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):

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.]







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.




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 Alan Robertson Fund for Animal Genetics

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:

Useful Links:

Research on Intelligent Design


Tasters of the Word (YouTube), videos recientes: "Astronomía y Nacimiento de Jesucristo: Once de Septiembre Año Tres A.C.", "Estudio sobre Sanidades" (en 20 episodios), "Jesus Christ, Son or God?" and "We've the Power to Heal":

Tasters of the Word (the blog, with: "Astronomy and the Birth of Jesus Christ"):


And a commercial before we go:

Window Cleaning of Ronnie Petree, where my wife works (smile): Good Looking Glass of Houston (serving also at: Katy, Surgarland, Conroe, Kingwood, Woodlands, Galveston).