The Dynamics of Territory Acquisition: A Model of Two Coexisting Strategies

Two potential strategies for acquiring territories are (1) fighting and taking over a territory from its owner, or (2) waiting until a territory owner dies and then taking its place. In this paper we explore territory acquisition using these two strategies, using a population dynamical model. Factors expected to affect the predominance of each strategy are injury rate, rate of successful territory takeover, birth and death rates on the territory, and birth and death rates while non-territorial. We explore the effects of these parameters on numbers of territorial and nonterritorial fighters and waiters. Waiters predominate when injury rate, birth rate of nonterritorial individuals, and death rate of territory owners are high. Fighters predominate when rate of successful territory takeover, death rate of nonterritorial individuals, and birth rate of territory owners are high. We present supportive evidence for these preditions from the literature.     

Extinction times and moment closure in the stochastic logistic process

We investigate the statistics of extinction times for an isolated population, with an initially modest number M of individuals, whose dynamics are controlled by a stochastic logistic process (SLP). The coefficient of variation in the extinction time V is found to have a maximum value when the death and birth rates are close in value. For large habitat size K we find that Vmax is of order K1/4 / M1/2, which is much larger than unity so long as M is small compared to K1/2. We also present a study of the SLP using the moment closure approximation (MCA), and discuss the successes and failures of this method. Regarding the former, the MCA yields a steady-state distribution for the population when the death rate is low. Although not correct for the SLP model, the first three moments of this distribution coincide with those calculated exactly for an adjusted SLP in which extinction is forbidden. These exact calculations also pinpoint the breakdown of the MCA as the death rate is increased.     

A strategy of movement and resource utilization

A set of age-specific rates of birth and death implies expected numbers of kin. An individual girl or woman chosen at random out of a population whose birth and death rates are specified can be expected to have a certain number of older sisters, younger sisters, nieces, cousins; expressions for these values are provided for both total kin and kin who are still living. Included also are the probabilities of living mother, grandmother, and great grandmother for girls and women of various ages. The methods are applicable to the size of the nuclear and the extended family. All formulas have been programmed and specimen numerical values are given.     

Mortality of bereavement.

The death rate of a group of 87 widowers and 279 widows was followed for two years from the death of their spouses. The life tables for England and Wales 1970-2 indicated that the expected number of deaths would be 6 men and 11 women. The actual numbers (9 men and 11 women, 5.5%) were not significantly different, though there were more widowers'' deaths during the first six months of bereavement. There was no significantly greater mortality among those whose spouses had died in hospital; but when this had occurred the health of the second spouse was likely to have been poorer than that of those whose spouses had died at home.     

Determination of proliferative parameters from growth curves

Abstract. Data on total cell numbers and proportions of non-proliferative cells during the development of a tissue can be obtained by experiment. This paper shows, via a simple mathematical model, that data collected over a period of time determine the time profile of two proliferative parameters. These are the rate per proliferative cell per day at which cells divide and the average number of proliferative daughters which result from the division of a proliferative cell. One dataset alone does not provide sufficient information to determine either time profile. The findings are applicable where there is no significant cell death during the growth period. The mathematical model is fitted to data from chick neural retina.     

Determination of proliferative parameters from growth curves

Data on total cell numbers and proportions of non-proliferative cells during the development of a tissue can be obtained by experiment. This paper shows, via a simple mathematical model, that data collected over a period of time determine the time profile of two proliferative parameters. These are the rate per proliferative cell per day at which cells divide and the average number of proliferative daughters which result from the division of a proliferative cell. One dataset alone does not provide sufficient information to determine either time profile. The findings are applicable where there is no significant cell death during the growth period. The mathematical model is fitted to data from chick neural retina.     

Effect of time and temperature of fermentation on the microflora of grape pomace

The effects of fermentation time and temperature of grape pomace on the number of bacteria and yeasts were assessed using ANOVA of experimentally generated data, as well as analysis of models derived from first principles and fitted by non-linear regression to such data. Specific rates of death of yeasts and bacteria were experimentally obtained at different fermentation times (pilot scale), and at different fermentation times and different temperatures (laboratory scale) for pomace of Alvarinho and Loureiro grape varieties obtained after vinification at two different locations. Viable numbers of yeasts and bacteria in grape pomace were high, especially in the first 3 week of fermentation; for bacteria, there was an increase of their levels during the first 3 week, followed by a significant decrease towards 9 week; for yeasts there was a monotonic decrease throughout such whole period. The numbers of viable microorganisms were mathematically correlated with time and temperature for both wineries using mechanistic models and following a methodology of increasing model complexity. After having checked the validity of underlying assumptions of normal distribution and constant variance of residuals of the experimental data, determination of the best nested model was based on an F-test; such model considered that the behavior of the microbial population is well described by a constant specific growth rate and an increasing specific death rate, both of which vary with temperature following Arrhenius relationships. Activation energies for the specific death rates of yeasts and bacteria were (1.469-1.560)᎒⁴ and (2.584-4.152)᎒⁴ cal/mol, respectively, for the temperature range 20-35 ^:C. Prediction of the time profile of viable numbers of the major families in the adventitious microflora of grape pomace, as a function of fermentation parameters that are easily manipulated is important in attempts to eventually standardize this solid-state, ill-defined fermentation and so eventually optimize the manufacture of marcs obtained by steam distillation of such fermented pomaces.     

Joint Modeling for Cognitive Trajectory and Risk of Dementia in the Presence of Death

Summary .  Dementia is characterized by accelerated cognitive decline before and after diagnosis as compared to normal aging. It has been known that cognitive impairment occurs long before the diagnosis of dementia. For individuals who develop dementia, it is important to determine the time when the rate of cognitive decline begins to accelerate and the subsequent gap time to dementia diagnosis. For normal aging individuals, it is also useful to understand the trajectory of cognitive function until their death. A Bayesian change-point model is proposed to fit the trajectory of cognitive function for individuals who develop dementia. In real life, people in older ages are subject to two competing risks, e.g., dementia and dementia-free death. Because the majority of people do not develop dementia, a mixture model is used for survival data with competing risks, which consists of dementia onset time after the change point of cognitive function decline for demented individuals and death time for nondemented individuals. The cognitive trajectories and the survival process are modeled jointly and the parameters are estimated using the Markov chain Monte Carlo method. Using data from the Honolulu Asia Aging Study, we show the trajectories of cognitive function and the effect of education, apolipoprotein E 4 genotype, and hypertension on cognitive decline and the risk of dementia.     

Growth and death of Rohon-Beard cells in Rana pipiens and Ceratophrys ornata

Rohon-Beard (R-B) neurons of the medulla oblongata and spinal cord of anurans originate during gastrulation, become distinguishable just after closure of the neural tube, and are present in maximum numbers at the end of the embryonic period, just before feeding begins. Cell deaths are first seen in the earliest larval stages; in Rana pipiens and Ceratophrys ornata, they may not be complete until the very end of larval development or a day or two later, in the juvenile froglet. This is in sharp contrast with Xenopus laevis, in which the last R-B cells die well before the onset of metamorphic climax. Cell losses tend to reach completion in the trunk in a craniocaudal progression, that is, first in the medulla oblongata, then sequentially at brachial, postbrachial, and lumbar levels. Nuclei and cells increase in size through embryonic and early larval stages, reaching maxima at stages X–XIV (of 25 larval stages), then shrinking before cell death occurs. While Ceratophrys produces only two-thirds as many R-B cells as does R. pipiens, its rate of cell death is slower, gauged by attained stage, and at every stage, X–XXIV, Ceratophrys displays a greater number of surviving cells. In hypophysectomized Rana pipiens larvae some 7–15% of the peak numbers of R-B cells are still present after 400 days, more than 4 times the length of the usual larval period. Most or all of these surviving cells are in the tail. The extreme persistence of R-B cells in hypophysectomized larvae is consistent with the view that the R-B cell population can be characterized as being divided into those cells whose death occurs relatively early and those in which cell destruction occurs late, presumably dependent upon different factors. The critical factor for onset of cell death in late larvae may well be the surge in thyroid hormone concentration, which characterizes metamorphic climax. J Morphol 232:67–78, 1997. © 1997 Wiley-Liss, Inc.     

Predictions and tests of climate-based hypotheses of broad-scale variation in taxonomic richness

Broad‐scale variation in taxonomic richness is strongly correlated with climate. Many mechanisms have been hypothesized to explain these patterns; however, testable predictions that would distinguish among them have rarely been derived. Here, we examine several prominent hypotheses for climate–richness relationships, deriving and testing predictions based on their hypothesized mechanisms. The ‘energy–richness hypothesis’ (also called the ‘more individuals hypothesis’) postulates that more productive areas have more individuals and therefore more species. More productive areas do often have more species, but extant data are not consistent with the expected causal relationship from energy to numbers of individuals to numbers of species. We reject the energy–richness hypothesis in its standard form and consider some proposed modifications. The ‘physiological tolerance hypothesis’ postulates that richness varies according to the tolerances of individual species for different sets of climatic conditions. This hypothesis predicts that more combinations of physiological parameters can survive under warm and wet than cold or dry conditions. Data are qualitatively consistent with this prediction, but are inconsistent with the prediction that species should fill climatically suitable areas. Finally, the ‘speciation rate hypothesis’ postulates that speciation rates should vary with climate, due either to faster evolutionary rates or stronger biotic interactions increasing the opportunity for evolutionary diversification in some regions. The biotic interactions mechanism also has the potential to amplify shallower, underlying gradients in richness. Tests of speciation rate hypotheses are few (to date), and their results are mixed.     

Iteroparous reproduction strategies and population dynamics

Asymptotic relationships between a class of continuous partial differential equation population models and a class of discrete matrix equations are derived for iteroparous populations. First, the governing equations are presented for the dynamics of an individual with juvenile and adult life stages. The organisms reproduce after maturation, as determined by the juvenile period, and at specific equidistant ages, which are determined by the iteroparous reproductive period. A discrete population matrix model is constructed that utilizes the reproductive information and a density-dependent mortality function. Mortality in the period between two reproductive events is assumed to be a continuous process where the death rate for the adults is a function of the number of adults and environmental conditions. The asymptotic dynamic behaviour of the discrete population model is related to the steady-state solution of the continuous-time formulation. Conclusions include that there can be a lack of convergence to the steady-state age distribution in discrete event reproduction models. The iteroparous vital ratio (the ratio between the maximal age and the reproductive period) is fundamental to determining this convergence. When the vital ratio is rational, an equivalent discrete-time model for the population can be derived whose asymptotic dynamics are periodic and when there are a finite number of founder cohorts, the number of cohorts remains finite. When the ratio is an irrational number, effectively there is convergence to the steady-state age distribution. With a finite number of founder cohorts, the number of cohorts becomes countably infinite. The matrix model is useful to clarify numerical results for population models with continuous densities as well as delta measure age distribution. The applicability in ecotoxicology of the population matrix model formulation for iteroparous populations is discussed.     

Effect of daily spermatozoan production but not age on transit time of spermatozoa through the human epididymis

Daily spermatozoan production, numbers of epididymal spermatozoa, and transit times of spermatozoa through different regions of the epididymis were determined in 38 men, aged 20-49 or 50-79 yr. Specimens were obtained at autopsy within 24 h of death due to traumatic injury or heart failure. Subjects were in apparent good health prior to death, and death was not preceded by an extended period of hospitalization. Daily spermatozoan production per testis (DSP/T) and numbers of epididymal spermatozoa were determined from counts of maturation-phase spermatids or epididymal spermatozoa in tissue homogenized in a Waring blender. Epididymal transit time was calculated as the number of spermatozoa in a given region of the epididymis or in the entire epididymis divided by DSP/T of the connected testis. Parenchymal weight, spermatozoan production rate, numbers of epididymal spermatozoa, and epididymal transit time were similar (p greater than 0.05) between paired testes or epididymides. Men were divided into four groups on the basis of age and DSP/T. Since there was no (p greater than 0.05) effect of age on epididymal transit time, men in different age groups were combined within their respective group on the basis of DSP/T. In the group with high DSP/T, DSP/g parenchyma was much higher and epididymal transit time was much faster. However, parenchymal weights and numbers of epididymal spermatozoa were similar (p greater than 0.05) between DSP/T groups. The similarity in number of spermatozoa in epididymides of men whose DSP/T differed by threefold is consistent with the inability of the human epididymis to store many spermatozoa when no blockage is present.(ABSTRACT TRUNCATED AT 250 WORDS)     

Programmed cell death without DNA fragmentation in the jimpy mouse: secreted factors can enhance survival

Jimpy is one of many related mutations affecting the myelin proteolipid protein gene that causes severe hypomyelination in the central nervous system (CNS). Underlying the hypomyelination is a failure of oligodendrocytes (OLs) to differentiate, and the premature death of large numbers of OLs during the developmental period. Previous light and electron microscopic evidence suggested that jimpy OLs die in a manner consistent with programmed cell death. We have used TUNEL staining as a biochemical marker for apoptosis in conjunction with immunostaining for OL and myelin markers. At 13 - 14 days postnatal, a time when the number of dying OLs in jimpy CNS is increased more than five times normal, there are only modest increases (70% in spinal cord; 20% in cerebral cortex) in TUNEL labeled cells in mutant CNS tissues. The results in vitro are similar, and only a small per cent of TUNEL labeled cells have the antigenic phenotype of OLs. The discrepancy between numbers of dying and TUNEL labeled cells suggests either that most jimpy OLs do not undergo programmed cell death or that the biochemical pathways leading to their death do not involve DNA fragmentation which is detected by the TUNEL method. We also present evidence that jimpy OLs show increased survival and enhanced differentiation when they are grown in vitro in medium conditioned by cells lines which express products of the proteolipid protein gene. Cell lines expressing proteolipid protein and the alternatively spliced DM20 protein have differential effects on cell numbers and production of myelin-like membranes.     

Familial Sinistrals Avoid Exact Numbers

We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals – individuals who are left-handed themselves or have a left-handed close blood-relative – with those of pure familial dextrals – right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd’s (1988, Language in Society) index of the roundness of a number and report that familial sinistrals’ responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere.     

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.     

Analysis of an SEIRS epidemic model with two delays

 A disease transmission model of SEIRS type with exponential demographic structure is formulated. All newborns are assumed susceptible, there is a natural death rate constant, and an excess death rate constant for infective individuals. Latent and immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form, namely proportional to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The model consists of a set of integro-differential equations. Stability of the disease free proportion equilibrium, and existence, uniqueness, and stability of an endemic proportion equilibrium, are investigated. The stability results are stated in terms of a key threshold parameter. More detailed analyses are given for two cases, the SEIS model (with no immune period), and the SIRS model (with no latent period). Several threshold parameters quantify the two ways that the disease can be controlled, by forcing the number or the proportion of infectives to zero. Received 8 May 1995; received in revised form 7 November 1995     

Seasonal programming of adult longevity in Ukraine

Longevity was significantly associated with season of birth in 101,634 individuals who died in Kiev during the period 1990-2000. The relationship between age at death and month of birth showed a very similar pattern for both men and women. Mean values for the age at death were lowest for subjects born in April-July, and highest for individuals born at the beginning and end of the year. Minimum and maximum ages at death, analysed according to month of birth, differed by 2.6 years in men and 2.3 years in women. For all major causes of death causes, the mean age at death for persons born in the fourth quarter was the highest. These results suggest that, in this population, longevity is affected by prenatal or early postnatal seasonal factors. This is consistent with the hypothesis that the rate of ageing may be programmed in response to environmental influences at critical periods of early development.     

Linking immunological and epidemiological dynamics of HIV: the case of super-infection

In this paper, a two-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the two strains eliminate each other with the strain with the larger immunological reproduction persisting. However, on the population scale superinfection is possible, with the strain with larger immunological reproduction number super-infecting the strain with the smaller immunological reproduction number. The two models are linked through the age-since-infection structure of the epidemiological variables. In addition, the between-host transmission and the disease-induced death rate depend on the within-host viral load. The immunological reproduction numbers, the epidemiological reproduction numbers and invasion reproduction numbers are computed. Besides the disease-free equilibrium, there are two population-level strain one and strain two isolated equilibria, as well as a population-level coexistence equilibrium when both invasion reproduction numbers are greater than one. The single-strain population-level equilibria are locally asymptotically stable suggesting that in the absence of superinfection oscillations do not occur, a result contrasting previous studies of HIV age-since-infection structured models. Simulations suggest that the epidemiological reproduction number and HIV population prevalence are monotone functions of the within-host parameters with reciprocal trends. In particular, HIV medications that decrease within-host viral load also increase overall population prevalence. The effect of the immunological parameters on the population reproduction number and prevalence is more pronounced when the initial viral load is lower.     

Bayes Estimator of Survival Probability from Randomly Censored Observations with Weibull Distribution of Time to Death

This paper deals with Bayes estimation of survival probability when the data are randomly censored. Such a situation arises in case of a clinical trial which extends for a limited period T. A fixed number of patients (n) are observed whose times to death have identical Weibull distribution with parameters β and θ. The maximum times of observation for different patients are also independent uniform variables as the patients arrive randomly throughout the trial. For the joint prior distribution of (β, θ) as suggested by Sinha and Kale (1980, page 137) Bayes estimator of survival probability at time t (0<t<T) has been obtained. Considering squared error loss function it is the mean of the survival probability with respect to the posterior distribution of (β, θ). This estimator is then compared with the maximum likelihood estimator, by simulation, for various values of β, θ and censoring percentage. The proposed estimator is found to be better under certain conditions.     

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.