Heredity 84 (2000) 193±200 Received 24 May 1999, accepted 30 September 1999

A quantitative genetic analysis of of diapause induction in the cricket socius

DEREK A. ROFF* & MICHAEL J. BRADFORDà Department of Biology, McGill University, 1205 Dr Pen®eld Ave., Montreal, Quebec, Canada, H3A 1B1 and àFisheries and Oceans Canada and School of Resource and Environmental Management, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6

Although numerous studies have indicated that diapause is heritable and phenotypically plastic, none of them has examined the quantitative genetic basis of this plasticity. In this paper we report such an analysis for egg diapause in the cricket , the induction of which appears to be largely determined by the mother. We analysed the quantitative genetic basis of the phenotypically plastic response of female A. socius to age and environmental conditions. We measured the production of diapause eggs on four occasions over a 16-day period, and in two environments; one mimicking an `early' period of the year and another mimicking a `late' period. We analysed genetic variation in phenotypic plasticity using the character-state approach. Diapause proportion was heritable (h2 ranged from 0.17 to 0.49, being larger in the `early' environment), and the genetic correlation between ages in proportion of diapausing eggs was close to 1 but showed a decrease with increased di€erence between ages. There were signi®cant genetic correlations between environments for all ages. Because of the reduction in genetic correlation as the di€erence in ages increases, selection will be more e€ective at changing the overall shape of the reaction norm than causing local changes. Furthermore, the high genetic correlations may constrain the of the reaction norm. When the two environments are converted into the estimated days in the year the two reaction norms form approximately a single curve as predicted from previous theoretical analysis of the optimal reaction norm.

Keywords: character-state approach, diapause, genetic correlation, , phenotypic plasticity, reaction norms.

Introduction Diapause induction is an ideal model for the genetic analysis of the evolution of reaction norms, because the In a heterogeneous environment there may be selection ®tness advantages of entering diapause at a particular for the ability to respond to cues that give information time can be readily modelled using life-history data and about the present or future state of the environment. historical data such as temperature records (Bradford & Such phenotypic plasticity results in a mapping between Ro€, 1997). There is considerable evidence that dia- and environment that is known as the pause induction is heritable and is phenotypically plastic reaction norm (for a review of the concept see Schlichting (Tauber et al., 1986), although to our knowledge there & Pigliucci, 1998). Reaction norms are found in a wide are no studies showing that this phenotypic plasticity is range of characters, particularly life-history traits under polygenic control. The purpose of the present (Travis, 1994). It is a general ®nding that phenotypic study was to analyse the genetic variability of pheno- plasticity is genetically variable (e.g. see table 6.1 in typic plasticity for diapause induction in the cricket Ro€, 1997) and hence selection should generally be Allonemobius socius. capable of moulding the reaction norm to its optimum Sib analysis and common garden experiments have (De Jong, 1990; but see Ro€, 1994 and De Jong, 1999 shown genetic di€erentiation among populations for for cases in which evolution will be constrained). diapause induction in the eggs of A. socius (Mousseau & Ro€, 1989; Mousseau, 1991; Bradford & Ro€, 1995), and that diapause is sensitive to temperature, photoperiod *Correspondence. E-mail: dro€@bio1.lan.mcgill.ca (Bradford & Ro€, 1995) and maternal age (Mousseau,

Ó 2000 The Genetical Society of Great Britain. 193 194 D. A. ROFF & M. J. BRADFORD

1991; Bradford & Ro€, 1993). Female A. socius from a generation in this population. The `early' environment bivoltine population lay a larger proportion of nondia- consisted of a photoperiod of 15.5:8.5 h light:dark (L:D) pausing eggs when reared under conditions mimicking for nymphs and 15:9 h L:D for adults, corresponding early summer than when reared under late summer approximately to photoperiods (including civil twilight) conditions (Bradford & Ro€, 1995), whereas the pro- between Julian days 195 and 210 at the collection site of portion of diapausing eggs increases with the age of the the experimental population. In the `late' environment, female (Bradford & Ro€, 1993). The speci®c objective of conditions were set at 15:9 h L:D for the nymphs and the present study was to determine the quantitative 14.5:9.5 h L:D for the adults, simulating Julian days 210 genetic basis of these two types of phenotypic plasticity and 225. In all environments a 31:19°C thermoperiod (between environment, between ages). was used on a 12-h cycle, with the increase in temper- ature set at 1.5 h before lights on. These are average Materials and methods midsummer temperatures for the collection site. There were 56 families that had sucient (>20) eggs to make up two replicates per environment and nine families that Species description yielded enough eggs for only two replicates in a single Allonemobius socius is a small (»0.07 g) common ground environment; the latter were all placed in the early cricket of the subfamily . It is found in wet environment. grasslands in the south-eastern United States from Mousseau & Ro€ (1989) estimated the heritability of Florida to New Jersey (Howard & Furth, 1986). In diapause propensity, assuming that it was a trait of the the northern part of its range A. socius is univoltine, o€spring. Further research suggested that it might more becoming bivoltine in Virginia and possibly multivoltine properly be considered a maternal trait (Tanaka, 1986; in Florida (Howard & Furth, 1986). The transition from Mousseau, 1991; Bradford & Ro€, 1995) and thus in the a univoltine to bivoltine phenology occurs between present experiment we used the proportion of eggs latitudes 34±37°N, in which region voltinism is primarily diapausing as a trait of the female, not the egg itself. For a conditional strategy and not a simple genetic poly- each environment 6±8 females were chosen haphazardly morphism (Bradford & Ro€, 1995). In the transition from each family and mated and allowed to reproduce area, overwintering eggs hatch in May and ®rst-genera- for the estimation of diapause proportion. To ensure tion adults appear in July and early August. Females of successful mating each female was provided with two the ®rst generation produce mixtures of nondiapausing randomly chosen males, either from the pool of males and diapausing eggs (Mousseau, 1991). Eggs laid in emerging from the experiment or from a separate August or later typically diapause: thus second-genera- rearing of the surplus nymphs. We collected four tion females produce only diapausing eggs. batches of eggs at 4-day intervals from each female, Individuals used in the present experiment were from beginning on the ninth day after the ®nal moult (i.e. the third generation of a stock descended from approxi- covering days 9±12, 13±16, 17±20, 21±24). Eggs were mately 100 adults collected in July (1988) from Danville, incubated in the same environment as the mothers for Virginia (36°40¢N). Husbandry methods were as des- 14±18 days, at which point diapause, direct-developing cribed in Bradford & Ro€ (1993). and infertile eggs were scored. Infertile eggs were not used in the calculation of diapause proportion and batches of fewer than four eggs were excluded from the Experimental design analysis. The total number of egg batches (where one A split family full-sib design was employed to estimate egg batch corresponds to the output of a single female) genetic parameters. Although such estimates are poten- obtained for each period and in each environment were: tially biased by nonadditive genetic e€ects, space limi- `early' environment, 392, 433, 401, 365; `late' environ- tations and diculties with mating prevented us from ment, 345, 370, 372, 338. using the preferred half-sib design. The parental generation was reared under short Statistical methods: initial test photoperiods so that all eggs from the pair-mating were in diapause. The eggs were kept at 4°C for 3 months, We ®rst tested for variation in proportion diapause and were then warmed to 28°C to initiate hatching. This between environments, among ages and families using synchronized development such that the hatching of both univariate and multivariate repeated measures o€spring after diapause was concentrated over a 2- to ANOVA. For these analyses we used only families that 3-day period. Upon hatching, nymphs from each family were represented in both environments. Additionally were placed in one of two environments designed to two families had to be dropped, as their inclusion, for span the range of conditions experienced by the ®rst reasons we could not ascertain, generated a matrix

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singularity. Following the ®nding that there was signi®- where rA and SE were estimated using the jackknife and cant variation attributable to both age and environment x was zero or one (Knapp et al., 1989). we estimated and genetic correlations (rA) There are two `types' of genetic correlations between separately for each environment/age combination as environments: that between the same trait (e.g. P1) and described below. that between two di€erent traits (e.g. P1 and P2). In the ®rst case there is only one way to obtain the jackknifed estimate. In the second case there are two ways, e.g. P Statistical methods: female age and proportion 1 in the `early' environment vs. P in the `late' environ- of diapause eggs 2 ment, or P2 in the `early' environment vs. P1 in the `late' We calculated the heritability of the proportion of environment. Thus two sets of pseudovalues from the diapause eggs at each age (designated Pi, where i ˆ 1, 2, jackknife procedure are estimated; under the null 3, 4, for the ®rst, second, third and fourth collection) hypothesis that the two sets of data do not di€er the and the genetic correlation between them (use of the di€erence between the mean pseudovalues will be zero. arcsine square root transformation did not change the This was tested by means of a two-sample t-test. If the results and we report here the results on the raw scores). two samples were not found to di€er, the genetic Heritabilities and their associated standard errors were correlation was estimated using the combined sample estimated using a delete-one (ˆ family) jackknife with of jackknife pseudovalues. the pseudovalues estimated from a nested (nymphal rearing cage nested within family) one-way ANOVA as Results described in Simons & Ro€ (1994); as there was no signi®cant e€ect attributable to rearing cage for the The proportion of eggs laid in the `late' environment nymphs the results presented here are for the combined that were in diapause was approximately 0.1 greater data (no nesting). than in the `early' environment (Fig. 1). In both The distribution of diapause proportions among environments there was a trend towards a decline in females was skewed, with approximately 50% of females proportion of diapause eggs at age 16. The univariate in any sample producing only diapause eggs, which and multivariate repeated measures ANOVAs gave the potentially biased the ANOVA estimates. Therefore, we con®rmed the ANOVA results with the randomization method described in Ro€ & Bradford (1996). Genetic correlations between ages within the same environment were estimated using ANOVA combined with the delete-one (family) jackknife as described in Ro€ & Preziosi (1994). Only families for which data were available for both environments were used in this analysis (this is necessary for the jackknife procedure used). This reduced the number of families to 56.

Statistical methods: estimation of the genetic correlations between environments

We used the mixed-model ANOVA method with families as a random e€ect and environments and age as ®xed e€ects to test for a positive genetic correlation (Fry, 1992). Because the data were not fully balanced, this test should be considered approximate. Genetic correlations were determined by estimating separately by REML (using the varcomp procedure in SPLUS) the covariance and the two variances (Fry, 1992; correlations obtained from family mean values were used to con®rm that the correlations were positive). Standard errors were estimated using the jackknife (Ro€ & Simons, 1997; Fig. 1 Mean proportion of diapausing eggs for all females of Windig, 1997). As an alternative to the mixed-model Allonemobius socius (solid lines, ‹1 SE) as a function of age ANOVA we used a one-sample t-test [t ˆ (rA ) x)/SE], and environment.

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2 Table 1 Repeated-measures ANOVA of the proportion Table 2 Estimates of heritability (h ), additive genetic of diapause eggs produced by Allonemobius socius as a variance (VA) and environmental variance (VE) for the function of age, family and environment proportion of diapausing eggs produced by Allonemobius socius at four ages Source d.f. MS FP Traits h2 SE P V V Between females rand A E Family 53 1.058 3.6 <0.00001 `Early' environment Environment 1 6.178 21.03 <0.00001 P1 0.40 0.10 0.0002 0.065 0.097 Family ´ environment 53 0.387 1.32 0.076 P2 0.43 0.11 0.0002 0.069 0.090 Error 376 0.294 P3 0.49 0.11 0.0002 0.078 0.082 P 0.48 0.13 0.0002 0.069 0.074 Within females 4 Age 3 0.835 18 <0.00001 `Late' environment Age ´ family 159 0.059 1.27 0.019 P1 0.23 0.10 0.0038 0.030 0.097 Age ´ environment 3 0.057 1.22 0.301 P2 0.29 0.09 0.0004 0.041 0.098 Age ´ environment ´ family 159 0.047 1.014 0.443 P3 0.30 0.10 0.0004 0.035 0.080 Error 1128 0.046 P4 0.17 0.09 0.0184 0.015 0.073 Probability obtained from randomization method. same results as did the probabilities estimated from the F, Greenhouse±Geiser and Huynh±Feldt statistics: we were signi®cantly di€erent from zero (mean ) 2SE>0 present only the results for the univariate test using the in all cases; note that because of sample size this test is F-values (Table 1). There were highly signi®cant e€ects equivalent to a test based on the estimated t-value, of family, environment and age but the only signi®cant Table 3). The phenotypic correlation was approximately interaction was between age and family. These results 0.60 and was signi®cantly less than 1 (mean + 2 SE <1 suggest that the shapes of the reaction norms were the in all cases), whereas the genetic correlation was same in both environments, which is apparent from the generally very close to 1 and in no case was it signi®- plots of the means (Fig. 1), but that there was also cantly di€erent from 1 (mean + 2 SE > 1 in all cases). signi®cant genetic variation averaged over environments In all cases the genetic correlation was larger than the in age-speci®c tendency to produce diapausing eggs. phenotypic correlation (Table 3); because these two statistics are not independent there is no appropriate statistical test for the observed di€erence, but the Heritabilities consistency of the result does suggest that the di€erence Both the estimated standard errors and randomization is real. The di€erence between the genetic and pheno- test indicated that there was signi®cant genetic variation typic correlations results from di€erence in both for diapause proportion at all ages (Table 2). The the covariances (Cov) (`early' environment: mean heritability estimates for the proportion of diapause CovA ˆ 0.070, mean CovP ˆ 0.102, mean ratio of CovA/ eggs at each age did not vary substantially with age but CovP ˆ 0.69; `late' environment: mean CovA ˆ 0.024, were consistently higher in the `early' environment mean CovP ˆ 0.073, mean ratio of CovA/ CovP ˆ 0.33) (Table 2). We tested for a di€erence between heritabil- and the denominators (Denom) (`early' environment: ities in the di€erent environments by means of a paired mean DenomA ˆ 0.072, mean DenomP ˆ 0.152, mean t-test (i.e. the signed di€erence between Pi in the two ratio of DenomA/DenomP ˆ 0.46; `late' environment: environments). The mean di€erence of 0.20 was highly mean DenomA ˆ 0.029, mean DenomP ˆ 0.115, mean signi®cant (t3 ˆ 5.43, P ˆ 0.012). The increased herit- ratio of DenomA/DenomP ˆ 0.25). ability in the `early' environment was caused primarily by The `within-environmental' genetic and phenotypic an increase in the additive genetic variance (mean VA in correlations were larger, on average, in the `early' `early' environment ˆ 0.07 vs. 0.03 in the `late' environ- environment (`early' environment: mean rP ˆ 0.66, ment), with the environmental variance remaining more mean rA ˆ 0.97; `late' environment: mean rP ˆ 0.63, or less constant (mean VE in both environments ˆ 0.09: mean rA ˆ 0.84). As an approximate test of whether Table 2). the `within-environmental' correlations di€ered we used a paired t-test. The genetic correlations did not di€er (t ˆ 1.60, P ˆ 0.170), whereas the phenotypic cor- Genetic correlations between ages 5 relations were marginally nonsigni®cant (t ˆ 2.33, within each environment 5 P ˆ 0.067). All phenotypic and genetic correlations between the In general, we might expect that the more distant two proportion of diapausing eggs produced at di€erent ages traits are then the lower will be the genetic correlation

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Table 3 Phenotypic and genetic correlations in Allonemobius socius between age- speci®c diapause proportions (Pi) within environments. Values for the `early' environment are shown above the diagonal, values for the `late' environment are shown below the diagonal. Standard errors are given in parentheses

P1 P2 P3 P4 Phenotypic correlations P1 0.67 (0.04) 0.61 (0.04) 0.53 (0.05) P2 0.65 (0.05) 0.75 (0.03) 0.64 (0.04) P3 0.61 (0.05) 0.71 (0.05) 0.74 (0.03) P4 0.54 (0.06) 0.59 (0.05) 0.68 (0.04) Genetic correlations P1 1.00 (0.06) 0.99 (0.07) 0.95 (0.09) P2 0.78 (0.23) 1.01 (0.04) 0.90 (0.06) P3 0.74 (0.23) 1.05 (0.06) 0.95 (0.06) P4 0.55 (0.39) 0.96 (0.16) 0.97 (0.17)

between them: thus the genetic correlation between two ures ANOVA (Table 1). The grand mean of all estimates ages is predicted to decline as the di€erence in ages equalled 0.67 (SE ˆ 0.065, n ˆ 10) which was signi®- increases. For both the phenotypic and genetic correla- cantly di€erent from unity (t9 ˆ 5.03, P ˆ 0.001). tions there was a statistically signi®cant decline in the correlation as the di€erence between ages increased. For each type of correlation there are six comparisons and in Discussion all comparisons the correlation declined; from the bino- By using a growth chamber programmed to produce a mial test the probability of all six comparisons going in continuously changing environment that mimicked the the predicted direction is 0.015 (one-tailed probability). area from where the present stock of A. socius was collected, Bradford & Ro€ (1993) found that females Genetic correlations between environments laid approximately 30% of diapausing eggs on day 210 of the year (`early' environment) and 78% of diapausing The two-sample t-tests indicated no di€erence between eggs on day 225 (`late' environment). The latter the two possible estimates of rA for di€erent traits proportion is approximately what we obtained in the (P > 0.2 in all six possible combinations); we therefore `late' environment but the former is less than one-half combined the data. With one exception (P4) the genetic that observed in the `early' environment (Fig. 1). This correlations were all highly signi®cantly di€erent from discrepancy suggests that a continuously changing zero (P < 0.001, one-tailed t-tests: Table 4). As with the photoperiod and/or temperature is important in induc- genetic correlations within environments, there was ing diapause, as has been found in the butter¯y, a trend for the correlation to decrease as the di€erence Polygonia c-album (Nylin, 1989). Nevertheless, there in ages increased (®ve decreases out of six possible, was a signi®cant di€erence in the diapause response that P ˆ 0.1094, binomial one-tailed test). The overall pat- was qualitatively consistent with the expected pattern of tern (nine of 10 estimates <1) suggests that rA was less increased proportion diapause in the `late' environment. than one. This is also suggested by the almost signi®cant Thus under the two experimental regimes females family ´ environment interaction in the repeated meas- showed phenotypic plasticity for diapause induction. The proportion of diapause eggs increased overall Table 4 Cross-environment genetic correlations in with female age (Fig. 1; Mousseau, 1991; Bradford & Allonemobius socius between proportion of diapause eggs Ro€, 1993), indicating that diapause was at least in the two environments. Standard errors shown in partially determined by the mother. The slight decrease parentheses in proportion of diapause eggs produced during the

P1 P2 P3 P4 second period (age 13±16 days) may be a consequence of the sudden shift between photoperiods at the time of P1 0.65 (0.26) 0.89 (0.17) 0.64 (0.18) 0.42 (0.23) eclosion into the adult. However, given that the photo- P 1.04 (0.16) 0.81 (0.17) 0.67 (0.21) 2 periodic shift should have indicated less time remaining P 0.72 (0.15) 0.52 (0.20) 3 before the end of the growing season, we would have P 0.38 (0.34) 4 expected an increase rather than a decrease.

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In this paper we have assumed that diapause was a In each year there is a particular day on which a maternal trait that in a given environment can be female should switch from laying nondiapausing eggs to characterized by the proportion of diapause eggs pro- diapausing eggs; in some populations of copepods duced at di€erent ages (Pi). The heritabilities of Pi were this switch is determined ultimately by ®sh predation larger in the `early' than the `late' environment but (Hairston & Dillon, 1990), whereas in A. socius the signi®cant in both (Table 2). The genetic correlations important selective factor appears to be the probability between days were all very close to one but did show a that there remains sucient time to complete develop- signi®cant decline as the di€erences in ages increased ment and produce another batch of eggs, which is the (Table 3). Such declines have been observed between only stage that can diapause (Bradford & Ro€, 1997). morphological traits at di€erent ages in mammals Interannual variation in the occurrence of ®sh or length (Atchley, 1984) and fecundity in Drosophila melanogas- of time suitable for development will favour a ¯exible ter (Engstrom et al., 1992). If the genetic correlation timing for the switch between diapause and nondia- between ages were actually one, then selection could not pausing eggs. If a female A. socius can assess the day of change the shape of the reaction norm. The slight the year but not the remaining length of the growing reduction below one means that the reaction norm can season, selection will favour a reaction norm in which evolve. Furthermore, the decline with the age di€erence mixed batches of diapause and nondiapause eggs are means that selection can more readily change the overall produced on some days. Using historical temperature shape of the reaction norm than it can make local data Bradford & Ro€ (1997) determined this reaction variation in shape. norm for A. socius in the region from which the Mousseau & Ro€ (1989) estimated the heritability of experimental originated. The transition from diapause on the assumption that it was a trait of the laying only nondiapause eggs to laying only diapause o€spring. They obtained an average estimate of 0.74, eggs was predicted to be very narrow, covering approx- which is higher than obtained in the present analysis. If, imately a 12-day period. This rapid change is consistent as appears to be the case, the assumption that diapause with the observed coecient of variation in season induction is an o€spring trait is incorrect then their length of only 10±15% (Bradford & Ro€, 1997). These previous estimates of heritability are in¯ated, and are results are also consistent with other studies of risk- equal to twice the repeatability of the trait (i.e. twice spreading in (Hopper, 1999). the intraclass correlation; Lessells & Boag, 1987). The According to the assumptions of the model of population (Richmond) studied in Mousseau & Ro€ Bradford & Ro€ (1997) the reaction norms obtained (1989) that was geographically the closest to the in the two experimental environments should be the population in the present study gave a repeatability of `lower' and `upper' portions of a single reaction norm. 0.45. The conditions under which the Richmond popu- Alternatively, the reaction norm might consist of a lation was raised (30°C, 14:10 h L:D) most closely more complex function that includes both age and match the `early' environment of the present experiment environment, as suggested by the nearly signi®cant under which conditions the heritability of diapause family ´ environment interaction (Table 1). However, proportion varied from 0.40 to 0.49, with a mean of 0.45 the following evidence suggests that the major factor is (Table 2), which is the same as the repeatability from the relative age. The early environment covers approximate- Mousseau & Ro€ study. This suggests that the correct ly the period encountered by the adult during the heritability of diapause for the populations analysed in monitored egg-laying period from day 222 to 234 Mousseau & Ro€ (1989) can be obtained by halving whereas the late environment covers days 237 to 249 their reported values. Using this correction, the herit- and therefore the curve for the late environment should abilities ranged from 0.15 to 0.55, with a mean of 0.37, be a continuation of that found in the early environ- which is similar to that obtained in the present analysis. ment. A right translational shift of the curve from the Similar estimates for the heritability of diapause have late environment does produce a more or less single been obtained in a lepidopteran, Choristoneura rosace- reaction norm (Fig. 2). Under the hypothesis of a single anna (h2 ˆ 0.38, SE ˆ 0.10; CarrieÁ re, 1994) and a reaction norm the genetic correlation across environ- copepod, Diaptomus sanguineus (h2 ˆ 0.60, SE ˆ 0.35; ments corresponds to the genetic correlation between Hairston & Dillon, 1990). Signi®cant additive genetic days that are separated by the appropriate number of variance has also been found in two other aspects of days. Thus, for example, the genetic correlation between diapause; degree days from chilling to adult eclosion in P1 in the `early' environment and P1 in the `late' Hyphantria cunea (h2 ˆ 0.60, SE ˆ 0.22; Morris, 1971), environment should correspond to the genetic correla- and the critical photoperiod for the induction of tion between any two ages separated by approximately diapause in Wyeomyia smithii (h2 ˆ 0.70, SE ˆ 0.16; 15 days (i.e. days 222 and 237 in Fig. 2). Using this Bradshaw & Holzapfel, 1990). criterion we plotted the genetic correlation as a function

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(conditions mimicking early summer) produced only direct-developing eggs, whereas females from the uni- voltine and mixed populations produced some diapaus- ing eggs. In any particular environment the proportion of diapausing eggs increased with the latitude of origin of the females. Diapause is a central feature of the life histories of many invertebrates, as is its equivalent, dormancy, in many plant species. Whereas there is evidence that diapause induction is, in general heritable, the present study is the ®rst to estimate the genetic parameters of the reaction norm. The high genetic correlations between ages and between environments indicate that the evolu- tion of the reaction norm can be constrained and the evolutionary trajectory towards at least some reaction Fig. 2 Diapause curves as shown in Fig. 1 but plotted norms may be very long. according to the approximate day of the year. Acknowledgements of the expected or `perceived' separation in days and, as We gratefully thank J. Windig, P. Crnokrak and predicted, found a highly signi®cant negative regression G. Stirling for their helpful comments. This research (r ˆ )0.70, n ˆ 21, P ˆ 0.0005). was supported by a grant to D.A.R. from the Natural Genetic variation in the reaction norm will allow Sciences and Engineering Council of Canada, and by selection to modify the proportion of diapause eggs grants from NSERC and Max Bell postgraduate schol- produced as conditions change either over time or over arships to M.J.B. space. This prediction has been veri®ed by a common garden experiment using three geographical stocks of A. socius raised in three environments mimicking the References locations from where the stocks were collected (Brad- ATCHLEY, W. R. 1984. , timing of development, and ford & Ro€, 1995). Diapause propensity varied with genetic variance±covariance structure. Am. Nat., 123, environment and stock, indicating genetic variation 519±540. among populations and a response to selection, pre- BRADFORD, M. J.AND ROFF , D. A. 1993. Bet hedging and the sumably caused in part by the di€erent season lengths at diapause strategies of the cricket . the di€erent locations. In an environment in which the Ecology, 74, 1129±1135. season length is typically too short for more than a BRADFORD, M. J.AND ROFF , D. A. 1995. Genetic and phenotypic single generation, selection will favour females in which sources of life history variation along a cline in voltinism in there is an early age-speci®c switch to diapausing eggs the cricket Allonemobius socius. Oecologia, 103, 319±326. , M. J.AND ROFF , D. A. 1997. An empirical model of and the reaction norm is largely una€ected by external BRADFORD diapause strategies in the cricket Allonemobius socius. cues. Similarly, at a location at which a bivoltine life Ecology, 78, 442±451. history is favoured, in most years selection will favour BRADSHAW, W. E.AND HOLZAPFEL , C. M. 1990. Evolution of females with reaction norms that show a strong inter- phenology and demography in the pitcher plant mosquito, action with external cues (e.g. photoperiod and/or Wyeomyia smithii. In: Gilbert, F. (ed.) Life Cycles: temperature) such that ®rst generation females show a Genetics, Evolution, and Co-ordination, pp. 47±67. Springer, very late age-speci®c switch to diapause whereas females London. from the second generation show an early age-speci®c CARRIECARRIEREÁ RE, Y. 1994. Evolution of phenotypic variance: non- switch to diapausing eggs. The common garden exper- Mendelian parental in¯uences on phenotypic and genetic iments described above support these predictions: a components of life-history traits in a generalist herbivore. univoltine population raised in its natal environment Heredity, 72, 420±430. , G. 1990. of reaction norms. produced only diapause eggs, whereas females from a DEJONG J. Evol. Biol., 3, 447±468. bivoltine population and females from a mixed (transi- DEJONG , G. 1999. Unpredictable selection in a structured tional) population produced some direct developing population leads to local genetic di€erentiation in evolved eggs early in their reproductive schedule (Bradford & reaction norms. J. Evol. Biol., 12, 839±851. Ro€, 1995). Similarly, females from the bivoltine ENGSTROM, G., LILJEDAHL, L.-E.AND BJORKLUND , T. 1992. population when raised in their natal environment Expression of genetic and environmental variation during

Ó The Genetical Society of Great Britain, Heredity, 84, 193±200. 200 D. A. ROFF & M. J. BRADFORD

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