Age-dependent Growth Research Articles

On the dynamics of chemically stressed populations: The deduction of population consequences from effects on individuals

A general, simple, and explicit model for the age-dependent growth and reproduction of individuals as a function of food supply is presented. The model assumes a Holling-type functional response coupled with a von Bertalanffy body growth law, a fixed ratio between the energy utilized for reproduction and respiration, and a juvenile stage that ends as soon as the animal attains a sufficient weight. This model is shown to fit the available data on the development of Daphnia magna quite well. The model is used as a basis for studying the effects of chemicals on population growth rate, given the effects on individuals. Effects on individual growth and reproduction are reflected in a concentration-dependent relative reduction of the population growth rate. Effects on feeding rate, digestion, basal metabolism, and survival work out much more dramatically at low natural population growth rates. This already follows from a much simpler model that assumes age-independent reproduction, as exempblified to a good approximation by the rotifer Brachionus rubens. The theoretical results are supplemented with experimental evidence, implying that the stress on a population at a certain concentration of a chemical may indeed be strongly dependent on the feeding state of that population.

Constant-Rate Harvesting of Age-Structured Populations

We consider the nonlinear age-dependent population growth model introduced by Gurtin and MacCamy [Arch. Rat. Mech. Anal., 54 (1974), pp. 281–300] with birth and death moduli depending on age and total population size, to which is added a harvest of members at a rate which is constant in time but may depend on the age of members being harvested. We formulate the problem as a pair of equations for the total population size and the birth rate, and discuss the behaviour of solutions when the birth and death moduli depend on either the age or the total population size, but not both.

On the dynamics of chemically stressed populations: The deduction of population consequences from effects on individuals

A general, simple and explicit model has been constructed for the age-dependent growth and reproduction of individuals in relation to their food supply. The model assumes a Holling type functional response coupled to a Von Bertalanffy body growth law, a fixed ratio between the energy channelled to reproduction and respiration and a juvenile state, that ends as soon as the animal reaches a sufficient weight. This model is shown to fit the available data on the development ofDaphnia magna quite well. Using this model as a base the effects of chemicals on the population growth rate are studied, given the effects on the individuals. Effects on individual growth and reproduction are reflected in a concentration-dependent, relative reduction of the population growth rate. Effects on feeding rate, digestion, basal metabolism and survival, turn out to have a much more dramatic effect at low natural population growth rates. This effect can already be demonstrated on a much simpler model, which assumes age independent reproduction, as examplified to a good approximation by the rotiferBrachionus rubens. The theoretical results are supplemented with experimental evidence, implying that the stress on a population at a certain concentration of a chemical may indeed be strongly dependent on the feeding state of that population.

Sonometrics of the Prostate

Determination of prostatic size by rectal examination is inaccurate if objective and reproducible values are desired. Sonometrics, a combination of transrectal sonography and biometrics, is a simple method to determine prostatic weight. The optomanual image analyzing system (BIT PAD-TRS 80) consists of a digitizer tablet, cursor, processing unit and keyboard (TRS 80). The photographic records or the image of the prostate on the scan can be measured with the optomanual image analysis system by tracing the circumference of the prostate. Using the computer one can calculate length, area and circumference of the sonogram. When the postoperative and sonometrically estimated weights were compared a good correlation coefficient was found. The studies on age-dependent growth of the prostate show an age-volume relationship similar to that shown in the study by Swyer. As demonstrated in patients with hypothalamic hypogonadotropic hypogonadism changes in prostatic volume also can be assessed in small prostates.

A growth function for a column of cells

Recently Tognetti and Winley have extended the age dependent integral formulation of demography to account for position dependence. This extended integral model may be used to describe the one dimensional growth of a column of fissioning cells such as in a root. An input to this model is a growth function which characterizes the age, position, and time dependent growth of an average cell. This paper establishes a growth function which is appropriate for a dividing cell in which fission is merely the formation ofa new cell wall. Also this growth function is reconciled with the mean length of dividing mother cells at the time of birth of the average cell.

The Bilinear, Modal State Equations for Age-Dependent Growth Control

There have been previous attempts to model biological processes as bilinear systems [4,9,10]. In these early studies any member of a population was taken to be quite like any other so that the variation of fertility and susceptibility to mortality with age was ignored. In this paper, however, the age-dependent nature of biological growth [5] is accounted for. The modal (eigenfunction) analysis of the basic partial differential equation of age-dependent growth is shown to result in a system of bilinear equations. (The basic mathematical model is a non-self-adjoint operator with a discrete spectrum and the modes are coupled by the control term.) The impulse control of a truncated version of this system of equations is then discussed. It is anticipated that the results presented here will aid planning for optimal amounts of pesticides to agro-ecosystems or for optimal amounts of drugs (or radiations) to unwanted cell populations.

Non-linear age-dependent population growth.

A non-linear problem arising from age-dependent population dynamics is studied. Existence and uniqueness and a priori bounds for the growth of population are proved. Moreover the existence and the stability of equilibrium age distributions is investigated.

Linear age-dependent population growth with seasonal harvesting.

A population growth is modelled by the Von Foerster PDE with accompanying Lotka-Volterra integral equation describing the birth rate; the age specific death and fertility rates are assumed to depend only on age and not time. A harvesting policy where a fraction of the population of age greater than a given age is harvested for a fraction of a given season. This introduces a time dependence, but this difficulty is circumvented by devising approximate time-independent models whose birthrates bracket the true birthrate--the standard renewal equation theory applies to the approximate models so quantitative results can be obtained.

A mathematical model for the uptake of heavy metals in benthic algae

A mathematical model for the uptake of heavy metals in the benthic algae Ascophyllum nodosum has been developed. The model allows assignment of age-dependent growth parameters which also may be a function of external factors. Mortality curves for A. nodosum corresponding to a highly polluted and a nearly unpolluted area have been used in the study of metal uptake. Uptake has been simulated for different values of growth parameters and different concentrations of heavy metals in seawater. Emphasis has been on the uptake of zinc. The simulations showed that the concentration of zinc in the algae changed much less (6%) than the biomass (30%) with changes in intrinsic growth rate, mortality and carrying capacity. The concentration in the algae was found to be an approximately linear function of the mean concentration in seawater up to about 100 ppb. At very high concentrations, associated with high mortality, the deviation from linearity may be significant (about 13% at 162 ppb at one locality). The calculation indicates further that variations in the zinc concentration in the seawater are considerably damped in the algae. Simulations have also been performed to study the effects of sampling different parts of the algae, and some initial simulations have been performed to study the effects of heavy metal exchange between algae and sea water.

Linear age-dependent population growth with harvesting

Linear age-dependent population growth with harvesting

An Age Dependent Epidemic Model

The model presented here describes the spread of an infection in a population by keeping track of the chronological ages of the participants as well as their “class ages” (i.e. the length of time since entering their present state). The reasoning behind this model is similar to that used in the equation of age dependent population growth.

Functional differential equations and age dependent population growth

Growth equations are established for a population of individuals that have fixed age dependent reproduction and mortality rates. Equations are obtained both for the population density and for the numerical size of the population in a fixed age group. Age and time dependent migration is taken into consideration. The usual integral equation of renewal type for these variables is shown to be equivalent to a functional differential equation of retarded type; these differential equations are of main interest in this work. The role of initial data in characterizing a unique solution of the functional differential equation is examined in detail. Finally, some special cases for the reproduction and mortality rates are considered where the functional differential equations take a reasonably simple form.