Evolutionary tracking is determined by differential selection on demographic rates and density dependence

Recent ecological forecasts predict that ~25% of species worldwide will go extinct by 2050. However, these estimates are primarily based on environmental changes alone and fail to incorporate important biological mechanisms such as genetic adaptation via evolution. Thus, environmental change can affect population dynamics in ways that classical frameworks can neither describe nor predict. Furthermore, often due to a lack of data, forecasting models commonly describe changes in population demography by summarizing changes in fecundity and survival concurrently with the intrinsic growth rate (r). This has been shown to be an oversimplification as the environment may impose selective pressure on specific demographic rates (birth and death) rather than directly on r (the difference between the birth and death rates). This differential pressure may alter population response to density, in each demographic rate, further diluting the information combined to produce r. Thus, when we consider the potential for persistence via adaptive evolution, populations with the same r can have different abilities to persist amidst environmental change. Therefore, we cannot adequately forecast population response to climate change without accounting for demography and selection on density dependence. Using a continuous‐time Markov chain model to describe the stochastic dynamics of the logistic model of population growth and allow for trait evolution via mutations arising during birth events, we find persistence via evolutionary tracking more likely when environmental change alters birth rather than the death rate. Furthermore, species that evolve responses to changes in the strength of density dependence due to environmental change are less vulnerable to extinction than species that undergo selection independent of population density. By incorporating these key demographic considerations into our predictive models, we can better understand how species will respond to climate change.     

Life history elasticity and the population-level effect of p-nonylphenol on Daphnia galeata

In order to evaluate population-level effects of p-nonylphenol on a cladoceran zooplankton (Daphnia galeata), the chronic effects on survival and reproduction were estimated with partial life table tests, which examined responses in life history characters until 3 weeks after birth. The observed responses in survival and reproduction were converted to reductions of the intrinsic rate of natural increase r. The population level EC₅₀, which is defined as the exposure concentration that reduces r by 50%, was estimated as 16.1 g l^–1. In order to examine the extent to which the population-level effect in terms of r is influenced by extra mortality in nature, which is induced by predation, starvation, etc., sensitivity (elasticity) measures of the intrinsic rate of natural increase to reductions in age-specific survival and reproduction were calculated under hypothetical predation schemes. The sensitivities of the intrinsic rate to changes in survival and reproduction invariably decline rapidly after the onset of reproduction irrespective of predation schemes. This implies that partial life cycle tests until 21 days after birth can provide reliable estimates of the population-level effects.     

Estimating population birth rates of zooplankton when rates of egg deposition and hatching are periodic

Summary I present a general method of computing finite birth and death rates of natural zooplankton populations from changes in the age distribution of eggs and changes in population size. The method is applicable to cases in which eggs hatch periodically owing to variable rates of oviposition. When morphological criteria are used to determine the age distribution of eggs at the beginning and end of a sampling interval, egg mortality can be incorporated in estimates of population birth rate. I raised laboratory populations of Asplanchna priodonta, a common planktonic rotifer, in semicontinuous culture to evaluate my method of computing finite birth rate. The Asplanchna population became synchronized to a daily addition of food but grew by the same amount each day once steady state was achieved. The steady-state rate of growth, which can be computed from the volume-specific dilution rate of the culture, was consistent with the finite birth rate predicted from the population's egg ratio and egg age distribution.     

On the interpretation of some planktonology equations

Summary The concept of the mean value of a function is used to interpret some population-dynamics equations. The well-known formula for the per capita growth rate r gives a precise mean value for any (not only exponentially growing) populations. This result is used to derive the birth and death rate equations of Paloheimo (1974) with minimal initial limitations.Abbreviations t time - N number of animals - E number of eggs - r specific (i.e. per capita) population growth rate - b specific birth rate - d specific death rate - D duration of embryonic development     

A stochastic computer model for simulating population growth

A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model's behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka's Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values or r_m and K. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetle Tribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

DENSITY-DEPENDENT SELECTION ON CONTINUOUS CHARACTERS: A QUANTITATIVE GENETIC MODEL

A quantitative genetic model of density-dependent selection is presented and analysed with parameter values obtained from laboratory selection experiments conducted by Mueller and his coworkers. The ecological concept of r- and K-selection is formulated in terms of selection gradients on underlying phenotypic characters that influence the density-dependent measure of fitness. Hence the selection gradients on traits are decomposed into two components, one that changes in the direction to increase r, and one that changes in the direction to increase K. The relative importance of the two components is determined by temporal fluctuations in population density. The evolutionary rate of r and K (per-generation changes in r and K due to the genetic responses of the underlying traits) is also formulated. Numerical simulation has shown that with moderate genetic variances of the underlying characters, r and K can evolve rapidly and the evolutionary rate is influenced by synergistic interaction between characters that contribute to r and K. But strong r-selection can occur only with severe and continuous disturbances of populations so that the population density is kept low enough to prevent K-selection.     

Demography of the twospotted spider mite,Tetranychus urticae Koch

Summary A simple life table model was constructed for Tetranychus urticae in which daily survivorship of eggs and motil stages, fecundity, and development time was altered to assess the impact of each parameter on the intrinsic rate of increase. r. Interpretation of the trade-offs focused on management considerations.A second aspect of the study concerned age and stage structure in mite populations including the time path of convergence to a stable age distribution and the effect of changes in birth and death rates on the age profile. The stable stage distributions of 7 tetranychid mite species were computed using 25 separate life tables. In spite of the wide range of r-values induced by different experimental conditions, all of the stage distributions were quite similar averaging roughly 66% eggs, 26% immatures, and 8% adults. Several population studies were cited which reported stage distributions of growing mite populations. The empirical evidence suggested that natural mite populations are often quite near this stable distribution.A practical problem involving the extent to which hormoligosis (insecticide stimulation) affects mite population growth rate was addressed using the life table model and laboratory data from controlled studies. The findings suggested that mite populations treated with insecticide may attain a 1.4- to a 4.2-fold difference in population size relative to an untreated population after 2 generations and over a 1,300-fold potential difference after 10 generations.     

Seasonality,Population Dynamics and Production of Daphnia longispina in the Subtropical Lake Bhimtal (U.P.), India

Seasonal variation in population density, birth rate, mortality and production of a daphnid was studied in a high, altitude sub-tropical lake. A bimodal growth curve with maxima during summer and autumn was observed. A positive correlation was reported between fecundity and death rate, probably due to a difference in age specific death rate combined with a high relative frequency of juveniles in a growing population. The production of Daphnia longispina correlates better with temperature than with food. The P/B ratio was higher during summer and autumn months.     

Life history of a neotropical marsupial: Evaluating potential contributions of survival and reproduction to population growth rate

The relative effect of survival and reproductive rates to population growth rate is expected to be similar across species with similar life-histories. We employed a matrix population model and sensitivity and elasticity analysis to assess the absolute and relative importance of age-specific survival and fertility to population growth rate of Didelphis aurita (Didelphimorphia, Didelphidae) in a rural area of Rio de Janeiro, southeastern Brazil. The results were compared to expectations for mammals that mature early and have short generation time, such as D. aurita. Prospective analysis showed that changes in pouch young and juveniles survival would have large effects on population growth rate, relative to other vital rates, being the most critical time periods in the life cycle of D. aurita, whereas the effect of fertilities were always low. These findings do not fit to the observed pattern in mammals that mature early, where reproductive parameters have the largest relative influence on population growth rate. Although reproductive rates were characterized by a relatively small influence on population growth rate, they are still relevant because of their high variability and response to potential environmental disturbances. The first application of matrix population models to a neotropical rainforest marsupial provides information on marsupial demography and life-history strategy, increasing comprehension of this unknown group.     

Validity of Using Background Leukemia Incidence Rates with Cohort Mortality-Based Potency Estimates to Calculate Excess Lifetime Risk

Data from occupational cohort mortality studies have been used to derive exposure-response curves and general population excess lifetime cancer risks, given low-level, chronic exposure. Using an actuarial method, mortality-based rate ratios associated with cumulative exposures are applied to age-specific background cancer mortality rates for a theoretical population aged birth to 70 years. In one recent U.S. Environmental Protection Agency health assessment, a mortality-based leukemia relative rate model was used with background leukemia incidence rates, rather than mortality rates, to calculate excess lifetime risk of leukemia incidence. We examined the validity and implications of this novel approach, while considering possible bias if a potential leukemogen did not pose equal risk by cell type. Limited sensitivity analyses were also conducted. Our analyses show that using total leukemia mortality-based potency estimates with background incidence rates will introduce a biased estimate of excess lifetime risk, the direction of which varies by potency and the histological type of leukemia. These biases were somewhat increased on adjustment for possible greater susceptibility of children. For potent carcinogens, the traditional approach provides a reasonable approximation of excess lifetime mortality risk for both the more and less fatal forms of leukemia, even after adjustments for children and is, therefore, to be preferred. Less consistency by leukemia cell type and background rate was observed for flatter exposure-response curves. This evaluation illustrates the importance of carefully examining the impact of methodological changes to calculations of excess lifetime risk before implementation.     

Evolution of senescence: Influence of age-dependent death rates on the natural increase of a hypothetical population

A hypothetical population is characterized by functions of age which describe its longevity and its maternity rate. Solution of the renewal equation for the birth rate of the population yields a characteristic equation which, in contradiction to the results of previous studies, may have more than one real root. The largest real root of the characteristic equation is the rate of natural increase, r, of the population and is used as a measure of its selective advantage.The maternity rate is represented by a rising or falling exponential function of age. Longevity is represented by a series each term of which has the form of a gamma distribution function. As the number of terms increases, the mean longevity remains constant, but the function becomes progressively more rectangular in shape; the early death rate declines, while the death rate in old age increases. Unless the reproductive fraction is small, each such decrease in the youthful death rate more than compensates for the corresponding increase in old age and causes an increment in r which is interpreted as a step toward the evolution of senescence. Although the degree of change in r attendant upon a change in the age-dependency of the death rate is related to the initial value of the maternity function, it is not influenced by the age dependency of the maternity function.     

Erratum to: Using multistate capture–mark–recapture models to quantify effects of predation on age-specific survival and population growth in black-tailed deer

Effective species management and conservation relies on accurate estimates of vital rates and an understanding of their link to environmental variables. We used multistate capture–mark–recapture models to directly quantify effects of predation on age-specific survival of black-tailed deer Odocoileus hemionus columbianus in California, USA. Survival probabilities were derived from individual encounter histories of 136 fawns and 57 adults monitored over 4 years. Based on results from our survival analysis we parameterized a Lefkovitch matrix and used elasticity analyses to investigate contributions of mortality due to predation to changes in population growth. We found strong evidence for age-specific survival including senescence. Survival of females >1 year old was consistently low (0.56 ± 0.18 for yearlings, 0.77 ± 0.13 for prime-aged females, and 0.55 ± 0.08 for senescent individuals), primarily due to high puma Puma concolor predation during summer. Predation from black bears Ursus americanus and coyotes Canis latrans was the primary cause for low annual survival of fawns (0.24 ± 0.16). Resulting estimates of population growth rates were indicative of a strongly declining population (λ = 0.82 ± 0.13). Despite high sensitivity to changes in adult survival, results from a lower-level elasticity analysis suggested that predation on fawns was the most significant individual mortality component affecting population decline. Our results provide a rare, direct link between predation, age-specific survival and the predicted population decline of a common ungulate species. The magnitude of predation was unexpected and suggests that ungulates in multi-predator systems struggle to cope with simultaneous reductions in survival probabilities from predators targeting different age classes.     

Demographic Modeling of a Predator-Prey System and Its implication for the Gombe Population of <Emphasis Type="Italic">Procolobus rufomitratus tephrosceles</Emphasis>

We evaluated the viability of colobus populations under conservative estimates of predation by chimpanzees. If fertility and mortality schedules remain constant, intensely hunted red colobus populations will experience negative growth rates if one allows the assumption of stable age structure to persist into the future. Demographic models have many advantages in studies of primate behavior and ecology. Researchers use them to investigate the quality of observed data and to project population growth rates to changes in mortality, fertility, and migration schedules. We used published age-specific death rates for red colobus (Procolobus rufomitratus tephrosceles) in Gombe National Park, Tanzania, to construct model life tables under various mortality scenarios. Selection in life-history traits toward shorter interbirth intervals, reduction in gestation length, and increased dispersal of individuals from source to sink populations and antipredator behavior, show a limited ability to counter the effects of intense predation. At Gombe, where factors such as small reserve size and isolation prevail, current levels of predation by chimpanzees may depress intrinsic growth rates low enough to cause the extirpation of red colobus in the near future.     

IMPLICATIONS OF NON-LINEAR DENSITY DEPENDENCE

Abstract: Ranges of the ratio of maximum net productivity level (MNPL) to carrying capacity (K) are explored in general models for pinnipeds and odontocetes. MNPL/K is used in management of marine mammals but no empirical evidence exists to limit the range of values expected. Density dependent changes in age-specific birth and death rates have been used to infer MNPL/K. Non-linearities in these rates do not translate directly to population growth curves. The simple models demonstrate: (1) density dependence is likely to involve more than a single parameter (such as birth rate), (2) MNPL/K can be greatly reduced from that inferred from one strongly non-linear parameter when changes in other parameters are linear, (3) ranges of MNPL/K depend on biological limits on ranges of fecundity and survival rates, and (4) the magnitude and sign of bias incurred by inferring MNPL/K from functional forms of single parameters cannot be determined. Given current empirical evidence the range of MNPL/K for marine mammals as a group is large. Although MNPL/K should not be inferred from single parameter non-linearities, distributions of MNPL/K values can be generated through models which account for single species ranges for birth and death rates and maximum population growth rate.     

The fall and rise of US inequities in premature mortality: 1960-2002

Background

Debates exist as to whether, as overall population health improves, the absolute and relative magnitude of income- and race/ethnicity-related health disparities necessarily increase—or derease. We accordingly decided to test the hypothesis that health inequities widen—or shrink—in a context of declining mortality rates, by examining annual US mortality data over a 42 year period.

Methods and Findings

Using US county mortality data from 1960–2002 and county median family income data from the 1960–2000 decennial censuses, we analyzed the rates of premature mortality (deaths among persons under age 65) and infant death (deaths among persons under age 1) by quintiles of county median family income weighted by county population size. Between 1960 and 2002, as US premature mortality and infant death rates declined in all county income quintiles, socioeconomic and racial/ethnic inequities in premature mortality and infant death (both relative and absolute) shrank between 1966 and 1980, especially for US populations of color; thereafter, the relative health inequities widened and the absolute differences barely changed in magnitude. Had all persons experienced the same yearly age-specific premature mortality rates as the white population living in the highest income quintile, between 1960 and 2002, 14% of the white premature deaths and 30% of the premature deaths among populations of color would not have occurred.

Conclusions

The observed trends refute arguments that health inequities inevitably widen—or shrink—as population health improves. Instead, the magnitude of health inequalities can fall or rise; it is our job to understand why.     

Culling Versus Density Effects in Management of a Deer Population

Abstract: Wildlife managers often manipulate hunting regulations to control deer populations. However, few empirical studies have examined the level of hunting effort (hunter-days) required to limit population growth and demographic effects through harvesting of females. Moreover, the relative importance of density effects on population growth has not been quantified. We reconstructed a sika deer [Cervus nippon] population over a period of 12 years (1990–2001) using age- and sex-specific harvest data. Using cohort analysis, we analyzed population dynamics, focusing on 1) the relationship between hunting effort and hunting-induced mortality rate, 2) relative contributions of hunting mortality and recruitment of yearlings to annual changes in population growth rate, and 3) annual variation in recruitment rate. Population size increased until 1998 and declined thereafter. The population growth rate changed more in response to annual changes in recruitment rate than hunting mortality rate. Temporal variation in recruitment rate was not controlled by birth rate alone; direct density dependence, intensities of hunting mortality for fawns, and for females (≥2 yr of age), which accounted for the fawn survival rate, were required as factors to explain temporal variation. Density effects on the recruitment rate were not strong enough to regulate the population within the study period; high hunting mortality, with intensive female harvesting, was necessary to prevent population growth. Hunting effort was a good predictor of the hunting mortality rate, and female harvest had a negative effect on the recruitment rate through fawn survival. We suggest that >3,500 hunter-days and prioritization of female harvesting are required to prevent increases in this deer population.     

Population dynamics of Daphnia spp. and implications for trophic interactions in small, monomictic lake

In Lake Oglethorpe, Georgia, USA, herbivorous crustacean zooplankton are abundant and dominate zooplankton biomass in winter, but are scarce throughout most of the summer. We used a 3.5 year study of Daphnia population dynamics to infer when food, predators or temperature constrained growth of this population. Transitions between winter and summer consumer assemblages are concurrent with seasonal changes in water temperature, thermal structure (stratification/destratification), resources (autotrophic/heterotrophic-domained production), and predator abundance and activity (e.g. Lepomis macrochirus and Chaoborus punctipennis. We sampled at weekly or less intervals from April 1992 to September 1995, and determined population abundances for all cladoceran species. For the Daphnia population (Daphnia ambigua + Daphnia parvula, we measured clutch size and length for all individuals. We used average water column temperature (where dissolved oxygen is >1 mg l^-1) to estimate egg development time from an empirical model. Estimates of Daphnia population birth and death rate were thus generated from abundance, egg ratio and temperature/dissolved oxygen data. We compared observed birth rate (bobs) with expected birth rate (bexp>95% CI; predicted for food-saturated conditions at ambient temperature). For variable (1-13 week) periods between later November and March, 1992-1995, water temperature was the primary factor constraining Daphnia population growth (bobs = bexp). From about April to early November, bobs < bexp suggested food-limited population growth. In spring, summer and early fall (March-October), population densities were several-fold lower than in late fall and winter (November-February). However, all else being equal, egg ratio and population birth rate data would have predicted that Daphnia abundance fluctuates over equivalent ranges in spring and fall. We interpret this discrepancy as evidence for increased rates of extrinsic mortality during the growing season and a seasonal shift in the relative importance of resource and predator regulation. The duration of predator suppression of crustacean population abundance in Lake Oglethorpe and other warm-latitude lakes (36N-27°S) is longer (3-7 months) than that observed in north temperate lakes (1-2.5 months; 41-52°N).      

A quantitative test of the size efficiency hypothesis by means of a physiologically structured model

According to the size‐efficiency hypothesis (SEH) larger bodied cladocerans are better competitors for food than small bodied species. In environments with fish, however, the higher losses of the large bodied species due to size‐selective predation may shift the balance in favor of the small bodied species. Here we present a theoretical framework for the analysis of the competitive abilities of zooplankton species that takes both competition and predation into account in one coherent analysis. By applying the conceptually well‐understood framework of physiologically structured population models we were able to predict the relative difference in predation rates necessary to cause a shift in dominance of the large‐bodied species (Daphnia pulicaria) to the small‐bodied species (D. galeata). These predictions depend only on seven easily interpretable parameters per species: size at birth, size at maturity and maximum size, age at maturity, maximal clutch size, egg development time and finally the half‐saturation constant for food. The critical equilibrium mortality of D. pulicaria was 0.16 d^?1 at food concentrations close to the critical food concentration of D. galeata, i.e. D. pulicaria will win the competition as long as its mortality rate is below 0.16 d^?1. At higher food concentrations the differential mortality curve (plotting equilibrium mortalities of both species against each other) approached a linear function with a slope of one and an intercept equal to the difference in maximal population birth rates. The prediction of critical predation rates was independent of the ingestion rate of the cladocerans and the algal carrying capacity and food regeneration rate of the environment although the mechanism works through competition for a shared algal food resource. We interpret these findings in terms of the relative predation risk large and small‐bodied cladocerans will face in various freshwater ecosystems.     

Age- and density-dependent population dynamics in static and variable environments

We consider a general model of a single-species population with age- and density-dependent per capita birth and death rates. In a static environment we show that if the per capita death rate is independent of age, then the local stability of any stationary state is guaranteed by the requirement that, in the region of the steady state, the density dependence of the birth rate should be negative and that of the death rate positive. In a variable environment we show that, provided the system is locally stable, small environmental fluctuations will give rise to small age structure and population fluctuations which are related to the driving environmental fluctuations by a simple “transfer function.” We illustrate our general theory by examining a model with a per capita death rate which is age and density independent and a per capita birth rate which is zero up to some threshold age a₀, adopts a finite density-dependent value up to a maximum age a_o + α, and is zero thereafter. We conclude from this model that resonance due specifically to single-species age-structure effects will only be of practical importance in populations whose members have a life cycle consisting of a long immature phase followed by a short burst of intense reproductive effort (α a_o).     

Impact of fear effect on the growth of prey in a predator-prey interaction model

Several field data and experiments on a terrestrial vertebrates exhibited that the fear of predators would cause a substantial variability of prey demography. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. Based on the experimental evidence, we proposed and analyzed a prey-predator system introducing the cost of fear into prey reproduction with Holling type-II functional response. We investigate all the biologically feasible equilibrium points, and their stability is analyzed in terms of the model parameters. Our mathematical analysis exhibits that for strong anti-predator responses can stabilize the prey-predator interactions by ignoring the existence of periodic behaviors. Our model system undergoes Hopf bifurcation by considering the birth rate r₀ as a bifurcation parameter. For larger prey birth rate, we investigate the transition to a stable coexisting equilibrium state, with oscillatory approach to this equilibrium state, indicating that the greatest characteristic eigenvalues are actually a pair of imaginary eigenvalues with real part negative, which is increasing for r₀. We obtained the conditions for the occurrence of Hopf bifurcation and conditions governing the direction of Hopf bifurcation, which imply that the prey birth rate will not only influence the occurrence of Hopf bifurcation but also alter the direction of Hopf bifurcation. We identify the parameter regions associated with the extinct equilibria, predator-free equilibria and coexisting equilibria with respect to prey birth rate, predator mortality rates. Fear can stabilize the predator-prey system at an interior steady state, where all the species can exists together, or it can create the oscillatory coexistence of all the populations. We performed some numerical simulations to investigate the relationship between the effects of fear and other biologically related parameters (including growth/decay rate of prey/predator), which exhibit the impact that fear can have in prey-predator system. Our numerical illustrations also demonstrate that the prey become less sensitive to perceive the risk of predation with increasing prey growth rate or increasing predators decay rate.