On a new perspective of the basic reproduction number in heterogeneous environments

Although its usefulness and possibility of the well-known definition of the basic reproduction number R0 for structured populations by Diekmann, Heesterbeek and Metz (J Math Biol 28:365-382, 1990) (the DHM definition) have been widely recognized mainly in the context of epidemic models, originally it deals with population dynamics in a constant environment, so it cannot be applied to formulate the threshold principle for population growth in time-heterogeneous environments. Since the mid-1990s, several authors proposed some ideas to extend the definition of R0 to the case of a periodic environment. In particular, the definition of R0 in a periodic environment by Baca?r and Guernaoui (J Math Biol 53:421-436, 2006) (the BG definition) is most important, because their definition of periodic R0 can be interpreted as the asymptotic per generation growth rate, which is an essential feature of the DHM definition. In this paper, we introduce a new definition of R0 based on the generation evolution operator (GEO), which has intuitively clear biological meaning and can be applied to structured populations in any heterogeneous environment. Using the generation evolution operator, we show that the DHM definition and the BG definition completely allow the generational interpretation and, in those two cases, the spectral radius of GEO equals the spectral radius of the next generation operator, so it gives the basic reproduction number. Hence the new definition is an extension of the DHM definition and the BG definition. Finally we prove a weak sign relation that if the average Malthusian parameter exists, it is nonnegative when R0>1 and it is nonpositive when R0<1.     

Clupeoid life-history styles in variable environments

Synopsis Marine fish species with planktonic larval stages experience high and variable pre-adult mortality, and in accordance with general life-history theory have evolved iteroparity to reduce the uncertainty in reproductive success of individuals. In this paper we use a Monte Carlo model to explore the influence of spawning style and adult survival of clupeoids on the spawning success of individual fish during their life span, when early stage survival is determined according to different spectra of environmental variability. In these simulations the variation in reproductive success was governed first by the number of batches of eggs spawned by each adult fish over its lifespan (as determined by its pattern of spawning and the adult survival rate), and secondly by the patterning of environmental variability affecting early stage survival. We consider that the life history styles of the clupeoids are based on co-evolved traits in which the different patterns of iteroparity represent different solutions for coping with the variable nature of early-stage survival. When these life history traits are compared on time scales appropriate to each species, they are therefore unlikely to provide the correlation between brood strength variation and the life span of adults proposed in Murphy's (1968) contribution to this aspect of life history theory.     

Evolution of thermotolerance in seasonal environments: the effects of annual temperature variation and life-history timing in Wyeomyia smithii

In organisms with complex life cycles, the adaptive value of thermotolerance depends on life-history timing and seasonal temperature profiles. We illustrate this concept by examining variation in annual thermal environments and thermal acclimation among four geographic populations of the pitcher plant mosquito. Only diapausing larvae experience winter, whereas both postdiapause and nondiapause adults occur only during the growing season. Thus, adults experience transient cold stress primarily during the spring. We show that adult cold tolerance (chill coma recovery) is enhanced in spring-like conditions via thermal acclimation but is unaffected by diapause state. Moreover, adult mosquitoes from northern populations were more cold tolerant than those from southern populations largely because acclimation responses were steeper in the north. In contrast to cold tolerance, there was no significant acclimation of heat tolerance (heat knockdown), and no significant differences in heat tolerance between northern and southern populations. Field temperature data show that because of evolved differences in diapause timing, adult exposure to cold stress is remarkably consistent across geography. This suggests that geographic variation in cold tolerance may not be the result of direct selection on adults. Our results illustrate the importance of the interplay between phenological and thermal adaptation for understanding variation along climatic gradients.     

An uncertain life: demography in random environments

This paper concisely reviews the demography of populations with random vital rates, highlights examples and techniques which yield insight into population dynamics, summarizes the state of significant applications of the theory, and points to open problems. The central picture in this theory is of a time-varying but statistically stationary equilibrium for population, sharply distinct from the notions of classical demography. The deepest biological insights from the theory reveal the temporal structure of life histories to be a rich arena for natural selection.     

Costs of reproduction in a historical perspective

Costs of reproduction constitute a core assumption of life history theory. After reformulation by G.C. Williams, the cost hypothesis soon became a major foundation of phenotypic life history models. More-recent studies have approached reproductive costs from the perspective of quantitative genetics. Here, we present a brief historical perspective to the development of the cost of reproduction hypothesis. We evaluate the status and heuristic value of the different approaches, and outline how the approaches have originated.     

Early is better: seasonal egg fitness and timing of reproduction in a zooplankton life-history model

Timing of reproduction influences future prospects of offspring and therefore the reproductive value of parents. Early offspring are often more valuable than later ones when food availability and predation risk fluctuate seasonally. Marine zooplankton have evolved a diversity of life history strategies in response to seasonality. We present a state-dependent life history model for the annual and herbivorous high-latitude copepod Calanoides acutus . Individuals are characterised by four states; developmental stage, structural size, energy reserves and vertical location. There are two habitats, a surface habitat with seasonal predation risk and food availability, and a safer deep habitat with no food and low metabolism (diapause). Optimal life histories (diapause and energy allocation strategies) are found by dynamic programming. Seasonal egg fitness (reproductive value) emerges from the model and peak values are typically before the feeding season. Disentangling the fitness components, we conclude that seasonality in egg fitness is caused both by environmental seasonality in food and predation risk and by time-constraints on development and diapause preparation. Realised egg production, as predicted from population simulations, does not match the seasonal peak in offspring fitness but is delayed relative to peak egg fitness. We term this an 'internal life history mismatch' as constraints and tradeoffs cause sub-optimal birth dates for most eggs whereas mothers maximise their reproductive value by high number of eggs rather than few and optimally timed eggs. The earliest eggs have a disproportionately high contribution to population recruitment, emphasising the importance of early eggs and the need to understand seasonal patterns in offspring fitness.     

The evolution of life-history traits in parasitic and free-living platyhelminthes: a new perspective

Parasite life histories have been assumed to be shaped by their particular mode of existence. To test this hypothesis, we investigate the relationships between life-history traits of free-living and parasitic platyhelminthes. Using phylogenetically independent contrasts we examine patterns of interspecific covariation in adult size, progeny volume, daily fecundity, total reproductive capacity, age at first reproduction and longevity. The correlations obtained indicate a similar causal chain of life history variations for free-living and parasitic platyhelminthes. These results suggest that increased longevity favours delayed reproduction. Furthermore, growth pattern determines adult body size and age at maturity. For platyhelminthes, whether free-living or parasitic, the total reproductive capacity is found to be directly determined by the size of the worm. Within this group the parasitic way of life does not seem to influence the basic patterns of life history evolution. Received: 20 September 1997 / Accepted: 1 March 1998     

Evolution of host life-history traits in a spatially structured host-parasite system

Most models for the evolution of host defense against parasites assume that host populations are not spatially structured. Yet local interactions and limited dispersal can strongly affect the evolutionary outcome, because they significantly alter epidemiological feedbacks and the spatial genetic structuring of the host and pathogen populations. We provide a general framework to study the evolution of a number of host life-history traits in a spatially structured host population infected by a horizontally transmitted parasite. Our analysis teases apart the selective pressures on hosts and helps disentangle the direct fitness effect of mutations and their indirect effects via the influence of spatial structure on the genetic, demographic, and epidemiological structure of the host population. We then illustrate the evolutionary consequences of spatial structure by focusing on the evolution of two host defense strategies against parasitism: suicide upon infection and reduced transmission. Because they bring no direct fitness benefit, these strategies are counterselected or selectively neutral in a nonspatial setting, but we show that they can be selected for in a spatially structured environment. Our study thus sheds light on the evolution of altruistic defense mechanisms that have been observed in various biological systems.     

Evolution: sociality as a driver of unorthodox reproduction

An unusual reproductive system was discovered in desert ants, in which daughter queens are produced asexually via parthenogenesis, whereas workers develop from hybrid crosses between genetically divergent lineages. The system appears to be doomed to extinction.     

Generalists versus specialists in fluctuating environments: a bet-hedging perspective

Bet-hedging evolves in fluctuating environments because long-term genotype success is determined by geometric (rather than arithmetic) mean fitness across generations. Diversifying bet-hedging produces different specialist offspring, whereas conservative bet-hedging produces similar generalist offspring. However, many fields, such as behavioral ecology and thermal physiology, typically consider specialist versus generalist strategies only in terms of maximizing arithmetic mean fitness benefits to individuals. Here we model how environmental variability affects optimal amounts of phenotypic variation within and among individuals to maximise genotype fitness, and we disentangle the effects of individual-level optimization and genotype-level bet-hedging by comparing long-term arithmetic versus geometric mean fitness. For traits with additive fitness effects within lifetimes (e.g. foraging-related traits), genotypes of similar generalists or diversified specialists perform equally well. However, if fitness effects are multiplicative within lifetimes (e.g. sequential survival probabilities), generalist individuals are always favored. In this case, geometric mean fitness optimization requires even more within-individual phenotypic variation than does arithmetic mean fitness, causing individuals to be more generalist than required to simply maximize their own expected fitness. In contrast to previous results in the bet-hedging literature, this generalist conservative bet-hedging effect is always favored over diversifying bet-hedging. These results link the evolution of behavioral and ecological specialization with earlier models of bet-hedging, and we apply our framework to a range of natural phenomena from habitat choice to host specificity in parasites.     

Life-history evolution in uncertain environments: bet hedging in time

Many vertebrates, forest herbs, and trees exhibit both variable age at maturity and iteroparity as adaptations to uncertain environments. We analyze a stochastic model that combines these two life-history adaptations with density-dependent fertility. Results for a model with only iteroparity are consistent with previous work; environmental uncertainty favors adult survival over juvenile survival. This holds true even if there is a moderately strong convex trade-off between adult survival and fecundity, but the direction of selection can depend on which life-history trait is considered a random variable. A life history with only developmental delay favors juvenile survival in uncertain environments, consistent with previous models of seed banks. When both developmental delay and iteroparity are included in the model, both adaptations are favored in uncertain environments. Our simulations show that selection is not necessarily a runaway process in which either developmental delay or iteroparity is favored, as recently proposed by Tuljapurkar and Wiener, but rather that selection can favor both mechanisms. Invasion analysis shows that selective pressure on life-history delays increases as environmental variation increases. Reproductive delay and adult survival can be either adaptations or constraints. Natural-history studies that estimate model parameters can resolve this uncertainty.     

Chaoborus predation and delayed reproduction in Daphnia: a demographic modeling approach

I develop a demographic model that examines the impact of Chaoborus predation on the population dynamics and life history of Daphnia. Predation effects are determined through analysis of the various components of the predator-prey interaction (encounter, attack, strike efficiency), and are integrated into a stage-classified matrix population model. The model is parameterized with data from interactions between D. pulex and fourth-instar C. americanus. I test this model with two laboratory experiments that examine population growth of D. pulex under the influence of five different levels of Chaoborus predation. With the exception of a single predation treatment in each experiment, the model accurately predicted the observed reduction in Daphnia numbers with increasing Chaoborus predation. I then use this model to investigate the evolution of delayed reproduction in D. pulex that are exposed to Chaoborus. I ask whether delayed reproduction may evolve in Daphnia that are subjected to Chaoborus predation as a trade-off for the benefits of larger body size. The model predicts that the effectiveness of such a life history trade-off depends on the relative sizes of predator and prey. In some interactions between Chaoborus and Daphnia, increasing Daphnia body length by as little as 5% from base growth trajectories sufficiently increases fitness (by reducing vulnerability to Chaoborus predation) to compensate for the cost of delayed reproduction. In other interactions, however, increased body length provides no benefit to Daphnia (and may even reduce fitness), and selection would act against the evolution of delayed reproduction. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evolution of enzymes in metabolism: a network perspective

Several models have been proposed to explain the origin and evolution of enzymes in metabolic pathways. Initially, the retro-evolution model proposed that, as enzymes at the end of pathways depleted their substrates in the primordial soup, there was a pressure for earlier enzymes in pathways to be created, using the later ones as initial template, in order to replenish the pools of depleted metabolites. Later, the recruitment model proposed that initial templates from other pathways could be used as long as those enzymes were similar in chemistry or substrate specificity. These two models have dominated recent studies of enzyme evolution. These studies are constrained by either the small scale of the study or the artificial restrictions imposed by pathway definitions. Here, a network approach is used to study enzyme evolution in fully sequenced genomes, thus removing both constraints. We find that homologous pairs of enzymes are roughly twice as likely to have evolved from enzymes that are less than three steps away from each other in the reaction network than pairs of non-homologous enzymes. These results, together with the conservation of the type of chemical reaction catalyzed by evolutionarily related enzymes, suggest that functional blocks of similar chemistry have evolved within metabolic networks. One possible explanation for these observations is that this local evolution phenomenon is likely to cause less global physiological disruptions in metabolism than evolution of enzymes from other enzymes that are distant from them in the metabolic network.     

Mammalian reproduction: an ecological perspective

The objectives of this paper are to organize our concepts about the environmental regulation of reproduction in mammals and to delineate important gaps in our knowledge of this subject. The environmental factors of major importance for mammalian reproduction are food availability, ambient temperature, rainfall, the day/night cycle and a variety of social cues. The synthesis offered here uses as its core the bioenergetic control of reproduction. Thus, for example, annual patterns of breeding are viewed as reflecting primarily the caloric costs of the female's reproductive effort as they relate to the energetic costs and gains associated with her foraging effort. Body size of the female is an important consideration since it is correlated with both potential fat reserves and life span. Variation in nutrient availability may or may not be an important consideration. The evolutionary forces that have shaped the breeding success of males usually are fundamentally different from those acting on females and, by implication, the environmental controls governing reproduction probably also often differ either qualitatively or quantitatively in the two sexes. Mammals often live in habitats where energetic and nutrient challenges vary seasonally, even in the tropics. When seasonal breeding is required, a mammal may use a predictor such as photoperiod or a secondary plant compound to prepare metabolically for reproduction. A reasonable argument can be made, however, that opportunistic breeding, unenforced by a predictor, may be the most prevalent strategy extant among today's mammals. Social cues can have potent modulating actions. They can act either via discrete neural and endocrine pathways to alter specific processes such as ovulation, or they can induce nonspecific emotional states that secondarily affect reproduction. Many major gaps remain in our knowledge about the environmental regulation of mammalian reproduction. For one, we have a paucity of information about the annual patterns of breeding and about the mechanisms controlling these patterns in the most common mammals on the planet-the small to average-sized mammals living in the tropics. We probably have only a shallow conceptualization of the way available energy and nutrients control reproduction and, likewise, we may have only a narrow view of the potential kinds and uses of seasonal predictors. Finally, we have little appreciation of the way environmental cues interact with each other to control reproduction.     

Evolution by phenotype: a biomedical perspective

Genes are widely assumed to play a major role in the epidemiology of complex chronic diseases, yet attempts to characterize the genetic architecture of such traits have been frustrating. Understanding that evolution works by screening phenotypes rather than genotypes can help explain the source of this frustration. Complex traits are usually the result of long-term, often subtle, gene-environment interactions, such that individual life histories may be as important as population histories in predicting and explaining these traits. Recognizing that the problem is not due to technological limitations can help temper expectations and guide the design of future work in biomedical genetics, by allowing us to focus on better approaches where they exist and on those problems most likely to yield a genetic solution. We may even be forced to re-conceive complex biological causation.     

Nothofagus: Evolution from a southern perspective

Nothofagus holds a premier position in the study of Southern Hemisphere plant evolution and biogeography, and many have attempted to reconstruct its history. A recent surge of research on both living and fossil species has added valuable data to the debate, but has also introduced complications, including the now less certain familial relationships of the genus. The vast quantity of fossil evidence provides an extremely firm base for reconstruction of the past distribution of Nothofagus, and allows informed speculation on the time and places of origin and major speciation events.     

Evolution of life-history traits collapses competitive coexistence

Trade-offs between competitive ability and the other life-history traits are considered to be a major mechanism of competitive coexistence. Many theoretical studies have demonstrated the robustness of such a coexistence mechanism ecologically; however, it is unknown whether the coexistence is robust evolutionarily. Here, we report that evolution of life-history traits not directly related to competition, such as longevity, and predator avoidance, easily collapses competitive coexistence in several competition systems: spatially structured, and predator-mediated two-species competition systems. In addition, we found that a superior competitor can be excluded by an inferior one by common mechanisms among the models. Our results suggest that ecological competitive coexistence due to a life-history trait trade-off balance may not be balanced on an evolutionary timescale, that is, it may be evolutionarily fragile.     

Timing of avian reproduction in unpredictable environments

Organisms living in periodically varying environments adjust their life history events to the changes in food availability. When these changes are not entirely predictable animals face a trade-off between maintaining physiological preparedness (which can be costly) and being unprepared (which decreases the chances of successful reproduction). To investigate this problem, we developed an optimal annual routine model of gonad regulation in birds. Most birds regress their reproductive organs during non-breeding periods, but to start breeding again they need to have functional gonads. Maintaining the gonads in this state is costly, but because it takes time to achieve this state, if gonads are not functional the bird may miss a possible breeding opportunity. We explore the resolution of this trade-off in environments where favorable periods can occur at any time of the year and variability in the length of good and bad periods can be altered. Consistent with empirical studies of reproductive behavior in unpredictable environments, we find that birds maintain the gonads partially activated during unfavorable conditions in many cases. However, gonad regulation may differ strikingly depending on the consistency of the good and bad periods. Furthermore, seasonal changes in food availability lead to the entrainment of reproduction and the segregation of the breeding and non-breeding season, even if the magnitude of seasonality is small compared to the degree of environmental fluctuations. These results indicate that several aspects of the environment need to be taken into account to understand reproductive behavior in unpredictable environments. Given that the trade-off between the costs and benefits of maintaining physiological preparedness is not limited to birds, our results have implications for understanding behavioral flexibility in other organisms as well.