Buffering of life histories against environmental stochasticity: accounting for a spurious correlation between the variabilities of vital rates and their contributions to fitness

Life-history theory predicts vital rates that on average make large contributions to the annual multiplication rate of a lineage should be highly buffered against environmental variability. This prediction has been tested by looking for a negative correlation between the sensitivities (or elasticities) of the elements in a projection matrix and their variances (or coefficients of variation). Here, we show by constructing random matrices that a spurious negative correlation exists between the sensitivities and variances, and between the elasticities and coefficients of variation, of matrix elements. This spurious correlation arises in part because size transition probabilities, which are bounded by 0 and 1, have a limit to their variability that often does not apply to matrix elements representing reproduction. We advocate an alternative analysis based on the underlying vital rates (not the matrix elements) that accounts for the inherent limit to the variability of zero-to-one vital rates, corrects for sampling variation, and tests for a declining upper limit to variability as a vital rate's fitness contribution increases. Applying this analysis to demographic data from five populations of the alpine cushion plant Silene acaulis, we provide evidence of stronger buffering in the vital rates that most influence fitness.     

The reproductive rates of Australian rodents

Summary The reproductive rates of about 50 species of Australian rodents were studied by calculating allometric equations for the relationships between female body weight, litter size, length of gestation and weaning periods as well as age of sexual maturity.Members of the subfamily Hydromyinae, which invaded Australia 5–10 million years ago, are characterised by small litters, long gestation and weaning periods and late maturity. The opposite is true for the Murinae (Rattus and Mus) which invaded Australia during the Pleistocene. Among the species of this latter group, those which invaded earlier have reproductive rates closer to the old invaders, while those which arrived with the Europeans during the last 200 years have the highest reproductive rates.Possible reasons for the low reproductive rates of Australian rodents are discussed. It is concluded that the rain forest origin of the hydromyinids is one of the factors responsible for their low reproductive rate. They maintained this rate to the present time because of the unpredictability of the climate and the low productivity of many Australian habitats.     

Density-dependent vital rates and their population dynamic consequences

We explore a set of simple, nonlinear, two-stage models that allow us to compare the effects of density dependence on population dynamics among different kinds of life cycles. We characterize the behavior of these models in terms of their equilibria, bifurcations, and nonlinear dynamics, for a wide range of parameters. Our analyses lead to several generalizations about the effects of life history and density dependence on population dynamics. Among these are: (1) iteroparous life histories are more likely to be stable than semelparous life histories; (2) an increase in juvenile survivorship tends to be stabilizing; (3) density-dependent adult survival cannot control population growth when reproductive output is high; (4) density-dependent reproduction is more likely to cause chaotic dynamics than density dependence in other vital rates; and (5) changes in development rate have only small effects on bifurcation patterns. Received: 12 April 1999 / Published online: 3 August 2000     

Comparative evolutionary rates of introns and exons in murine rodents

Analysis of DNA sequences of 132 introns and 140 exons from 42 pairs of orthologous genes of mouse and rat was used to compare patterns of evolutionary change between introns and exons. The mean of the absolute difference in length (measured in base pairs) between the two species was nearly five times as high in the case of introns as in the case of exons. The average rate of nucleotide substitution in introns was very similar to the rate of synonymous substitution in exons, and both were about three times the rate of substitution at nonsynonymous sites in exons. G+C content of introns and exons of the same gene were correlated; but mean G+C content at the third positions of exons was significantly higher than that of introns or positions 1–2 of exons from the same gene. G+C content was conserved over evolutionary time, as indicated by strong correlations between mouse and rat; but the change in G+C content was greatest at position 3 of exons, intermediate in introns, and lowest at positions 1–2 in introns. Received: 23 December 1996 / Accepted: 1 April 1997     

The natural variability of vital rates and associated statistics

The first concern of this work is the development of approximations to the distributions of crude mortality rates, age-specific mortality rates, age-standardized rates, standardized mortality ratios, and the like for the case of a closed population or period study. It is found that assuming Poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate Poisson distribution. The Lexis diagram is seen to make direct use of the result. It is suggested that in a variety of cases, it will be satisfactory to approximate the distribution of the number of deaths given the population size, by a Poisson with mean proportional to the population size. It is further suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic Poisson distribution for the number of deaths, with mean proportional to the population size and an exponential function of a linear combination of the explanatories. Such a model is fit to mortality data for Canadian females classified by age and year. A dynamic variant of the model is further fit to the time series of total female deaths alone by year. The models with extra-Poisson variation are found to lead to substantially improved fits.     

A juvenile-adult model with periodic vital rates

A global branch of positive cycles is shown to exist for a general discrete time, juvenile-adult model with periodically varying coefficients. The branch bifurcates from the extinction state at a critical value of the mean, inherent fertility rate. In comparison to the autonomous system with the same mean fertility rate, the critical bifurcation value can either increase or decrease with the introduction of periodicities. Thus, periodic oscillations in vital parameter can be either advantageous or deleterious. A determining factor is the phase relationship among the oscillations in the inherent fertility and survival rates.Research supported by NSF grant DMS-0414212.     

Cheek pouch capacities and loading rates of heteromyid rodents

Rodents of the family Heteromyidae are proficient gatherers and hoarders of seeds. A major component of their adaptive specialization for harvesting and transporting seeds is their spacious, fur-lined cheek pouches. Precise measurements of cheek pouch capacities are essential if ecologists are to understand the foraging ecology, possible constraints on locomotion patterns, and competitive relationships of heteromyid rodents. To measure the size of these cheek pouches and the rate at which animals load seeds into their pouches during seed harvest, we attracted 56 individuals representing ten species of heteromyid rodents to bait stations in the field and allowed them to fill their cheek pouches with seeds several times while we observed and timed the events with the aid of night-vision equipment. The largest load taken by each individual was used as an estimate of its cheek pouch capacity. At the end of observations, each subject was captured and its mass and other data gathered. The allometric relationship between cheek pouch capacity and body mass for ten species of heteromyids was significant [pouch capacity (ml) = 0.148 body mass (g)^0.992, r ²=0.91, P<0.0001]. The regression coefficient is ≈1.0, which indicates that the volume of the cheek pouches scales in direct proportion to body size. When the data were subdivided into quadrupeds (Perognathus and Chaetodipus) and bipeds (Dipodomys) (n=5 for each), the relationships between pouch capacity and body mass were significant, but the two regressions were not significantly different from each other. When all loads (full and partial) were considered, subjects filled their cheek pouches an average of 93 ± 10% of pouch capacity (n=185). Cheek pouch capacities from published studies of artificially filled pouches of heteromyids in the laboratory averaged about 40% below the field measurements obtained here. The allometric relationship between mean loading rate and body mass was also significant [seeds/s=1.067 bodymass (g)^0.830, r ²=0.85,P=0.0011), but when quadrupeds and bipeds were considered separately, the relationships were not significant. Seed densities and bulk densities were used to calculate packing coefficients for seed species, which, when used in conjunction with the allometric relationship between cheek pouch capacity and body size, can be used to estimate the maximum load carried by a heteromyid. Except for the very largest kangaroo rat species, a full pouch load of Indian ricegrass seeds represents less than the daily energy requirements of an active heteromyid. Received: 3 March 1997 / Accepted: 15 July 1997     

Artificial selection on metabolic rates and related traits in rodents

Artificial selection experiments are potentially powerful, yetunder-utilized tool of evolutionary and physiological ecology.Here we analyze and review three important aspects of such experiments.First, we consider the effects of instrumental measurement errorsand random fluctuations of body mass on the total phenotypicvariation. We illustrate this with the analysis of measurementsof oxygen consumption in an open-flow respirometry set-ups.We conclude that measurement errors and fluctuations of bodymass are likely to reduce the repeatability of oxygen consumptionby about one third. Using published estimates of repeatabilityof metabolic rates we also showed that it does not tend to declinewith increasing time between measurements. Second, we reviewdata on narrow sense heritability (h²) of metabolic rates inmammals. The results are equivocal: many studies report verylow (     

Divergence in rates of phenotypic plasticity among ectotherms

An individual's fitness cost associated with environmental change likely depends on the rate of adaptive phenotypic plasticity, and yet our understanding of plasticity rates in an ecological and evolutionary context remains limited. We provide the first quantitative synthesis of existing plasticity rate data, focusing on acclimation of temperature tolerance in ectothermic animals, where we demonstrate applicability of a recently proposed analytical approach. The analyses reveal considerable variation in plasticity rates of this trait among species, with half-times (how long it takes for the initial deviation from the acclimated phenotype to be reduced by 50% when individuals are shifted to a new environment) ranging from 3.7 to 770.2 h. Furthermore, rates differ among higher taxa, being higher for amphibians and reptiles than for crustaceans and fishes, and with insects being intermediate. We argue that a more comprehensive understanding of phenotypic plasticity will be attained through increased focus on the rate parameter.     

Reproductive rates in Australian rodents are related to phylogeny

Background

The native rodents of Australia are commonly divided into two groups based on the time of their colonization of the Sahulian continent, which encompasses Australia, New Guinea, and the adjacent islands. The first group, the “old endemics,” is a diverse assemblage of 34 genera that are descended from a single colonization of the continent during the Pliocene. A second group, the “new endemics,” is composed of several native Rattus species that are descended from a single colonization during the Pleistocene. Finally, a third group is composed of three non-native species of Rattus and Mus introduced into Australia by humans over the last 200 years. Previous studies have claimed that the three groups differ in their reproductive rates and that this variation in rates is associated with the unique environmental conditions across Australia. We examined these hypotheses using phylogenetically controlled methods.

Methodology and Results

We examined the relationship between the reproductive rates of the Australian rodents and the environmental variations across the continent, as well as the epoch of their colonization of the continent. Our results revealed no significant correlation with environmental variables but a significant association between colonization age and all the reproductive parameters examined.

Discussion

Based on a larger phylogeny of the subfamily Murinae, we showed that significant differences in reproductive rates among colonization groups are shared with their closest relatives outside Sahul. Therefore, the lower reproductive rates in the old endemics are more likely to be the result of phylogenetic history and conservation of traits than an adaptation to the Australian environment. In the new endemics, we found a trend of increasing reproductive rates with diversification. We suggest that the differences in reproductive rates of the old endemic rodents and the native Rattus represent alternative adaptive strategies that have allowed them to utilize similar ecological niches across Australia.     

Building integral projection models with nonindependent vital rates

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co‐vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co‐vary as a function of time (temporal variation), co‐vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population‐level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life‐history evolution.     

Modeling vital rates improves estimation of population projection matrices

Population projection matrices are commonly used by ecologists and managers to analyze the dynamics of stage-structured populations. Building projection matrices from data requires estimating transition rates among stages, a task that often entails estimating many parameters with few data. Consequently, large sampling variability in the estimated transition rates increases the uncertainty in the estimated matrix and quantities derived from it, such as the population multiplication rate and sensitivities of matrix elements. Here, we propose a strategy to avoid overparameterized matrix models. This strategy involves fitting models to the vital rates that determine matrix elements, evaluating both these models and ones that estimate matrix elements individually with model selection via information criteria, and averaging competing models with multimodel averaging. We illustrate this idea with data from a population of Silene acaulis (Caryophyllaceae), and conduct a simulation to investigate the statistical properties of the matrices estimated in this way. The simulation shows that compared with estimating matrix elements individually, building population projection matrices by fitting and averaging models of vital-rate estimates can reduce the statistical error in the population projection matrix and quantities derived from it.     

Linking vital rates to invasiveness of a perennial herb

Invaders generally show better individual performance than non-invaders and, therefore, vital rates (survival, growth, fecundity) could potentially be used to predict species invasiveness outside their native range. Comparative studies have usually correlated vital rates with the invasiveness status of species, while few studies have investigated them in relation to population growth rate. Here, I examined the influence of five vital rates (plant establishment, survival, growth, flowering probability, seed production) and their variability (across geographic regions, habitat types, population sizes and population densities) on population growth rate (λ) using data from 37 populations of an invasive, iteroparous herb (Lupinus polyphyllus) in a part of its invaded range in Finland. Variation in vital rates was often related to habitat type and population density. The performance of the populations varied from declining to rapidly increasing independently of habitat type, population size or population density, but differed between regions. The population growth rate increased linearly with plant establishment, and with the survival and growth of vegetative individuals, while the survival of flowering individuals and annual seed production were not related to λ. The vital rates responsible for rapid population growth varied among populations. These findings highlight the importance of both regional and local conditions to plant population dynamics, demonstrating that individual vital rates do not necessarily correlate with λ. Therefore, to understand the role of individual vital rates in a species ability to invade, it is necessary to quantify their effect on population growth rate.     

Response of population size to changing vital rates in random environments

Population size and population growth rate respond to changes in vital rates like survival and fertility. In deterministic environments change in population growth rate alone determines change in population size. In random environments, population size at any time t is a random variable so that change in population size obeys a probability distribution. We analytically show that, in a density-independent population, the proportional change in population size with respect to a small proportional change in a vital rate has an asymptotic normal distribution. Its mean grows linearly at a rate equal to the elasticity of the long-term stochastic growth rate λ _S while the standard deviation scales as $\sqrt t$ . Consequently, a vital rate with a larger elasticity of λ _S may produce a larger mean change in population size compared to one with a smaller elasticity of λ _S. But a given percentage change in population size may be more likely when the vital rate with smaller elasticity is perturbed. Hence, the response of population size to perturbation of a vital rate depends not only on the elasticity of the population growth rate but also on the variance in change in population size. Our results provide a formula to calculate the probability that population size changes by a given percentage that works well even for short time periods.