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Keywords:

  • development time;
  • fecundity;
  • genetic correlation;
  • growth rate;
  • phenotypic correlation;
  • trade-offs

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References

The assumption of a trade-off between development time and fecundity, resulting from a positive correlation between body size and fecundity and between body size and development time, is a common feature of life history models. The present paper examines the evidence for such a trade-off as indicated by genetic correlations between traits. The genetic covariances between traits are derived using a model in which maturation occurs when the organism achieves a genetically variable size threshold, and fecundity is an allometric function of body size with one genetically variable parameter (excluding body size itself). This model predicts that the heritabilities of the life history traits (growth rate, development time, fecundity) will not necessarily be less than the heritability of adult size (i.e. morphological traits). It is shown that if growth rate is genetically correlated with adult size then it is not possible, in general, to predict the sign of the genetic correlation between development time and fecundity. For particular cases the signs of the covariances between traits can be predicted. These predictions are tested using data drawn from the literature.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References

Life history theory is based on the hypothesis that evolution is constrained by the presence of trade-offs among some of the traits that contribute to fitness ( Roff, 1992; Stearns, 1992). One of the most commonly assumed trade-offs is that between size and age at maturity, the fitness trade-off arising, at least in part, from a correlation between fecundity and body size (e.g. McLaren, 1966; Kachi & Hirose, 1973; Roff, 1981, 1984; Stearns & Crandall, 1981; Abrams et al., 1996 ). A generally unstated assumption of the foregoing is that all individuals follow more or less the same growth trajectory ( Roff, 1992; Klingenberg & Spence, 1997). At the present time there is no study that critically examines which, if any, of these assumptions has sufficient empirical support to be made as a general assumption in life history models. The purpose of the present paper is to fill this important lacuna first by developing a simple quantitative genetic model of growth and reproduction, and second by testing the predictions of this model using data gleaned from the literature.

Trade-offs are manifested at two levels: firstly, we observe a phenotypic correlation between traits such that a change in one trait that by itself increases fitness is opposed by the antagonistic effect of a change in another trait. For example, a decreased age to maturity will, all other things being held constant, increase fitness ( Fisher, 1930; Lewontin, 1965). However, due to the reduced time for growth, a decreased age at maturity might result in a decreased adult body size. In many species fecundity and fighting ability are correlated with body size and hence a reduced age at maturity could result in a loss of fecundity in females and reduced matings in males ( Roff, 1992). Phenotypic correlations indicative of a trade-off will produce a selection differential but will not produce a corresponding evolutionary change unless the trade-off is genetically determined, as indicated by a genetic correlation of the same sign as the phenotypic correlation ( Reznick, 1985).

An increased body size can be achieved either by an increased development time or an increased rate of growth. In the latter case there may be no resulting correlation between development time and adult body size. On the other hand, such an increased growth rate could be selected against because of a trade-off between growth rate and mortality rate ( Roff, 1992; Arendt, 1997). The analysis of trade-offs between growth and fecundity must therefore consider the interactions among growth rate (i.e. the growth trajectory), development time, adult size, immature survival and fecundity. The purpose of the present paper is to test if there are general patterns of trade-offs demonstrable by the appropriate genetic correlations between the aforementioned traits. Because of a lack of data on genetic variation in survival rates, I restrict the present analysis to the question of whether there is a trade-off between growth and fecundity. Specifically, I address the following questions: (1) is there a positive genetic correlation between development time and adult (mature) body size?; (2) is there a genetic correlation (positive or negative) between growth rate and the two previous traits?; (3) is there a positive genetic correlation between adult size and fecundity?; (4) is there a positive genetic correlation between development time and fecundity? An affirmative answer to question 4 indicates the presence of an evolutionarily important trade-off. However, the expectation of such a trade-off is contingent on answers to the previous three questions and in particular the potential confounding influence of genetic variation in growth rates. To examine the possible complexity of the predictions I first consider some simple models of growth and reproduction.

Some simple models of growth, maturity and fecundity

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References

For any given individual only two of the three traits, adult size, development time and growth rate, are independent. Suppose, for example, that growth is linear on some scale,

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where D is development time and A is size at maturity (=adult size). In the first case adult size is determined by the coefficients of the growth function (c0, c1), which can themselves be regarded as traits, and development time. In the second case development time is determined by the two coefficients and adult size. Typically, growth rate is measured as some index of size, such as weight, at a fixed age rather than the growth coefficients per se: for operational purposes I shall equate growth rate with size at some given immature age, assuming that this correlates with the growth trajectory.

There is considerable experimental evidence that maturity is frequently initiated when an individual exceeds a critical size threshold (insects –Wigglesworth, 1934; Nijhout, 1975, 1979; Blakley & Goodner, 1978; Woodring, 1983; Bakker, 1959; Nijhout & Williams, 1974a, b: mammals –Riska et al., 1984 ; Skogland, 1989; Childs, 1991: plants –Werner, 1975; Harper, 1977 [p. 687]; Kachi & Hirose, 1973; Yokoi, 1989). The general finding of additive genetic variance in morphological traits, particularly adult body size ( Mousseau & Roff, 1987), suggests that this size threshold will be genetically variable. Assuming that maturation is cued by a size threshold then development time is itself a compound trait composed of the two traits, size at maturity and growth rate. Now assume that there is some transformation that linearizes the growth rate (this is for illustrative purposes only: the general principles outlined below apply to nonlinear growth trajectories but there will be several component parameters [for examples of such curves see Barbato, 1991; Gebhardt-Henrich, 1992; Danjon, 1994]). Further, assume that the initial size is sufficiently small relative to the adult size that it can be ignored. Hence we have D=A/G, where, in this instance, G is the slope of the growth function. Taking logs we have log(D)=log(A) – log(G). Assuming that these traits are normally distributed on the log scale, and for simplicity writing the foregoing equation as Dtime=Asize – Grate, then the variance of development time, V(Dtime), can be written as a function of the variances of growth rate and adult size and their covariance: V(Dtime)=V(Asize) + V(Grate) – 2Cov(Asize, Grate).

A typical assumption in life history analysis is that an increased body size will require an increased development time ( Roff, 1992). The argument for this rests on the implicit assumption that individuals are all genetically programmed to follow the same growth trajectory. Therefore, the first case I shall consider is that in which there is no additive genetic variance in growth rate, Va(Grate), from which it also follows that there is no genetic covariance between adult size and growth rate. An environmental covariance between growth rate and adult size (CovE(Asize, Grate)) could arise and be either positive or negative, but it would most likely be positive. Suppose, for example, that there were no genetic variation in any of the components (this for simplicity of exposition), and that the process of maturation commenced when the organism exceeded some size threshold. If the period of maturation were constant then fast growing individuals, if they continued to grow relatively fast after the initiation of maturation, would be relatively large. Therefore, in this case the covariance between growth rate and adult size would be positive. A positive covariance would also ensue if maturation were initiated after a fixed development time. An apparent covariance could arise if the laboratory environment is not entirely homogeneous, because, in general, there will be selection for a reaction norm between growth rate and adult size ( Roff, 1992; Stearns, 1992). The evolution of such a reaction norm is beyond the scope of the present paper. I shall assume, unless otherwise stated, that CovE(Asize, Grate) ≥ 0.

Model 1: Va(Asize) > 0, Va(Grate) = 0, Cova(Asize, Grate) = 0

From the relationship Dtime=AsizeGrate, and the above conditions, it follows that Va(Dtime)=Va(Asize) and Vp(Dtime)=Vp(Asize) + Vp(Grate) – 2Covp(Asize,Grate). Hence,

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and

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If there were no covariance between growth rate and adult size then, because Vp(Grate) will generally be greater than zero, h2(Asize) > h2(Dtime). With a large enough environmental covariance the inequality could be reversed. Because of the common occurrence of the additive and phenotypic variances of adult size, the two heritabilities will be correlated. To obtain the genetic correlation between development time and size at maturity we proceed as follows:

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Rearranging, gives

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The genetic correlation is therefore

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Thus we have two predictions:Prediction 1: h2(Asize) > h2(Dtime), depending on the value of Covp(Asize, Grate)Prediction 2: ra(Asize,Dtime)=1.

Now consider the consequences when there is genetic variation in growth rate but there is no genetic covariance between growth rate and size at maturity.

Model 2: Va(Asize) > 0, Va(Grate) > 0, Cova(Asize, Grate) = 0

Proceeding in the same manner as before: Va(Dtime) =Va(Asize) + Va(Grate), Vp(Dtime)=Vp(Asize) + Vp(Grate) – 2CovP(Asize, Grate) and, hence,

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and

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Therefore, the difference in the two heritabilities will depend upon the relative size of the variances and the covariance, and no general statement can be made.

To obtain the genetic correlations we proceed as follows:

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Rearranging,

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The genetic correlation is thus

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The genetic correlation between adult size and development time will be positive but less than one.

Thus the two predictions from case 1 become:

Prediction 1: relative sizes of the heritabilities are dependent upon the relative values of the variances and covariance: no general relationships emerge.

Prediction 2: 0 < ra(Asize, Dtime) < 1.

Finally, consider the consequences when there is genetic variation in growth rate and a genetic covariance between growth rate and size at maturity.

Model 3: Va(Asize) > 0, Va(Grate) > 0, Cova(Asize,Grate) ≠ 0

Now Va(Dtime)=Va(Asize) + Va(Grate) – 2Cova(Asize, Grate), Vp(Dtime)=Vp(Asize) + Vp(Grate) – 2Covp(Asize, Grate): hence,

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and

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As in the previous model there is no simple relationship between the heritabilities.

To obtain the genetic correlation we proceed as follows

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Rearranging,

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Thus the genetic correlation will be negative if Cova(Asize, Grate) > Va(Asize), i.e. under this condition an increased body size will be accompanied by a decrease in development time. Following the same procedure we obtain the genetic covariance between development time and growth rate as

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To summarize, the predictions (findings) for this case are:

Prediction 1: relative sizes of the heritabilities are dependent upon the relative values of the variances and covariances: no general relationships emerge.

Prediction 2:

0 < ra(Asize, Dtime) < 1 if Cova(Asize, Grate) < Va(Asize)

–1 < ra(Asize, Dtime) < 0 if Cova(Asize, Grate) > Va(Asize)

Prediction 3:

0 < ra(Grate, Dtime) < 1 if Cova(Asize, Grate) > Va(Grate)

–1 < ra(Grate, Dtime) < 0 if Cova(Asize, Grate) < Va(Grate).

The above analyses show that the genetic correlation between development time and adult size can be either positive or negative. How will this impact upon the genetic correlation between fecundity and development time? In what follows I shall show that even with a very simple model the genetic correlation between fecundity and development time can be either negative or positive even if both the genetic correlation between adult size and fecundity and the genetic correlation between development time and adult size are positive.

In general, fecundity can be related to body size by the relationship F=CAB, where C and B are parameters ( Roff, 1992). Genetic variation in fecundity implies only genetic variation in A, although there may also be variation in C and/or B. Analysis becomes quite complex if B is variable, because we have the product of two random variables. To keep the analysis simple I shall assume that B is a constant equal to 1 (this does not qualitatively change the results) and that there is genetic variation in A and C. Taking logs we have log F=log C + log A, which for simplicity shall be written as Feggs=C0 + Asize. As before, to fulfil the quantitative genetic assumptions, I shall assume that the traits are normally distributed on the log scale. Hence, Va(Feggs)=Va(Asize) + Va(C0) + 2Cova(Asize + C0) and the heritability of fecundity is

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A positive environmental covariance might be expected, given that conditions that promote large phenotypic size might also be expected to promote high fecundity. Under constant laboratory conditions the covariance should be zero. As in the previous model there are no simple general qualitative relationships between the relative size of h2(Feggs) and h2(Asize).

I shall assume that fecundity and adult size are positively genetically correlated: this could arise indirectly from geometric constraints of body size on fecundity and/or from a positive correlation between resource acquisition and body size. There seems no a priori reason to suppose that C0 and Feggs are genetically correlated and so I shall assume that Cova(C0, Feggs)=0.

From the above, Asize=Dtime – Grate, and thus Feggs=C0 + Dtime – Grate, and rearranging Grate=C0 + Dtime – Feggs. The variance relationship is then Va(Grate)=Va(c) + Va(Dtime) + Va(Feggs) – 2Cova(Feggs, Dtime). Rearranging gives

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If Va(Grate)=0 then

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and Cova(Feggs, Dtime) > 0. However, if Va(Grate) > 0 then

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and Cova(Feggs, Dtime) could be negative. This can occur even if the covariance between Asize and Dtime is positive (recall from previously that Cova(Asize, Grate)=Va(Asize) –Cova(Asize, Grate)). Thus it is possible to have a positive genetic correlation between fecundity and adult size (Cova(Feggs, Asize) > 0), a positive genetic correlation between adult size and development time (Cova(Asize, Dtime) > 0) but a negative genetic correlation between fecundity and development time (Cova(Feggs, Dtime) < 0) or any other combination for the last two. Further, it is possible to have a negative genetic correlation between adult size and development time (Cova(Asize, Dtime) < 0) but a positive genetic correlation between fecundity and development time (Cova(Feggs, Dtime) > 0). Predictions of the sign of the genetic correlation between development time and fecundity (and hence the existence of a trade-off) cannot be made on the basis of the signs of the genetic correlation between these and other traits, such as adult body size.

The foregoing analysis shows that the addition of genetic variation in growth rate can greatly complicate the predicted correlations between development time and adult size and between development time and fecundity. In the remainder of this paper I examine the empirical evidence for this complexity.

Description of the data set

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References

I surveyed the literature for studies reporting genetic correlations between two or more of the traits, development time, growth rate, size at maturity (which I shall also refer to as simply adult size) and fecundity. I include only data for nondomesticated species. To avoid pseudoreplication I used mean values per species unless the data were highly discrepant in which case I report both individual values and means. If both male and female estimates were given I used only the female estimates. If possible, I used the heritability estimate for adult size that was reported in the same paper as the other trait (Grate, Dtime, Feggs): this means that in a few cases the heritability estimate for adult size may differ among comparisons. Where multiple indexes of size were given (e.g. head width, femur length) I used the averaged value of the heritability or correlation. Where possible, estimates were only used for animals reared in the laboratory under ‘normal’ conditions (e.g. not an obviously novel food source). Traits were defined as follows:

1 Development time: For insects, which are the majority of organisms, the time from hatching to final eclosion. For the other invertebrate (Helix aspersa, a snail), hatching to first reproduction. For vertebrates, the time from ‘hatching’ to first reproduction. For plants, the time from seedling emergence to flowering.

2 Size at maturity: For insects, this is either the size at eclosion or a closely correlated trait such as pupal weight. For other organisms it is the size at first reproduction.

3 Growth rate: The ideal measure would be the slope of the linearized relationship between size at age t and t. In the absence of this measure I have used size at some immature age as a surrogate. In some papers growth rate is defined as adult size/development time: this would only be ‘growth rate’ as defined previously if the growth trajectory were linear. Because no evidence is presented for this, and because this measure is confounded with the other two traits (adult size, development time) under study, I have not used this measure of growth rate.

4 Fecundity: Some measure of the number of propagules produced during some defined period.

The phenotypic correlation is a complex function of the genetic correlation and therefore it has been suggested that the phenotypic correlation cannot be assumed to be a reliable guide to the evolutionary importance of a trade-off ( Reznick, 1985; Van Noordwijk & de Jong, 1986; Roff, 1992, 1996; Stearns, 1992). To see if this admonition holds true across different categories of trade-offs I compare the genetic (ra) and phenotypic (rp) correlations, asking first if there is a correspondence between the signs, which at least indicates that the phenotypic correlation is a guide to the presence of a trade-off, and, second, if the value of rp is a reasonable surrogate for ra.

Analysis

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References

Is the heritability of the growth rate, development time or fecundity less than the heritability of adult size?

Previous analysis indicated that the average heritability of life history traits was less than the average heritability of morphological traits ( Mousseau & Roff, 1987). No such general prediction emerged from the above theoretical analysis. Overall, the heritability of development time is quite large and similar to that of adult size (Table 2), that for development time averaging 0.32 (range 0.01–0.81, SE=0.04, n=19) and that for adult size averaging 0.41 (range 0.09–0.90, SE=0.05, n=18). With either a paired or two-sample t-test there is no significant difference between the two sets of estimates (P > 0.3 in both cases). There is also no significant correlation between the two estimates (r=–0.20, d.f.=16, P=0.42). There are too few data to compare the heritabilities of growth rate and adult size (Table 3). The heritability of fecundity is relatively large (range 0.07–1.27, mean=0.42, SE=0.12; Table 4) and not significantly different from the heritability of adult size (paired t=0.28, d.f.=9, P=0.79). The two heritabilities are significantly correlated (r=0.703, d.f.=8, P=0.023).

Table 2.   Heritabilities of development time (Dtime) and size at maturity (Asize) and the genetic correlation between them in various species, arranged in ascending order of the genetic correlation. Thumbnail image of
Table 3.   Heritabilities of growth rate (Grate), adult size (Asize) and development time (Dtime) and the genetic correlation between them, arranged in ascending order of the genetic correlation. Thumbnail image of
Table 4.   Heritabilities of adult size (Asize) and fecundity (Feggs) and the genetic correlation between them in nine species, arranged in ascending order of the genetic correlation. Thumbnail image of

Is size at maturity genetically correlated with development time?

There are 15 estimated genetic correlations that are significantly different from zero, which represents 60% of the cases listed in Table 2, indicating that a genetic correlation between development time and adult size is a common phenomenon. There are 17 positive and six negative genetic correlations (the two zeros are ignored), which is significantly different from the null hypothesis of a 1:1 ratio (χ2=5.26, d.f.=1, P=0.02): thus we can conclude that there is typically a positive genetic correlation between development time and size at maturity. The negative genetic correlations cannot be dismissed as due to small sample size, because in three cases they are significantly different from zero (Table 2). In general, the genetic correlation is significantly less than one (11 significantly less than 1 and five with 95% confidence limits that include 1; Table 2). These results indicate that Model 1 can be rejected, suggesting that, in general, there will be genetic variation in growth rate.

The phenotypic and genetic correlations are highly correlated (r=0.65, d.f.=16, P=0.003) and the genetic correlation can be predicted from the phenotypic with the regression equation, ra=0.207 + 1.224rp. The genetic correlation is significantly larger than the phenotypic correlation (paired t=2.831, d.f.=17, P=0.012). In all but two cases, the sign of the phenotypic correlation is the same as the genetic correlation.

Can a genetic correlation with growth rate account for the above variation in genetic correlations?

Table 1 summarizes the predictions of the signs of the three genetic correlations given information on one or more of the genetic correlations. A negative genetic correlation between development time and adult size, Cova(Asize, Dtime), will result if the covariance between adult size and growth rate is greater than the additive genetic variance in adult size (i.e. Va(Asize) < Cova(Asize, Grate)). A necessary but not sufficient condition for a negative genetic correlation between development time and adult size is that the genetic correlation between adult size and growth rate be positive. A sufficient condition for a positive genetic correlation between adult size and development time is that the genetic correlation between adult size and growth rate be negative. A negative covariance between adult size and growth rate will result in a negative genetic correlation between growth rate and development time. No such prediction can be made if the former covariance is positive.

Table 1.   Summary of predictions on the sign of the covariances between pairs of the three traits, adult size, development time and growth rate. Symbols indicate the relative value of a covariance, while the labels indicate the sign of the covariance resulting in the other covariance(s). Thumbnail image of

There are, unfortunately, few estimates of the genetic correlation between growth rate and the previous two traits (development time, size at maturity: Table 2). There is a significant negative genetic correlation between growth rate and adult size in the fall armyworm, Spodoptera frugiperda, from which leads the predictions (see above) that ra(Grate, Dtime) < 0 and ra(Asize, Dtime) > 0. Both of these predictions are confirmed (Tables 2, 3. In the other two insect species, Tribolium casteneum and Gryllus pennsylvanicus, the genetic correlation between growth rate and adult size is positive, while that between growth rate and development time is negative (Table 3). According to the foregoing analysis, the genetic correlation between growth rate and development time will only be positive if ra(Asize, Grate) > 0 (Table 1). This prediction is confirmed for both species (Table 3). In summary, the results shown in Table 3 are all in accord with the predictions of Model 3, and provide an adequate explanation for the variation in sign of the genetic correlation observed between development time and adult size (Table 2).

Is fecundity genetically correlated with adult size and development time?

There is abundant phenotypic data showing that fecundity typically increases with body size ( Roff, 1992). Genetic correlations between fecundity and body size range from –0.16 to 1.00 (Table 4), although the low correlations are associated with relatively large standard errors. There are 10 positive genetic correlations and one negative, which is significantly different from the null hypothesis of no association (P=0.006, one-sided binomial test). Thus, overall, there is strong evidence for a positive genetic correlation between body size and fecundity. This supports the assumption previously made in the development of predictions for the genetic correlation between fecundity and development time.

As with the previous cases, there is a significant regression between the phenotypic and genetic correlations (ra=–0.051 + 1.22rp, n=9, r=0.70, P=0.035). There is no significant difference between the two types of correlation (paired t=0.26, P=0.80).

A positive correlation between fecundity and body size will itself represent a fitness trade-off if the large size is bought at the expense of a long development time. The previous analysis has shown that the sign of the genetic correlation between fecundity and development times depends upon the covariance between adult size and growth rate, being positive if the covariance is negative or Cova(Asize, Grate) < Va(C0) + Va(Feggs) + Va(Asize). Importantly, the sign cannot be predicted from the sign of the genetic correlation between body size and development time. Because of substantial variation in the genetic correlation estimates, both between and within studies, I present the individual and averaged estimates in Table 5. In all cases the phenotypic correlation between development time and fecundity is small and generally negative. Thus at the phenotypic level there is not only no evidence of a trade-off but there are indications of the opposite. Unfortunately, the large standard errors and wide variation in the genetic correlations makes interpretation difficult. Where multiple estimates are available (G. aculeatus, O. fasciatus, D. melanogaster) there are both positive and negative genetic correlations, depending on the population or fecundity measure analysed. Further, there are both statistically significant positive and negative genetic correlations (Table 5).

Table 5.   Heritabilities of development time (Dtime) and fecundity (Feggs) and the genetic correlation between them in five species. Because of substantial disparities, individual estimates in addition to the averages are presented. Thumbnail image of

There is no correlation between the phenotypic and genetic correlations (r=0.58, d.f.=4, P=0.23) but, given the few data points and the wide standard errors, this result is not consequential.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References

Empirical evidence, reviewed above, suggests that, typically, maturity is initiated when an individual exceeds a critical size during development. Taking this as a starting assumption I developed a simple model predicting the genetic relationships between the four traits, growth rate, adult size, development time and fecundity. From this model the following general predictions can be made:

1 Although a previous theoretical analysis found the average heritability of life history traits to be less than that of morphological traits ( Mousseau & Roff, 1987) no such prediction emerges from the present theory;

2Cova(Asize, Dtime)=Va(Asize) – Cova(Asize) – Cova(Asize, Grate) and Cova(Grate, Dtime)=Cova(Asize, Grate) – Va(Grate);

3 From (2) we obtain the set of relationships shown in Table 1

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5 From (4) we have Cova(Feggs, Dtime) > 0 if Cova(Asize, Grate) < 0;

6 From (4) it can also be seen that it is possible for there to be a positive covariance between adult size and fecundity (assumed in the derivation) and a positive covariance between adult size and development time but, if Va(Asize) is sufficiently large, a negative covariance between fecundity and development time. Without specific parameter values the sign of the covariance between fecundity and development time is generally undetermined.

With respect to prediction 1, the heritabilities of development time and fecundity are less than the heritability of adult size, but the difference is not statistically significant. The heritability of fecundity is highly correlated with the heritability of adult size. The overall mean of the life history heritabilities (Grate, Dtime, Frate) is 0.37 (SE=0.05, n=31), whereas that for adult size is 0.40 (SE=0.04, n=20; the difference in sample size is due to h2(Asize) being duplicated in several tables). The overall conclusion to be drawn is that while the heritability of the three life history traits may be less than that of adult size, the difference is small. This conclusion contrasts with that reached by Mousseau & Roff (1987) who obtained estimates for the heritability of life history traits of 0.26 (SE=0.03, n=79) and for morphological traits of 0.51 (SE=0.02, n=140). The two data sets differ in that the latter includes a wider array of traits than included in the present analysis. To see if this could account for the difference I reanalysed the data set used by Mousseau and Roff using species means per trait category and using only traits that would be included in the present analysis (i.e. traits classified as Asize, Grate, Dtime, Feggs). The mean heritability of the life history traits (Grate, Dtime, Feggs) is now 0.34 (SE=0.04, n=20) and that for adult size is 0.46 (SE=0.04, n=37). These values are significantly different (t=2.01, d.f.=55, P= 0.025; Mann–Whitney test, χ2=4.58, d.f.=1, P=0.016; tests one-tailed) but suggest that the difference is not as great as in the original data set of Mousseau and Roff. The primary difference between the estimates is that the heritability of life history traits in Mousseau and Roff is substantially less than that obtained if the data set is restricted to the three traits of the present paper (0.26 vs. 0.34). This difference is largely due to the low heritability of survival (h2=0.19) in the data set of Mousseau & Roff (1987). This is illustrated also by the one species, G. pennsylvanicus, for which we have estimates of all the above traits: h2(Asize)=0.60, h2(Dtime)=0.31, h2(Grate)=0.44, h2(Feggs)=0.55, h2(survival)=0.07 (survival estimate from Simons et al., 1998 ). In G. pennsylvanicus the heritability of adult size is the largest but the heritabilities of Grate, Dtime and Feggs are quite substantial whereas that for survival is very low (but statistically significant).

Although the data do not permit a quantitative assessment of the algebraic relationships between variances and covariances as specified in point 2 above, it is possible to test the predictions given in Table 1. In the three available tests these predictions are upheld. The model used to derive these predictions was relatively simple and assumed that on some scale the growth curve will be linear and that size at some immature age is an index of growth rate. Plotted on an untransformed scale, growth trajectories are typically sigmoidal or at least concave (e.g. Atchley, 1984; Gebhardt-Henrich, 1992; Roff, 1992), but transformations such as the logarithmic may make the curves more or less linear (e.g. Simons et al., 1998 ). The predictions of the simple model should still apply in general if the genetic correlation between estimates of growth rate at different ages are positively genetically correlated. This has been found to be the case for mice ( Riska et al., 1984 ), rats ( Atchley & Rutledge, 1980), pigs ( Ahlschwede & Robison, 1971), chickens ( Chamber, 1990), clams ( Hilbish et al., 1993 ) and trees ( Danjon, 1994). Where there is no simple transformation the growth trajectory could be analysed using either a nonlinear or a polynomial function ( De Jong, 1990; Gebhardt-Henrich & Marks, 1993; Roff, 1994; Van Tienderen & Koelewijn, 1994) or the infinite dimensional approach of Kirkpatrick & Heckman (1989). In these cases there is no longer any single metric for ‘growth rate’ and analyses would have to focus upon either particular parameters or ages. Detailed analyses of growth trajectories are uncommon but represent an important area of investigation.

A typical assumption in life history analysis is that an increased body size will require an increased development time and this results in a trade-off (see introduction), because increased development time decreases r but an increased body size increases fecundity and hence increases r ( Roff, 1992; Stearns, 1992). The argument for this rests on the implicit assumption that individuals are all genetically programmed to follow the same growth trajectory. As shown in the present paper, this assumption is manifestly not true in some organisms. Without this assumption the above sequence of arguments is not necessarily true. Most particularly, the quantitative genetic model investigated shows that the genetic correlation between development time and fecundity (which is the ultimate source of the trade-off) cannot be predicted from the sign of the genetic correlation between development time and adult size. The empirical data show that negative genetic correlations between these two traits are common and, while they suggest that growth rate is genetically variable, they cannot be used to argue for the lack of a trade-off, as was suggested by Klingenberg & Spence (1997). Similarly, the presence of a positive genetic correlation between development time and adult size is insufficient evidence for a positive genetic correlation between development time and fecundity.

There is a consistent pattern of a positive genetic correlation between body size and fecundity (Table 4). Therefore, as frequently assumed, large body size will be favoured as a correlated response to selection for increased fecundity. The difficulty, as described above, is relating this response via the developmental parameters. Thus, for example, large body size is favoured in G. pennsylvanicus both because it is positively genetically correlated with fecundity (0.52, Table 4) and negatively correlated with development time (–0.14, Table 2). The latter genetic correlation indicates the lack of trade-off, although the positive (but nonsignificant) genetic correlation between development time and fecundity (0.16, Table 5) would suggest a trade-off. Under different environmental conditions the latter genetic correlation was significantly negative (–0.35, Simons & Roff, 1996). Two important messages can be derived from this example: first, the genetic basis of trade-offs should be measured directly and not inferred, and, secondly, conclusions on the sign of the genetic correlation should take into account the confidence region about the estimate.

Given the usually large standard errors associated with the genetic correlation estimate, it would be very useful if at least the sign, if not the value, of the genetic correlation could be inferred from the phenotypic correlation. Caution is generally advised in using phenotypic correlations as indicators of trade-offs or underlying genetic correlations ( Reznick, 1985; Van Noordwijk & de Jong, 1986; Roff, 1992, 1996; Stearns, 1992). The present data suggest that phenotypic correlations may be generally reliable both with respect to sign and approximate value for the genetic correlation between adult size and development (Dtime, Grate) or fecundity (f). The phenotypic correlation had the same sign as the genetic correlation 27 times and a different sign three times (i.e. 10% of cases differed), which is highly significantly different from random (P < 10–4, binomial test). For the combined data there is also a highly significant regression (r=0.68, n=30, P < 0.0005, rp=0.13[0.07]+ 1.11[0.21]ra) in which the intercept is not significantly different from zero nor the slope from one. However, the mean genetic correlation is significantly larger than the phenotypic correlation (a=0.31, p=0.15, paired t=2.62, P=0.014), which suggests that the phenotypic correlation can be used as a minimal estimate of the genetic correlation. These results are in accord with the findings reported earlier ( Roff, 1996) in which was found that for correlations between morphological and life history traits the regression model was rp=0.06 + 1.14ra. Unfortunately, this relationship cannot be extended to correlations between two life history traits ( Roff, 1996). This is important in the present analysis because most of the phenotypic correlations between development time and fecundity are negative while the standard errors on the genetic correlations are typically so large that the confidence region makes the genetic correlation estimates worthless (Table 5). Thus the generality of a trade-off between development time and fecundity remains to be demonstrated.

Given the central evolutionary role of trade-offs between growth rate, development time, adult size and fecundity, the number of studies that determined the interaction among the components is surprisingly small. Except for the positive genetic correlation between body size and fecundity, no general patterns are clearly discernible. The present analysis shows that, given the potential complexity of interactions among the traits, more quantitative genetic analyses of growth and reproduction are necessary.

Acknowledgment

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References

This work was supported by a grant from the Natural Sciences and Engineering Council of Canada.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Some simple models of growth, maturity and fecundity
  5. Description of the data set
  6. Analysis
  7. Discussion
  8. Acknowledgment
  9. References
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