Global asymptotic stability and the ideal free distribution in a starvation driven diffusion

We study a logistic model with a nonlinear random diffusion in a Fokker-Planck type law, but not in Fick’s law. In the model individuals are assumed to increase their motility if they starve. Any directional information to resource is not assumed in this starvation driven diffusion and individuals disperse in a random walk style strategy. However, the non-uniformity in the motility produces an advection toward surplus resource. Several basic properties of the model are obtained including the global asymptotic stability and the acquisition of the ideal free distribution.     

Evolution of dispersal in a multi‐trophic community context

Much is known about the evolution of dispersal when species interact with their resources or natural enemies, but very little is known about dispersal evolution when species interact with both resources and natural enemies. Here I investigate how the dispersal of an intermediate consumer evolves in response to its interactions with a basal resource and top predator. I find that dispersal evolution is possible even when the consumer species is not directly affected by environmental variability, but rather experiences the consequences that such variability has on its resource and predator. Spatial variation in the consumer's fitness is driven by spatial heterogeneity in resource productivity, which determines whether a predator can colonize a resource‐consumer community. Temporal variation in the consumer's fitness is driven by random disturbances that cause periodic local extinctions of the predator, followed by recolonizations that lead to transient fluctuations in consumer abundance. When spatial variation in resource productivity is low and the predator can colonize all patches in the landscape, there is no spatial variation in consumer fitness but temporal variation in fitness favors the evolution of a dispersal monomorphism. When spatial variation in resource productivity is high and the predator cannot colonize many patches in the landscape, spatial variation in fitness selects against dispersal. In this case, temporal variation can promote the evolution of a dispersal polymorphism with sedentary and mobile phenotypes, but only for certain types of tri‐trophic interactions. This finding underscores the importance of indirect interactions in shaping the evolution of dispersal. While the ecological community can provide a strong selective environment for the evolution of dispersal, the nature of interactions between trophic levels can also impose constraints on evolution.     

Starvation Driven Diffusion as a Survival Strategy of Biological Organisms

The purpose of this article is to introduce a diffusion model for biological organisms that increase their motility when food or other resource is insufficient. It is shown in this paper that Fick’s diffusion law does not explain such a starvation driven diffusion correctly. The diffusion model for nonuniform Brownian motion in Kim (Einstein’s random walk and thermal diffusion, preprint http://amath.kaist.ac.kr/papers/Kim/31.pdf, 2013) is employed in this paper and a Fokker–Planck type diffusion law is obtained. Lotka–Volterra type competition systems with spatial heterogeneity are tested, where one species follows the starvation driven diffusion and the other follows the linear diffusion. In heterogeneous environments, the starvation driven diffusion turns out to be a better survival strategy than the linear one. Various issues such as the global asymptotic stability, convergence to an ideal free distribution, the extinction and coexistence of competing species are discussed.     

On evolutionary stability of carrying capacity driven dispersal in competition with regularly diffusing populations

Two competing populations in spatially heterogeneous but temporarily constant environment are investigated: one is subject to regular movements to lower density areas (random diffusion) while the dispersal of the other is in the direction of the highest per capita available resources (carrying capacity driven diffusion). The growth of both species is subject to the same general growth law which involves Gilpin–Ayala, Gompertz and some other equations as particular cases. The growth rate, carrying capacity and dispersal rate are the same for both population types, the only difference is the dispersal strategy. The main result of the paper is that the two species cannot coexist (unless the environment is spatially homogeneous), and the carrying capacity driven diffusion strategy is evolutionarily stable in the sense that the species adopting this strategy cannot be invaded by randomly diffusing population. Moreover, once the invasive species inhabits some open nonempty domain, it would spread over any available area bringing the native species diffusing randomly to extinction. One of the important technical results used in the proofs can be interpreted in the form that the limit solution of the equation with a regular diffusion leads to lower total population fitness than the ideal free distribution.     

Gains of Bacterial Flagellar Motility in a Fungal World

The maintenance of energetically costly flagella by bacteria in non-water-saturated media, such as soil, still presents an evolutionary conundrum. Potential explanations have focused on rare flooding events allowing dispersal. Such scenarios, however, overlook bacterial dispersal along mycelia as a possible transport mechanism in soils. The hypothesis tested in this study is that dispersal along fungal hyphae may lead to an increase in the fitness of flagellated bacteria and thus offer an alternative explanation for the maintenance of flagella even in unsaturated soils. Dispersal along fungal hyphae was shown for a diverse array of motile bacteria. To measure the fitness effect of dispersal, additional experiments were conducted in a model system mimicking limited dispersal, using Pseudomonas putida KT2440 and its nonflagellated (ΔfliM) isogenic mutant in the absence or presence of Morchella crassipes mycelia. In the absence of the fungus, flagellar motility was beneficial solely under conditions of water saturation allowing dispersal, while under conditions limiting dispersal, the nonflagellated mutant exhibited a higher level of fitness than the wild-type strain. In contrast, in the presence of a mycelial network under conditions limiting dispersal, the flagellated strain was able to disperse using the mycelial network and had a higher level of fitness than the mutant. On the basis of these results, we propose that the benefit of mycelium-associated dispersal helps explain the persistence of flagellar motility in non-water-saturated environments.     

Prospecting and informed dispersal: Understanding and predicting their joint eco‐evolutionary dynamics

The ability of individuals to leave a current breeding area and select a future one is important, because such decisions can have multiple consequences for individual fitness, but also for metapopulation dynamics, structure, and long‐term persistence through non‐random dispersal patterns. In the wild, many colonial and territorial animal species display informed dispersal strategies, where individuals use information, such as conspecific breeding success gathered during prospecting, to decide whether and where to disperse. Understanding informed dispersal strategies is essential for relating individual behavior to subsequent movements and then determining how emigration and settlement decisions affect individual fitness and demography. Although numerous theoretical studies have explored the eco‐evolutionary dynamics of dispersal, very few have integrated prospecting and public information use in both emigration and settlement phases. Here, we develop an individual‐based model that fills this gap and use it to explore the eco‐evolutionary dynamics of informed dispersal. In a first experiment, in which only prospecting evolves, we demonstrate that selection always favors informed dispersal based on a low number of prospected patches relative to random dispersal or fully informed dispersal, except when individuals fail to discriminate better patches from worse ones. In a second experiment, which allows the concomitant evolution of both emigration probability and prospecting, we show the same prospecting strategy evolving. However, a plastic emigration strategy evolves, where individuals that breed successfully are always philopatric, while failed breeders are more likely to emigrate, especially when conspecific breeding success is low. Embedding information use and prospecting behavior in eco‐evolutionary models will provide new fundamental understanding of informed dispersal and its consequences for spatial population dynamics.     

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.     

The new kid on the block: immigrant males win big whereas females pay fitness cost after dispersal

Dispersal is nearly universal; yet, which sex tends to disperse more and their success thereafter depends on the fitness consequences of dispersal. We asked if lifetime fitness differed between residents and immigrants (successful between‐population dispersers) and their offspring using 29 years of monitoring from North American red squirrels (Tamiasciurus hudsonicus) in Canada. Compared to residents, immigrant females had 23% lower lifetime breeding success (LBS), while immigrant males had 29% higher LBS. Male immigration and female residency were favoured. Offspring born to immigrants had 15–43% lower LBS than offspring born to residents. We conclude that immigration benefitted males, but not females, which appeared to be making the best of a bad lot. Our results are in line with male‐biased dispersal being driven by local mate competition and local resource enhancement, while the intergenerational cost to immigration is a new complication in explaining the drivers of sex‐biased dispersal.     

Artificial selection for increased dispersal results in lower fitness

Dispersal often covaries with other traits, and this covariation was shown to have a genetic basis. Here, we wanted to explore to what extent genetic constraints and correlational selection can explain patterns of covariation between dispersal and key life‐history traits—lifespan and reproduction. A prediction from the fitness‐associated dispersal hypothesis was that lower genetic quality is associated with higher dispersal propensity as driven by the benefits of genetic mixing. We wanted to contrast it with a prediction from a different model that individuals putting more emphasis on current rather than future reproduction disperse more, as they are expected to be more risk‐prone and exploratory. However, if dispersal has inherent costs, this will also result in a negative genetic correlation between higher rates of dispersal and some aspects of performance. To explore this issue, we used the dioecious nematode Caenorhabditis remanei and selected for increased and decreased dispersal propensity for 10 generations, followed by five generations of relaxed selection. Dispersal propensity responded to selection, and females from high‐dispersal lines dispersed more than females from low‐dispersal lines. Females selected for increased dispersal propensity produced fewer offspring and were more likely to die from matricide, which is associated with a low physiological condition in Caenorhabditis nematodes. There was no evidence for differences in age‐specific reproductive effort between high‐ and low‐dispersal females. Rather, reproductive output of high‐dispersal females was consistently reduced. We argue that our data provide support for the fitness‐associated dispersal hypothesis.     

Transgenerational Effects of Early Life Starvation on Growth,Reproduction, and Stress Resistance in Caenorhabditis elegans

Starvation during early development can have lasting effects that influence organismal fitness and disease risk. We characterized the long-term phenotypic consequences of starvation during early larval development in Caenorhabditis elegans to determine potential fitness effects and develop it as a model for mechanistic studies. We varied the amount of time that larvae were developmentally arrested by starvation after hatching (“L1 arrest”). Worms recovering from extended starvation grew slowly, taking longer to become reproductive, and were smaller as adults. Fecundity was also reduced, with the smallest individuals most severely affected. Feeding behavior was impaired, possibly contributing to deficits in growth and reproduction. Previously starved larvae were more sensitive to subsequent starvation, suggesting decreased fitness even in poor conditions. We discovered that smaller larvae are more resistant to heat, but this correlation does not require passage through L1 arrest. The progeny of starved animals were also adversely affected: Embryo quality was diminished, incidence of males was increased, progeny were smaller, and their brood size was reduced. However, the progeny and grandprogeny of starved larvae were more resistant to starvation. In addition, the progeny, grandprogeny, and great-grandprogeny were more resistant to heat, suggesting epigenetic inheritance of acquired resistance to starvation and heat. Notably, such resistance was inherited exclusively from individuals most severely affected by starvation in the first generation, suggesting an evolutionary bet-hedging strategy. In summary, our results demonstrate that starvation affects a variety of life-history traits in the exposed animals and their descendants, some presumably reflecting fitness costs but others potentially adaptive.     

Evolutionarily Stable and Convergent Stable Strategies in Reaction–Diffusion Models for Conditional Dispersal

We consider a mathematical model of two competing species for the evolution of conditional dispersal in a spatially varying, but temporally constant environment. Two species are different only in their dispersal strategies, which are a combination of random dispersal and biased movement upward along the resource gradient. In the absence of biased movement or advection, Hastings showed that the mutant can invade when rare if and only if it has smaller random dispersal rate than the resident. When there is a small amount of biased movement or advection, we show that there is a positive random dispersal rate that is both locally evolutionarily stable and convergent stable. Our analysis of the model suggests that a balanced combination of random and biased movement might be a better habitat selection strategy for populations.     

Can natural selection maintain long-distance dispersal? Insight from a stream salamander system

Dispersal distributions are often characterized by many individuals that stay close to their origin and large variation in the distances moved by those that leave. This variation in dispersal distance can strongly influence demographic, ecological, and evolutionary processes. However, a lack of data on the fitness and phenotype of individual dispersers has impeded research on the role of natural selection in maintaining variation in dispersal distance. Six years of spatially explicit capture-mark-recapture data showed that survival increased with dispersal distance in the stream salamander Gyrinophilus porphyriticus. To understand the evolutionary implications of this fitness response, we tested whether variation in dispersal distance has a phenotypic basis. We used photographs of marked individuals to measure head, trunk, and leg morphology. We then tested whether dispersal distances over the six-year study period were predicted by these traits. Dispersal distance was significantly related to leg morphology: individuals with relatively long forelimbs and short hindlimbs dispersed the farthest. These results support the hypothesis that positive fitness consequences maintain phenotypes enabling long-distance dispersal. More broadly, they suggest that natural selection can promote variation in dispersal distance and associated phenotypes, offering an alternative to the view that dispersal distance is driven by stochastic or landscape-specific mechanisms.     

No evidence for divergence in male harmfulness or female resistance in response to changes in the opportunity for dispersal

The outcome of sexual conflict can depend on the social environment, as males respond to changes in the inclusive fitness payoffs of harmfulness and harm females less when they compete with familiar relatives. Theoretical models also predict that if limited male dispersal predictably enhances local relatedness while maintaining global competition, kin selection can produce evolutionary divergences in male harmfulness among populations. Experimental tests of these predictions, however, are rare. We assessed rates of dispersal in female and male seed beetles Callosobruchus maculatus, a model species for studies of sexual conflict, in an experimental setting. Females dispersed significantly more often than males, but dispersing males travelled just as far as dispersing females. Next, we used experimental evolution to test whether limiting dispersal allowed the action of kin selection to affect divergence in male harmfulness and female resistance. Populations of C. maculatus were evolved for 20 and 25 generations under one of three dispersal regimens: completely free dispersal, limited dispersal and no dispersal. There was no divergence among treatments in female reproductive tract scarring, ejaculate size, mating behaviour, fitness of experimental females mated to stock males or fitness of stock females mated to experimental males. We suggest that this is likely due to insufficient strength of kin selection rather than a lack of genetic variation or time for selection. Limited dispersal alone is therefore not sufficient for kin selection to reduce male harmfulness in this species, consistent with general predictions that limited dispersal will only allow kin selection if local relatedness is independent of the intensity of competition among kin.     

Evolutionary Convergence to Ideal Free Dispersal Strategies and Coexistence

We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For nonmonotone resource functions, our findings suggest that there may exist some dispersal strategies which are not ideal free, but could be locally evolutionarily stable and/or convergent stable, and allow for the coexistence of more than one species.     

Spatial dynamics of communities with intraguild predation: the role of dispersal strategies

I investigate the influence of dispersal strategies on intraguild prey and predators (competing species that prey on each other). I find an asymmetry between the intraguild prey and predator in their responses to each other's dispersal. The intraguild predator's dispersal strategy and dispersal behavior have strong effects on the intraguild prey's abundance pattern, but the intraguild prey's dispersal strategy and behavior have little or no effect on the intraguild predator's abundance pattern. This asymmetry arises from the different constraints faced by the two species: the intraguild prey has to acquire resources while avoiding predation, but the intraguild predator only has to acquire resources. It leads to puzzling distribution patterns: when the intraguild prey and predator both move away from areas of high density, they become aggregated to high-density habitats, but when they both move toward areas of high resource productivity, they become segregated to resource-poor and resource-rich habitats. Aggregation is more likely when dispersal is random or less optimal, and segregation is more likely as dispersal becomes more optimal. The crucial implication is that trophic constraints dictate the fitness benefits of using dispersal strategies to sample environmental heterogeneity. A strategy that affords greater benefits to an intraguild predator can lead to a more optimal outcome for both the intraguild predator and prey than a strategy that affords greater benefits to an intraguild prey.     

Effects of dispersal plasticity on population divergence and speciation

Phenotypic plasticity is thought to have a role in driving population establishment, local adaptation and speciation. However, dispersal plasticity has been underappreciated in this literature. Plasticity in the decision to disperse is taxonomically widespread and I provide examples for insects, molluscs, polychaetes, vertebrates and flowering plants. Theoretical work is limited but indicates an interaction between dispersal distance and plasticity in the decision to disperse. When dispersal is confined to adjacent patches, dispersal plasticity may enhance local adaptation over unconditional (non-plastic) dispersal. However, when dispersal distances are greater, plasticity in dispersal decisions strongly reduces the potential for local adaptation and population divergence. Upon dispersal, settlement may be random, biased but genetically determined, or biased but plastically determined. Theory shows that biased settlement of either type increases population divergence over random settlement. One model suggests that plasticity further enhances chances of speciation. However, there are many strategies for deciding on where to settle such as a best-of-N strategy, sequential sampling with a threshold for acceptance or matching with natal habitat. To date, these strategies do not seem to have been compared within a single model. Although we are just beginning to explore evolutionary effects of dispersal plasticity, it clearly has the potential to enhance as well as inhibit population divergence. Additional work should pay particular attention to dispersal distance and the strategy used to decide on where to settle.     

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.     

Biased dispersal of Metrioptera bicolor,a wing dimorphic bush‐cricket

In the highly fragmented landscape of central Europe, dispersal is of particular importance as it determines the long‐term survival of animal populations. Dispersal not only secures the recolonization of patches where populations went extinct, it may also rescue small populations and thus prevent local extinction events. As dispersal involves different individual fitness costs, the decision to disperse should not be random but context‐dependent and often will be biased toward a certain group of individuals (e.g., sex‐ and wing morph‐biased dispersal). Although biased dispersal has far‐reaching consequences for animal populations, immediate studies of sex‐ and wing morph‐biased dispersal in orthopterans are very rare. Here, we used a combined approach of morphological and genetic analyses to investigate biased dispersal of Metrioptera bicolor, a wing dimorphic bush‐cricket. Our results clearly show wing morph‐biased dispersal for both sexes of M. bicolor. In addition, we found sex‐biased dispersal for macropterous individuals, but not for micropters. Both, morphological and genetic data, favor macropterous males as dispersal unit of this bush‐cricket species. To get an idea of the flight ability of M. bicolor, we compared our morphological data with that of Locusta migratoria and Schistocerca gregaria, which are very good flyers. Based on our morphological data, we suggest a good flight ability for macropters of M. bicolor, although flying individuals of this species are seldom observed.     

A comparison of sexual and asexual replication strategies in a simplified model based on the yeast life cycle

This paper develops simplified mathematical models describing the mutation-selection balance for the asexual and sexual replication pathways in Saccharomyces cerevisiae, or Baker’s yeast. The simplified models are based on the single-fitness-peak approximation in quasispecies theory. We assume diploid genomes consisting of two chromosomes, and we assume that each chromosome is functional if and only if its base sequence is identical to some master sequence. The growth and replication of the yeast cells is modeled as a first-order process, with first-order growth rate constants that are determined by whether a given genome consists of zero, one, or two functional chromosomes. In the asexual pathway, we assume that a given diploid cell divides into two diploids. For the sake of generality, our model allows for mitotic recombination and asymmetric chromosome segregation. In the sexual pathway, we assume that a given diploid cell divides into two diploids, each of which then divide into two haploids. The resulting four haploids enter a haploid pool, where they grow and replicate until they meet another haploid with which to fuse. In the sexual pathway, we consider two mating strategies: (1) a selective strategy, where only haploids with functional chromosomes can fuse with one another; (2) a random strategy, where haploids randomly fuse with one another. When the cost for sex is low, we find that the selective mating strategy leads to the highest mean fitness of the population, when compared to all of the other strategies. When the cost for sex is low, sexual replication with random mating also has a higher mean fitness than asexual replication without mitotic recombination or asymmetric chromosome segregation. We also show that, at low replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. If the fitness penalty for having a defective chromosome is sufficiently high and the cost for sex sufficiently low, then at low replication fidelities the random mating strategy has a mean fitness that is a factor of larger than the asexual mean fitness. We argue that for yeast, the selective mating strategy is the one that is closer to reality, which if true suggests that sex may provide a selective advantage under considerably more relaxed conditions than previous research has indicated. The results of this paper also suggest that S. cerevisiae switches from asexual to sexual replication when stressed, because stressful growth conditions provide an opportunity for the yeast to clear out deleterious mutations from their genomes. That being said, our model does not contradict theories for the evolution of sex that argue that sex evolved because it allows a population to more easily adapt to changing conditions.     

Scale of dispersal in varying environments and its implications for life histories of marine invertebrates

Summary We present several models concerning the short term consequences of spreading offspring in varying environments. Our goal is to determine what patterns of spatial and temporal variation yield an advantage to increasing scale of dispersal. Of necessity, the models are somewhat artificial but we feel they are a reasonable approximation of and hence generalizable to natural systems. With these models we examine consequences of dispersal arising from environmental variation: increased environmental variance, different degrees of spatial and temporal correlation, some arbitrary spatial patterns of favorability and finally some patterns derived from long-term, large-scale weather data collected along a contiguous stretch of coastline from southern Oregon to northern Washington (USA). We examine the costs and benefits of increasing sclae of dispersal in both density dependent and density independent models.Several conclusions may be drawn from the results of these models. In the absence of any spatial or temporal order to favorability (where favorability is directly proportional to either fitness or carrying capacity) increasing scale of spread produces a higher tate of population increase. At larger scales, though, an asymptote of maximum relative advantage is approached, so each added increment of spread has a smaller contribution to fitness. This asymptote is higher and the approach to it relatively slower with increasing environmental variance. For a given environmental variance, increasing spatial correlation results in a slower approach to the same asymptote. In density independent models, increasing temporal correlation of fitness selects against increased dispersal if expected differences between sites are sufficiently great relative to variation within sites; but in this instance, density dependence yields a somewhat different result: dispersers have a refuge at sites of low carrying capacity or sites lacking non-dispersers. Finally, optimum intermediate scales of dispersal can occur where differences in expected fitness increase with increasing distance from the parental site, such as in a gradient, but where the environmental variation at a given site is fairly large relative to differences in expected fitness between adjacent sites.The foregoing results are extended for the following predictions. When greater longevity in a resistant phase of the life cycle reduces temporal variation in survival and fecundity, increased generation time should decrease the benefits of spreading offspring in an environment that would otherwise favor spread and could either increase or decrease the costs of spreading offspring in an environment selecting against spread. We speculate that if large scale patterns of varying survival and fecundity are similar to the variation in the physical environment which we examined with weather data, there should be little or no short term advantage to large scale spread of offspring (on the order of 50 kilometers or more) because expected differences increase and seldom if ever decrease with increasing distance between sites.This suggests that feeding larvae of benthic invertebrates with their concomitant long planktonic period, receive little if any advantage from increased scale of dispersal, and consequently that the advantages to planktotrophy over lecithotrophy must lie in other life history aspects, such as the ability to produce a greater number of smaller eggs.Order of authorship alphabetical and by increasing age and height