THE NATURAL LIMITS TO BIOLOGICAL
VARIABILITY:
AN EXAMPLE (excerpts: Works of Roberts and
Robertson):
In a recent
internal seminar (April 2002), I presented the next introduction:
“The Nucleic
Acids: DNA and RNA are the Biological Software (you can see that there was a
designer of them, The God Creator)”.
“The knowledge
of the RNA Assembly (RNA Editing, RNA Splicing, RNA Trans-Splicing, RNA
Post-transcriptional Modifications, etc…) can help us to understand the
Abundance and Types of mRNA in the Cell, and vice-versa”.
The next expressions summarize some of
our most recent research concerns: “The proteome is astoundingly more complex
than the genome. And it is not just the numbers, though they are staggering:
30,000 genes could well translate into one million proteins.” "We have to
remember," says Marc Vidal, assistant professor of
genetics, Dana Farber Cancer Institute in Boston, "that the proteome is
vast. It's like terra incognita.... We have a few settlers, we have to explore
a huge amount of space." Vidal says, "If you know what the binding
partners [of a protein] were, and when it and neighboring genes were expressed,
and if in addition you know the phenotype of the loss of function of these genes,
then you can start building models of what those genes might do and also how
they do it." Vidal warns about being too quick to throw out the false
positives that inevitably come from large-scale screening efforts. While in the
past, he has recommended care in interpreting data, he now wonders whether
important or novel interactions might be overlooked. "We must be careful
about the judgments that we make, we might miss some very interesting biology.
Why do you want to know an interaction takes place—you want to know when it's
surprising, when it makes you think differently." (The
Scientist 16[8]:28, Apr. 15, 2002).
Linking the Past with the Present:
The next, is a
Figure with it’s Conclusions, Discussion and Summaries (after that, a review of
Contributions and a Biographical sketch of Alan Robertson):
A figure that
talks more than thousands of “mathematical words” (Taken from: Roberts, Genet. Res.
8:361-375, 1966):
http://personales.com/mexico/guadalajara/RV1960/robertsgraph.gif
FIGURE 1. Long-Term Responses to Selection of CL (long mice) and CS (small
mice) Lines.
[Note on Figure
1: The experiments described in the first part of that study (see below)
describe until the 30 generation, the second part (see below) deals with later
generations. A similar graphic was previously described by Falconer (Falconer, D. S. Selection for large
and small size in mice. J. Genet. 51:470-501, 1953) for the big line NF, that attained a limit of 28 g after 52
generations and the small line NS, that attained a limit of 11 g after
42 generations, that graphic is shown in the Fig. 1 of the first part of the
study published by Roberts, also in Figure 2 (Falconer, D. S. Selection of Mice for Growth on High
and Low Planes of Nutrition. Genet Res. 1:91-113, 1960b) and Figure 3 (For the upper line: Falconer, D. S. & King, J. W. B. A Study of
selection Limits in the Mouse. J. Genet. 51:561-81, 1953; for the lower line: MacArthur, J. W. Genetics of Body Size and Related Characters. I.
Selecting Small and Large Races of the Laboratory Mouse. Am. Nat. 78:142-157,
1944; MacArthur, J. W. Selection for Small and Large Body Size in the House
Mouse. Genetics 34:196-209, 1949; King, J. W. B. Pygmy, a Dwarfing Gene
in the House Mouse. J. Hered. 41:249-252, 1950) Roberts show similar differences from other studies.]
Conclusions (of
part one of the study):
This survey of
previous selection experiments for body weight indicates to within a fairly
narrow range the limits that can be expected, under the conditions of our
laboratory, when selection is applied to a heterogeneous population… These
figures set standards for further experimental studies on the limits…
The experiments
discussed here seem to have featured high initial responses to selection
without a sacrifice of ultimate gain, if we can safely conclude that
unfavorable alleles have not been fixed. To combine these two objectives
appropriately is a problem in practice, and one that has proved intractable to
theoretical treatment.
The experiments
reviewed in this paper seem to agree reasonably well with a model of selection
limits based on the exhaustion of the additive genetic variance. It is
emphasized however that this does not necessarily establish that model as the
exclusive explanation of the phenomena. The genetic nature of the limits can be
exposed to experimental investigation…
SUMMARY (of part one of
the study):
1.
The
results of some selection experiments for body weight in the mouse, conducted
in the past in this laboratory, have been examined from the point of view of
the limits ultimately reached.
2.
The
limits that are apparently attained do not necessarily remain stable over
prolonged periods of time; two large lines (CL and CFL) showed marked decrease
despite continued selection for high body weight.
3.
Selection
for high body weight (CL) reached a limit in the region of 30 g. at 6 weeks of
age; small mice (CS) reached their limit at around 12 g.
4.
The
time taken to reach the limit may vary from ten to thirty generations, even for
this one trait.
5.
The
total response for unidirectional selection was between two and six times the
phenotypic standard deviation, or three to twelve times the additive genetic
standard deviation.
6.
Consideration
of the half-life of the selection responses excluded the likelihood of the chance
of fixation of alleles unfavorable to the direction of selection.
7.
The loci
contributing to the response could each have an effect amounting to anything
from one-half to one phenotypic standard deviation in the base population.
8.
This
indicated that up to twenty loci had contributed to the response.
9.
The
intensity of selection practiced was close to the optimum for obtaining the
maximum total response.
10.
The
rule of parsimony would indicate the exhaustion of the additive genetic
variance as an adequate explanation of the limit attained.
I should like to
acknowledge the profit and pleasure of discussions with Drs. D. S. Falconer,
Alan Robertson and W. G. Hill on various issues that arose during the
preparation of this manuscript. Dr. Falconer kindly provided me with data to
supplement his original publications. This facilitated greatly the examination
of several points.
DISCUSSION (of part two of
the study):
It was seen in
the preceding sections that the limit to artificial selection had been reached
for very different reasons in the large and small lines. In the large line the
additive genetic variance had been effectively exhausted. In the small line,
however, a substantial proportion of the remaining variance was additive
genetic, and a response to reversed selection was readily obtained.
It was explained
earlier that only two of the seven selected lines available for study were
subjected to further experimental investigation of the nature of the limits.
However, Falconer (Falconer,
D.S. Patterns of Response in Selection Experiments with Mice. Cold Spring
Harb. Symp. Quant. Biol. 20:178-96, 1955) reports some
short-term studies of a similar kind on two of the other five lines. Reversed
selection was carried out from the small (NS) line on two separate occasions.
The first (from generation 12) was at a time when the line was still
responding, but by the second time (from generation 20) the line was
approaching its ultimate limit. Over four generations, the response to the
reversed selection was unmistakable. The other study described by Falconer was the
relaxation of selection from the 24th generation of the large (NF)
line, after the line had reached its limit. Over six generations, there was no
indication that the relaxation of selection resulted in any separation from the
line under continued selection.
Though the
evidence just quoted is fragmentary, it does encourage some thought of the
possible generality of the phenomena described in this paper, with respect to
selection for body weight in the mouse, namely that selection for large size
may lead to the exhaustion of the additive genetic variance whereas selection
for small size may reach a limit despite the detectable presence of additive
variance. If this is so, then the genetic nature of the limits were reversed
from the ones that appear to obtain in Drosophila; in this organism, it
is selection for small size that seems to lead to fixation. Reeve &
F. W. Robertson (Reeve,
E. C. R. & Robertson, F. W. Studies in Quantitative Inheritance. II
Analysis of a Strain of Drosophila melanogaster Selected for Long Wings.
J. Genet. 51:276-316, 1953) described a
strain, selected for fifty generations for long wings, in which the additive
genetic variance was much greater than in the base population and from which relaxed
and reversed selection yielded read responses. F. W. Robertson (Robertson, F. W. Selection Response
and Properties of Genetic Variation. Cold Spring Harb. Symp. Quant. Biol.
20:166-177, 1955) reported a parallel but extended study,
using thorax length as his criterion of size. After twenty generations of
selection, the small flies failed to yield any response to further selection
after twelve to fifteen generations but quickly returned to the level of the
base population on the reversal of selection. Detailed analyses in both of
these Drosophila studies indicated to the authors that genetic
mechanisms of some complexity operated to preserve heterozygosity in the lines
selected for large size.
Another Drosophila
study on the long-term effects of selection, this time for a bristle score, was
reported by Clayton & A. Robertson (Clayton, G. A. & Robertson, A. An Experimental
Check on Quantitative Genetical Theory. II. The Long-Term effects of Selection.
J. Genet. 55:152-170, 1957). Despite the
highly additive genetic basis of the character selected, a limit to the
response in either direction was still compatible with a considerable amount of
residual genetic variance.
The results so
far available on selection limits suggest that models based on the exhaustion
of the additive variance may not be sufficiently comprehensive to describe
fully many of the situations derived in practice. They therefore underscore the
need for more detailed investigations of specific cases, if we are to gain a
deeper appreciation of the genetic nature of the limits to artificial selection…
SUMMARY (of part two of
the study):
1.
The
effects of long-continued selection for body weight in two lines of mice, one
large and one small, are described.
2.
The
large line showed sharp increase in weight after remaining at an apparent limit
for twenty generations. A rare combinational event is suggested as the most
likely explanation.
3.
Reversed
and relaxed selection from the large line at the limit failed to yield any
response. This indicates that effectively, the additive genetic variance in the
line had been exhausted.
4.
In
contrast, the small line at the limit regressed slightly towards the base
population when selection was relaxed. Reversed selection yielded a ready
response until a new limit was apparently reached. Loci affecting body
weight in this line had therefore not been fixed by selection.
5.
Natural
selection, operating on viability between conception and the time when the
selection was made, appears to explain best the lack of fixation in the small
line.
6.
Attention is drawn to the necessity of
more experimental work to elucidate the genetic nature of the limits to
artificial selection.
[Source: Roberts, R. C. The Limits to Artificial Selection
for Body Weight in the Mouse. II. The Genetic Nature of the Limits. Genet.
Res. 8:361-375, 1966, and I. The Limits Attained in Earlier Experiments. Genet.
Res. 8:347-360, 1966.]
ALAN ROBERTSON
(1920-1989)
HIS PIONEERING CONTRIBUTION TO THE BIOLOGICAL
LIMITS OF VARIABILITY
The Theory of
Limits to Artificial Selection
For a simple
additive model, Alan Robertson showed in 1960 (Robertson, 1960) that the
expected limit to artificial selection is equal to the expected response in the
first generation multiplied by twice the effective population size, with a half
life of 1.4 times the effective population size. The theoretical limit is the
same if two populations of size N are selected independently and then
crossed and reselected, or if a single population of size 2N is
selected. These predictions were found to hold generally true for experimental
populations (Jones et al, 1968; Madalena & Robertson, 1975).
The Theory of
Limits to artificial selection was later extended to include the effects of linkage
(Hill & Robertson, 1966; Robertson, 1970; Robertson 1977). The effect of
linkage on the final limit depends on population size, the problem being
whether the negative associations between linked loci with opposite
effects on the trait caused by selection can be broken by recombination before
they are fixed. The general consensus is that linkage will not substantially
reduce the limit to selection expected with free recombination for most
combinations of parameters relevant to selected populations. This was confirmed
experimentally in Drosophila selection lines, in which recombination was
suppressed over 80 % of the genome, reaching limits to selection for
sternopleural bristle number that were reduced 25 % from limits achieved with
free recombination (Mc Phee & Robertson, 1970).
The Theory of
Limits to artificial selection was further extended to the case where the limit
is caused by a balance between natural and artificial selection, showing a
reduction in the final limit and maintenance of genetic variation at the limit,
as observed experimentally (Nicholas & Robertson, 1980). Natural selection
must be very strong before this sort of plateau is achieved.
The Theory of
Limits and The Quantitative Trait Loci (QTL)
The description
of quantitative variation in terms of the gene frequencies, numbers and
effects, and the interaction of the individual loci controlling the
traits is necessary if quantitative genetics wishes to go beyond statistical
descriptions (Robertson, 1967; Robertson, 1968), Alan was actively involved in
experiments to address these questions. The Theory of Limits to artificial
selection (Robertson, 1960) in fact suggests an experimental approach to
inferring gene frequencies at loci involved in selection response. If
the initial population size is restricted by inbreeding, the limit to selection
from the bottlenecked lines will be reduced over that obtained from selection
from a large base population by an amount that depends on how important are
initially rare genes (eliminated from the bottlenecked lines) in determining
selection limits. Da Silva (1961), a student of Alan Robertson, showed that
selection from a single pair resulted in a reduction of the limit by 30 %,
suggesting that the majority of alleles fixed by selection were not initially
rare.
The ultimate
goal is to identify the individual loci responsible for quantitative
variation, and in this context, Alan Robertson was encouraged by the work of
Thoday (1979) in mapping QTLs. Robertson, had pointed out that the question
addressed was not how many loci affect the variation for a quantitative
trait but, rather, how many loci account for the bulk of the difference
between selected lines (Robertson, 1967 & 1968). Alan Robertson viewed the distribution
of gene effects on quantitative traits as being such that most loci have
small effects, but a few have large effects and cause most of the variation.
Mc Millan and
Robertson (1974) showed that the results of QTL mapping experiments using recombination
of an extreme-scoring chromosome with a multiply marked tester chromosome to
identify regions with significant effects on the trait, will always
overestimate the effect of detected loci and underestimate their number,
because several linked loci affecting the trait may occur in a segment,
and can even identify loci that do not exist, if the next assumption is
violated: that a loci on the tested chromosomes carry “higher” alleles
than the loci on the tester chromosome. A practical suggestion for partially
alleviation the latter problem is to ensure that tester and tested chromosomes
are selected in opposite directions from the same base population, with
subsequent backcrossing of the marker gene into the tester chromosome. Such a
third chromosome was synthesized in Alan Robertson’s lab and used by his Ph.D.
students L. R. Piper and A. E. Shrimpton to partition the effect of a high
sternopleural bristle number chromosome into segments bounded by recessive
visible markers. The results (Shrimpton & Robertson, 1988a and 1988b)
support the model of distribution of gene effects outlined above, despite the
methodological problems.
References
quoted:
Robertson, A. A
Theory of Limits in Artificial Selection. Proceedings of the Royal Society
of London. Series B, Biological Sciences, 153(951):234-249. Nov. 29, 1960.
Jones, L. P., R.
Frankham & J. S. F. Barker. The Effects of Population Size and Selection
Intensity in Selection for a Quantitative Character in Drosophila. II
Long Term Response to Selection. Genet Res. 12:249-66, 1968.
Madalena, F. E.
& A. Robertson. Population Structure in Artificial Selection: Studies With Drosophila
melanogaster. Genet Res. 24:113-26, 1975.
Hill, W. G.
& A. Robertson. The Effect of Linkage on Limits to Artificial Selection. Genet
Res. 8:269-94, 1966.
Robertson, A. A
Theory of Limits in Artificial Selection with Many Linked loci, pp.
246-88, in: “Mathematical Topics in Population Genetics”, edited by K.
Kojima. Springer, Berlin, 1970.
Robertson, A.
Artificial Selection With a Large Number of Linked loci, pp. 307-22, in
“Proceedings of the International conference on Quantitative Genetics”,
edited by E. Pollak, O. Kempthorne & T. B. Baily. Iowa State University
Press, Ames, 1977.
Mc Phee, C. P.
& A. Robertson. The Effect of Suppressing Crossing-Over on the Response to
Selection in Drosophila melanogaster. Genet Res. 16:1-16, 1970.
Nicholas, F. W.
& A. Robertson. The Conflict Between Natural and Artificial Selection in
Finite Populations. Theor. Appl. Genet. 56:57-64, 1980.
Robertson, A.
The Nature of Quantitative Genetic Variation, pp: 265-80, in: “Heritage From
Mendel”, edited by A. Brink. University of Wisconsin Press, Madison,
1967. [a review].
Robertson, A.
The Spectrum of Genetic Variation, pp: 5-16, in: “Population Biology and
Evolution”, edited by R. C. Lewontin. Syracuse University Press,
Syracuse, N. Y., 1968. [a review].
Da Silva, J. M.
P. Limits of Response to Selection, PhD. Thesis, University of Edinburgh,
1961.
Thoday, J. M.
Polygene Mapping: Uses and Limitations, pp: 219-33, in: “Quantitative
Genetic Variation”, edited by J. N. Thompson, Jr. & J. M. Thoday. Academic
Press, N. Y., 1979. [a review].
Mc Millan, I.
& A. Robertson. The Power of Methods for the Detection of Major Genes
Affecting Quantitative Characters. Heredity 32:349-56, 1974.
Shrimpton, A. E.
& A. Robertson. The Isolation of Polygenic Factors Controlling Bristle
Score in Drosophila melanogaster. I Allocation of Third Chromosome
Sternopleural Bristle Effects to Chromosome Sections. Genetics 118:437-43,
1988a.
Shrimpton, A. E.
& A. Robertson. The Isolation of Polygenic Factors Controlling Bristle
Score in Drosophila melanogaster. II Distribution of Third Chromosome
Sternopleural Bristle Effects Within Chromosome Sections. Genetics 118:445-9,
1988b.
BIOGRAPHICAL
SKETCH:
The Contribution
of Alan Robertson was to quantitative genetics from its most practical
application in animal breeding, through statistical methodology, theoretical
underpinnings and tests of the theory, to arrive to the Mendelian Genetics of
Quantitative Trait Loci (QTL).
B. A. Chemistry,
Cambridge Univ., 1941.
Operational
researcher during WWII with C. H. Waddington, and after that continued with him
in ABGRO (Animal Breeding & Genetics Research Organization, in the
Agricultural Research Council), initially in Henson and later in Edinburgh.
Student of
Sewall Wright in Chicago and Jay Lush in Ames in 1947.
Married with Meg
in 1947, they had three children: Mark, Hilary and Michael.
Returned to
ABGRO for the rest of his career, working in the ARC Unit of Animal Genetics,
directed first by Waddington and later by Douglas S. Falconer (who had written
the article: Falconer, D. S. & King, J. W. B. A Study of selection Limits
in the Mouse. J. Genet. 51:561-81, 1953).
He received a
D.Sc. from the University of Edinburgh in 1951 for his work in genetics and was
appointed an Honorary Professor in 1967.
Promoted to
deputy Chief Scientific Officer in 1966.
Order of the
British Empire (OBE), 1965, Fellow of the Royal Society of London, 1964 and of
Edinburgh, 1966, Foreign member of the Association of the National Academy of
Sciences, U.S.A., 1979. Also Foreign Honorary member of the Genetics Society of
Japan and of the Spanish “Real Academia de Ciencias Veterinarias”. Honorary
Doctorates from the University of Stuttgart-Hohenheim, the Agricultural
University of Norway, the State University of Liège, the Danish Agricultural
University, etc…
Although his
scientific publications reveal an astonishing range of interests, Alan’s
influence through personal contact was undoubtedly his most lasting
contribution. Alan was invariably generous with his time and ideas, and could
always be approached for advice by students and colleagues alike. Many
Scientists currently working on quantitative genetics can trace their roots
either directly or indirectly to Alan Robertson at the institute of Animal
Genetics of the University of Edinburgh; more than anything this must be a
tribute to his influence.
Mackay, T.F.C., Genetics 125(1):1-7, 1990 (This is paper No.
12532 of the Journal Series of the North Carolina Agricultural Research
Service)
Trudy F. C.
MacKay. Dept. of Genetics, North Carolina State University, Raleigh, North
Carolina 27695-7614.
See also Hill,
W. G., Biogr. Memb. Fellows R. Soc. 36:465-8, 1990.
The fund is in memory of Professor Alan
Robertson FRS, formerly of the Institute of Animal Genetics in Edinburgh and a
past President of both the British Society of Animal Science and of the World
Congress in Genetics Applied to Livestock Production.
The
aim of the fund is to "further research and education in the application
of genetics to livestock production ". About £1400 is available per annum.
Awards
shall be made to persons with an interest in Animal Genetics, particularly:
Candidates need not be members of BSAS.
Selection will be based on the importance or relevance of the proposal, project
or study and how well the candidate or organization may benefit.
The
successful candidates will be expected to provide the Secretary of BSAS with a
short written report within 3 months of the end of the study/project/proposal.
Copies will then be available on request from the BSAS secretariat.
Applications should be received by end of October.
Click
to download application form (.pdf, 10K)
The Alan Robertson
Fund for Animal Genetics
An award aimed
at those interested in animal genetics, aimed at allowing people to attend
meetings and undertake study tours or projects, it can also be used to bring
animal geneticists to UK meetings. Applications should reflect areas of current
or future interest that will advance research and education in the application
of genetics to livestock production. Around £1400 is available annually. This
scholarship is open to both members and non-members of BSAS.
Taken from: http://www.bsas.org.uk/socinfo/scholrps.htm
