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.     

Population dynamics of Walia ibex (Capra walie) at Simien Mountains National Park,Ethiopia

Intensive total direct counts of Walia ibex (Capra walie) population were performed at Simien Mountains National Park (SMNP) in 2009. Historical data were collected from SMNP and literature reviews. Different models were suited to determine population growth rates and intrinsic rate of increase. The population size estimated was 745 animals. The correlation between the two repeated counts was significant (r = 0.99 and P < 0.01). Mean instantaneous growth rate (r), growth rate per capita (λ) and population annual growth rate (Λ) were 2.6 ± 2.6, 0.03 ± 0.18 and 19.5 ± 50.4, respectively. Instantaneous growth rate and growth rate per capita were positively correlated (r = 0.958, P < 0.01). Average growth rate (rΛ) and intrinsic rate of increase (rr) under ideal (r = 0.950, P < 0.01) and random environments (r = 0.810, P < 0.01) were positively correlated. The population grows by 2.5% under ideal environments with an intrinsic increase of 0.04 (0.006%) and by 0.13% under random environments with intrinsic rate of decrease of ?0.184 or ?0.025% per year, respectively. The mean rank of the flock structure of whole population was 3.13, 3.88, 2.00 and 1.00 for males, females, juveniles and unidentified, respectively.     

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).     

The relative importance to population increase of fluctuations in mortality,fecundity and the time variables of the reproductive schedule

Summary Previous authors have used simple models to investigate the relative importance to population increase of variations in the total and age-specific reproductive rates. But while acknowledging that the latter were the product of the age specific birth and death rates, they have used their models only to investigate changes in total or age-specific birth rates and have not been concerned with variations in death rates. This paper extends the use of Lewontin's (1965) model, to a wide range of values of r, the exponential rate of population increase. It shows how the relative importance of changes in certain life-history features can change with r and be reversed when r is near to zero. It is also shown that variations in mortality rate are not necessarily best expressed in analogous terms to variations in birth rate. If more suitable terms are used it is seen that changes in mortality rate can be of varying importance depending on the existing mortality rate. They can be overwhelmingly important when the mortality rate is high.     

Kinetic study on pH dependence of growth and death of Streptococcus faecalis

A chemostat culture was used for lactic acid fermentation with Streptococcus faecalis at various pH values (8.0, 7.0, 6.0, 5.5, 5.0) and glucose concentrations (10, 20, 30 g/l). At every pH value, the reciprocals of the specific consumption rate of glucose and the specific production rate of lactic acid were linearly correlated to the reciprocal of the specific growth rate. The product, lactic acid, caused non-competitive inhibition of the specific growth rate at every pH value. Moreover, it was found that the cell death rate was dependent on pH and lactic acid. The death rate was smallest at pH 7.0 and increased with increasing lactic acid concentration. The kinetic equations of growth and death are proposed in a broader pH range. Correspondence to: H. Ohara     

The optimal sex ratio for age-structured populations

A new nonlinear age-dependent model for age-structured sexual populations is introduced, based on two assumptions: (1) the birth function depends on the ages of the two parents; and (2) the death functions of the two sexes are composed of two types of additive terms depending on age and sex and on time evolution of population densities, respectively. Formal arguments are given that suggest that time-persistent age profiles may exist and that the intrinsic rate of growth for the two sexes is the same. If the ratio between the number of newborn females and the number of newborn males is equal to the square root of the ratio of the corresponding per capita birth rates, then the intrinsic rate of growth has an optimal value. The optimal sex ratio for the whole population is equal to the reciprocal value of the sex ratio at birth.     

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.     

A population dynamics perspective on effect of irrigation regimes and plant densities on greenbug abundance in grain sorghum using regression

• 1 A dataset generated from previous experiments on greenbug Schizaphis graminum (Rondani) (Hemiptera: Aphididae) response to irrigation and plant density in grain sorghum was reanalyzed using a recently‐developed mechanistic ecological model for describing aphid population density curves. The model was used to estimate seven response variables: observed peak aphid abundance, predicted peak aphid abundance, time of peak abundance, per capita birthrate, death rate coefficient, final cumulative density and duration of substantial aphid infestation across three irrigation regimes and five plant densities.
• 2 Using regression, the observed peak aphid abundance, predicted peak aphid abundance, per capita birthrate and final cumulative abundance were shown to decrease significantly, whereas the death rate coefficient and duration of the infestation were shown to increase significantly for each 100 000 plant/ha increase.
• 3 Although significant results were found for a number of variables generated from the specific data set used in the analyses, of perhaps greater importance is the potential use of these equations in future predictions of aphid population dynamics. An example of projecting population curves based on estimated peak and cumulative counts and an example of projecting population curves based on estimated birth and death rate coefficients are provided.

     

Effects of demographic parameters on metapopulation size and persistence: an analytical stochastic model

An analytical stochastic metapopulation model is developed. It describes how individuals will be distributed among patches as a function of density-dependent birth, death and emigration rates, and the probability of successful dispersal. The model includes demographic stochasticity, but not catastrophes, environmental stochasticity or variation in patch size and suitability. All patches are equally likely to be colonized by migrants. The model predicts: (a) mean and variance of the number of individuals per patch; (b) probability distribution of individuals per patch; (c) mean number of individuals in transit; and (d) turn-over rate and expected persistence time of a single patch. The model shows that (a) dispersal rates must be intermediate in order to ensure metapopulation persistence; (b) the mean number of individuals per patch is often well below the carrying capacity; (c) long transit times and/or high mortality during dispersal reduce the mean number of individuals per patch; (d) density-dependent emigration responses will usually increase metapopulation size and persistence compared with density-independent dispersal; (e) an increase in the per capita net growth rate can both increase and decrease metapopulation size and persistence depending on whether dispersal rates are high or low; (f) density-independent birth, death, and emigration rates lead to a spatial pattern described by the negative binomial distribution.     

Survivorship and fertility schedules of two Sumatran tortoise beetles,Aspidomorpha miliaris andA. sanctaecrucis (Coleoptera: Chrysomelidae) under laboratory conditions

Two species of tortoise beetles, Aspidomorpha miliaris (AM) and A. sanctaecrucis (AS) feeding on a shrub-like morning glory, Ipomoea carnea, were reared under laboratory conditions to study their survivorship and fertility schedules. AM and AS required 34–39 days and 30–37, respectively, for the development of the immature stages. The mean longevity of the males was 88.4 days in AM and 63.8 in AS, and that of females was 87.9 days in AM and 83.3 in AS. The mean length of the pre-reproductive period (27.2 days in AM and 33.8 in AS) was much longer than that of the post-reproductive period (10.9 days in AM and 14.3 in AS). Females laid eggs at a nearly constant rate throughout their reproductive period. The reproductive value V_x/V₀ of the two species remained high for most of their adult life, as a result of prolonged survivorship and fertility periods. The total number of eggs produced per female was 442.9 (AM) and 80.1 (AS). The intrinsic rate of natural increase r was 0.070 (AM) and 0.044 (AS) per capita per day. The prolonged reproductive schedules, coupled with strong dispersal power, of these species no doubt have an adaptive value for living in highly disturbed tropical environments, where rainfall is ample but unpredictable and food resources are available throughout the year in a wide area, but distributed in widely flung patches.     

Experimental evidence for density-dependent reproductive output in a coral reef fish

We tested for density-dependent reproduction in a small coral reef fish using field manipulations of density and observational data. Males of the study species, the bridled goby (Coryphopterus glaucofraenum Gill), defend benthic nest sites, within which they spawn with females, and females can spawn repeatedly over an extended breeding season. In small areas, usually only a single male nested at any one time regardless of how many males were present, so the probability of nesting was inversely proportional to density. Nesting males were almost always the largest in the vicinity, suggesting that, for males whose home ranges overlap, social interactions dictate opportunities to nest. Both the per capita rate at which clutches were laid and the number of eggs produced per clutch declined with increasing density, so the per capita rate of egg production was also density dependent. All three measures of fecundity were better predicted by numerical density (numbers per unit area) than biomass (mass of fish per unit area), and were well described as an inverse function of the number of gobies in the vicinity. A simple hypothesis consistent with these results is that a constant number of females spawn, regardless of density. Alternately, the effect of crowding may depend primarily on the number of interacting individuals and affect all females relatively equally. This density dependence could thus contribute to population regulation at the spatial scale over which populations become reproductively closed.     

Growth and reproduction of three cladoceran species from a small wetland in the south-eastern U.S.A.

SUMMARY 1. Growth, reproduction and life‐history parameters were measured for three cladoceran species from a small south‐eastern wetland, U.S.A. Simocephalus serrulatus, Diaphanosoma brachyurum and Scapholeberis mucronata juveniles were reared at temperatures between 10 and 25 °C on natural food resources. 2. Growth rate increased with temperature and decreased with individual size for all three species. Maximum somatic growth rate was higher for Simocephalus (49–72% day^?1) and Diaphanosoma (21–91% day^?1) than for Scapholeberis (11–45% day^?1). Multiple regression equations were developed which predict temperature‐ and mass‐specific growth rates for each species. 3. Scapholeberis egg production was positively related to temperature; however, maximum egg production occurred at intermediate temperatures for Simocephalus and Diaphanosoma. Mean cumulative egg production was higher for Scapholeberis (28–92 eggs per female) than for Simocephalus (18–25 eggs per female) and Diaphanosoma (1–41 eggs per female), and was related to differences in reproductive strategy and survival. 4. Survival was inversely related to temperature in most cases. For all three cladocerans, the intrinsic rate of increase (r) and net reproductive rate (R₀) increased with temperature, whereas generation time (G) decreased. Greater egg production by Scapholeberis compared with the other two cladocerans was consistent with higher R₀ values for Scapholeberis at any given temperature. Although r was very similar among species, G was typically longer for Scapholeberis than for Simocephalus and Diaphanosoma. 5. This analysis provides basic information about the population parameters of these coexisting wetland species, and the growth rate models can be applied to field data to determine production dynamics.     

Effects of population density on the sediment mixing induced by the gallery-diffusor Hediste (Nereis) diversicolor O.F. Müller, 1776

The aim of this work was to quantify the intensity of sediment mixing induced by the gallery-diffusor (functional bioturbation group) Hediste diversicolor as a function of density, using particles tracers (luminophores). In order to assess the impact of density on sediment reworking, a 1-D model was used to obtain sediment reworking coefficients such as Db (biodiffusion-like) and r (biotransport). Densities used in this experiment corresponded to population densities observed in the sampling area (Saint-Antoine Canal, Gulf of Fos, France): 144, 288, 577, 1153 indiv/m². At first, results showed that neither luminophore maximum burying depth nor the more marked tracer accumulation areas were influenced by density. Thus density did not seem to have any influence on size of galleries or complexity of structure. Then, density-dependent relations with Db (biodiffusion-like mixing) and r (biotransport) were highlighted with an observed process intensity rate twice as high at highest worm density. On the other hand, Db and r per capita coefficients were negatively influenced by density. Db and r per capita at highest density were equal to ∼ 20% of individual Db and r obtained at the lowest density. Finally, this study showed the importance of density which appears to be a key parameter in the functioning of the sedimentary ecosystem.     

Effect of pH on survival,reproduction, egg viability and growth rate of five closely related rotifer species

In the laboratory we examined the effect of pH (5–10 with one interval) on survival, reproduction, egg viability and growth rate (intrinsic growth rate—r _m and population growth rate—r) of five Brachionus rotifer species (B. calyciflorus, B. quadridentatus, B. urceolaris, B. patulus and B. angularis). The pH was shown to exert a major influence on egg viability and growth rate (r _m and r) for each species. The age-specific survivorship curves within a species were not significantly different at pH 6–10. The optimal pH for each species is near-neutral pH (pH 6–8), and the fecundity decreased as the pH deviated from these values. For each Brachionus species, there was no significant difference between age-specific fecundity curves at pH 7 and 8. At acid pH (pH 5 or 6) higher egg mortality was observed for each species. The r _m and population r of the five Brachionus species incubated at different pHs were significantly influenced by pH. The pH supporting the highest r _m or r was obtained at pH 6–8, but varied due to species. In this study B. urceolaris and B. patulus could tolerate a broad range of pH, while the populations of B. calyciflorus, B. quadridentatus and B. angulari declined at acid conditions.     

Interactions in a tritrophic acarine predator-prey metapopulation system IV: effects of host plant condition on Tetranychus urticae (Acari: Tetranychidae)

Feeding by spider mites can cause severe injury to a host plant and lead to a decreasing per capita growth rate and an increasing per capita emigration rate. Such density-dependent responses to local conditions are important in a metapopulation context because they allow the herbivores to colonize new host plants and thereby prolong the time until regional (metapopulation) extinction. In order to include density-dependent responses of the two-spotted spider mite (Tetranychus urticae) in a realistic metapopulation model, a series of greenhouse experiments was conducted with the purpose to quantify how the condition of bean plants (Phaseolus vulgaris) influences the demographic parameters of T. urticae. Plant age per se reduced the growth rate of the spider mites only slightly, whereas the growth rate declined significantly as the plants were injured by the mites. The relationships between plant condition (expressed by the plant injury index D) and the birth and loss (death + emigration) rates of the mites were quantified so as to predict population growth as a function of D. Maximum per capita growth rate (r) was estimated to be c. 0.21 day⁻¹. The growth rate is expected to be negative when D exceeds 0.8. When mites were allowed to emigrate to neighbouring plants via bridges, the per capita emigration rate increased almost exponentially with D. The proportion of eggs in the population decreased with D while the numerical ratio between immatures to adults and the sex ratio did not change with D. Overall, immatures and adults constituted 74% and 26%, respectively, of the active mites and c. 46% of the adults were males. The bridges that connected a donor plant with the surrounding recipient plants were responsible for the majority of the emigrations from donor plants. Most mites stopped after having crossed a single bridge, but a few crossed two bridges while none crossed three bridges within 24 h. The significance of the results for biological control is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Slow‐motion population dynamics in Mojave Desert perennial plants

Abstract. To investigate survivorship and regeneration in desert perennial plants, individual shrubs were mapped, measured and tagged on a nearly level 360 m² plot of diverse Mojave Desert vegetation in 1981, they were re‐mapped and measured 15 years later, in 1996. A large majority of the shrubs persisted between censuses. Modest birth (establishment) and death rates indicate that plants are replaced approximately every century, while the median longevity of several species is much longer. A 15‐yr intercensus interval, appropriate for most species (i.e. birth and death rates were measurable), is too short for several larger shrubs (including Larrea divaricata, Ephedra nevadensis, Yucca schidigera and the larger Opuntia spp.) in which virtually no births or deaths occurred and in which longevity must be extremely high. While individuals of most species grew over the 15‐yr interval, others did not, and some individuals shrank in size. In a number of species, individual growth rates were significantly reduced according to the number of neighbouring plants rooted 0.5–2.0 m distant. Even Larrea tridentata, one of the largest species, showed significant effects of growth rate reduction where crowded by allospecific plants, despite the generally much smaller sizes of these neighbours.     

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.     

A stage structured predator-prey model and its dependence on maturation delay and death rate

Many of the existing models on stage structured populations are single species models or models which assume a constant resource supply. In reality, growth is a combined result of birth and death processes, both of which are closely linked to the resource supply which is dynamic in nature. From this basic standpoint, we formulate a general and robust predator-prey model with stage structure with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and computational study. Our work indicates that if the juvenile death rate (through-stage death rate) is nonzero, then for small and large values of maturation time delays, the population dynamics takes the simple form of a globally attractive steady state. Our linear stability work shows that if the resource is dynamic, as in nature, there is a window in maturation time delay parameter that generates sustainable oscillatory dynamics.Work is partially supported by NSF grant DMS-0077790.Mathamatics Subject Classification (2000):92D25, 35R10Revised version: 26 February 2004     

Constitution and By-Laws of the American Association of Physical Anthropologists

From parent populations (N = 50,000) statistically generated, representing different levels of correlation (r) between the age at death and a hypothetical biological indicator (r = 0.8-0.98), reference samples and target demographic samples are randomly drawn. Two iterative techniques, proportional fitting procedure and Bayesian, are used to estimate from the reference samples the age distribution of the targets. Due to the random fluctuations of the pattern of aging, both in the reference and target samples, these techniques converge only in expectation toward the true value of a distribution, but not in practice for any particular realization. Nevertheless, these techniques allow the estimation of the average of an age distribution, even if its shape is unknown. Under the hypothesis that the target sample is drawn from a stationary population, this average represents the life expectancy at 20 years (plus 20 years). Using this mean age at death for the adults and the juvenility index at death (D5-14/D20-ω), a new set of paleodemographic estimators were derived from 40 archaic life tables. For a hypothesized stable population, they give the life expectancy at birth and at 20 years, and the probability of death at 1 and 5 years. © 1996 Wiley-Liss, Inc.     

Time-specific life tables for the pea aphid,Acyrthosiphon pisum (Harris), on alfalfa

Time-specific life tables were constructed for three pea aphid, Acyrthosiphon pisum (Harris ) (Homoptera: Aphididae), populations using a modification ofHughes' analytical procedure. All populations were studied on second-growth alfalfa (mid-June to mid-July) in south central Wisconsin; data for two populations were collected during 1980, and data for the third population were collected during 1982. The intrinsic rate of increase (r_m) estimated on a physiological time (day-degree) scale under field conditions but in the absence of natural enemies, provided a reliable estimate of potential population growth rate and was used in preference toHughes' approach of estimating potential population growth rates directly from stage structure data. Emigration by adult alatae and fungal disease were the major sources of A. pisum mortality in each of the three populations studied. These factors were most important because of their impact on reducing birth rates within the local population. Parasitism was never greater than 9 percent. Mortality attributable to predation ranged from 0.0 to about 30.0%; however, even at the highest predator densities A. pisum populations increased exponentially.