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).     

New data on programmed risks of death in normal mice and mutants with growth delay

Study of the lifespans of normal (non mutant) mice and growth delay mutants has shown that mortality rates for both kinds of animals exhibit reproducible fluctuations. In the case of the mutant mice, the positions of peaks on the differential mortality curves (mortality rate plotted against lifespan) coincided in different-sex groups of animals and in same-sex subgroups of animals. Differential mortality curves of the mutant mice also had a peak at 1 month of age that was absent from the differential mortality curves of the normal mice. In the case of normal animals, positions of most peaks were the same in the studied independent subgroups of males, and to a lesser extent – independent subgroups of females, which might be explained by a shift in mortality peak positions due to the reproductive activity of females. Similar positions of mortality rate peaks in the differential mortality curves for animals from independent groups and subgroups indicate the existence of increased risks of death at specific ages. The observed pattern could be due to the programming in the genome of both the periods of increased risk of death and the intermitting intervals of stable development.     

Optimal reproductive strategies in age-structured populations of zooplankton

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

Age-specific mortality rates in reef fishes: Evidence and implications

Abstract Mortality is a fundamental demographic rate, the nature of which has profound consequences for both the dynamics of populations and the life-history evolution of species. For example, if per capita mortality rates are age- or stage-specific, life-history traits should evolve in response to age- and stage-specific differences in selection arising from these temporally variable rates. Similarly, variation in the average mortality rate across ages and/or stages can also select for shifts in life history. Mortality rates of recently settled reef fishes can be very high and per capita mortality is commonly assumed to decrease with increasing age. A review of evidence for age-specific per capita mortality rates in reef fishes from early postsettlement up to 13 months postsettlement suggests that during this period these rates are often age invariant. The data on which these interpretations are based, however, are extremely limited both in terms of the proportion of the life cycle over which mortality rates have been sampled and the quality of these data. Nonetheless, these data do suggest that selective pressures associated with patterns of mortality may vary among species of reef fishes and that these species therefore could be more effectively used in the study of life-history evolution. At present, reef fishes are under-represented in the study of life-history evolution compared with other vertebrate taxa.     

Tyrannosaur ageing

Rate of ageing in tyrannosaurs was calculated from parameters of Weibull functions fitted to survival curves based on the estimated ages at death of fossilized remains. Although tyrannosaurs are more closely related to birds than to mammals, they apparently aged at rates similar to mammals of comparable size. Rate of growth in body mass of tyrannosaurs was similar to that of large mammals, and their rates of ageing were consistent with the estimated extrinsic mortality, which is strongly correlated with the rate of ageing across birds and mammals. Thus, tyrannosaurs appear to have had life histories resembling present-day large terrestrial mammals. Rate of ageing in warm-blooded vertebrates appears to be adjusted in response to extrinsic mortality and potential lifespan, independently of both physiological and developmental rates. However, individuals in species with the slowest rates of ageing suffer the highest proportion of ageing-related mortality, hence potentially strong selection to further postpone senescence. Thus, the longest observed lifespans in birds, tyrannosaurs and mammals might be close to the maximum possible.     

Social and demographic effects of anthropogenic mortality: a test of the compensatory mortality hypothesis in the red wolf

Whether anthropogenic mortality is additive or compensatory to natural mortality in animal populations has long been a question of theoretical and practical importance. Theoretically, under density-dependent conditions populations compensate for anthropogenic mortality through decreases in natural mortality and/or increases in productivity, but recent studies of large carnivores suggest that anthropogenic mortality can be fully additive to natural mortality and thereby constrain annual survival and population growth rate. Nevertheless, mechanisms underlying either compensatory or additive effects continue to be poorly understood. Using long-term data on a reintroduced population of the red wolf, we tested for evidence of additive vs. compensatory effects of anthropogenic mortality on annual survival and population growth rates, and the preservation and reproductive success of breeding pairs. We found that anthropogenic mortality had a strong additive effect on annual survival and population growth rate at low population density, though there was evidence for compensation in population growth at high density. When involving the death of a breeder, anthropogenic mortality was also additive to natural rates of breeding pair dissolution, resulting in a net decrease in the annual preservation of existing breeding pairs. However, though the disbanding of a pack following death of a breeder resulted in fewer recruits per litter relative to stable packs, there was no relationship between natural rates of pair dissolution and population growth rate at either high or low density. Thus we propose that short-term additive effects of anthropogenic mortality on population growth in the red wolf population at low density were primarily a result of direct mortality of adults rather than indirect socially-mediated effects resulting in reduced recruitment. Finally, we also demonstrate that per capita recruitment and the proportion of adults that became reproductive declined steeply with increasing population density, suggesting that there is potential for density-dependent compensation of anthropogenically-mediated population regulation.     

Post-settlement emigration affects mortality estimates for two Bahamian wrasses

Understanding the dynamics of open marine populations is inherently complex, and this complexity has led to decades of debate regarding the relative importance of pre- versus post-settlement processes in structuring these populations. Movement between patches may be an important modifier of patterns established at settlement, yet local immigration and emigration have received less attention than other demographic rates. I examined loss rates from tagged populations of juvenile wrasses (yellowhead wrasse Halichoeres garnoti and bluehead wrasse Thalassoma bifasciatum) at two sites in the Bahamas. Assuming that all losses were due solely to mortality would have significantly underestimated survivorship of yellowhead wrasse by 29% and bluehead wrasse by 14%. On average, per capita mortality and emigration rates were higher for yellowhead than bluehead wrasse, but neither demographic rate differed between sites for either species. With respect to within-species density, bluehead wrasse mortality was density-dependent at the patch reef site, but mortality rates of yellowhead wrasse were consistently density-independent. Evaluating the effects of between-species density, yellowhead wrasse mortality increased with a decrease in bluehead wrasse density, but this effect was limited to the patch reef site. Emigration rates were not a function of either within-species or between-species density, but instead varied inversely with isolation distance. Numerous previous studies of coral-reef fish, conducted on patch reefs separated by only a few meters of sand and often using untagged fish, may have confounded losses due to emigration with those due to mortality. A better understanding of the factors affecting emigration in marine fishes is important to their effective management using spatial tools such as marine protected areas.     

The Evolution of Senescence and Post-Reproductive Lifespan in Guppies (Poecilia reticulata)

The study of post-reproductive lifespan has been of interest primarily with regard to the extended post-menopausal lifespan seen in humans. This unusual feature of human demography has been hypothesized to have evolved because of the “grandmother” effect, or the contributions that post-reproductive females make to the fitness of their children and grandchildren. While some correlative analyses of human populations support this hypothesis, few formal, experimental studies have addressed the evolution of post-reproductive lifespan. As part of an ongoing study of life history evolution in guppies, we compared lifespans of individual guppies derived from populations that differ in their extrinsic mortality rates. Some of these populations co-occur with predators that increase mortality rate, whereas other nearby populations above barrier waterfalls are relatively free from predation. Theory predicts that such differences in extrinsic mortality will select for differences in the age at maturity, allocation of resources to reproduction, and patterns of senescence, including reproductive declines. As part of our evaluation of these predictions, we quantified differences among populations in post-reproductive lifespan. We present here the first formal, comparative study of the evolution of post-reproductive lifespan as a component of the evolution of the entire life history. Guppies that evolved with predators and that experienced high extrinsic mortality mature at an earlier age but also have longer lifespans. We divided the lifespan into three non-overlapping components: birth to age at first reproduction, age at first reproduction to age at last reproduction (reproductive lifespan), and age at last reproduction to age at death (post-reproductive lifespan). Guppies from high-predation environments live longer because they have a longer reproductive lifespan, which is the component of the life history that can make a direct contribution to individual fitness. We found no differences among populations in post-reproductive lifespan, which is as predicted since there can be no contribution of this segment of the life history to an individual's fitness. Prior work on the evolution of post-reproductive lifespan has been dominated by speculation and correlative analyses. We show here that this component of the life history is accessible to formal study as part of experiments that quantify the different segments of an individual's life history. Populations of guppies subject to different mortality pressures from predation evolved differences in total lifespan, but not in post-reproductive lifespan. Rather than showing the direct effects of selection characterizing other life-history traits, post-reproductive lifespan in these fish appears to be a random add-on at the end of the life history. These findings support the hypothesis that differences in lifespan evolving in response to selection are confined to the reproductive lifespan, or those segments of the life history that make a direct contribution to fitness. We also show, for the first time, that fish can have reproductive senescence and extended post-reproductive lifespans despite the general observation that they are capable of producing new primary oocytes throughout their lives.     

An explanation for negligible senescence in animals

Negligible or negative senescence occurs when mortality risk is stable or decreases with age, and has been observed in some wild animals. Age‐independent mortality in animals may lead to an abnormally long maximum individual lifespans and be incompatible with evolutionary theories of senescence. The reason why there is no evidence of senescence in these animals has not been fully understood. Recovery rates are usually very low for wild animals with high dispersal ability and/or small body size (e.g., bats, rodents, and most birds). The only information concerning senescence for most of these species is the reported lifespan when individuals are last seen or caught. We deduced the probability density function of the reported lifespan based on the assumption that the real lifespan corresponding to Weibull or Gompertz distribution. We show that the magnitude of the increase in mortality risk is largely underestimated based on the reported lifespans with low recovery probability. The risk of mortality can aberrantly appear to have a negative correlation with age when it actually increases with increasing lifespan. We demonstrated that the underestimated aging rate for wild animals with low recovery probability can be generalizable to any aging models. Our work provides an explanation for the appearance of negligible senescence in many wild animals. Humans attempt to obtain insights from other creatures to better understand our own biology and its gain insight into how to enhance and extended human health. Our advice is to take a second glance before admiring the negligible senescence in other animals. This ability to escape from senescence is possibly only as beautiful illusion in animals.     

Dynamics of cannibalism in equal‐aged cohorts of Spodoptera frugiperda

1. Antagonistic interactions in herbivorous insects are often density‐dependent, so rates are predicted to vary dynamically over time as density changes. Fatal intraspecific interactions, especially cannibalism, occur between equal‐aged larvae in young first‐ and second‐instar Spodoptera frugiperda (J.E. Smith). 2. A cannibalism experiment was conducted, starting with seven different densities of neonate S. frugiperda larvae, each replicated 50 times. Larvae were examined daily for the duration of the first and second instars (7 days). Seven‐day mortality was density‐dependent. 3. A stochastic mathematical model was developed in which per‐capita mortality from antagonistic interactions among equal‐aged larvae varies dynamically as density changes. A maximum likelihood method was developed to estimate the conditional per‐capita mortality rate from antagonistic interactions given an intraspecific encounter. An alternative model with mean‐mortality from antagonistic interactions that depends only on the initial larval density was also developed. 4. The models were fitted to the experimental data, and compared using log‐likelihood. The dynamic model fitted the cannibalism data significantly better than the time‐averaged mortality model for all starting densities for the experimental data, implying that density‐dependent mortality varied dynamically over time even within short 7‐day periods. 5. The conditional per‐capita mortality rate from antagonistic interactions was also density‐dependent, possibly because encounters became more aggregated at higher density, or because the probability that a larva died from the interaction was higher at higher density, or both.     

A statistical model for red blood cell survival

A statistical model for the survival time of red blood cells (RBCs) with a continuous distribution of cell lifespans is presented. The underlying distribution of RBC lifespans is derived from a probability density function with a bathtub-shaped hazard curve, and accounts for death of RBCs due to senescence (age-dependent increasing hazard rate) and random destruction (constant hazard), as well as for death due to initial or delayed failures and neocytolysis (equivalent to early red cell mortality). The model yields survival times similar to those of previously published studies of RBC survival and is easily amenable to inclusion of drug effects and haemolytic disorders.     

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     

The evolution of senescence and post-reproductive lifespan in guppies (Poecilia reticulata)

The study of post-reproductive lifespan has been of interest primarily with regard to the extended post-menopausal lifespan seen in humans. This unusual feature of human demography has been hypothesized to have evolved because of the “grandmother” effect, or the contributions that post-reproductive females make to the fitness of their children and grandchildren. While some correlative analyses of human populations support this hypothesis, few formal, experimental studies have addressed the evolution of post-reproductive lifespan. As part of an ongoing study of life history evolution in guppies, we compared lifespans of individual guppies derived from populations that differ in their extrinsic mortality rates. Some of these populations co-occur with predators that increase mortality rate, whereas other nearby populations above barrier waterfalls are relatively free from predation. Theory predicts that such differences in extrinsic mortality will select for differences in the age at maturity, allocation of resources to reproduction, and patterns of senescence, including reproductive declines. As part of our evaluation of these predictions, we quantified differences among populations in post-reproductive lifespan. We present here the first formal, comparative study of the evolution of post-reproductive lifespan as a component of the evolution of the entire life history.

Guppies that evolved with predators and that experienced high extrinsic mortality mature at an earlier age but also have longer lifespans. We divided the lifespan into three non-overlapping components: birth to age at first reproduction, age at first reproduction to age at last reproduction (reproductive lifespan), and age at last reproduction to age at death (post-reproductive lifespan). Guppies from high-predation environments live longer because they have a longer reproductive lifespan, which is the component of the life history that can make a direct contribution to individual fitness. We found no differences among populations in post-reproductive lifespan, which is as predicted since there can be no contribution of this segment of the life history to an individual's fitness.

Prior work on the evolution of post-reproductive lifespan has been dominated by speculation and correlative analyses. We show here that this component of the life history is accessible to formal study as part of experiments that quantify the different segments of an individual's life history. Populations of guppies subject to different mortality pressures from predation evolved differences in total lifespan, but not in post-reproductive lifespan. Rather than showing the direct effects of selection characterizing other life-history traits, post-reproductive lifespan in these fish appears to be a random add-on at the end of the life history. These findings support the hypothesis that differences in lifespan evolving in response to selection are confined to the reproductive lifespan, or those segments of the life history that make a direct contribution to fitness. We also show, for the first time, that fish can have reproductive senescence and extended post-reproductive lifespans despite the general observation that they are capable of producing new primary oocytes throughout their lives.

     

Regulation of local populations of a coral reef fish via joint effects of density- and number-dependent mortality

Density-dependent mortality can regulate local populations - effectively minimizing the likelihood of local extinctions and unchecked population growth. It is considered particularly important for many marine reef organisms with demographically open populations that lack potential regulatory mechanisms tied to local reproduction. While density-dependent mortality has been documented frequently for reef fishes, few studies have explored how the strength of density-dependence varies with density, or how density-dependence may be modified by numerical effects (i.e., number-dependent mortality). Both issues can have profound effects on spatial patterns of abundance and the regulation of local populations. I address these issues through empirical studies in Moorea, French Polynesia, of the six bar wrasse (Thalassoma hardwicke), a reef fish that settles to isolated patch reefs. Per capita mortality rates of newly settled wrasse increased as a function of density and were well approximated by the Beverton-Holt function for both naturally formed and experimentally generated juvenile cohorts. Average instantaneous mortality rates were a decelerating function of initial densities, indicating the per capita strength of density-dependence decreased with density. Results of a factorial manipulation of density and group size indicate that per capita mortality rates were simultaneously density- and number-dependent; fish at higher densities and/or in groups had higher probabilities of disappearing from patch reefs compared with fish that were solitary and/or at lower densities. Mortality rates were ~30% higher for fish at densities of 0.5 fish/m² than at 0.25 fish/m². Similarly, mortality rates increased by ~45% when group size was increased from 1 to 2 individuals per patch, even when density was kept constant. These observations suggest that the number of interacting individuals, independent of patch size (i.e., density-independent effects) can contribute to regulation of local populations. Overall, this work highlights a greater need to consider numerical effects in addition to density effects when exploring sources of population regulation.     

The maximum yield problem: Distortion in the yield curve due to age structure

An unselective harvest is sustainable if the per capita removal rate balances the net per capita growth rate of the population. If the function relating the growth rate to population density is known, finding the density at which the maximal total harvest rate may be achieved is a simple exercise in parameter optimization. In age-structured populations the per capita growth rate is related in a complicated way to the age-specific vital rates upon which density feedbacks directly operate. Generally, the function relating the per capita growth rate to density will resemble a log transform of the function relating age-specific fecundities to density. Accordingly, maximum yield is attained at a population density that is closer to the saturation density than we would expect on the basis simply of substituting the functional form of the density dependence of fecundity into the parameter optimization model derived for the case without age structure. The amount of the discrepancy increases with the intensity of the density feedback and with the degree to which the reproduction of a cohort is dominated by reproduction taking place during a span of ages that is small relative to the generation time.     

Allee effects and population regulation: a test for biotic resistance against an invasive leafroller by resident parasitoids

Resident natural enemies can impact invasive species by causing Allee effects, leading to a reduction in establishment success of small founder populations, or by regulating or merely suppressing the abundance of established populations. Epiphyas postvittana, the Light Brown Apple Moth, an invasive leafroller in California, has been found to be attacked by a large assemblage of resident parasitoids that cause relatively high rates of parasitism. Over a 4-year period, we measured the abundance and per capita growth rates of four E. postvittana populations in California and determined parasitism rates. We found that at two of the sites, parasitism caused a component Allee effect, a reduction in individual survivorship at lower E. postvittana population densities, although it did not translate into a demographic Allee effect, an impact on per capita population growth rates at low densities. Instead, E. postvittana populations at all four sites exhibited strong compensatory density feedback throughout the entire range of densities observed at each site. As we found no evidence for a negative relationship between per capita population growth rates and parasitism rates, we concluded that resident parasitoids were unable to regulate E. postvittana populations in California. Despite a lack of evidence for regulation or a demographic Allee effect, the impact of resident parasitoids on E. postvittana populations is substantial and demonstrates significant biotic resistance against this new invader.     

Mortality estimates for Penaeus vannamei boone in a Mexican coastal lagoon

Marked and unmarked shrimp were maintained in enclosures in order to estimate mortality rates. Regular sampling and measurement of shrimp in small enclosures (10 m²) resulted in higher mean mortality rates for tagged shrimp (34% per wk) than for untagged shrimp (12% per wk). These estimates include death due to handling in addition to natural mortality. Laboratory tests also indicated higher mortality rates in tagged shrimp. In larger enclosures (2100 m²) where sampling was restricted, lower rates were obtained for tagged shrimp (17% per wk) even though predators were present. Freshly tagged shrimp were found to be vulnerable to sudden changes in environmental conditions.A tag-release experiment indicated a maximum natural mortality rate of 31% per wk in the open lagoon. This is a high estimate, and the natural mortality rate of untagged shrimp in the lagoon probably lies at the lower end of the range 12–31% per wk.     

Growth and population dynamic model of the reef coral Fungia granulosa Klunzinger, 1879 at Eilat, northern Red Sea

The lack of population dynamic information for most species of stony corals is due in part to their complicated life histories that may include fission, fusion and partial mortality of colonies, leading to an uncoupling of coral age and size. However, some reef-building corals may produce compact upright or free-living individuals in which the above processes rarely occur, or are clearly detectable. In some of these corals, individual age may be determined from size, and standard growth and population dynamic models may be applied to gain an accurate picture of their life history. We measured long-term growth rates (up to 2.5 years) of individuals of the free-living mushroom coral Fungia granulosa Klunzinger, 1879 at Eilat, northern Red Sea, and determined the size structure of a population on the shallow reef slope. We then applied growth and population models to the data to obtain estimates of coral age, mortality rate, and life expectancy in members of this species. In the field, few F. granulosa polyps suffered partial mortality of >10% of their tissues. Thus, the majority of polyps grew isometrically and determinately, virtually ceasing growth by about 30-40 years of age. Coral ages as revealed by skeletal growth rings were similar to those estimated from a growth curve based on field data. The frequency of individuals in each age class on the reef slope decreased exponentially with coral age, indicating high mortality rates when corals were young. The maximum coral age observed in the field population (31 years) was similar to that estimated by application of a population dynamic model (30 years). Calculated rates of growth, mortality and life expectancy for F. granulosa were within the range of those known for other stony corals. Our results reveal a young, dynamic population of this species on Eilat reefs, with high turnover rates and short lifespans. Such information is important for understanding recovery of coral reefs from disturbances, and for application to the management of commercially exploited coral populations.     

Is height related to longevity?

Over the last 100 years, studies have provided mixed results on the mortality and health of tall and short people. However, during the last 30 years, several researchers have found a negative correlation between greater height and longevity based on relatively homogeneous deceased population samples. Findings based on millions of deaths suggest that shorter, smaller bodies have lower death rates and fewer diet-related chronic diseases, especially past middle age. Shorter people also appear to have longer average lifespans. The authors suggest that the differences in longevity between the sexes is due to their height differences because men average about 8.0% taller than women and have a 7.9% lower life expectancy at birth. Animal experiments also show that smaller animals within the same species generally live longer. The relation between height and health has become more important in recent years because rapid developments in genetic engineering will offer parents the opportunity to increase the heights of their children in the near future. The authors contend that we should not be swept along into a new world of increasingly taller generations without careful consideration of the impact of a worldwide population of taller and heavier people.     

Dynamics of an age‐structured population drawn from a random numbers table

I constructed age‐structured populations by drawing numbers from a random numbers table, the constraints being that within a cohort each number be smaller than the preceding number (indicating that some individuals died between one year and the next) and that the first two‐digit number following 00 or 01 ending one cohort’s life be the number born into the next cohort. Populations constructed in this way showed prolonged existence with total population numbers fluctuating about a mean size and with long‐term growth rate (r) ≈ 0. The populations’ birth rates and growth rates and the females’ per capita fecundity decreased significantly with population size, whereas the death rates showed no significant relationship to population size. These results indicate that age‐structured populations can persist for long periods of time with long‐term growth rates of zero in the absence of negative‐feedback loops between a population’s present or prior density and its birth rate, growth rate, and fecundity, contrary to the assumption of density‐dependent regulation hypotheses. Thus, a long‐term growth rate of zero found in natural populations need not indicate that a population’s numbers are regulated by density‐dependent factors.