1 INTRODUCTION

As is well known that a quantitative trait is affected by polygenes. When these polygenes at many loci segregate simultaneously, genetic variability of the quantitative trait will be modified by non-genetic interactions such as intra-locus (dominance) and inter-locus interaction (epistasis) (Lynch and Walsh, 1998; Lutz, 2001). In conjunction with the modification by environment, the underlying genetic control of a quantitative trait may change significantly during ontogeny of organisms (Walsh and Lynch, 2018). For example, Vasemägi et al. (2016) reported that a substantial proportion of growth-related quantitative trait Loci (QTLs) detected in farmed conditions had no effect on Salmo salar growth in the wild. Similar results were documented in Salvelinus alpinus by Chiasson et al. (2013). Accordingly, the genetic assessment for a population should be carried out in a dynamic manner. Based upon the individual animal model, researchers have conducted the genetic assessment in some populations of aquatic animals, such as Oncorhynichus mykiss and Salmo trutta (Bonnet et al., 1999), Oreochromis niloticus (Lozano et al., 2011), Megalobrama amblycephala (Luo et al., 2014; Zhao et al., 2016), Crassostrea gigas (Kong et al., 2015), and Scophthalmus maximus (Wang et al., 2019b). Furthermore, environmental effects were eliminated from phenotypic variation when genetically evaluating the population of O. niloticus (Trong et al., 2013), and of Sparus aurata (García-Celdrán et al., 2015). Predicated upon the genetic model with additive, dominance and genotype by environment interaction, non-genetic effects such as dominance and dominance by environment interaction were removed from phenotypic variation in Procambarus clarkii (Wang et al., 2019a). Nevertheless, these assessments of genetic variability were undertaken only using the phenotypes at a specific temporal point of ontogeny. For instance, He et al. (2011) utilized the phenotypic values obtained at 150 days of age to evaluate the genetic variability in Fenneropenaeus chinensis while Lozano et al. (2013) assessed the genetic variability using the phenotypes at 53 days of age in O. niloticus. The genetic variation revealed by analyzing the phenotypic values in the above studies can provide knowledge about accumulated genetic effects only suitable for a specific developmental phase. In this case, the dynamic changes in genetic variability cannot be embodied, since the actions and interactions of genes vary over time (Walsh and Lynch, 2018).

To understand the longitudinal changes in genetic variability, researchers have examined the variations of genetic effects with time (day/month or generation) in some populations of aquatic animals, such as Penaeus vannamei (Campos-Montes et al., 2013), Haliotis rufescens (Brokordt et al., 2015), Macrobrachium rosenbergii (Luan et al., 2015), and S. salar (Thorland et al., 2020). For example, Domingos et al. (2013) evaluated the genetic variability for traits (weight, standard length, body depth, Fulton's condition factor, and body shape index) at 62 and 273–469 days post hatch in Lates calcarifer. The genetic variability was examined only at several isolated time points in these studies, and no information attained at prior time points was used upon conducting the genetic evaluation. Due to existence of a common genetic base, there exist a correlation to varying extents between the same traits measured at different time points (Zhu, 1996; Atchley and Zhu, 1997; Lynch and Walsh, 1998; Wang et al., 2006, 2015). When the information derived at prior time point(s) is used, the dynamics of genetic variability at a posterior time point would be more accurately exhibited (Zhu, 1996; Wang et al., 2006, 2015).

Procambarus clarkii is a species that is widely distributed over the world, occupying different kinds of habitats, including subterranean situations, wet meadows, seasonally flooded swamps and marshes, and permanent lakes and streams (Lutz, 2001; Holdich, 2002; Longshaw and Stebbing, 2016). As with all other crustaceans, crayfish are protected by their jointed exoskeleton. This seriously constrains growth or ultimate size, since any permanent increase in size is only possible after shedding the rigid exoskeleton. Meanwhile, it also imposes important constraints on management practices involved in their culture. Crayfish thus grow not continuously, but stepwise morphologically. Hence, the growth process of crayfish involves periodic molting interspersed with intermolt periods. The exoskeleton and its molting cycle dominate the life of these animals. Molting means growth. That is, molting is the crucial growth point over ontogeny of this species. Increase in size depends on both growth/molt (growth increment) as well as molt frequency. Crayfish require at least eleven molts to sexual maturity (Holdich, 2002; Longshaw and Stebbing, 2016). Under optimum conditions, for example, crayfish can increase up to 15% in length and 40% in weight in a single molt, depending on temperature and food abundance (Holdich, 2002; Longshaw and Stebbing, 2016). In P. clarkii, genetic evaluation for growth-related traits has been documented by Lutz and Wolters (1999), Li et al. (2016), and Wang et al. (2019a), but these genetic evaluations are carried out using only the phenotypes measured at 150 days of age.

Red swamp crayfish are now commercially very important in China. Its total production has reached one million tons with a gross output value of ca.＄40 billion (Wang et al., 2019a). Due to indeterminate growth, crayfish continue to molt throughout their lives (Holdich, 2002; Longshaw and Stebbing, 2016). A knowledge of the genetic dynamics underlying the growth-related traits at important molting points is fundamental to the production of this species. Since the causal components of phenotypic variability in a population is usually analyzed by genetic variance components for the traits of interest (Zhu, 1996; Atchley and Zhu, 1997; Lynch and Walsh, 1998; Lutz, 2001; Walsh and Lynch, 2018), the causal genetic components of phenotypic variability for four growth-related traits measured at different molting times in P. clarkii are examined in this study. The objective of the present study is to clarify the longitudinal dynamics of genetic effects for the growth-related traits measured at different molting points by using a conditional genetic analysis method. Based upon the architecture and characteristics of the conditional genetic and non-genetic effects obtained, the genetic changes over the ontogeny of P. clarkii would be elucidated. Results would provide valuable information for commercialized production of the red swamp crayfish.

2 MATERIAL AND METHOD 2.1 Broodstock sourcing

In the crayfish cultivation base, Huai'an Xindayun Eco-Fisheries Development Co., Ltd., which is located in Huaihe Town, Xuyi County, Huai'an City, Jiangsu Province. There are three different geographic crayfish populations reserved: Guantan population, Yanghe population, and Dapu population. These populations were collected respectively from Guantan township of Xuyi county, Yanghe township of Suqian city, and Dapu township of Yixing city of Jiangsu Province, China. Sufficient female P. clarkii that had displayed moderate to advanced cement gland development were chosen from each population in May of 2019, and were held individually in partitioned 50-L polyethylene tanks supplied with aerated tap water recirculated through a biological filter in our laboratory (Jiangsu Engineering Laboratory for Breeding of Special Aquatic Organisms). Together with the females, mature males from each geographic population were also chosen for reproduction. These broodstocks were acclimated in our laboratory for one week. Over the acclimation, broodstocks were given a commercial pelleted feed (40% crude protein, 9% lipid), supplemented with the aquatic weeds, Alternanthera philoxeroides (Mart.) Griseb and Elodea nuttallii. Temperature was 25-27 ℃.

2.2 Mating design

The diallel cross mating design was used in our study. Since late May 2019, a complete diallel cross (male: female=1꞉4 within each mating combination) among these geographical populations of P. clarkii was conducted in our laboratory to construct the offspring populations of red swamp crayfish. There were a total of 9 offspring populations produced, 3 for within-population combinations, and 6 for reciprocal combinations. Each mating combination was conducted in a polyethylene tank (120 cm×100 cm× 60 cm, water depth 10-15 cm). Several arc shaped tiles were placed at the bottom of each tank as nests to prevent cannibalism. Aeration was exercised continuously to provide enough dissolved oxygen. Broodstocks were fed once daily with the diet as given above. Feces were siphoned off daily. After mating, berried females were collected from the tank for each mating combination, and cultured individually in a round polyethylene tank (diameter 50 cm, height 60 cm) for hatching. Daily management for the berried females were the same as given above. When the larvae were hatched out and began to leave the brood females to fend themselves after larvae molted two times, the brood females were taken out from the round tank. Thus, third-instar larvae for each mating combination that were used for our experiment were obtained.

2.3 Identification of crayfish

Polyethylene tanks (3.2 m×0.65 m×0.15 m, water depth 10-15 cm) were each partitioned as small divisions (0.3 m×0.3 m) using nylon net (mesh size 2 mm). Only one third-instar larva (0.04-0.03 g) was cultured in each small division. For all practical purposes, third-stage (instar) crayfish are miniature adults and are fully capable of living apart from their mother (Holdich, 2002; Longshaw and Stebbing, 2016). A total of 450 third-instar larvae were used for the experiment, 50 third-instar larvae for each mating combination. Due to being individually partitioned, each crayfish could be completely identified, and thus its ecdysis observed and recorded. Exuviated shells were removed timely to prevent from eating them after it had molted. The survival of crayfish was monitored every day. Water ionic calcium content was regularly checked to ensure its levels were not lower than 2 mg/L (Longshaw and Stebbing, 2016). Other daily managements were the same as described above. The same experiment was carried out once more in May of 2020 in our laboratory.

2.4 Data measuring

Although an increase in growth and length occurs only at the molt, the internal physiological growth is continuous. Crayfish growth is typically determined from external measurements of a known hard part or from weight increments at molt (Jussila and Evans, 1998; Lutz, 2001). According to Holdich (2002) and Longshaw and Stebbing (2016), the number of molts from third-instar larvae to maturity in the red swamp crayfish is nine. In our study, following four growth-related traits over the entire experimental period (from third-instar larvae to maturity) were measured at different molting points: total body weight (BW, g), body length (BL, mm, from tip of rostrum to hind edge of telson), chela length (CHL, mm, from tip of chela to hind edge of propodite), and cephalothorax length (CL, mm, from tip of rostrum to hind edge of cephalothorax). The four growth-related traits were measured after 2 days of each molting when the new cuticle was hardened (at this time the final shell layer, the thin and inner un-calcified membranous layer was complete). All measurements of the four growth-related traits were obtained at nine molts each. Size traits were measured microscopically (Olympus, CX21) to 5^th molt, then measured using a Vernier caliper to 9^th molt. Body weight was measured using an electronic balance (Ohaus, AR224CN).

2.5 Genetic analysis model

For longitudinal data of a quantitative trait, the genetic effect at time t can be broken down into two portions, the accumulated genetic effect at a prior time t-1 and the incremental genetic effect from time t-1 to t (Zhu, 1996; Atchley and Zhu, 1997). The phenotypic values observed at time t are to varying degrees correlated with the ones observed at time t-1 (Lynch and Walsh, 1998). In this study, the following matrix-form mixed genetic model with fixed and random effects (additive, dominance, and genotype × environment interactive effects) was used for analyzing the conditional phenotypic data at t^th molt of red swamp crayfish:

where P_(t|t-1) is the conditional phenotypic value of the trait of interest at t^th molt; b_(t|t–1) is the conditional fixed effect vector at t^th molt, including conditional population mean and environmental effect (year) and tank effect. X is the incidence matrix of conditional fixed effects with coefficients 1 or 0. e_A(t|t–1) is the random conditional additive effect vector at t^th molting, e_A(t|t–1) ~ (0, σ_A(t|t-1)²I). U_A is the incidence matrix of conditional additive effect. e_D(t|t–1) is the random conditional dominance effect vector at t^th molt, e_D(t|t–1) ~ (0, σ_D(t|t-1)²I). U_D is the incidence matrix of conditional dominance effect. e_AE(t|t–1) is the random conditional additive × environment effect vector at t^th molt, e_AE(t|t–1) ~ (0, σ_AE(t|t–1)²I). U_AE is the incidence matrix of conditional additive × environment effect. e_DE(t|t–1) is the random conditional dominance × environment effect vector at t^th molt, e_DE(t|t–1) ~ (0, σ_DE(t|t–1)²I). U_DE is the incidence matrix of conditional additive effect. e_ε(t|t–1) is the random conditional error effect vector at t^th molt, e_ε(t|t–1) ~ (0, σ_ε(t|t–1)²I). I is an identity matrix.

The conditional variance components included in the above analysis model were estimated using the approach of minimum norm quadratic unbiased estimation (MINQUE) (Zhu, 1996), and their standard errors were estimated using the Jackknife method (Zhu, 1996; Lynch and Walsh, 1998). With the standard errors estimated, significance of various conditional variance components was given by the Student's t-test. Using the method of Zhu (1996), the conditional variance components from a certain time t to final time f, σ_(f|t)², were also estimated to understand the net genetic effects expressed during the period (from a prior time t to the final observation time f).

3 RESULT 3.1 Trait descriptive

In P. clarkii, the newly hatched crayfish is basically equipped with all the parts necessary for survival, but it must remain with its mother and undergo two molts before it can fend for itself.

During this early period, larvae are attached to their mother's pleopods. Certain death awaits a young crayfish that becomes detached from the mother, as it is unable to take care of itself. For this reason, the larvae before the two molts were excluded, and only third-instar larvae were used in our study. Survival rates were recorded to range between 76% and 84% for different mating combinations among three geographic populations of P. clarkii. The numbers of survived crayfish that completed nine molts during 106 days of experiment (from stocking of third-instar larvae to completion of 9^th ecdysis) were observed to vary from 29 to 38 for different mating combinations. Since the experiments were rigorously controlled, these crayfish molted basically at the same time. The time was 10 days for each intermolt from 1^st to 4^th molt, 15 days for each intermolt from 5^th to 7^th molt, and 14 days for each intermolt from 8^th to 9^th molt. Variations in phenotypic grand means (±SD) of 4 traits at varying molting points for the whole F₁ offspring population of three intra-population and six reciprocal cross combinations are presented in Fig. 1 for body length, chela length, cephalothorax length, and body weight. It could be found that there occurred different patterns with the growth curves between body weight and 3 morphological traits. Body weight increased slowly before 4^th molt, and thereafter increased rapidly. The three size traits grew in nearly a linear manner from 1^st molt to 9^th molt. It was necessary to point out that since those crayfish had yet to mature after 9^th molt, the difference in growth between two sexes could be dismissed (Holdich, 2002). Thereby sex was not put into our model for analysis as a factor. In addition, the tank effect was found nonsignificant.

3.2 Conditional variance components at a molt conditional on the prior one molt

The conditional variance components (additive, dominance, and genotype × environment) for body weight are given in Table 1, where the genetic effects were conditional on the gene expression of the traits at a prior molt. The new genetic effects at a molt conditional on the causal genetic effects at the prior molt were independent of the causal genetic effects during the intermolt. Thus, body weight at second molt was conditional on body weight at first molt, body weight at third molt on body weight at second molt, and the like.

For body weight (Table 1), the conditional additive variance components were not detected at 2^nd molt. They were detected at 3^rd and 4^th molt, but not significant. Since 5^th molt, the conditional additive variance components became significant, and peaked at 9^th molt. This suggested that there had been new expression of additive effect genes from 5^th molt to 9^th molt, especially from 7^th molt to 9^th molt. Conditional dominance variances were found significant from 2^nd molt to 5^th molt, and then decreased to nearly zero at 9^th molt. Genotype × environment interaction variances, including additive × environment and dominance × environment, were decreased gradually to nearly zero at the final molt. This showed that different environments in two years (2019 and 2020) had significant influences on the expression of additive effect genes and on body weight.

For body length (Table 2), the additive conditional variances were not detected prior to 4^th molt. They were detected since 5^th molt, and peaked at the final molt (9^th molt), demonstrating that additive effect genes were significantly expressed at this interval, especially from 7^th molt to 9^th molt. Conditional dominance variances were found significant from 2^nd molt to 5^th molt, and then decreased to nearly zero at 9^th molt. Additive × environment and dominance × environment interaction variances were significant before 5^th molt, and then decreased gradually to nearly zero at the final molt. Considering that crayfish were very small in size, and were sensitive to environmental changes, resulting in significant G×E interaction. This showed that different environments in two years (2019 and 2020) had significant influences on the expression of additive effect genes and on body length.

For chela length (Table 3), the conditional additive variances were not detected at 2^nd and 3^rd molt. They were significant at 4^th and 5^th, and highly significant from 6^th to 9^th molt. The conditional additive variance components peaked at 9^th molt. This suggested that there have been new expression of additive effect genes from 4^th molt to 9^th molt, especially from 6^th molt to 9^th molt, showing that the expression of additive effect genes was turned on over this period. Conditional dominance variances were found significant from 2^nd to 4^th molt, decreased to nearly zero at 5^th molt, and then increased at 6^th and 8^th molt, showing a fluctuating pattern. Additive × environment interaction variance was significant at 4^th and 5^th molt, and nonsignificant at other molts. Dominance × environment interaction variance was detected from 2^nd to final molt, and not detected at 8^th and 9^th molt. This showed that the expression of additive effect genes affecting chela length varied with different environments.

For cephalothorax length (Table 4), the conditional additive variance components were not detected before 5^th molt. They occurred at 5^th and 6^th molt, and highly significant from 7^th to 9^th molt. The conditional additive variance components peaked at 9^th molt. This suggested that there had been new expression of additive effect genes from 5^th to 9^th molt, especially from 7^th to 9^th molt that gave rise to new additive genetic variability. Conditional dominance variances occurred at 2^nd and 3^rd molt, and then decreased to zero at 9^th molt. Additive × environment interaction variance occurred from 2^nd to 8^th molt, and were decreased to zero at the final molt; it peaked at 6^th molt. Dominance × environment interaction variance occurred at 2^nd, 3^rd, 5^th, 7^th, and 8^th molt; it peaked at 2^nd molt, significantly increased at 8^th molt (2^nd peak), and then decreased to zero at 9^th molt. This showed that the expression of additive genes for cephalothorax length was significantly influence by environmental effects.

3.3 Conditional variance components at 9^th molt conditional on prior molts

To compare the magnitude of genetic effects at different molts on the final molt (9^th molt), the conditional variance components, i.e., , for growth-related traits are presented in Figs. 2-5. Obviously, size of this conditional variance component would vary with the time span between two molts. In this sense, the conditional genetic variances at 9^th molt for growth-related traits would be the largest when conditional on 1^st molt. For body weight (Fig. 2), it could be clearly found that the various conditional variances at 9^th molt gradually decreased as the time span between a prior molt and the final molt was decreased. The conditional additive variance was numerically higher than other conditional nonadditive variances. From 5^th to 9^th molt, conditional additive variance decreased very slowly, but the other conditional non-additive variances decreased rapidly, nearly to zero at 9^th molt.

For the other morphological traits: body length, chela length, and cephalothorax length (Figs. 3-5), the values of conditional additive variance components were all higher than those of other conditional nonadditive variances. The change in the conditional additive variances for body length was very similar to that in cephalothorax length, and decreased very slowly from 4^th to 9^th molt. In contrast to the conditional additive variances for body length and cephalothorax length, the conditional additive variances for chela length were decreased sharply from 1^st to 3^rd molt, and then decreased very slowly from 4^th to 9^th molt. The conditional dominance variance for body length was analogous to that of cephalothorax length, albeit the rates of change being different. The conditional dominance variance for chela length was decreased slowly from 1^st to 4^th molt, but significantly increased at 5^th molt, and then again decreased slowly to 9^th molt. The conditional additive × environment interaction variances for chela length and cephalothorax length were similar, all decreased slowly from 1^st to 9^th molt. In contrast, the conditional additive × environment interaction variance for body length peaked at 1^st molt, decreased rapidly to 3^rd molt, again increased to its second peak at 5^th molt, and then decreased to 9^th molt. The conditional dominance × environment interaction variances for the three morphological traits were all decreased slowly from 1^st to 9^th molt.

4 DISCUSSION

Quantitative traits such as body weight consist of many different constituents morphogenetically, the growth patterns of which may vary considerably with distinct ontogenetic phases (Lynch and Walsh, 1998; Walsh and Lynch, 2018). For instance, in crayfish male chelae and female abdomens grow faster relative to other somatic parts (Lutz, 2001). As in many other decapods, growth of the abdomen in juvenile and male crayfish is nearly isometric throughout, but females display positive allometry prior to puberty and a pronounced increase in relative abdominal width at the puberty molt. This brings it to functional size (egg carrying) when needed (Holdich, 2002; Longshaw and Stebbing, 2016). In contrast, chelar growth is nearly isometric in juveniles and females, but in males, the level of allometry increases at the pre-puberty molt. There is a further marked increase in relative size of the chelae at the puberty molt. Allometric growth of the chelae continues after the puberty molt (Lutz and Wolters, 1999; Holdich, 2002; Longshaw and Stebbing, 2016). The result of the differential growth of males and females has commercial implications, in that male crayfish have more muscle (meat) in their chelae than females, whereas females have more tail meat in their abdomens than males.

The underlying governing agents for differential growth patterns over ontogeny can be molecularly demonstrated by the different temporal and spatial changes in expression of related genes (Walsh and Lynch, 2018). Due to quantitative differences are usually affected by gene differences at a multiplicity of loci, the individual genes cannot be discerned by their segregation and transmission (Lynch and Walsh, 1998; Lutz, 2001). However, as genome research has provided new techniques for constructing highdensity genetic linkage maps, major genes that affect a quantitative trait can be located on specific regions on chromosomes (Martyniuk et al., 2003; Gutierrez et al., 2012; Chiasson et al., 2013; Vasemägi et al., 2016; Kodama et al., 2018). For example, using a highdensity genetic linkage map, Wang et al. (2019c) located 1 major and 19 suggestive QTLs for 4 growth-related traits (body length, body height, head length, and body weight) in Hypophthalmichthys molitrix. The effects of QTLs in early growth stages (6 and 12 months post hatching) were significantly different from those of the QTLs detected in the middle and later growth stage (18 months post hatching). Effects of these QTLs explained 10.2%-19.5% of phenotypic variation. This indicates that the number of QTLs involved and size of QTL effects vary with ontogenetic stages in modulating the growth in this species. Similar results were also reported in Oncorhynchus mykiss (Martyniuk et al., 2003) and in S. salar (Gutierrez et al., 2012). In red swamp crayfish, since no genetic linkage map has been constructed, so growth-related QTLs cannot be mapped to date in this species. However, according to the temporal dynamics of conditional additive variance components at different molting points for the growth-related traits in our study (Tables 1-4 & Figs. 2-5), it can be speculated that there should be significant expressions of new related genes especially from 4^th molt to maturity, albeit the number and effect of the genes unknown.

For body weight, there is a consistent increasing pattern for the conditional additive genetic variance from 2^nd molt to 9^th molt. The conditional additive genetic variability is slightly increased from 2^nd molt to 4^th molt, but precipitously increased from 4^th molt and reached its maximum (0.373) at 9^th molt (Table 1). For example, the conditional additive variance from 4^th molt to 9^th molt accounted for 97.57% of total conditional additive variability from 2^nd molt to 9^th molt, and 38.45% of phenotypic variability from 2^nd molt to 9^th molt. Thus, the conditional genetic variance from 2^nd molt to 9^th molt was almost completely explained by the conditional additive genetic variance from 4^th molt to 9^th molt. Between 2^nd and 4^th molt there was new conditional additive genetic variance that accounted for ca. 0.81% of phenotypic variability. On the other hand, it can be clearly seen in Table 1 that the conditional additive variance was slowly decreased from 4^th molt to 8^th molt when conditional on 9^th molt. For example, the conditional additive variance was decreased by only 8.24% from 4^th molt to 8^th molt when conditional on 9^th molt. These show that the newly produced additive genetic variability after 4^th molt may probably be the result of high expression of genes influencing body weight. In P. clarkii, intermolts at later ontogenetic stage are typically much longer than those in early stage (Holdich, 2002; Longshaw and Stebbing, 2016), accordingly the additive genetic variability is more accumulated in later growth stage. The changes in additive genetic variability for body weight depend upon species. For example, decreasing trend for the additive genetic variation for body weight was documented by Atchley and Zhu (1997) in mice (Mus musculus albus). Wang et al. (2006) detected the additive genetic variation only at two time points over ontogeny in Cyprinus carpio, whereas Wang et al. (2015) reported that the additive genetic variation changed over time in a nonlinear way in Scophthalmus maximus. Compared with these studies, the additive genetic variation for body weight in our study was different. Species should be responsible for this difference.

In contrast, the patterns of conditional additive genetic variances of three morphological traits (body length, chela length, and cephalothorax length) were analogous to that of body weight in this study. When conditional on the variation at the prior one molt, there is still considerable new variability being introduced (Tables 2-4). For example, the conditional additive variance was increased from 0.05 at 4^th molt to 0.311 at 9^th molt for chela length, with the conditional additive variance accounting for 99.9% of total conditional additive variance from 2^nd molt to 9^th molt, and 30.22% of phenotypic variability from 2^nd to 9^th molt. When conditional on 9^th molt, from 4^th molt to 8^th mold there was a significant introduction of up to 49.02%-57.93% new additive genetic variability for the three length traits not explained by the previous intervals (Figs. 3-5). The age-dependent changes in additive genetic variability for tail length were found to be gradually decreased in mice (Atchley and Zhu, 1997), but were irregular for length traits in C. carpio (Wang et al., 2006) and S. maximus (Wang et al., 2015).

It should be pointed out that the conditional additive variances for 4 growth-related traits were higher than those conditional non-additive variances from 1^st to 9^th molt in red swamp crayfish (Figs. 2-5). During our experiment, several important factors such as temperature and food were held at suitable levels, this might provide better environmental conditions for the sufficient expression of additive genes affecting the growth-related traits. On the other hand, our experiment is carried out under controlled conditions; environmental influences are small in principle. Thus, G×E is relatively smaller.

In our study, the dominance effects were eliminated from phenotypic variability for growth-related traits. According to Lynch and Walsh (1998), Lutz (2001), this is very necessary in evaluating genetic variability of a population. Without dominance effect separated out, the additive genetic variability would be upwardly estimated (Walsh and Lynch, 2018). Wang et al. (2006) and Wang et al. (2015) also partitioned dominance effects out from phenotypic variability of growth-related traits. In the present study, the temporal changes in dominance effects for growth-related traits were decreased consistently (Tables 1-4 & Figs. 2-5). This is similar to the report of Atchley and Zhu (1997), but not to the reports of Wang et al. (2006) and Wang et al. (2015), who did not document a regular pattern of dominance effects for growth-related traits. Due to increased additive genetic variability for growth-related traits during later ontogenetic stage, the dynamic changes in gene expression led to decreased dominance variation (Zhu, 1996). It should be mentioned that maternal effect and epistatic effect, if any, were not partitioned out, i.e., maternal effect and epistatic effect may be confounded into the genetic effects for the growth-related traits in our study.

Since all metabolic and developmental pathways are affected to some extent by aspects of the environment, it makes sense that the expression of most quantitative traits is not solely under genetic control (Lynch and Walsh, 1998; Lutz, 2001). For example, Vasemägi et al. (2016) reported 3 QTLs affecting growth-related traits (fork length and body mass) in the hatchery environment were not detected in the wild, and 2 QTLs observed in the natural environment were not detected in the hatchery environment, thus concluded that growth-related QTLs were environment-specific in S. salar. Genotype by environment interactions, mainly including additive by environment interaction and dominance by environment interaction, should be examined as an important component of phenotypic value of a quantitative trait upon undertaking genetic assessment (Walsh and Lynch, 2018). In our study, the genotype by environment interactions were removed from phenotypic variability, thereby the longitudinal changes in the additive genetic effects for growth-related traits were more explicit. In the studies of Atchley and Zhu (1997) in mice, Wang et al. (2006) in C. carpio, and Wang et al. (2015) in S. maximus, due to environmental effect not checked, thus agedependent genotype by environment interactions were confounded into the genetic effects for growth-related traits. In addition, Kodama et al. (2018) concluded that the interaction between QTLs affecting growth-related traits and sex occurred in Oncorhynchus kisutch. In our study, the red swamp crayfish used were still not mature at 9^th molt, so the effect of sex could be ignored.

5 CONCLUSION

Since the conditional variance components were obtained subject to variability at earlier molts, significant episodes in the new generation of gene expression at specific intermolts during ontogeny were clearly exhibited. The changes in conditional additive variance components manifest the new genetic effects of gene expression over a specific developmental stage. With the conditional nonadditive genetic variations removed from phenotypic variability, the conditional additive variations were increased significantly for the growth-related traits. The cumulative conditional additive variation from 4^th molt to 9^th molt (maturity) predominated, showing that this ontogenetic period was most important for the growth of this species. Results of this study afford useful knowledge about improving the culture management of this species.

6 DATA AVAILABILITY STATEMENT

The experimental data obtained and used during the present study can be provided by the corresponding author at the request of any interested readers.