Life-history consequences of investment in free-spawned eggs and their accessory coats

The optimal trade-off between offspring size and number can depend on details of the mode of reproduction or development. In marine organisms, broadcast spawning is widespread, and external coats are a common feature of spawned eggs. Egg jelly coats are thought to influence several aspects of fertilization and early development, including the size of the target for sperm, fertilization efficiency, egg suspension time, polyspermy, embryo survival, and fecundity. These costs and benefits of investment in jelly result in trade-offs that can influence optimal reproductive allocation and the evolution of egg size. I develop an optimization model that sequentially incorporates assumptions about the function of egg coats in fertilization. The model predicts large variation in coat size and limited variation in ovum size under a broad range of conditions. Heterogeneity among spawning events further limits the range of ovum sizes predicted to evolve under sperm limitation. In contrast, variation in larval mortality predicts a broad range of optimal ovum sizes that more closely reflects natural variation among broadcast-spawning invertebrates. By decoupling physical and energetic size, egg coats can enhance fertilization, maintain high fecundity, and buffer the evolution of ovum size from variation in spawning conditions.     

A diffusion‐based approach to stochastic individual growth and energy budget,with consequences to life‐history optimization and population dynamics

Using diffusion processes, I model stochastic individual growth, given exogenous hazards and starvation risk. By maximizing survival to final size, optimal life histories (e.g. switching size for habitat/dietary shift) are determined by two ratios: mean growth rate over growth variance (diffusion coefficient) and mortality rate over mean growth rate; all are size dependent. For example, switching size decreases with either ratio, if both are positive. I provide examples and compare with previous work on risk‐sensitive foraging and the energy–predation trade‐off. I then decompose individual size into reversibly and irreversibly growing components, e.g. reserves and structure. I provide a general expression for optimal structural growth, when reserves grow stochastically. I conclude that increased growth variance of reserves delays structural growth (raises threshold size for its commencement) but may eventually lead to larger structures. The effect depends on whether the structural trait is related to foraging or defence. Implications for population dynamics are discussed.     

Growth after maturity as a sub-optimal strategy

Patterns of optimal resource allocation to growth and reproduction were investigated using a numerical simulation. As in most previous analyses, cessation of growth when reproduction begins (the determinate strategy) appeared optimal. Here, it was additionally found that fitness was only slightly lower for individuals that continue to grow after maturation. Therefore, it is argued that selection for a determinate strategy may be too weak to overwhelm random processes like environmental stochasticity or genetic drift that shape patterns of growth, especially under low mortality. The consequences of an indeterminate strategy for optimal size at maturity and final size were investigated: prolonging the period in which growth and reproduction co-occurred decreased size at maturity only slightly but markedly increased the final size.     

Growth strategies and optimal body size in temperate pararginii butterflies

In temperate insects the evolution of growth strategies andthe optimal age and size at maturity will depend strongly onseasonal variation in temperature and other resources. However,compared to photoperiod, temperature itself is a relativelypoor predictor of seasonal change and timing decisions in insectsare often most strongly influenced by the photoperiod. HereI review the evolution of seasonal growth strategies in thebutterfly tribe Pararginii (Satyrinae: Nymphalidae) and relateit to life history theory. The results indicate that individuallarvae may adjust their growth trajectories in relation to informationon time horizons obtained from the photoperiod. The growth strategiescan be characterized by a set of state-dependent decision rulesthat specify how an individual should respond to its internalstate and external circumstances. These decision rules may alsoinfluence how individual growth change with a rise in temperature,showing that the standard expectation of increased growth rateswith increasing temperatures may not always be true. With lesstime available individual larvae increase growth rates and therebyachieve shorter development times, most often without any effectson final sizes. One reason for the apparent optimization ofgrowth rate seems to be that growing fast may incur costs thatlarvae developing under lower time limitations chose to avoid.The patterns of growth found in these and many other studiesare difficult to reconcile with common assumptions of what typicallydetermines optimal body size in insects. In particular it seemsas if there should be some costs of a large body size that,so far, have been poorly documented.     

r- and K-tactics in the evolution of protist developmental systems: cell and genome size, phenotype diversifying selection, and cell cycle patterns

I outline the significance for protist evolution of the r-, K-selection spectrum,, and of my earlier theory that the most fundamental way organisms adapt to this spectrum is by evolutionary variations in their cell volumes, cell growth rates and genome sizes. Then I introduce the concept of phenotype diversifying selection; this refers to those selective forces which favour an increase in the number of phenotypes produced during a single life cycle by an organism's genotype and epigenetic system. These ideas are then used to discuss the evolution of protist development, with special reference to modifications of the cell cycle whose evolutionary causes and consequences can be related to K-selection for large size and r-selection for rapid reproduction. The significance of multiple fission, syncytia, multicellularity, nuclear dimorphism plus polyploidy, and reversible polyploidy, is treated in detail. Predictions are made of the effects of these different developmental patterns on genome size and the distribution and amounts of nucleoskeletal RNA and heterochromatin. I suggest that heterochromatin exists primarily because of phenotype diversifying selection for differing nuclear volumes. The possibility of applying these ideas to other cell properties like mitotic or cytokinetic mechanisms is also briefly discussed.     

Evolutionary demography of iteroparous plants: incorporating non-lethal costs of reproduction into integral projection models

Understanding the selective forces that shape reproductive strategies is a central goal of evolutionary ecology. Selection on the timing of reproduction is well studied in semelparous organisms because the cost of reproduction (death) can be easily incorporated into demographic models. Iteroparous organisms also exhibit delayed reproduction and experience reproductive costs, although these are not necessarily lethal. How non-lethal costs shape iteroparous life histories remains unresolved. We analysed long-term demographic data for the iteroparous orchid Orchis purpurea from two habitat types (light and shade). In both the habitats, flowering plants had lower growth rates and this cost was greater for smaller plants. We detected an additional growth cost of fruit production in the light habitat. We incorporated these non-lethal costs into integral projection models to identify the flowering size that maximizes fitness. In both habitats, observed flowering sizes were well predicted by the models. We also estimated optimal parameters for size-dependent flowering effort, but found a strong mismatch with the observed flower production. Our study highlights the role of context-dependent non-lethal reproductive costs as selective forces in the evolution of iteroparous life histories, and provides a novel and broadly applicable approach to studying the evolutionary demography of iteroparous organisms.     

A test of the reproductive cost hypothesis for sexual size dimorphism in Yarrow's spiny lizard Sceloporus jarrovii

1. Trade-offs between reproduction and growth are central assumptions of life-history theory, but their implications for sexual size dimorphism (SSD) are poorly understood. 2. Adult male Yarrow's spiny lizards Sceloporus jarrovii average 10% larger than adult females. In a low-altitude (1700 m) population, this SSD develops because males grow more quickly than females during the first year of life, particularly during the first female reproductive season. This study tests the hypothesis that SSD develops because female growth is constrained by energetic costs of reproduction. 3. To test for a growth cost of reproduction, I compared growth rates of free-living females that differed, either naturally or experimentally, in reproductive status. Females that naturally delayed reproduction until their second year grew more quickly than females that reproduced as yearlings, and ovariectomized yearlings grew more quickly and to larger sizes than reproductive controls. 4. To determine whether SSD develops in the absence of this inferred reproductive cost, I also studied a high-altitude (2500 m) population in which all females delay reproduction until their second year. Sex differences in growth trajectories were similar to those observed at low altitude, such that males averaged 10% larger than females even prior to female reproduction. 5. Although female growth may be constrained by reproduction, multiple lines of evidence indicate that this cost is insufficient to explain the full magnitude of SSD in S. jarrovii. First, differences in growth of reproductive and nonreproductive females are not observed until the final month of gestation, by which time SSD is already well developed. Second, the growth benefit accruing from experimental inhibition of reproduction accounts for only 32% of the natural sex difference in body size. Finally, SSD develops well in advance of female reproduction in a high-altitude population with delayed maturation.     

Heuristic optimization of the general life history problem: A novel approach

Summary The general life history problem concerns the optimal allocation of resources to growth, survival and reproduction. We analysed this problem for a perennial model organism that decides once each year to switch from growth to reproduction. As a fitness measure we used the Malthusian parameterr, which we calculated from the Euler-Lotka equation. Trade-offs were incorporated by assuming that fecundity is size dependent, so that increased fecundity could only be gained by devoting more time to growth and less time to reproduction. To calculate numerically the optimalr for different growth dynamics and mortality regimes, we used a simplified version of the simulated annealing method. The major differences among optimal life histories resulted from different accumulation patterns of intrinsic mortalities resulting from reproductive costs. If these mortalities were accumulated throughout life, i.e. if they were senescent, a bangbang strategy was optimal, in which there was a single switch from growth to reproduction: after the age at maturity all resources were allocated to reproduction. If reproductive costs did not carry over from year to year, i.e. if they were not senescent, the optimal resource allocation resulted in a graded switch strategy and growth became indeterminate. Our numerical approach brings two major advantages for solving optimization problems in life history theory. First, its implementation is very simple, even for complex models that are analytically intractable. Such intractability emerged in our model when we introduced reproductive costs representing an intrinsic mortality. Second, it is not a backward algorithm. This means that lifespan does not have to be fixed at the begining of the computation. Instead, lifespan itself is a trait that can evolve. We suggest that heuristic algorithms are good tools for solving complex optimality problems in life history theory, in particular questions concerning the evolution of lifespan and senescence.     

Accessory costs of seed production and the evolution of angiosperms

Accessory costs of reproduction frequently equal or exceed direct investment in offspring, and can limit the evolution of small offspring sizes. Early angiosperms had minimum seed sizes, an order of magnitude smaller than their contemporaries. It has been proposed that changes to reproductive features at the base of the angiosperm clade reduced accessory costs thus removing the fitness disadvantage of small seeds. We measured accessory costs of reproduction in 25 extant gymnosperms and angiosperms, to test whether angiosperms can produce small seeds more economically than gymnosperms. Total accessory costs scaled isometrically to seed mass for angiosperms but less than isometrically for gymnosperms, so that smaller seeds were proportionally more expensive for gymnosperms to produce. In particular, costs of abortions and packaging structures were significantly higher in gymnosperms. Also, the relationship between seed:ovule ratio and seed size was negative in angiosperms but positive in gymnosperms. We argue that the carpel was a key evolutionary innovation reducing accessory costs in angiosperms by allowing sporophytic control of pre- and postzygotic mate selection and timing of resource allocation. The resulting reduction in costs of aborting unfertilized ovules or genetically inferior embryos would have lowered total reproductive costs enabling early angiosperms to evolve small seed sizes and short generation times.     

Strategic diel regulation of body mass in European robins

Stochastic dynamic programming (SDP) is a computational technique that has been used to model daily routines of foraging in small birds. A diurnal bird must build up its fat reserves towards dusk in order to avoid starvation during the night, when it cannot feed. However, as well as the benefits of avoiding starvation, storing fat imposes costs such as an increased predation risk and higher flight and metabolic costs. There is therefore an optimal level of fat reserves for a bird to reach at dusk in order to survive overnight without being left with excessive fat reserves at dawn. I tested a prediction common to all SDP models of daily foraging routines, that a bird will attempt to reach this level at dusk, regardless of its fat reserves the previous dawn. I provided supplementary food to manipulate the fat reserves at dawn of free-living European robins, Erithacus rubecula. Diurnal changes in body mass (a reliable estimate of fat reserves) were then monitored remotely. Robins provided with an ad libitum food supply reached almost exactly the same body mass at dusk, regardless of their body mass at dawn, supporting the prediction that birds attempt to reach a target level of reserves at dusk. Copyright 2000 The Association for the Study of Animal Behaviour.     

Estimation of the reproduction number of dengue fever from spatial epidemic data

Dengue, a vector-borne disease, thrives in tropical and subtropical regions worldwide. A retrospective analysis of the 2002 dengue epidemic in Colima located on the Mexican central Pacific coast is carried out. We estimate the reproduction number from spatial epidemic data at the level of municipalities using two different methods: (1) Using a standard dengue epidemic model and assuming pure exponential initial epidemic growth and (2) Fitting a more realistic epidemic model to the initial phase of the dengue epidemic curve. Using Method I, we estimate an overall mean reproduction number of 3.09 (95% CI: 2.34,3.84) as well as local reproduction numbers whose values range from 1.24 (1.15,1.33) to 4.22 (2.90,5.54). Using Method II, the overall mean reproduction number is estimated to be 2.0 (1.75,2.23) and local reproduction numbers ranging from 0.49 (0.0,1.0) to 3.30 (1.63,4.97). Method I systematically overestimates the reproduction number relative to the refined Method II, and hence it would overestimate the intensity of interventions required for containment. Moreover, optimal intervention with defined resources demands different levels of locally tailored mitigation. Local epidemic peaks occur between the 24th and 35th week of the year, and correlate positively with the final local epidemic sizes (rho=0.92, P-value<0.001). Moreover, final local epidemic sizes are found to be linearly related to the local population size (P-value<0.001). This observation supports a roughly constant number of female mosquitoes per person across urban and rural regions.     

Optimal patterns of growth and reproduction for perennial plants with persisting or not persisting vegetative parts

Summary Optimal allocation of energy to growth, reproduction and storage was considered for perennial plants differing in the proportion of vegetative structures persisting over winter and/or in the amount of resources which can be relocated to storage before abscission of some organs. It was found that for every mortality level there exists a critical proportion of persistent organs. Below this critical value it is optimal to grow without reproduction for the first years until a characteristic size is reached; afterwards, that size is maintained year after year and all extra resources are devoted to reproduction. Some storage is also necessary to maintain constant size. If the proportion of retained vegetative mass is above the critical value, the optimal strategy is gradual growth to an asymptotic size, with growth and reproduction occurring in several years following maturation. In this case real storage occurs only until maturation is reached, then storage is realized only by energy relocation from the vegetative body. Although the optimal solution changes abruptly qualitatively at a given proportion of resources saved from year to year, further growth of this proportion above the critical level brings about a greater difference between size reached at maturity and final size. The predictions of the model seem to follow the pattern of nature qualitatively.     

Cost of reproduction and allocation of food between parent and young in the swift (Apus apus)

We manipulated brood sizes to promote different levels of parentaleffort in the common swift (Apus apus). This provided a powerfulmethod for testing hypotheses regarding parental investmentdecisions concerning optimal allocation strategies between parentsand young. Data were analyzed on a visit-by-visit basis regardingchanges in parental and chick body mass, the mass of prey delivered,and the estimated mass of parental self-feeding. Our resultswere consistent with current theory in that food delivery increasedwith brood size, whereas the food received per chick, and hencemean chick body mass, decreased with brood size. Parental bodymass decreased with brood size and increasing parental effortbut recovered quickly during lower levels of chick feeding immediatelybefore fledging, suggesting some short-term cost of reproduction.Parents feeding at the highest level experienced criticallylow body mass and responded by a temporary cessation of chickfeeding. On any one foraging trip, total mass of prey captureddid not differ between brood sizes, but load mass deliveredto the young was negatively related to the amount of estimatedparental self-feeding. Allocation decisions of parents feedingthemselves and their young matched differential allocation theories,but estimated provisioning efficiency of parents at differentbody masses did not suggest any adaptive advantage from parentalmass loss.     

THE EVOLUTION OF REPRODUCTIVE EFFORT IN LIZARDS AND SNAKES

Life history theory suggests that the optimal evolved level of reproductive effort (RE) for an organism depends upon the degree to which additional current reproductive investment reduces future reproductive output. Future reproduction can be decreased in two ways, through (i) decreases in the organism's survival rate, and/or (ii) decreases in the organism's growth (and hence subsequent fecundity). The latter tradeoff–that is, the “potential fecundity cost”—should affect the evolution of RE only in species with relatively high survival rate, a relatively high rate of fecundity increase with body size, or a relatively high reproductive frequency per annum. Unless these conditions are met, the probable benefit in future fecundity obtained from decreasing present reproductive output is too low for natural selection to favor any reduction in RE below the maximum physiologically possible. Published data on survival rate, reproductive frequency and relative clutch mass (RCM) suggest that many lizard species fall well below the level at which natural selection can be expected to influence RE through such “potential fecundity” tradeoffs. Hence, the relative allocation of resources between growth and reproduction is unlikely to be directly optimized by natural selection in these animals. Instead, energy allocation should influence the evolution of RE only indirectly, via effects on an organism's probability of survival during reproduction. Survival costs of reproduction may be the most important evolutionary determinants of RE in many reptiles, and information on the nature and extent of such costs is needed before valid measures of reptilian RE can be constructed.     

A Dynamic Energy Budget model based on partitioning of net production

We formulate a Dynamic Energy Budget (DEB) model for the growth and reproduction of individual organisms based on partitioning of net production (i.e. energy acquisition rate minus maintenance rate) between growth and energy reserves. Reproduction uses energy from reserves. The model describes both feeding and non-feeding stages, and hence is applicable to embryos (which neither feed nor reproduce), juveniles (which feed but do not reproduce), and adults (which commonly both feed and reproduce). Embryonic growth can have two forms depending on the assumptions for acquisition of energy from yolk. By default, when the energy acquisition rate exceeds the maintenance rate, a fixed proportion of the resulting net production is spent on growth (increase in structural biomass), and the remaining portion is channelled to the reserves. Feeding organisms, however, modulate their allocation of net production energy in response to their total energy content (energy in the reserves plus energy bounded to structural biomass). In variable food environment an organism alternates between periods of growth, no-growth, and balanced-growth. In the latter case the organism adopts an allocation strategy that keeps its total energy constant. Under constant environmental conditions, the growth of a juvenile is always of von Bertalanffy type. Depending on the values of model parameters there are two long-time possibilities for adults: (a) von Bertalanffy growth accompanied by reproduction at a rate that approaches zero as the organism approaches asymptotic size, or (b) abrupt cessation of growth at some finite time, following which, the rate of reproduction is constant. We illustrate the model's applicability in life history theory by studying the optimum values of the energy allocation parameters for constant environment and for each of the dynamic regimes described above. Received: 11 May 1998 / Revised version: 18 February 2000 / Published online: 4 October 2000     

Optimal resource allocation of the marine bivalve Yoldia notabilis: The effects of size-limited reproductive capacity and size-dependent mortality

The effects of the morphological constraint of maximum reproductive output (reproductive capacity) and the size at which individuals can avoid heavy mortality (refuge size) on the resource allocation pattern between growth and reproduction are investigated using a dynamic modelling approach for a population of Yoldia notabilis (Mollusca: Bivalvia) in Otsuchi Bay, northeastern Japan. A state variable model is developed using field data on shell length, somatic weight, production, survivorship and reproductive capacity of the bivalve. The optimal allocation pattern is characterized by sudden switching from growth to reproduction without the assumption of reproductive capacity, while simultaneous investment in growth and reproduction becomes optimal when maximum reproductive output is limited by reproductive capacity. Size-specific reproductive effort, size at maturity and the growth curve predicted by the latter model fit more closely to the field data, suggesting that size-limited reproductive capacity can play an important role in the evolution of the observed resource allocation pattern. The mortality pattern affects optimal size at maturity, but not size-specific reproductive effort after maturity. When refuge size is fixed, optimal size at maturity increases with survivorship above refuge size. Optimal size at maturity changes in a more complex way with changes in refuge size. Size at maturity remains constant when refuge size is small, increases when it is intermediate, and decreases when it is large. The results suggest that refuge size is an important factor in the evolution of size at maturity, although its contribution varies depending on the values of other factors, such as size-dependent production and survivorship above refuge size. This revised version was published online in July 2006 with corrections to the Cover Date.     

Unexpected discontinuities in life-history evolution under size-dependent mortality

In many organisms survival depends on body size. We investigate the implications of size-selective mortality on life-history evolution by introducing and analysing a new and particularly flexible life-history model with the following key features: the lengths of growth and reproductive periods in successive reproductive cycles can vary evolutionarily, the model does not constrain evolution to patterns of either determinate or indeterminate growth, and lifetime number and sizes of broods are the outcomes of evolutionarily optimal life-history decisions. We find that small changes in environmental conditions can lead to abrupt transitions in optimal life histories when size-dependent mortality is sufficiently strong. Such discontinuous switching results from antagonistic selection pressures and occurs between strategies of early maturation with short reproductive periods and late maturation with long reproductive cycles. When mortality is size-selective and the size-independent component is not too high, selection favours prolonged juvenile growth, thereby allowing individuals to reach a mortality refuge at large body size before the onset of reproduction. When either component of mortality is then increased, the mortality refuge first becomes unattractive and eventually closes up altogether, resulting in short juvenile growth and frequent reproduction. Our results suggest a new mechanism for the evolution of life-history dimorphisms.     

Which proximate factor determines sexual size dimorphism in tiger snakes?

Diverse interactions between factors that influence body size complicate the identification of the primary determinants of sexual size dimorphism. Using data from a long‐term field study (1997–2009), we examined the contributions of the main proximate factors potentially influencing sexual size dimorphism from birth to adulthood in tiger snakes (Notechis scutatus). Data on body size, body mass and body condition of neonates, juveniles and adults were obtained by mark–recapture. Frequent recaptures allowed us to monitor reproductive status, diet and food intake, and to estimate survival and growth rates in age and sex classes. Additional data from females held briefly in captivity enabled us to assess reproductive output and the body mass lost at parturition (proxies for reproductive effort). From birth to maturity, individuals of both sexes experienced similar growth and mortality rates. We found no difference in diet, feeding and survival rates between the sexes, nor between juveniles and adults. On maturity, despite comparable diet and food intake by both sexes, the high energy requirements of vitellogenesis and gestation were responsible for a depletion of body reserves and probably resulted in a marked decrease in growth rates. Males were largely exempt from such costs of reproduction, and so could grow faster than females and attain larger body sizes. The absence of niche divergence between the sexes (uniformity of habitat, lack of predators) suggests that the impact of differential energetic investment for reproduction on growth rate is probably the main proximate factor influencing sexual size dimorphism in this species. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 103 , 668–680.     

Herbivore-mediated ecological costs of reproduction shape the life history of an iteroparous plant

Plant reproduction yields immediate fitness benefits but can be costly in terms of survival, growth, and future fecundity. Life-history theory posits that reproductive strategies are shaped by trade-offs between current and future fitness that result from these direct costs of reproduction. Plant reproduction may also incur indirect ecological costs if it increases susceptibility to herbivores. Yet ecological costs of reproduction have received little empirical attention and remain poorly integrated into life-history theory. Here, we provide evidence for herbivore-mediated ecological costs of reproduction, and we develop theory to examine how these costs influence plant life-history strategies. Field experiments with an iteroparous cactus (Opuntia imbricata) indicated that greater reproductive effort (proportion of meristems allocated to reproduction) led to greater attack by a cactus-feeding insect (Narnia pallidicornis) and that damage by this herbivore reduced reproductive success. A dynamic programming model predicted strongly divergent optimal reproductive strategies when ecological costs were included, compared with when these costs were ignored. Meristem allocation by cacti in the field matched the optimal strategy expected under ecological costs of reproduction. The results indicate that plant reproductive allocation can strongly influence the intensity of interactions with herbivores and that associated ecological costs can play an important selective role in the evolution of plant life histories.     

Overcompensation in response to simulated herbivory in the perennial herb <Emphasis Type="Italic">Sedum maximum</Emphasis>

A positive effect of herbivory on plant reproduction (overcompensation) has been documented mostly in monocarpic plants. Iteroparous perennials can be used to test whether enhanced reproduction in 1 year has negative future consequences as predicted by optimal allocation models. This study was intended to verify this prediction in the iteroparous herb Sedum maximum, applying mechanically simulated herbivory. I monitored 132 labelled S. maximum individuals during 2 years of study. They were randomly assigned to two groups: clipped and control. Infructescence dry mass, total seed dry mass, seed size, germination rate and an increase of root dry mass during the season were assessed in the experimental plants. Since only roots can survive to the next season, root dry mass was considered a reliable measure of allocation to future performance. Clipped plants showed increased fruit and seed dry mass versus the controls, with no other aspect of reproduction affected. Apical bud removal also had a positive effect on increase of root dry mass. The results indicate true overcompensation in response to simulated herbivory with no future costs of increased reproduction. Moreover, increased plant reproduction as a result of herbivory is likely to persist in the following years: clipping increased not only seed production but also root growth. This response is inconsistent with the results of optimal allocation models and the discrepancy is probably due to violation of the resource limitation assumption. Plants adapted to tolerate herbivory seem not to reproduce at the maximum rate when undamaged, but rather withhold resources to be allocated to reproduction after herbivory.