How to compare geometric mean fitness
This study is a rare case comparing geometric mean fitness in empirical studies to test the bet-hedging polyandry hypothesis (but see Fox and Rauter 2003; Garcia-Gonzalez et al. 2015; Matsumura et al. 2021). Fox and Rauter (2003) did a pioneer study of this issue, however, their calculations of geometric mean fitness are not entirely correct in our view because their method tends to produce higher geometric mean in polyandry than monandry (see Appendix 1). We have established the correct method to evaluate geometric mean fitness in this paper.
Bet-hedging in the field crickets
This study shows that 3 different types of bet-hedging worked in the crickets as follows: (1) the bet-hedging polyandry to avoid male-caused reproductive failures, (2) metapopulation bet-hedging to spread the extinction risks over multiple habitats and (3) reproduction itself as bet-hedging.
Polyandry as bet-hedging
Compared to monandry, mating with 3 or more males reduced the occurrence of total reproductive failures (Table 3c) and achieved higher geometric mean fitness over multiple blocks (Fig. 4). This means that polyandry works as bet-hedging to reduce extinction risk of the female “genotype” over multiple “generations” (Yasui 2001; Yasui and Garcia-Gonzalez 2016; Yasui and Yoshimura 2018) although to separate the effects of bet-hedging (stochastic process) from that of sexual selection (deterministic process) is difficult (we discuss this issue later). The trade-off between the mean and variance of fitness, a definition of bet-hedging (Slatkin 1974; Gillespie 1977; Philippi and Seger 1989) was not detected because the polyandrous treatments showed higher arithmetic mean fitness than monandry in some blocks (Fig. 3). The rationale of this definition is that the bet-hedging traits (e.g., seed dormancy; Cohen 1966) suppressing intergenerational fitness fluctuation, which necessarily increases between-generation geometric mean fitness (GMF; the long-term persistence), should be costly in the term of within-generation arithmetic mean fitness (AMF; moment rate of increase). Consequently, the trade-off (negative correlation) appears between AMF and GMF via AMF variance across generations. This is, traditionally, a prerequisite to invoke bet-hedging strategies. However, this requirement needs further theoretical testing. Such theoretical investigations are not the scope of the current study, but, in short, the negative correlation between AMF and GMF should be genetic but would not be necessarily realized at the phenotype level because an individual of bet-hedger genotype with good conditions would be superior to that of non-bet-hedger genotype with bad condition in single generation. Moreover, even if the AMF of monandry is greater than that of polyandry as expected from the trade-off assumption, it can be also explained by the fitness cost of remating (cost associated with sexual selection). Therefore, we hold that the trade-off is not a necessary condition to confirm bet-hedging in empirical studies.
We focused the accidental mating failures and male infertility at the phenotype level. The compensation of mating failure by multiple mating might have occurred in the following cases: 5–2, 6–3, 7–3, 5–3, 7–1, 7–4 and 5–1 (see Table 2). In these cases, offspring of only one morph (black eye or white eye) were born. If such absence of paternity share of a part of the mates was caused by his (their) mating failure (especially early spermatophore separation), it follows that it was compensated by the existence of other partner(s).
Polyandry corresponds to “within-generation bet-hedging” (Hopper 1999; Hopper et al. 2003) and its efficiency depends on the female population size (Yasui 2001; Yasui and Garcia-Gonzalez 2016). If the sufficient number of monandrous females exist in a large panmictic population, the probability that all monandrous females unluckily encounter unsuitable males is low, and thus, the GMF of monandry is not inferior to that of polyandry (Yasui 2001; Yasui and Garcia-Gonzalez 2016). However, many organisms live in more or less structured population (Levin 1974; Hanski 1999; Marsh and Trenham 2001). In metapopulations that consists of small patches, polyandry is favored (Yasui and Garcia-Gonzalez 2016). Even in single large population containing many males, if the opportunity of mate choice for a single female may be limited to a few males, bet-hedging polyandry can work (Yasui and Garcia-Gonzalez 2016; Yasui and Yoshimura 2018). In this study, where each block can be taken as corresponding to a single small population, this theory is applicable.
The egg allocation to the 4 petri dishes with different conditions (temperature and salinity) can be interpreted not only as the unpredictable environmental changes after oviposition but also as the female strategy to migrate and distribute eggs to 4 different patches (i.e., metapopulation bet-hedging; Hopper 1999). In metapopulations, if some patches crashed completely by unpredictable catastrophe (e.g., pesticide spraying) but others were unaffected (i.e., spatial fine-grained environments), migration strategies can spread the risk of extinction. In fact, the 0-hatching rate in the block 2 salt water was compensated with the success of the eggs of the same genotype allocated to fresh water (Fig. 2). Thus, even monandrous females can tolerate the environmental fluctuation if they distribute offspring to multiple environments, suggesting metapopulation bet-hedging is more powerful than within-generation bet-hedging (Hopper 1999; Hopper et al. 2003).
Reproduction is bet-hedging
Moreover, the existence of multiple females of the same strategy (i.e., homologous individuals descended from single mutant) in the population offsets the fitness fluctuation among females. Thus, reproduction itself can be considered as bet-hedging to make spare individuals to offset fitness variance among mothers. There are no organisms lacking the intrinsic tendency to increase. Indeed, numbers are power.
The risk of small population when spare individual of the same strategy (genotype) is absent was also detected. Considering each block as a population in a discrete generation, block 5 contained only one monandrous female (5–4) and this female failed reproduction (0-hatching rate in all petri dishes), resulting in the extinction of the monandrous “genotype”. On the other hand, the fertilization failure of 7–5(M) was compensated by 7–2(M) within the same population. The blocks in this study can be also interpreted as the small population of endangered species. Yasui and Garcia-Gonzalez (2016) suggested that the bet-hedging polyandry can delay the extinction of demes. Therefore, the present study provides good verifications of various aspects of the bet-hedging theory.
What causes the reproductive failures
The standard way of polyandry study has adopting the repeated mating with the same male as “monandry” treatment (Tregenza and Wedell 1998; Simmons 2001; Garcia-Gonzalez and Simmons 2007). It surely adjusts the number of mating between polyandry and monandry. However, in natural environment, a female of solitary insect usually does not mate repeatedly with the same male. In such design, even if the male fails single copulation, he can be eventually successful via the repeated mating. In the bet-hedging theory, we should focus accidental mating failure which is unpredictable and thus unavoidable for females. If we use the repeated mating design as monandry, the mating failure risk in single mating would be underestimated. Although some studies (Rodríguez-Muñoz et al. 2010, 2011) have shown the congeneric field cricket Gryllus campestris females frequently mate repeatedly with the same male sharing the same burrow, as well as showing high degrees of polyandry, our study does not focus cricket biology but the empirical test of the hypothesis using the cricket as the model system. If mating failure in a single mating can be compensated with repeated mating, such cohabitation behavior as like as pair-bonding in birds and mammals can be interpreted as bet-hedging against mating failure and temporal infertility. Therefore, the G. campestris example enhances the bet-hedging hypothesis.
This study shows that even in the laboratory conditions, which are more favorably controlled regarding, e.g., food supply than natural populations, reproductive failures frequently occurs. Out of 34 females investigated, one was unable to copulate due to physical disability (loss of hind legs) and another one mated with four males but did not lay eggs. Out of 123 petri dishes obtained from the remaining 32 females, 31 dishes (3 out of which was under the “best”, 25 °C fresh water condition) recorded the 0-hatching rate. Because such reproductive failures are usually not reported in the literature as they are most of the times deemed inconvenient or non-informative for the purpose of particular studies conducted, their prevalence and evolutionary significance are greatly underestimated (García-González 2004; Greenway et al. 2015; Balfour et al. 2020). Considering the publication bias against negative data, analysis including negative data like as this study is necessary to test this hypothesis.
Among the various causes of reproductive failures (García-González 2004; Balfour et al. 2020), this study focused on the infertile mating (fertilization failure) and developing environments after fertilization. Causes of the infertile mating may come from female-side, male-side or their interaction (García-González 2004). Of course, if females are permanently infertile because of new mutations and some postnatal (nongenetic) disabilities such as loss of legs observed at female 3–1, and obstruction of oviducts etc. (Rhainds 2010), polyandry cannot rescue it. The male-side causes are genetic (e.g., deleterious mutations and genetic incompatibilities) or environmental (e.g., abnormal spermatophore attachment, spermatophore aplasia, empty spermatophore and early detachment of spermatophore) are possible (García-González 2004). Bet-hedging polyandry can cope with most of them.
When analyzing the early (from copulation to egg swelling) and late (from swelling to hatch) embryonic development separately, the compensation by multiple mating functioned especially in the early stage (Table 3). Hence, in this experiment, the bet-hedging polyandry mainly worked to offset mating failure but could not deal with the postfertilization environmental changes. To tolerate such environmental changes, genetic variance about e.g., temperature adaptability and salinity tolerance is needed in male genes (i.e., genotype-by-environment interaction within multiply-sired clutches; Yasui 1998). Because the small laboratory population of G. bimaculatus unlikely sustains the enough genetic variance, our results are reasonable. However, in natural populations maintaining genetic diversity, bet-hedging polyandry possibly works against unpredictable fluctuation of egg-hatching conditions.
A serious and very difficult-to-handle issue with the design of the study is that in the polyandry groups, females that failed to mate the designated number of times were discarded from the treatment of original plan. This means that in the higher-degree polyandry groups only those females willing to mate a set number of times were used, these are unlikely to be a random sample of the population and indeed it is easy to imagine they might be the healthier individuals. This will tend to create a bias in favor of the polyandry treatments. Unless using artificial insemination, it is impossible to coerce the unwilling female to mate. The future development of such technique is awaited.