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Group selection and kin selection
TREE vol. 6, no. 2, February
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Group Selection and Kin Selection I wish to raise two issues concerning Breden’s recent advocacy’ of an alternative2z3 to the usual inclusivefitness approach4 to studying kin selection. First, his description of the approach as the method of covariance partitioning is confusing because partition of Price’s covarianceselection rule5 also generates inclusive-fitness results6g. Breden’s approach is better described as a group-selection method. second issue concerns The whether this group-selection approach is superior to the inclusivefitness approach. I think the two approaches are very similar; most of the differences arise from presenting the results in different ways. Inclusive fitness has always been framed in terms of the effects of phenotypes. In contrast, the group-selection approach has usually been expressed purely in terms of genotypes. This can lead to cleaner theoretical results, but leaves it unclear how to apply the results in the real world. For example, consider the claim that the group-selection approach is superior because it actually predicts gene-frequency change. While Hamilton’s inclusive-fitness rule does
not do this, it is not an intrinsic limitation of the method. In the derivation from Price’s rule, the penultimate step looks something like this:
WAG = -cCov(G,,f,) +
bCov(G,,/=,)
where W is mean fitness, c and b are the cost and benefit of altruism, F’, is the phenotype of the actor, and G, and G, are the frequencies of the gene in the actor and its partner. SG is the change in population gene frequency, but it is eliminated if we simplify by asking when AG>O.Dividing through by Cov(G,,P,) then gives Hamilton’s rule, -c + rb > 0, where relatedness (r) is the ratio of the two covariances. We sacrifice prediction of AG but gain something else crucial. Relatedness is often independent of gene frequency and dosage6,8, allowing estimation from pedigrees or from marker alleles. In contrast, the group-selection result (Breden’s Eqn 1) requires detailed knowledge of the genetics of the trait itself, which is rarely available. It is not surprising, then, that when it comes to actually applying the method, genefrequency change is dispensed with, and instead relatedness is estimatedlo.
1997
--_
The group-selection perspective, while valid, should not lead to rejection of the inclusive-fitness viewpoint. Future theoretical work should reveal which differences are trivial matters of presentation and which, if any, are fundamental.
David C. Queller Dept of Ecologyand Evolution,RiceUwerslty. PO Box 1892.Houston,TX 77251,USA
1 Breden, F. (1990) Trends Ecol. Evol. 5, 224-228 2 Hamilton, W.D. (1964) J. Theor. &o/. 7. I-52 3 Price, G.R. (1972) Ann. Hum. Genet. 35, 485-490 4 Wade, M.J. (1985) Am. Nat. 125, 61-73 5 Price. G.R. (1970) Nature 227. 520-521 6 Sege;, J. (1981) J. Theor. Biol. 91, 191-213 7 Queller, D.C. 11985) Nature 318, 366-367 8 Grafen, A. (1985) Uxf. Surv. Evoi. Biol. 2, 28-89 9 Taylor, P.D. (1990) Theor. Popul BIO/. 34, 145-168
10 McCauley, D., Wade, M.J., Breden, F. and Wohltmann, M. (1988) Evolution 42, 182-l 94
Recruitment in Marine Fish Populations Rather than providing a clarification, S.J. Holt’s letter in your July issue gives a misleading impression both of how he and I originally tackled the problem of recruitment in fish populations’ and of how it is dealt with in modern fisheries research and management. The time and context are important. Holt and I came together in 1947, with the taskof developing a rigorous ‘theory of fishing’ and applying it to the long-established trawl fisheries of the North Sea, which were suspected by some - rightly as it turned out-to be ‘overfished’. We first established from yield-per-recruit models with density-independent growth and mortality parameters that the prewar fishing rate for both North Sea plaice and haddock - the only two stocks for which there were enough data-was several times that needed to maximize the yield per recruit. The reliability of those simple assessments was then tested by introducing, separately and together, the density dependence of growth and natural mortality and, in particular, the dependence of recruitment on parent stock. For the latter we developed what has become known as
64
the Beverton-Holt stock-recruitment function, which, together with the alternative formulation due to W.E. Ricker*, has been in universal use for the past three decades. Applied to the haddock, for which total egg production could be computed, we showed that a weakly curved relationship between stock (as egg production) and subsequent recruits, which could not be rejected by the available data, caused the population to go extinct through recruitment failure at a level of fishing only a little higher than that in the pre-war years. Subsequent events have confirmed the essential correctness of those original assessments. The fishing rate on plaice has declined and the yield has increased. Fishing on haddock has remained too high for its growth productivity to be used efficiently, but the stock has held up until recently, when a serious decline in recruitment has set in. Whether this is due to the incipient instability that we had detected from our ‘selfregenerating’ stock-recruit model some 40 years before or to adverse environmental changes has yet to be established. Be that as it may, Holt and I certainly did not exclude the
possibility that there might be a strong underlying stock-recruit relationship that could not be rejected by the available data. However, our 1957 book was a limited edition (a second edition is planned) and it is understandable that some who have never seen a copy may think we dealt only with ‘per-recruit’ models. The dramatic ‘collapses’ came later, towards the end of the 1960s not in the trawl fisheries for the demersal species with which Holt and I were concerned but in herring and other pelagic shoaling fish. They were due primarily to new powerful purse seines and fish-detection sonars, which caused the fishing rate to escalate at a speed and to an extent inconceivable a decade before in the trawl and gill-net fisheries, and which rendered the conventional catch-perunit-effort index unreliable as a timely indicator of stock decline. Whether the management at that time had any chance of restraining those rapid escalations of fishing rate is very doubtfui3, but its failure to act had little to do with stock-recruit relationships or null hypotheses. More to the point was that the scientists were in dispute as to how much of the
_-..-._.--
Group Selection and Kin Selection I wish to raise two issues concerning Breden’s recent advocacy’ of an alternative2z3 to the usual inclusivefitness approach4 to studying kin selection. First, his description of the approach as the method of covariance partitioning is confusing because partition of Price’s covarianceselection rule5 also generates inclusive-fitness results6g. Breden’s approach is better described as a group-selection method. second issue concerns The whether this group-selection approach is superior to the inclusivefitness approach. I think the two approaches are very similar; most of the differences arise from presenting the results in different ways. Inclusive fitness has always been framed in terms of the effects of phenotypes. In contrast, the group-selection approach has usually been expressed purely in terms of genotypes. This can lead to cleaner theoretical results, but leaves it unclear how to apply the results in the real world. For example, consider the claim that the group-selection approach is superior because it actually predicts gene-frequency change. While Hamilton’s inclusive-fitness rule does
not do this, it is not an intrinsic limitation of the method. In the derivation from Price’s rule, the penultimate step looks something like this:
WAG = -cCov(G,,f,) +
bCov(G,,/=,)
where W is mean fitness, c and b are the cost and benefit of altruism, F’, is the phenotype of the actor, and G, and G, are the frequencies of the gene in the actor and its partner. SG is the change in population gene frequency, but it is eliminated if we simplify by asking when AG>O.Dividing through by Cov(G,,P,) then gives Hamilton’s rule, -c + rb > 0, where relatedness (r) is the ratio of the two covariances. We sacrifice prediction of AG but gain something else crucial. Relatedness is often independent of gene frequency and dosage6,8, allowing estimation from pedigrees or from marker alleles. In contrast, the group-selection result (Breden’s Eqn 1) requires detailed knowledge of the genetics of the trait itself, which is rarely available. It is not surprising, then, that when it comes to actually applying the method, genefrequency change is dispensed with, and instead relatedness is estimatedlo.
1997
--_
The group-selection perspective, while valid, should not lead to rejection of the inclusive-fitness viewpoint. Future theoretical work should reveal which differences are trivial matters of presentation and which, if any, are fundamental.
David C. Queller Dept of Ecologyand Evolution,RiceUwerslty. PO Box 1892.Houston,TX 77251,USA
1 Breden, F. (1990) Trends Ecol. Evol. 5, 224-228 2 Hamilton, W.D. (1964) J. Theor. &o/. 7. I-52 3 Price, G.R. (1972) Ann. Hum. Genet. 35, 485-490 4 Wade, M.J. (1985) Am. Nat. 125, 61-73 5 Price. G.R. (1970) Nature 227. 520-521 6 Sege;, J. (1981) J. Theor. Biol. 91, 191-213 7 Queller, D.C. 11985) Nature 318, 366-367 8 Grafen, A. (1985) Uxf. Surv. Evoi. Biol. 2, 28-89 9 Taylor, P.D. (1990) Theor. Popul BIO/. 34, 145-168
10 McCauley, D., Wade, M.J., Breden, F. and Wohltmann, M. (1988) Evolution 42, 182-l 94
Recruitment in Marine Fish Populations Rather than providing a clarification, S.J. Holt’s letter in your July issue gives a misleading impression both of how he and I originally tackled the problem of recruitment in fish populations’ and of how it is dealt with in modern fisheries research and management. The time and context are important. Holt and I came together in 1947, with the taskof developing a rigorous ‘theory of fishing’ and applying it to the long-established trawl fisheries of the North Sea, which were suspected by some - rightly as it turned out-to be ‘overfished’. We first established from yield-per-recruit models with density-independent growth and mortality parameters that the prewar fishing rate for both North Sea plaice and haddock - the only two stocks for which there were enough data-was several times that needed to maximize the yield per recruit. The reliability of those simple assessments was then tested by introducing, separately and together, the density dependence of growth and natural mortality and, in particular, the dependence of recruitment on parent stock. For the latter we developed what has become known as
64
the Beverton-Holt stock-recruitment function, which, together with the alternative formulation due to W.E. Ricker*, has been in universal use for the past three decades. Applied to the haddock, for which total egg production could be computed, we showed that a weakly curved relationship between stock (as egg production) and subsequent recruits, which could not be rejected by the available data, caused the population to go extinct through recruitment failure at a level of fishing only a little higher than that in the pre-war years. Subsequent events have confirmed the essential correctness of those original assessments. The fishing rate on plaice has declined and the yield has increased. Fishing on haddock has remained too high for its growth productivity to be used efficiently, but the stock has held up until recently, when a serious decline in recruitment has set in. Whether this is due to the incipient instability that we had detected from our ‘selfregenerating’ stock-recruit model some 40 years before or to adverse environmental changes has yet to be established. Be that as it may, Holt and I certainly did not exclude the
possibility that there might be a strong underlying stock-recruit relationship that could not be rejected by the available data. However, our 1957 book was a limited edition (a second edition is planned) and it is understandable that some who have never seen a copy may think we dealt only with ‘per-recruit’ models. The dramatic ‘collapses’ came later, towards the end of the 1960s not in the trawl fisheries for the demersal species with which Holt and I were concerned but in herring and other pelagic shoaling fish. They were due primarily to new powerful purse seines and fish-detection sonars, which caused the fishing rate to escalate at a speed and to an extent inconceivable a decade before in the trawl and gill-net fisheries, and which rendered the conventional catch-perunit-effort index unreliable as a timely indicator of stock decline. Whether the management at that time had any chance of restraining those rapid escalations of fishing rate is very doubtfui3, but its failure to act had little to do with stock-recruit relationships or null hypotheses. More to the point was that the scientists were in dispute as to how much of the