on the ground that to them the truth of their assumptions seems self-
evident. I have accepted the kind invitation of Professor Neyman to participate
in this Symposium with reluctance, because of my ignorance of mathematics;
all I can talk about are certain self-evident, and certain not so self-evident, bio-
logical premises and assumptions.
Let us restrict our attention to Mendelian populations. Mendelian popula-
tions are reproductive communities of sexual and either obligatorily or at least
facultatively cross fertilizing organisms. This leaves out of account the asexual,
exclusively self-fertilizing, parthenogenetic organisms, as well^ as some inter-
mediate situations^ in^ which^ cross^ fertilization^ is^ rare.^ A^ Mendelian^ population
is said^ to^ have^ a^ corporate genotype or^ gene pool. The gene pool of^ a^ population
may be^ envisaged as^ the^ genes in^ the^ array^ of the^ gametes,^ sex^ cells,^ which^ give
rise to^ the^ following generation. The^ composition of^ the^ gene pool^ can^ be^ de- scribed in terms of the numbers or of the (^) frequencies of the genes and linked gene complexes. The^ mechanisms^ of^ the^ replication^ of the^ hereditary^ materials tend to make the (^) gene pool constant (^) generation after (^) generation. Mutation, recombination, selection, sampling errors in small populations, vicissitudes of the environments, and variations of the reproductive habits and opportunities are liable to change the composition of the gene pool.
2. The classical model
Let us begin with a model which is probably the simplest, thoroughly un-
realistic biologically, tractable mathematically, and, therefore, the favorite with some mathematical geneticists anld genetical mathematicians. Assume a Men- 295
296 FIFTH BERKELEY SYMPOSIUM: DOBZHANSKY
delian population for which (a) the environment is constant in time and in
space for all members of the population; (b) the variable gene loci are each
represented by two or more alleles, one allele being "normal" and beneficial in
the environment, and all other alleles more or less disadvantageous in homozy-
gotes; (c) most of the gene loci are occupied by identical alleles in all individuals,
the variable loci are a minority; (d) the genes produce their effects each in-
dependently of the^ others; epistatic interactions, especially as concerns fitness,
do not occur or are negligible; the fitness variations caused by the alleles at the
unfixed loci are simply additive or multiplicative; (e) the population size is
infinite or large enough to be treated as such.
Genetic uniformity is clearly the ideal state under the above model. Natural,
artificial, or eugenic selection should eliminate all disadvantageous genotypes,
and establish the single optimal homozygous genotype. All members of the
population will be genetically identical, and all optimally fit. This paragon of
adaptive virtues is difficult to achieve because of mutation. In the absence of
known means to suppress all mutation, genetic variants, all or nearly all dele-
terious, will be injected into the gene pool in every generation. The fitness of
the population will always lag below the optimum. How far below will be
relatively easy to determine. If the mutation rates and the loss of fitness caused
by each mutant are known, the genetic equilibria of the mutants can be pre-
dicted. The magnitude of the genetic load which a population carries can be
estimated, as^ well^ as the^ numbers^ of the^ "genetic deaths" which^ the population
will suffer. These numbers can be made as frightening as you wish, especially
if you forget to state that a genetic death does not always produce a cadaver.
Having no children makes you genetically dead, having one child makes you
genetically half dead.
The model outlined makes all genetic diversity unwelcome departure from
the ideal optimal uniformity. Is it at all conceivable that this Platonic archetypal
state may ever be achieved? It is conceivable, but at a cost of truly heroic meas-
ures. The first is abandonment of sexual reproduction. A technique may con-
ceivably be invented to stimulate the development of human diploid cells from
a tissue culture to yield embryos and eventually adult bodies. Such a feat has
indeed been accomplished with cells of a lowly plant, the wild carrot. Assuming,
then, that^ one encounters^ and^ recognizes the carrier of the^ optimal genotype of
the species, obtains a tissue culture of his cells, avoids all mutation, makes the
cells develop without meiosis and fertilization, and accepts the genetic identity
as not (^) unbearably dull, then the "ideal" (^) mankind, or (^) any other (^) species, is
conceivable. This ideal is implicit in some eugenical writings, although their
authors (^) explicitly disclaim the (^) advocacy of any such ideal.
3. Requirements to be met by a more realistic model
3.1. Heterotic balance. Suppose now^ that some gene loci^ produce more^ than a single beneficial allele.^ Overdominance makes the^ heterozygote A1A2 not^ inter-
298 FIFTH BERKELEY SYMPOSIUM: DOBZHANSKY
same geographic locality. The environmental changes may be cyclic and recur-
ring regularly within a single generation of an organism or in different genera-
tions. Seasonal changes are an obvious example. Or, they may be recurrent in
space rather than in time, as with different food plants or other food sources
that may be present in a locality in which a population dependent upon these
food sources lives. This situation is sometimes described as the occupation of
a variety of ecological niches by a population. Some species of organisms and
some populations have a greater and others a more limited variety of ecological
niches available to them.
Abandonment of the assumption of environmental uniformity, and substitu-
tion of environmental diversity results in models of population structure that
are uncomfortably complex and relatively intractable. These are good reasons
why mathematicians as well as geneticists are reluctant to deal with them.
Unfortunately, nature has not been kind enough to make all things as simple
as we would like them to be. Complexities have to be faced. We know much
less about population genetics than is still unknown. To pretend otherwise is
to retard acquisition of more satisfactory knowledge. Among the colleagues
participating in the present Symposium, Bodmer, Dempster, and Levene have
made some pioneering studies of the consequences of environmental diversity;
they will not consider my saying that they have barely scratched the surface
an impertinence.
There are, in general, two ways of being adapted to environmental diversity.
One is physiological or developmental homeostasis. The other is genetic diversi-
fication, in which different genotypes within a population, or different popula-
tions, are adaptively specialized to^ fit^ different ecological niches^ or^ different
environmental contingencies. Maintenance of^ a^ constant body temperature de-
spite temperature changes in^ the^ environment is^ a^ good example of^ physiological
homeostasis; dependence of^ the^ body size^ in^ adult insects^ on^ the^ amount^ of^ food
available to^ nymphs or^ larvae is^ an^ instance^ of^ developmental homeostasis. Presence in^ a^ population of^ genetic variants with different^ food^ preferences, different temperature tolerances, and^ so^ forth, permits a^ fuller utilization^ of^ the environmental opportunities than^ could^ be^ achieved^ by a^ single genotype. Brazenly opportunistic, evolution^ utilizes^ homeostatic^ plasticity as^ well^ as genetic specialization and diversification^ to^ achieve^ adaptedness in^ its^ creations.
Is either of these methods superior to the other? It is intuitively obvious that a
genotype which could^ react^ to^ every^ environment^ by^ producing optimal pheno-
types would be ideal. This would, indeed, be that will-o'-the-wisp invented by some geneticists, the optimal genotype. Ours is, however, not only not the most
perfect of all conceivable worlds but not even^ the best of all^ possible worlds.
The adaptive capabilities of^ every genotype are^ circumscribed, more or^ less widely or narrowly. This makes^ adaptation by means^ of^ genetic diversification
sometimes preferable. In^ general, the^ more^ diversified^ is the environment the
less (^) likely is a (^) genotype fit to (^) occupy all the available (^) ecological niches. The problems that arise^ are^ those^ of^ evolutionary^ strategies.^ Mathematicians and
GENETIC (^) DIVERSITY 299
geneticists can play imagining themselves being gods, aiid decide what strategy
evolution could have used to achieve adaptedness most rapidly and effectively.
The optimal strategy would, of course, yield the most perfect possible adapted-
ness of a population to its environments. Such a strategy could, conceivably,
rely on a homeostatic plasticity given by a single or a few genotypes, or could
make use of an adaptive genetic polymorphism, or various combinations of these
methods. Levins [22], [23], [24] and Lewontin [26], [27], have produced very
interesting studies of optimal evolutionary strategies. There evidently exist
many fascinating and challenging problems in this field, both for theoreticians
and for experimentalists. One may inquire how evolution could be made adap-
tively most productive, and one may wish to find out whether evolution has
in actuality utilized anything resembling the methods which our mathematical
and biological wisdom indicates as most advisable.
Recognition of the importance of environmental diversity necessitates con-
sideration of some forms of selection which are rather more complex than the
classical ones. Although they were considered by the pioneers of mathematical
genetics, especially by Sewall Wright [47], [48], much remains to be done to
achieve a satisfactory understanding, both by way of mathematical models and
of their experimental applications. Suppose that there are two or more pheno-
types which confer a high Darwinian fitness on their possessors, while the
intermediates between them are less fit, or are culled and prevented from
reproducing by the breeder. This is diversifying selection, which will tend to
make the population genetically variable or polymorphic. (It is also termed
"disruptive" selection, which is a most unfortunate choice of word, since this
selection is biologically constructive rather than disruptive.) One of the situa-
tions in which diversifying selection will occur is when the fitness of a genotype
is a function of its frequency; in other words, the selection coefficient s is a
function of the gene frequency q.
An interesting, though perhaps rather special, example of this is the advantage
in mating of a type which is rare, and disadvantage of a type which is common
in a given environment. In the experiments of my colleague, Dr. Lee Ehrman
[13], females and males of two strains of Drosophila pseudoobscura are intro-
duced into an observation chamber, and the matings that occur are recorded.
The following data were obtained using strains derived from wild flies collected
in California (C) and flies collected in Texas (T). The numbers of the flies of
each sex (^) per chamber, the numbers of (^) females and of (^) males that mated (of course, in^ several chambers), and the chi squares (one degree of freedom) testing
the deviation from randomness of mating, are summarized in table I.
In Drosophila, males court all females rather (^) indiscriminately, but females accept only some and (^) reject other (^) courtships. Observed (^) courtships are several times more numerous than copulations in the observation chambers. (^) Now, with C and T females and males being equally numerous in a chamber, the C and T
flies mate about equally frequently; when C are four times more numerous
than (^) T, the number of C males (^) copulating is (^) only twice that of T (^) males; when
GENETIC DIVERSITY 301
biologists given to this possibility that I am unable to find in the literature a
convincing case that could be used here as an illustration.
There are, to be sure, excellent data of Birch on three species of the grain beetles Calandra and the related genus Rhizopertha, of Park^ [34]^ and his school
and of Lerner [17] and his colleagues on two species of the flour beetles Tribolium,
and of Moore [32] on two species of Drosophila. In all these studies, it has
been found that one species is better adapted to a certain food, or to a certain
temperature or humidity than the other species, while this latter is superior
under different conditions. In mixed populations one or the other species is
usually the winner, depending upon the environment. Most^ fascinating are the
recently published experiments of^ Sokoloff, Lerner and^ Ho^ [43] on^ mixed^ cul-
tures of^ Tribolium castaneum^ and^ T.^ confusum. The^ first of^ these^ does^ better
than the second on^ wheat^ flour, while^ the^ second^ does better^ in^ cornmeal.^ When
in competition on corn, castaneum is, however, the winner as long as confusum
is also present, but when the competitor is eliminated, the winner goes into
decline too. The solution of the puzzle is that these beetles are cannibals, and
while suffering from a nutritional deficiency on corn, castaneum is able to supple-
ment its diet by eating developmental stages of confusum. When the supply of
the latter species is exhausted, the^ species practicing "xenocide" commits un-
witting suicide.
In humid tropics, where there^ are^ many species of^ Drosophila developing^ in
fermenting fruits, Pipkin [40] and^ others^ found^ a^ remarkable differentiation^ of
ecological preferences. Although most^ species of^ Drosophila^ can^ feed^ on most
species of^ fruits,^ each^ Drosophila^ has^ a^ certain^ repertory^ of^ fruits which^ it
chooses if choice is available. This is an admirable arrangement, because when
there is a choice of fruits, different Drosophilae go after different fruits, thus
minimizing competition. The preference does not, however, reach the point
when a Drosophila could develop only in a single kind of fruit; so rigorous a
specialization would evidently endanger the continuation of^ the species if its
food source were owing to some^ accident^ temporarily unavailable. Differential
food preferences almost certainly exist^ within^ species as^ well, but the evidence
for this is^ circumstantial^ and^ inconclusive.
The evolutionary situations which arise when a Mendelian populationl faces
a diversity of environments^ have^ been^ surprisingly neglected by biologists, and perhaps because of this^ neglected also^ by mathematicians. Environments may vary in^ time, or^ in^ space, or^ both.^ Variation^ in^ time^ may^ be^ regularly^ cyclic,^ as
with seasons, or irregular, like wet and drought years. Variations in^ space may
recur mosaic fashion, as meadows, forests, and hill^ slopes in^ many countries,
or may be more systematic, as with the^ rainfall becoming greater or^ more scarce
as one approaches the ocean or^ ascends^ to^ higher altitudes^ in^ the mountains.
How will the population genotypes respond to these challenges? Under what
conditions will stably balanced polymorphisms be established? In a two page
article published some 13 years ago, Levene [18] has shown that when two or
302 FIFTH BERKELEY SYMPOSIUM: DOBZHANSKY
more ecological niches are available, two or more alleles may be held in stable
polymorphic equilibria, without the heterozygotes being heterotic. Dempster
[10], Li^ [29],^ [30],^ Lewontin^ [25],^ [27], [28],^ Haldane^ and^ Jayakar [14],^ Parsons
[35] to [39], and others have discussed Levene's and some other models. The
"polymorphism due to selection in varying direction" examined briefly by
Haldane and Jaykar seems particularly interesting, although it remains to be
discovered how often the biological situation postulated by them is encountered
in nature. They assumed a pair of alleles, one of which is dominant and the
other recessive, each of which makes its carrier fitter than its counterpart in
different generations. Now, if the arithmetic mean of the fitnesses of the^ re-
cessives in (^) different generations is greater than unity, while the geometric mean
is lower than unity, both alleles will persist in the population owing to this form
of balancing selection.
Very little^ attention^ has been^ given^ to^ the effects^ of^ epistatic^ interactions^ of
different genes affecting fitness. That such interactions occur, both for loci in
different chromosomes^ and for linked^ loci, is^ not^ denied^ by anyone; how^ preva-
lent epistatic phenomena are in reality is, however, an open question. I leave
it to you to judge whether it^ is advisable^ to^ build^ theories^ of^ population^ genetics
ignoring epistasis. Bodmer and^ Parsons^ [5],^ Lewontin^ and^ Kojima^ [28],^ and
some others have made theoretical studies of the situations that may arise
when linked genes affect fitness differentially when in coupling and when in
repulsion phase. As far^ as^ I^ know,^ epistasis^ by^ itself,^ without^ linkage^ or^ heterosis,
has not been shown to yield stable polymorphisms. The situations that might
arise when diversifying selection operates with epistatically interacting loci are,
however, in need of investigation.
4. Concluding remarks
I realize how unsatisfactory this article may appear to you. I have tossed
before you a host of problems, and have given no solution for any of them.
To give solutions was, however, not within my ambition, because this is beyond
my capabilities. The intention was rather to ask the^ mathematical^ colleagues
for help, which geneticists and evolutionists are so much in need. The classical
model of genetic population structure has until recently received the^ lion's^ share
of attention. It has the^ advantage of^ simplicity, but the^ disadvantage of^ mis-
representing reality. It is^ not^ entirely played out, and^ probably never^ will^ be,
since it does contain^ a^ grain of truth-for^ some^ genes and for^ some^ environments
its simplifying assumptions are^ satisfactory as^ approximations. But the bio-
logical reality is^ different, and if I may say so, more^ interesting than the classical
model suggests. Natural^ populations of^ many sexual^ species, including man, contain so much (^) genetic diversity at so (^) many loci that two individuals probably never have the same (^) genotypes, unless they are identical twins. Moreover, a good part of this diversity is not a sad accident, not a^ departure from^ this Platonic eidos called the (^) "optimum genotype," but^ a means^ whereby the^ popu-
304 FIFTH BERKELEY SYMPOSIIJM: DOBZHANSKY
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