Heredity 84 (2000) 193±200 Received 24 May 1999, accepted 30 September 1999 A quantitative genetic analysis of phenotypic plasticity of diapause induction in the cricket Allonemobius 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 Allonemobius socius, 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 dierence between ages. There were signi®cant genetic correlations between environments for all ages. Because of the reduction in genetic correlation as the dierence in ages increases, selection will be more eective at changing the overall shape of the reaction norm than causing local changes. Furthermore, the high genetic correlations may constrain the evolution 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, heritability, 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- phenotype 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 dierentiation 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: [email protected] (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 sucient (>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 Nemobiinae. 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, ospring. 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 eects, space limi- `early' environment, 392, 433, 401, 365; `late' environ- tations and diculties 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 ospring 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 Ó The Genetical Society of Great Britain, Heredity, 84, 193±200. GENETICS OF DIAPAUSE INDUCTION 195 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 heritabilities 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 dierent 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.