Demographic analysis of continuous-time life-history models

I present a computational approach to calculate the population growth rate, its sensitivity to life-history parameters and associated statistics like the stable population distribution and the reproductive value for exponentially growing populations, in which individual life history is described as a continuous development through time. The method is generally applicable to analyse population growth and performance for a wide range of individual life-history models, including cases in which the population consists of different types of individuals or in which the environment is fluctuating periodically. It complements comparable methods developed for discrete-time dynamics modelled with matrix or integral projection models. The basic idea behind the method is to use Lotka's integral equation for the population growth rate and compute the integral occurring in that equation by integrating an ordinary differential equation, analogous to recently derived methods to compute steady-states of physiologically structured population models. I illustrate application of the method using a number of published life-history models.     

A new demographic function maximized by life-history evolution

A goal of life-history theory has been to understand what combination of demographic traits is maximized by natural selection. In practice, researchers usually choose either density-independent population growth rate, lambda, or lifetime reproductive success, R0 (expected number of offspring produced in a lifetime). Others have shown that the maxima of density-independent lambda and R0 are evolutionarily stable strategies under specific density-dependent conditions: population regulation by equal density dependence among all age classes for lambda and by density dependence on a single age class for R0. Here I extend these connections between density-independent optimization models and density-dependent invasion function models in two ways. First, I derive a new demographic function for which a maximum corresponds to attainability of the equilibrium strategy or stability of the mean rather than stability of the variance of the strategy distribution. Second, I show explicitly a continuous range of cases with maxima between those for the lambda and R0. Graphical and biological interpretations are given for an example model. Finally, exceptions to a putative life-history generality (from lambda and R0 models), that high early-life mortality selects for high iteroparity, are shown.     

Are personality differences in a small iteroparous mammal maintained by a life-history trade-off?

Despite increasing interest, animal personality is still a puzzling phenomenon. Several theoretical models have been proposed to explain intraindividual consistency and interindividual variation in behaviour, which have been primarily supported by qualitative data and simulations. Using an empirical approach, I tested predictions of one main life-history hypothesis, which posits that consistent individual differences in behaviour are favoured by a trade-off between current and future reproduction. Data on life-history were collected for individuals of a natural population of grey mouse lemurs (Microcebus murinus). Using open-field and novel-object tests, I quantified variation in activity, exploration and boldness for 117 individuals over 3 years. I found systematic variation in boldness between individuals of different residual reproductive value. Young males with low current but high expected future fitness were less bold than older males with high current fecundity, and males might increase in boldness with age. Females have low variation in assets and in boldness with age. Body condition was not related to boldness and only explained marginal variation in exploration. Overall, these data indicate that a trade-off between current and future reproduction might maintain personality variation in mouse lemurs, and thus provide empirical support of this life-history trade-off hypothesis.     

Effects of an autocorrelated stochastic environment and fisheries on the age at maturity of Chinook salmon

Chinook salmon (Oncorhynchus tshawytscha) reproduce only once in their lifetime, and their age at reproduction varies among individuals (indeterminate semelparous). However, the factors that determine their spawning age still remain uncertain. Evidence from recent studies suggests that individual growth and reproduction of Chinook salmon are affected by the rate of coastal upwelling, which is shown to be positively autocorrelated between years. Therefore, the serially autocorrelated environmental is expected to play an important role in determining their spawning age. In the present study, I demonstrate the advantage of an indeterminate maturation strategy under a stochastic environment. I then present theoretical evidence for the advantage of adjusting the maturation probability based on the environment they experienced and demonstrate that fisheries reduce the fitness of the strategy to delay maturation. The results presented herein emphasize the importance of incorporating detailed life-history strategies of organisms when undertaking population management.     

Genotype-by-environment interactions leads to variable selection on life-history strategy in Common Evening Primrose (Oenothera biennis)

Monocarpic plant species, where reproduction is fatal, frequently exhibit variation in the length of their prereproductive period prior to flowering. If this life-history variation in flowering strategy has a genetic basis, genotype-by-environment interactions (G x E) may maintain phenotypic diversity in flowering strategy. The native monocarpic plant Common Evening Primrose (Oenothera biennis L., Onagraceae) exhibits phenotypic variation for annual vs. biennial flowering strategies. I tested whether there was a genetic basis to variation in flowering strategy in O. biennis, and whether environmental variation causes G x E that imposes variable selection on flowering strategy. In a field experiment, I randomized more than 900 plants from 14 clonal families (genotypes) into five distinct habitats that represented a natural productivity gradient. G x E strongly affected the lifetime fruit production of O. biennis, with the rank-order in relative fitness of genotypes changing substantially between habitats. I detected genetic variation in annual vs. biennial strategies in most habitats, as well as a G x E effect on flowering strategy. This variation in flowering strategy was correlated with genetic variation in relative fitness, and phenotypic and genotypic selection analyses revealed that environmental variation resulted in variable directional selection on annual vs. biennial strategies. Specifically, a biennial strategy was favoured in moderately productive environments, whereas an annual strategy was favoured in low-productivity environments. These results highlight the importance of variable selection for the maintenance of genetic variation in the life-history strategy of a monocarpic plant.     

Population responses to perturbations: the importance of trait-based analysis illustrated through a microcosm experiment

Environmental change continually perturbs populations from a stable state, leading to transient dynamics that can last multiple generations. Several long-term studies have reported changes in trait distributions along with demographic response to environmental change. Here we conducted an experimental study on soil mites and investigated the interaction between demography and an individual trait over a period of nonstationary dynamics. By following individual fates and body sizes at each life-history stage, we investigated how body size and population density influenced demographic rates. By comparing the ability of two alternative approaches, a matrix projection model and an integral projection model, we investigated whether consideration of trait-based demography enhances our ability to predict transient dynamics. By utilizing a prospective perturbation analysis, we addressed which stage-specific demographic or trait-transition rate had the greatest influence on population dynamics. Both body size and population density had important effects on most rates; however, these effects differed substantially among life-history stages. Considering the observed trait-demography relationships resulted in better predictions of a population's response to perturbations, which highlights the role of phenotypic plasticity in transient dynamics. Although the perturbation analyses provided comparable predictions of stage-specific elasticities between the matrix and integral projection models, the order of importance of the life-history stages differed between the two analyses. In conclusion, we demonstrate how a trait-based demographic approach provides further insight into transient population dynamics.     

On second order sensitivity for stage-based population projection matrix models

In this paper we present a simple method for identifying life-history perturbations in population projection matrices that yield an accelerating population growth rate. Accelerating growth means that the dependence of the growth rate on the perturbation is convex. Convexity, when the second sensitivity of the growth rate is positive, is calculated using a new formula derived from the transfer function of the perturbed system. This formula is used to explore the relationship between stasis and growth probabilities from stage-structured population projection matrices.     

Within-individual plasticity explains age-related decrease in stress response in a short-lived bird

A crucial problem for every organism is how to allocate energy between competing life-history components. The optimal allocation decision is often state-dependent and mediated by hormones. Here, we investigated how age, a major state variable affects individuals'' hormonal response to a standardized stressor: a trait that may reflect allocation between self-maintenance and reproduction. We caught free-living house sparrows and measured their hormonal (corticosterone) response to capture stress in consecutive years. Using a long-term ringing dataset, we determined the age of the birds, and we partitioned the variation into within- and among-individual age components to investigate the effects of plasticity versus selection or gene flow, respectively, on the stress response. We found large among-individual variation in the birds'' hormone profiles, but overall, birds responded less strongly to capture stress as they grew older. These results suggest that stress responsiveness is a plastic trait that may vary within individuals in an adaptive manner, and natural selection may act on the reaction norms producing optimal phenotypic response in the actual environment and life-history stage.     

Natural selection on female life-history traits in relation to socio-economic class in pre-industrial human populations

Life-history theory predicts that resource scarcity constrains individual optimal reproductive strategies and shapes the evolution of life-history traits. In species where the inherited structure of social class may lead to consistent resource differences among family lines, between-class variation in resource availability should select for divergence in optimal reproductive strategies. Evaluating this prediction requires information on the phenotypic selection and quantitative genetics of life-history trait variation in relation to individual lifetime access to resources. Here, we show using path analysis how resource availability, measured as the wealth class of the family, affected the opportunity and intensity of phenotypic selection on the key life-history traits of women living in pre-industrial Finland during the 1800s and 1900s. We found the highest opportunity for total selection and the strongest selection on earlier age at first reproduction in women of the poorest wealth class, whereas selection favoured older age at reproductive cessation in mothers of the wealthier classes. We also found clear differences in female life-history traits across wealth classes: the poorest women had the lowest age-specific survival throughout their lives, they started reproduction later, delivered fewer offspring during their lifetime, ceased reproduction younger, had poorer offspring survival to adulthood and, hence, had lower fitness compared to the wealthier women. Our results show that the amount of wealth affected the selection pressure on female life-history in a pre-industrial human population.     

TO AGE, TO DIE: PARITY, EVOLUTIONARY TRACKING AND COLE'S PARADOX

The existence of semelparity or "big bang" reproduction (reproducing only once in a lifetime) and iteroparity (reproducing more than once in a lifetime) has led to many questions investigating the evolution or persistence of these strategies. Here we investigate semelparity and iteroparity for their evolutionary importance. A mathematical model is used to illustrate how a population's ability to evolve depends on this life-history trait, and how this rate of evolution impacts the individual. We find that the ability of a trait to evolve is greater toward a semelparous strategy and this expresses a fitness advantage. This leads to an optimality between survival, population tracking ability, and lifetime fecundity.     

Strategic reduction of help before dispersal in a cooperative breeder

In cooperative breeders, sexually mature subordinates can either queue for chances to inherit the breeding position in their natal group, or disperse to reproduce independently. The choice of one or the other option may be flexible, as when individuals respond to attractive dispersal options, or they may reflect fixed life-history trajectories. Here, we show in a permanently marked, natural population of the cooperatively breeding cichlid fish Neolamprologus pulcher that subordinate helpers reduce investment in territory defence shortly before dispersing. Such reduction of effort is not shown by subordinates who stay and inherit the breeding position. This difference suggests that subordinates ready to leave reduce their investment in the natal territory strategically in favour of future life-history perspectives. It seems to be part of a conditional choice of the dispersal tactic, as this reduction in effort appears only shortly before dispersal, whereas philopatric and dispersing helpers do not differ in defence effort earlier in life. Hence, cooperative territory defence is state-dependent and plastic rather than a consistent part of a fixed life-history trajectory.     

Gonochorism vs. hermaphroditism: relationship between life history and fitness in three species of Ophryotrocha (Polychaeta: Dorvilleidae) with different forms of sexuality

1. The relationships between life history, fitness and sexuality, together with their ecological and evolutionary significance, has been analysed comparing the main life-history traits and demography in three closely related species belonging to the genus Ophryotrocha. The species are: the gonochoristic O. labronica, the simultaneous hermaphrodite O. diadema and the protandrous hermaphrodite O. puerilis. 2. Survivorship and reproductive data were collected weekly and were used to construct life tables and population projection matrices for each species and compare life-history characteristics. Elasticity, life-table response and decomposition analyses were performed to examine the relative contribution of fecundity and survivorship to differences in lamda between species. 3. The gonochoristic and hermaphroditic species differ in all the main life-history parameters and also in demographic characteristics. In particular the value of lamda, used commonly to express fitness, is markedly higher in the gonochoristic species while in terms of fitness simultaneous and sequential hermaphroditism are very similar. In the genus Ophryotrocha gonochorism currently represents the most widespread condition, being characteristic of the majority of the known species in the genus. 4. Given the demographic advantage ensured by gonochorism, it remains be understood why some species have retained simultaneous hermaphroditism and one has evolved a sequential type hermaphroditism; the most probable hypothesis is correlated with the density of the species in natural habitats.     

Accounting for wildlife life-history strategies when modeling stochastic density-dependent populations: A review

This article briefly reviews and provides discussion on the evidence for, and nature of, density-dependence patterns in r and K-selected species. In this review, I discuss how life-history strategies cause different nonlinear density-dependence patterns and I provide a simple modeling recommendation to incorporate nonlinear density dependence in population growth equations. Second, I discuss the importance of incorporation of environmental stochasticity and local extinction associated with nonlinear density dependence associated with life-history patterns through a novel modeling exercise. Last, I discuss the importance of considering how life-history nonlinear density dependence could affect optimal harvest yields. Though these topics are extensive, this review should spur wildlife biologists and managers to consider more inclusive population models that incorporate life-history strategies and stochasticity in their decision-making processes. © 2012 The Wildlife Society.     

To age or not to age

According to the antagonistic pleiotropy theory of ageing, natural selection has favoured genes conferring short-term benefits to the organism at the cost of deterioration in later life. The 'disposable soma' theory expresses this as a life-history strategy in which somatic maintenance is below the level required to prevent ageing, thus enabling higher immediate fertility. It has been argued that a non-ageing strategy will always be bettered by a low but non-zero rate of ageing, because the costs of such ageing will be felt only in the distant future when they are of negligible importance. Here, we examine this argument critically. We find that a non-ageing strategy will be locally optimal if, in the presence of ageing, the onset of deterioration is sufficiently rapid or early. Conversely, ageing will be optimal if deterioration is sufficiently slow or late. As the temporal profile of ageing changes from one of steady deterioration to one involving a sudden loss of vitality after a period of little or no decline, the conditions for a non-ageing strategy to be locally optimal become progressively more stringent. But for all forms of profile considered, conditions can be found for which a strategy involving no ageing is locally optimal.     

State-dependent life-history theory and its implications for optimal clutch size

Summary Life-history theory is usually based on an animal's age or size. McNamara describes a general technique for finding the optimal life-history when an organism's strategy is allowed to depend on other aspects of its state. In this paper we describe the technique in the context of previous work in life-history theory and discuss how it can be used to look at decisions on a finer time scale than the usual annual decisions. We show how it can be used to model optimal clutch size when there is a trade-off between number and quality of offspring. It is shown that the optimal clutch size is typically less than the most productive clutch size. Measuring the value of a clutch in terms of the number of offspring that survive to breed or even the number of grandchildren that survive to breed may give misleading results.     

The effect of socio-economic status and food availability on first birth interval in a pre-industrial human population

Individual variation in nutritional status has direct implications for fitness and thus is crucial in shaping patterns of life-history variation. Nevertheless, it is difficult to measure in natural populations, especially in humans. Here, we used longitudinal data on individual life-histories and annual crop yield variation collected from pre-industrial Finnish populations experiencing natural mortality and fertility to test the validity of first birth interval (FBI; time between marriage and first birth) as a surrogate measure of nutritional status. We evaluated whether women with different socio-economic groups differ in length of FBI, whether women of poorer socio-economic status and experiencing lower crop yields conceive slower following marriage, and whether shorter FBI is associated with higher lifetime breeding success. We found that poorer women had longer FBI and reduced probability of giving birth in months with low food availability, while the FBI of richer women was not affected by variation in food availability. Women with shorter FBI achieved higher lifetime breeding success and a faster reproductive rate. This is, to our knowledge, the first study to show a direct relationship between environmental conditions and speed of childbirth following marriage, highlighting the value of FBI as an indicator of nutritional status when direct data are lacking.     

Selection for increased allocation to offspring number under environmental unpredictability

According to life-history theory, the evolution of offspring size is constrained by the trade-off between allocation of resources to individual offspring and the number of offspring produced. Existing models explore the ecological consequences of offspring size, whereas number is invariably treated simply as an outcome of the trade-off with size. Here I ask whether there is a direct evolutionary advantage of increased allocation to offspring number under environmental unpredictability. Variable environments are expected to select for diversification in the timing of egg hatch and seed germination, yet the dependence of the expression of diversification strategies, and thus parental fitness, on offspring number has not previously been recognized. I begin by showing that well-established sampling theory predicts that a target bethedging diversification strategy is more reliably achieved as offspring number increases. I then use a simulation model to demonstrate that higher offspring number leads to greater geometric mean fitness under environmental uncertainty. Natural selection is thus expected to act directly to increase offspring number under assumptions of environmental unpredictability in season quality.     

Effect of periodical starvation on the life history of Brachionus plicatilis O.F. Müller (Rotifera): a possible strategy for population stability

To estimate the changes in the life history of the rotifer Brachionus plicatilis O.F. Müller under starvation, we carried out an individual culture and determined the effects of periodical food deprivation on its asexual reproductive characteristics such as lifespan, reproductive period, age at first egg and offspring production, and lifetime fecundity (total number of offspring produced in her lifetime). Rotifers were fed for 1-3 h daily, and were then starved until the next day. Control animals were fed throughout their lifespan. Starved rotifers matured and produced their first offspring at an older age than the control animals. The periodical starvation resulted in a decrease in the lifetime fecundity to less than half that of the non-starved control. The reproductive period and lifespan were 2-3 times longer in the starved animals than in the control animals. The negative relationship between lifespan and lifetime fecundity is interpreted as a trade-off in an alternative life-history strategy of rotifers under starved conditions. The great decrease in fecundity and extension of lifespan enables rotifers to compensate to keep the population in equilibrium.     

What pair formation can do to the battle of the sexes: towards more realistic game dynamics

In the various dynamic models of Dawkin's Battle of the Sexes, payoff matrices serve as the basic ingredients for the specification of a game-dynamic model. Here I model the sex war mechanistically, by expressing the costs of raising the offspring and performing a prolonged courtship via a time delay for the corresponding individuals, instead of via payoff matrices. During such a time delay an individual is not able to have new matings. Only after the delay has occurred, an individual (and its offspring) appears on the mating market again. From these assumptions I derive a pair-formation submodel, and a system of delay-differential equations describing the dynamics of the game. By a time-scale argument, I obtain an approximation of this system by means of a much simpler system of ordinary differential equations. Analysis of this simplified system shows that the model can give rise to two non-trivial asymptotically stable equilibrium points: an interior equilibrium where both female strategies and both male strategies are present, and a boundary equilibrium where only one of the female strategies and both male strategies are present. This behaviour is qualitatively different from that of models of the battle of the sexes formulated in the traditional framework of game-dynamic equations. In other words, the addition of a most elementary further assumption about individual life history fundamentally changes the model predictions. These results show that in analysing evolutionary games one should pay careful attention to the specific mechanisms involved in the conflict. In general, I advocate deriving simple models for evolutionary games, starting from more complex, mechanistic building blocks. The wide-spread method of modelling games at a high phenomenological level, through payoff matrices, can be misleading.