Optimal allocation of energy to growth and reproduction

The optimal allocation of energy to growth and reproduction is considered for three different cases, i.e., a single reproduction (semelparity), reproduction through repeated discrete clutches, and continuous reproduction. The problem reduces to optimizing age and size at maturity. The best strategy is to continue growth until the change of production rate with respect to increasing body size, multiplied by life expectancy for those attaining adulthood and reproducing successfully, is greater than one. The time at which semelparous species reproduce may also be optimized; for the other modes of reproduction only physiological factors or seasonality can limit the maximum age. A brief growing season or high mortality rate are factors leading to early maturity and small adult body size.     

Relationships of reproductive traits and body size with attainment of sexual maturity and age in Blanding's turtles (Emydoidea blandingi)

To place associations among body size, age at maturity, age, and reproductive traits of a long-lived organism in the context of current life history models based on the concept of norms of reaction, we examined data from a mark-recapture study of Blanding's turtles (Emydoidea blandingi) in southeastern Michigan during 24 of the years between 1953 and 1988. Females matured between 14 and 20 years of age. Both the smallest and largest adult females in the population were reproducing for the first time in their lives. This result suggests that a combination of differences in juvenile growth rates and ages at maturity, and not indeterminate growth, are the primary cause of variation in body size among adults. Body size variation among individuals was not related to age at sexual maturity. Females that had slower growth rates as juveniles matured later at similar mean body size compared to those with more rapid growth that matured at an earlier age. As a result, a linear model of age at sexual maturity with growth rates of primiparous females between hatching and maturity was significant and negative (R² = 0.76). Frequency of reproduction of the largest and smallest females was not significantly different. Clutch size did not vary significantly with age among either primiparous or multiparous females. Clutch sizes of primiparous females and multiparous females were not significantly different. However, older females (>55 years minimum age) reproduced more frequently than did younger females (minimum age <36 y).     

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.     

THE EFFECTS OF PREDATION ON THE AGE AND SIZE OF MATURITY OF PREY

The effects of nonselective predation on the optimal age and size of maturity of their prey are investigated using mathematical models of a simple life history with juvenile and adult stages. Fitness is measured by the product of survival to the adult stage and expected adult reproduction, which is usually an increasing function of size at maturity. Size is determined by both age at maturity and the value of costly traits that increase mean growth rate (growth effort). The analysis includes cases with fixed size but flexible time to maturity, fixed time but flexible size, and adaptively flexible values of both variables. In these analyses, growth effort is flexible. For comparison with previous theory, models with a fixed growth effort are analyzed. In each case, there may be indirect effects of predation on the prey's food supply. The effect of increased predation depends on (1) which variables are flexible; (2) whether increased growth effort requires increased exposure to predators; and (3) how increased predator density affects the abundance of food for juvenile prey. If there is no indirect effect of predators on prey food supply, size at maturity will generally decrease in response to increased predation. However, the indirect effect from increased food has the opposite effect, and the net result of predation is often increased size. Age at maturity may either increase or decrease, depending on functional forms and parameter values; this is true regardless of the presence of indirect effects. The results are compared with those of previous theoretical analyses. Observed shifts in life history in response to predation are reviewed, and the role of size-selective predation is reassessed.     

Optimal individual growth and reproduction in perennial species with indeterminate growth

Summary A model predicting optimal timing of growth and reproduction in perennial species with indeterminate growth living in a seasonal environment, is presented. According to the model, the optimal fraction of growing season devoted to growth decreases with increasing individual age and size, which leads to S-shaped growth curves. Winter mortality seems to be a crucial factor affecting the timing of growth and reproduction, under the same function describing the dependence of growth rate and reproductive rate on body size. When winter mortality is heavy, it is often optimal to start reproducing in the first year, and to devote a large proportion of the subsequent years to reproduction, thus leading to small adult body sizes.The model has been applied to two species of mollusc and one species of fish. The model predictions fit well to the field data for these three species.     

Evolution of longevity through optimal resource allocation

Models of life history evolution predict optimal traits of a simplified organism under various environmental conditions, but they at most acknowledge the existence of ageing. On the other hand, genetic models of ageing do not consider the effects of ageing on life histroy traits other than fecundity and longevity. This paper reports the results of a dynamic programming model which optimizes resource allocation to growth, reproduction and somatic repair. A low extrinsic (environmentally caused) mortality rate and high repair efficiency promote allocation to repair, especially early in life, resulting in delayed ageing and low growth rates, delayed maturity, large body size and dramatic enhancement of survival and maximum lifespan. The results are generally consistent with field, comprative and experimental data. They also suggest that the relationships between maximum lifespan and age at maturity and body size observed in nature may be by-products of optimal allocation strategies.     

Optimal reproductive strategies in age-structured populations of zooplankton

SUMMARY. We describe a model of zooplankton population dynamics that accounts for differences in mortality and physiology among animals of different ages or sizes. The model follows changes in numbers of individuals and changes in individual and egg biomass through time and it expresses mortality and net assimilation as functions of animal size.
We investigated the effect of egg size, age at first reproduction, and size at first reproduction on the per capita growth rates of populations growing under different conditions. In the absence of predation or when exposed to vertebrate predators that prefer large prey, populations achieve maximum growth rates when animals hatch from small eggs and reach maturity quickly at small sizes. Populations exposed to invertebrate predators that concentrate on small animals may increase r in two different ways. One way is for animals to increase juvenile survivorship by hatching from large eggs and by shortening the juvenile period. An alternative strategy is for animals to hatch from small eggs and to postpone maturity until they grow beyond the range of sizes available to their predators. Certain life history strategies maximize r if animals continue to grow after they reach maturity. By growing larger, non-primiparous females are able to hatch larger clutches and thereby increase the overall rate of population growth.
The model analysis shows how to assess age-dependent mortality rates from field data. The net rate of population increase and the age distribution of eggs together provide specific, quantitative information about mortality.     

Marker-assisted determination of the relationship between body size and reproductive success and consequences for evaluation of adaptive life histories

We tested for differences in the predicted optimal ages at first maturity in brook charr ( Salvelinus fontinalis ) in Freshwater River, Newfoundland, when life-history data were collated based on the marker-assisted estimation of the relationship between body size and reproductive success rather than using fecundity as a surrogate for reproductive success. Jointly with capture–recapture data to estimate the growth and survival costs of reproduction, we found that weak relationships between body size and reproductive success generate selection against delayed maturation. This finding would not have held for females if the relationship between body size and fecundity had been used as a surrogate for the relationship between body size and reproductive success. This shows that predictions of optimal life histories can be qualitatively changed when using molecular markers to directly evaluate age- and/or size-specific effects of body size on reproductive success.     

Ontogenetic Shifts in the Ability of the Cladoceran,Moina macrocopa Straus and Ceriodaphnia cornuta Sars to Utilize Ciliated Protists as Food Source

The ontogenetic diet shifts and age specific ability of the two cladoceran species Moina macrocopa and Ceriodaphnia cornuta to derive energy from ciliated protists have been investigated in laboratory. The postembryonic developmental rates and life table demography (longevity, age and size at first reproduction, fecundity and intrinsic rate of natural increase) of the cladocerans have been elucidated on algae (Chlorella vulgaris) and the ciliated protists (Tetrahymena pyriformis, Colpoda (c.f.) steini) as food. For either of the cladoceran, the somatic growth rate and average body size at first reproduction were higher with algal diet. During initial stages of development (0–5 days), either cladoceran realized higher rate of somatic growth on algal diet, subsequently ciliated protists supported significantly higher growth rate than the alga. Algal and ciliate diets did not differ in maximum body size (C. cornuta: 539–554 μm; M. macrocopa: 1274.8–1309 μm) reached by either of the cladocerans. The maximum body sizes were larger than size at first reproduction with either of the ciliated protists, however, with algal diet the maximum body sizes did not differ from the size at first reproduction in each case. In case of C. cornuta the generation time (20.5 ± 0.3 days on ciliate; 15.6 ± 0.17 days on algal diet), reproductive rates (net reproductive rate: 20.05 ± 3.2 on ciliate; 15.5 ± 1.2 on algal diet), and average life expectancy at hatching (27 ± 0.8 days on ciliate; 22.7 ± 0.71 days on alga) were higher, whereas the size at first reproduction (482 μm on ciliate; 521 μm on alga) was smaller with the ciliate than with an algal diet. The algal and the ciliate diets did not differ in survival (life expectancy at hatching: 9.2 ± 0.7 days) and fecundity (NRR: 23.6 ± 2.4) for M. macrocopa. The two ciliates used in the experiment did not differ in their performance as food source for either cladoceran species. Our results suggest that both the cladoceran species are able to utilize smaller ciliate (e.g., T. pyriformis, C. (c.f.) steini) as food; however with differential ability to derive energy from the ciliate diet and this ability is size and age structured in both cases. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Twelve fundamental life histories evolving through allocation‐dependent fecundity and survival

An organism's life history is closely interlinked with its allocation of energy between growth and reproduction at different life stages. Theoretical models have established that diminishing returns from reproductive investment promote strategies with simultaneous investment into growth and reproduction (indeterminate growth) over strategies with distinct phases of growth and reproduction (determinate growth). We extend this traditional, binary classification by showing that allocation‐dependent fecundity and mortality rates allow for a large diversity of optimal allocation schedules. By analyzing a model of organisms that allocate energy between growth and reproduction, we find twelve types of optimal allocation schedules, differing qualitatively in how reproductive allocation increases with body mass. These twelve optimal allocation schedules include types with different combinations of continuous and discontinuous increase in reproduction allocation, in which phases of continuous increase can be decelerating or accelerating. We furthermore investigate how this variation influences growth curves and the expected maximum life span and body size. Our study thus reveals new links between eco‐physiological constraints and life‐history evolution and underscores how allocation‐dependent fitness components may underlie biological diversity.     

Diversity of age‐specific reproductive rates may result from ageing and optimal resource allocation

This paper reports the results of a dynamic programming model which optimizes resource allocation to growth, reproduction and repair of somatic damage, based on the disposable soma theory of ageing. Here it is shown that different age‐dependent patterns of reproductive rates are products of optimal lifetime strategies of resource partitioning. The array of different reproductive patterns generated by the model includes those in which reproduction begins at the maximum rate at maturity and then declines to the end of life, or increases up to a certain age and then drops. The observed patterns reflect optimal resource allocation shaped by the level of extrinsic mortality. A continuous decline in the reproductive rate from the start of reproduction is associated with high extrinsic mortality, and an early increase in the reproductive rate occurs under low extrinsic mortality. A long‐lived organism shows a low reproductive rate early in life, and short‐lived organisms start reproduction at the maximum rate.     

What the egg can tell about its hen: Embryonic development on the basis of dynamic energy budgets

The energy cost of offspring is important in the conversion of resources allocated to reproduction to numbers of offspring, and in obtaining energy budget parameters from quantities that are easy to measure. An efficient numerical procedure is presented to obtain this cost for eggs and foetusses in the context of the dynamic energy budget theory, which specifies that birth occurs when maturity exceeds a threshold value and maternal effects determine the reserve density at birth. This paper extends previous work to arbitrary values of the ratio of the maturity and somatic maintenance costs. I discuss the body size scaling implications for the relative size and age at birth and conclude that the size at birth, contrary to the age at birth, covaries with the maintenance ratio. Apart from evolutionary adaptation of the maturity at birth, this covariation might explain some of the observed scatter in the relative length at birth. The theory can be used to evaluate the effects of the separation of cells in e.g. the two-cell stage of embryonic development, and of the removal of initial egg mass. If cell separation hardly affects energy parameters, body size scaling relationships imply that cell separation can only occur successfully in species with sufficiently large maximum body length (as adult); i.e. some two times that of Daphnia magna. Toxic compounds that increase the cost of synthesis of structure, decrease the allocation to reproduction indirectly via the life cycle, because food uptake is linked to size. They can also decrease the egg size, however, such that the reproduction rate is stimulated at low concentrations. The present theory offers a possible explanation for this well-known phenomenon.      

Correlated contemporary evolution of life history traits in New Zealand Chinook salmon, Oncorhynchus tshawytscha

Size at age and age at maturity are important life history traits, affecting individual fitness and population demography. In salmon and other organisms, size and growth rate are commonly considered cues for maturation and thus age at maturity may or may not evolve independently of these features. Recent concerns surrounding the potential phenotypic and demographic responses of populations facing anthropogenic disturbances, such as climate change and harvest, place a premium on understanding the evolutionary genetic basis for evolution in size at age and age at maturity. In this study, we present the findings from a set of common-garden rearing experiments that empirically assess the heritable basis of phenotypic divergence in size at age and age at maturity in Chinook salmon (Oncorhynchus tshawytscha) populations introduced to New Zealand. We found consistent evidence of heritable differences among populations in both size at age and age at maturity, often corresponding to patterns observed in the wild. Populations diverged in size and growth profiles, even when accounting for eventual age at maturation. By contrast, most, but not all, cases of divergence in age at maturity were driven by the differences in size or growth rate rather than differences in the threshold relationship linking growth rate and probability of maturation. These findings help us understand how life histories may evolve through trait interactions in populations exposed to natural and anthropogenic disturbances, and how we might best detect such evolution.     

When to parasitize? A dynamic optimization model of reproductive strategies in a cooperative breeder

We consider a cooperatively breeding group and find the optimal pattern of reproductive parasitism by a subordinate helper as a function of its body size, and hence the share of reproduction obtained by the subordinate. We develop the model for the social system of the cooperatively breeding cichlid fish Neolamprologus pulcher but the general framework is also applicable to other cooperative systems. In addition to behaving cooperatively by sharing tasks, sexually mature male cichlid helpers may directly parasitize the reproduction of dominant breeders in the group. We investigate the relative influence of life history and behavioural variables including growth, parasitism capacity, future reproductive fitness benefits and costs, relatedness and expulsion risk on the optimal reproductive strategy of subordinates. In a detailed analysis of the parameter space we show that a male helper should base its decision to parasitize primarily on an increase in expulsion risk resulting from reproductive parasitism (punishment), intra-group relatedness and the parasitism capacity. If expulsion risk is high then helpers should not parasitize reproduction at medium body size but should parasitize either when small or large.     

The evolution of complex life cycles when parasite mortality is size- or time-dependent

In complex cycles, helminth larvae in their intermediate hosts typically grow to a fixed size. We define this cessation of growth before transmission to the next host as growth arrest at larval maturity (GALM). Where the larval parasite controls its own growth in the intermediate host, in order that growth eventually arrests, some form of size- or time-dependent increase in its death rate must apply. In contrast, the switch from growth to sexual reproduction in the definitive host can be regulated by constant (time-independent) mortality as in standard life history theory. We here develop a step-wise model for the evolution of complex helminth life cycles through trophic transmission, based on the approach of Parker et al. [2003a. Evolution of complex life cycles in helminth parasites. Nature London 425, 480-484], but which includes size- or time-dependent increase in mortality rate. We assume that the growing larval parasite has two components to its death rate: (i) a constant, size- or time-independent component, and (ii) a component that increases with size or time in the intermediate host. When growth stops at larval maturity, there is a discontinuous change in mortality to a constant (time-independent) rate. This model generates the same optimal size for the parasite larva at GALM in the intermediate host whether the evolutionary approach to the complex life cycle is by adding a new host above the original definitive host (upward incorporation), or below the original definitive host (downward incorporation). We discuss some unexplored problems for cases where complex life cycles evolve through trophic transmission.     

Comparative analysis of phylogenetic and fishing effects in life history patterns of teleost fishes

The effects of fishing on life history traits and life history strategies of teleost fishes are analysed by a new comparative method that splits traits into an allometric part (size effect), an autoregressive phylogenetic component, and an environmental component (fishing effect). Both intra- and inter-specific variation of age and size at maturity, fecundity, adult size and egg size are analysed by comparing 84 populations of 49 species submitted to various fishing pressures. Two axes of life history diversification are found among teleosts. One is the well-known slow-fast continuum separating short-lived and early maturing species (like Clupeiformes) from longer-lived species that mature late relative to their size and spawn larger eggs (like salmonids or Scorpaeniformes). An additional strategy involves the schedule of resource allocation to growth and reproduction. Indeterminate growth allows higher teleosts (e.g. Gadiformes) to reach a large size while maturing early and laying small eggs. Increasing fishing pressure decreases age at maturity and egg size, and increases fecundity at maturity, the slope of the fecundity-length relationship and relative size at maturity. These compensations for higher adult mortality differ among life history strategies. Indeterminate growth is associated with a greater flexibility in resource allocation to growth and reproduction that facilitates greater resilience to fishing mortality.     

The temperature‐size rule in Daphnia magna across different genetic lines and ontogenetic stages: Multiple patterns and mechanisms

Ectotherms tend to grow faster, but reach a smaller size when reared under warmer conditions. This temperature‐size rule (TSR) is a widespread phenomenon. Despite the generality of this pattern, no general explanation has been found. We therefore tested the relative importance of two proposed mechanisms for the TSR: (1) a stronger increase in development rate relative to growth rate at higher temperatures, which would cause a smaller size at maturity, and (2) resource limitation placing stronger constraints on growth in large individuals at higher temperatures, which would cause problems with attaining a large size in warm conditions. We raised Daphnia magna at eight temperatures to assess their size at maturity, asymptotic size, and size of their offspring. We used three clonal lines that differed in asymptotic size and growth rate. A resource allocation model was developed and fitted to our empirical data to explore the effect of both mechanisms for the TSR. The genetic lines of D. magna showed different temperature dependence of growth and development rates resulting in different responses for size at maturity. Also, at warm temperatures, growth was constrained in large, but not in small individuals. The resource allocation model could fit these empirical data well. Based on our empirical results and model explorations, the TSR of D. magna at maturity is best explained by a stronger increase in development rate relative to growth rate at high temperature, and the TSR at asymptotic size is best explained by a size‐dependent and temperature‐dependent constraint on growth, although resource limitation could also affect size at maturity. In conclusion, the TSR can take different forms for offspring size, size at maturity, and asymptotic size and each form can arise from its own mechanism, which could be an essential step toward finding a solution to this century‐old puzzle.     

Contrasting life history strategies of sympatric Arctic charr morphs, Salvelinus alpinus

In polymorphic populations morphs usually diverge in morphology, ecology and life history, which is most likely driven by adaptations to different environments or resources. Sympatric morphs may develop differences in several life history traits to be able to maximize fitness in alternative niches and habitats. Here, the contrasting life history traits of three sympatric Arctic charr (Salvelinus alpinus (L.)) morphs in a deep and oligotrophic lake in sub-arctic Norway are addressed. The charr morphs differ in spawning habitat and trophic niche. One is a littoral spawning morph that feeds on benthic invertebrates and zooplankton in the littoral and pelagic zones (referred to as the LO-morph), and two other are profundal spawning morphs that either utilize profundal soft bottom benthos as food resource (the PB-morph) or are piscivorous (the PP-morph). The LO-morph typically had intermediate life-history traits relative to the two profundal morphs that had highly contrasting life history traits, especially in growth and age and size of maturity. The PB-morph matured at a young age (～3 years) and at a small body size (～8.5 cm), thereby increasing their fitness by investing in reproduction early in life, which results in a short generation time and decreased probability of being predated before first reproduction. The PP-morph on the other hand, matured at an old age (～9.2 years) and a large body size (～26 cm), thereby increasing their fitness by investing in somatic growth to enhance initial fecundity, and also to reach a large body size profitable for piscivory. The different trade-off regime between the PP- and PB-morphs seems to be caused by adaptation to alternative trophic niches, and appears to be an important factor for the co-occurrence of the two sister-morphs in the profundal zone.     

To grow or to seed: ecotypic variation in reproductive allocation and cone production by young female Aleppo pine (Pinus halepensis, Pinaceae)

Age and size at the first reproduction and the reproductive allocation of plants are linked to different life history strategies. Aleppo pine only reproduces through seed, and, as such, early female reproduction confers high fitness in its infertile highly fire-prone habitats along the Mediterranean coast because life expectancy is short. We investigated the extent of ecotypic differentiation in female reproductive allocation and examined the relation between early female reproduction and vegetative growth. In a common-garden experiment, the threshold age and size at first female reproduction and female reproductive allocation at age seven differed significantly among Aleppo pine provenances of ecologically distinct origin. Significant correlations among reproductive features of the provenances and the ecological traits of origin were found using different analytical tools. In nonlinear models of cone counts vs. stem volume, medium-sized trees (not the largest trees) produced the highest cone yield, confirming that, at the individual level, early female reproduction is incompatible with fast vegetative growth. The contribution of founder effects and adaptation to contrasting fire regimes may be confounding factors. But considering all traits analyzed, the geographical patterns of resource allocation by Aleppo pine suggest ecotypic specialization for either resource-poor (favoring early reproduction) or resource-rich (favoring vegetative growth) habitats.