- 15 l
SELECTION IN REFERENCE TO BIOLOGICAL GROUPS
Dr. Bruce Griffing
Dept. of Zoology and Entomology
Ohio State University
Columbus, Ohio
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SELECTION IN REFERENCE TO BIOLOGICAL GROUPS
This paper is concerned with the breeding dilemma which arises when
competitive interactions can occur between genotypes in the population
undergoing selection.
Interest in this problem was stimulated by the simple
but elegant study of competition between barley genotypes made by Wiebe et. al.
(1963).
In this study the authors discovered that yields of genetically
marked stocks were reversed in pure and mixed barley stands.
Obviously
this leads to a plant breeding dilemma since selection necessarily operates on
a mixed population but has as a goal the production of the highest yielding
pure stand.
The authors drew the following disturbing conclusions:
The reversal in yield performance of the same genotype in pure stand
vs. in a mixture is an important consideration when a population is
approached for selection. Where high yield is the criterion selected
for, say in the F6, and the selection is intended for use in pure stands_
then the instructions from the present study are that one should save
the poorest plants from the F6 rather than the good ones. This is a
paradox to the plant breeder; On the other hand, if the rule shown
has a degree of universality, it may explain why breeding for increased
yield has progressed so slowly.
This example implies that positive individual selection results in a
negative response in the population mean, and that continued selection causes
the population structure to deteriorate.
Of course, negative selection cannot be seriously recommended as a
solution to this problem.
The theoretical approach suggested here is to extend
the conceptual genetic population model to accommodate the phenomenon of
genotypic interaction (in this case competition) and then to examine the
consequences of different kinds of selection operating on this more complex
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model in order to identify those selection procedures which will invariably
give the desired result.
Clearly, the desired result is that positive selection
invariably produces a positive, or at least a non-negative response.
The biological model is extended in two ways:
(1)
Small groups of interacting genotypes are defined and the population
of such groups is generated;
(2)
the gene model associated with any individual is extended to include
not only the usual direct effects of the individual.s own genes, but also
associate effects of genes in other members of the group.
With Lintmembers in the group, the increment change in the population
mean due to individual selection is given by
where,
= standardized selection differential,
= phenotypic standard error,
d_i
= direct additive genetic effect of Ai, and
_i
= associate additive genetic effect of Ai.
In terms of variance and covariance components, this increment change is
},
where,
= additive genetic variance due to direct
gene effects, and
=
(_a)G_A
t
=
Z
_
= covariance of additive direct and additive
associate effects.
- 18 .
)
In groups of size one (the classical situation of no interaction among
members of the population), _
can be negative.
Therefore _
'n' is greater than one, _
quantities.
negative.
is a function of quantities_ none of which
is non-negative, i.e._>/O.
HOwever, when
is no longer a function of only non-negative
This is so because (_)_
is a sum of crossprodncts which can be
Under the situation in which plants are strongly competing for the
same environmental space (water, light and nutrients), it is logical to assume
that a negative relationship often exists between direct and associate effects.
Thus a gene which yields a positive direct advantage for the genotype containing
it, would tend to yield a negative associate stimulus to the competing member
ofthegroup.
Hence
if
< 0,
then positive individual selection results in a negative change in the population
mean.
Thus the model is capable of giving the results observed by Wiebe, et. al.
(1963).
The next problem is to find selection schemes that redirect the associate
effects into productive ways so as to aid rather than hinder the selective
process.
The solution is to identify 'balanced, selection procedures which
convert _4
from a negative sum of crossproducts into a positive sum of squares.
This ensures that n_ >/o.
The simplest such procedure is group selection in which the unit of
selection is the group rather than the individual, i.e. the entire group is
,
- 19
accepted or rejected on the basis of its average group performance.
In this
case, the increment change in the mean is transformed from a sum of crossproducts to a sum of squares;
oz-_ in
terms
of variarlce
ahd c:ovarianoe
components,
¢,).c-:-J,
I
&_
=
Thus group
group
_ _
selection
selection
satisfies
produces
E_-bension
of the
e_-ample_ selection
_:on,-.negative
_" (ac{_') "%
procedu-_s
responses
the
positive
group
_::_d_Ltive
necessary
associate
genetic
req,zirementsm
i.e.
variance.
positive
response°
theory
can be made in
based on indices
and which
1
are
a variety
of ways.
can be developed
more efficient
than
group
which
For
yield
selection.
extension to 'ordez:;_d:
gc'oup_ J,n which position is important can be made.
The
The
problem of selecting and e_m3uating in populations of differing group sizes
can be treated_
The precee_.ng
a'_--_;...._.,_:,
.,_,.............. are ._-a.dewith regard to interacting elements
witkin groups of olants_ _<ithspecial reference to densely planted small-grain
cereals°
Plant interactions a_e entirely concerned with utilization of the
physical environmental space°
E:_t.ension
of the argument to animals is made
more interesting by the fact that a new dimension is added to the competition
)
for space.
This dimension has to do with the utilization of the social space.
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Hence elements in animal groups can involve any one of the following four
combinations of physical or social interactions:
SOCIAL
Independence
Interaction
(Indep, for social space )
I_ependenc¢
Physica_
•
Interaction
[Indep. for physical spaceI
[Interaction for social space)
/Indep. for physical space
_Interaction for physical space_ /Interaction for physical space1
[Independence for social space J [Interaction for social space 1
Since my contact with the real world is only in plant research_ I cannot
speak with any authority in regard to the social structuring of animal populations.
However after a little study of the subject3 it appears to me that
a large flock of chickens may possibly be socially structured into small groups
(sa_lO
to 20_irds
in each group)in
such a way that one bird occupies the
dominant 'alpha, position, a number of birds each occupy a secondary Ibeta_
position and several occupy a tertiary 'gamma' position.
As the fleck density
is increased, the phenomenon of social 'stress' increases within the groups.
This accentuates the dominance relationships and may affect egg production.
Genes contributing directly to aggressiveness could very well have negative
associate effects.
If the above conjectures are essentially true, the results of selection
would be similar to those outlined above for the case of competition in plants.
In this case I suggest the first step would be to determine the optimum size
of the group in which the dominant bird can maintain control with minimum social
stress.
In this connection, Calhoun (1963), in a remarkable paper on the use
of social space, suggests that an average group size of 12 is found in a
wide range of social animals.
Once an optimum size has been determined, groups
of this size should be kept physically separated so that group performances
can be obtained.
Selection among g2oups can then be made on the basis of these
average records.
The objective, of course, is to u
•
e ...........
% ro
up select
or
some other 'balanced' procedure) which would modify the social behavior of
the animal to conform best with the aims of the breeder.
Finally, a possible explanation of the enigma of a plateaued egg production
when additive variance persists, can be made on the basis of the two-dimensionality
of gene effects in terms of the group theory.
It is easy to construct an
overdominance situation for the total effect of two alleles at a locus with a
model in which only partial dominance exists in each of the two (direct and
associate) components of gene action.
In this case, the total overdominance
effect would lead to a stable equilibrium under appropriate selection procedures.
The estimated additive genetic variance would not be equal to zero if the
estimation method did not correctly take into consideration both direct and
associate effects.
REFERENCES
Calhoun, J.B. (1963).-
The social use of space.
Physiological Mammalogy 1:1-187.
Griffing, B. 1967.- Selection in reference to biological groups. I Individual
and group selection applied to populations of unordered groups.
A.J.B.S. 20:127-39. (This paper is the first of a series on
biological group theory)
•
-22_
Lewontin, R.C. (1955).- The effects of population density and composition on
viability in Drosophila melano_aster. Evolution 9:27-41.
Lewontin, R.C. and Y. Matsuo (1963).- Interaction of genotypes determining
viability in Drosophila busckii. Proc. Nat. Acad. Sci. 49:270-78.
Wiebe, G.A., Petr, F.C., and Stevens, H. (1963).- Interplant competition
between barley genotypes. In "Statistical Genetics and Plant Breeding".
(Eds. _LD. Hanson and H.F. Robinson.) pp. 546-55. (National Academy
of Science: National Research Council Publ. No. 982.)
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DR. BRUCE GRIFFING - "SELECTION
R. C. LEWONTIN:
IN REFERENCE TO BIOLOGICAL GROUPS
There is extensive literature showing the effects you
describe in Drosophila and the house fly.
They show that in general the
group interaction effects are small, although there may be occasional
extreme interactions.
are usually small.
GRIFFING:
The imperical evidence then, is that these interactions
Is this your co$clusion?
On examining published material of Dr. Lewontin (Lewontin, 1935;
Lewontin and Matsuo, 1963) in which competition effects with Drosophila were
studied, it is rather surprising to note that Dr. Lewontin suggests group
interactions are, in general, small.
The summary of the 1963 paper contains
the following:
The results were:
(1) For all strains the highest viability
is at an intermediate density, not at the lowest. (2) For a given
density, especially at high density, the proportion of the two genotypes
in the mixture was important in determining viability. (3) Relative
viabilities observed in mixtures agreed with predicted viabilities
from pure cultures at intermediate (optimum densities) but deviated
strongly at high and low densities. (4) The genotype with higher
viability in pure culture often had lower viability in mixed culture.
The implication of this last observation is that the absolute fitness
of a population, may not have relation to the direction of genetic
change in that population, and that the population may evolve to a
lower state of absolute fitness°
Concerning this final statement the authors made the further elaboration:
Finally, from the evolutionary standpoint, such interactions as
seen at high densities in the 'cut' and 'yellow' series raise the question
of the relation between population fitness and genotype fitness. Since
Acme-A (wild-type) in pure culture has a lower viability than the mutants
in pure culture, a population of pure Acme-A is in some sense not as fit
as a population of pure mutant individuals. At least the load of larval
death is greater. Nevertheless, the presence of Acme-A and mutants
in the same population results in a dramatic increase in Acme-A
viability above that of the mutants. As a result the mutants will be
eliminated. We then have the paradox that a population will evolve
toward a lower absolute fitness, even though the value of intrapopulation fitness, W, seems to be increasing. Thus natural selection _
does not assure that the fitness of the population, as a whole, will be
increased.
The Drosophila data and interpretations for high density agree well
with the data and interpretations that Wiebe et. ai.(1963) made with respect
to the barley example which was discussed in the talk.
In fact if the
Drosophila data had to do with weights of the organisms (analogous to yield
of barley) instead of the all-or-none criterion of viability, the results would
probably have been even more similar to those of the barley example.
Hence
I see no conflict but rather a corraboration of results.
A note of caution about drawing inferences from simple mixtures about (_
should be made.
If group size is n> 2 but only two entities (A and B, say) are
being mixed, the correlation between members within groups does not directly
reflect (_(Y-A •
This is so because in such a mixture, pairwise interactions
would involve AxA and BxB as well as AxB.
If the simple mixture is (1/2)A to
(1/2)B the interaction, AxB, constitutes only 1/2 of all such pairwise
interactions.
As the mixture departs from (1/2)A to (1/2)B, the relative
frequency of AxB decreases.
Perhaps the differences of opinion relate to intensity of competition.
The example I used had to do with the intensely competitive situation which
exists in commercial stands of small-grained cereals.
are clear cut.
The results of Wiebe et. al.
The results of Lewontin and Matuso (1963) at the highest
25 -
density (the only density at which the wild-type flies showed a substantial
decreased viability) in combination with a l:l mixture, exhibited this same
negative relationship of direct and associate effects.
In three of the four
cases, the wild-type flies were more aggressive in mixtures but yet did not
yield as high viabilities in pure stands as the mutantse
The reverse was
true for the remaining mutant, 'claret,. However, when all possible pairwise
interactions were taken into consideration, the 'claret, contrast also
showed the negative relationship°
The important point I would like to make here is that the group theory
as it has been developed, is perfectly general.
It can accommodate any
degree of interaction and any class of interaction (competitive or cooperative)
regardless of whether the interaction involves use of only the physical space,
or only the social space, or if it involves both physical and social spaces.
R. C. LEWONTIN:
I would like to emphasize, as Dr. Griffing has done_
that negative correlations between fitness and frequency may maintain genetic
heterozygosity in a number of cases@
H. ALPLANALF:
Your random groups would have to be small in order that
genetic variance of group means is of reasonable magnitude°
t
GRIFFING:
Is this correct?
I think the most meaningful biological model which involves
genotypic interaction must incorporate the notion of small groups of individuals
within which genotypes may interact.
For example, plants are fixed in space
and hence each plant interacts with a small finite number of adjacent plants.
:
In hill-planted crops, each hill represents an extremely compact group of
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highly competitive members (3 to 5)_
In drill-planted crops, group size would
increase depending on the density of planting.
Even so, the effective group
size would be relatively small°
In social animals I am concerned primarily with those populations which
are socially structured with an ultimate group size in the range of 8 to 20.
Calhoun (1963) argues strongly for an optimum size of 12_
With regard to
chickens, my colleague Professor Jaap has directed my attention to a series
of papers by McBride (some of which are as yet unpublished) in which very
detailed analyses of g_oup formation in chickens has been made.
To answer your question, then,I am concerned with infinite population
theory which deals with small finite groups,
D. HARRIS:
This development is pertinent to the testing and selection of
_oultry in individual cages with commercial production in multiple bird cages.
Do these results have implications for genetically controlled maternal effects?
The difference seems to occur in that instead of random association there is
the association o_ parent and offspring_ - .............
GRIFFING:
A further extension of the group theory (which I did not mention
in the talk because of lack of time) relates to the problem of obtaining more
efficient selection procedures due to the use of groups whose elements are not
randomly associated°
An important example of this class of groups is that in
which the group members are relatives.
Group theory, then, provides the basis
for attack on problems due to interactions among relatives.
Use of plants can carry the relationship between group members to an
- 27 I
extreme.
For example,
with
groups
can be constituted
degree
of heterozygosityo
can be extracted,
genotype.
groups
plants that
entirely
can be separated
of the same genotype
In the case of those
plants
can be made up entirely
In both of these
cases,
into
propagules,
regardless
from which
of the
monoploids
of the same homozygous
the efficiency
of selection
is greatly
enhanced.
J. V. CRAIG:
I would
are found in animals.
previous
Poultry
Cos (Animal
(Poultry
Science,
commercial
This was pointed
Breeders
Behaviour,
like to comment
Roundtable
January
strains
were
in mixed
strains.
Peck
expected,
those
performed
at a lower level when
The opposite
formed
better
couldn,t
strains
worked
which
recently
experiment
to this
in mixed
out in the mixed
were low in social
of an interclass
this
in competition
groups,
discussion,
status
and
& Craig
in that
separate
We found
penned
that,
separately.
that is they peramong
themselves.
If so, the negative
associate
in this manner,
would
But a positive
it?
as
pens
effect"
could it?
six
by
in the mixed
than when
strains,
at a
effect,, and "associate
correlation?
be very large in large
effect wouldn,t be limited
different situation?
"direct
by Tindall
pens.
strain pens than when competing
Wouldntt
effects
by Bielherz
pens and also kept
was true of the highly aggressive
J. L. LUSH:
the nature
orders were
An
to be relevant
placed
composition
out by Dr. Guhl and myself
and more
1967).
1959) seems
that social
have
effect
associate
Or is this an utterly
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GRIFFING:
The intraclass correlation is not a direct measure of (d_
The numerator of the correlation can be shown to be a function of both (_)0_A
and _(T_ _.
_>o,
If (Ea)QAA remains negative, and of the same magnitude, and if
it can be shown that as 'n' increases the intraclass correlation may
change from negative to positive values.