Another Way to Calculate Fitness from Life History Variables: Solution of the Age-Structured Logistic Equation

The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the $\theta$-logistic, which generalises the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalises many growth functions. The reformula...

Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary differential equations. Among the various sigmoid models, the logistic and Gompertz equations are well established and widely used in fitting growth data in the fields of biology and ecology. This paper suggests a statistical interpretation of the l...

The paper was suggested by a brief note of the second author about the application of the Hubbert curve to predict decay of resource exploitation. A further suggestion came from the interpretation of the Hubbert curve in terms of a specific Lotka Volterra (LV) equation. The link with population dynamics was obvious as logistic function and LV equation were proposed within the demography science field. Mathematical population dynamics has a history of about two centuries. The ...

We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural selection. An exact solution without ageing is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourie...

Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology, population growth, economy...According to such a broad range of applications, there are different forms of functions and distributions which are recognized as generalized logistics. Sometimes they are obtained by fitting procedures. Therefo...

Two types of population models are well known -- the continuous and the discrete types.The two have very different characteristics and methods of solutions and analysis.In this note, we point out that an iterative technique when applied to the continuous case mimics, surprisingly the discrete theory. The implication is that techniques and conclusions of the latter theory can now be applied to the former case (and vice versa).

Motivated by recent research of aging in E. coli, we explore the effects of aging on bacterial fitness. The disposable soma theory of aging was developed to explain how differences in lifespans and aging rates could be linked to life history trade-offs. Although generally applied for multicellular organisms, it is also useful for exploring life history strategies of single celled organisms such as bacteria. Starting from the Euler-Lotka equation, we propose a mathematical mod...

Species coexistence is one of the central themes in modern ecology. Coexistence is a prerequisite of biological diversity. However, the question arises how biodiversity can be reconciled with the statement of competition theory, which asserts that competing species cannot coexist. To solve this problem natural selection theory is rejected because it contradicts kinetic models of interacting populations. Biological evolution is presented as a process equivalent to a chemical r...

Is there an advantage of displaying heterogeneity in a population where the individuals grow and divide by fission? This is a wide-ranging question, for which a universal answer cannot be easily provided. This article thus aims at providing a quantitative answer in the specific context of growth rate heterogeneity by comparing the fitness of homogeneous versus heterogeneous populations. We focus on a size-structured population, where an individual's growth rate is chosen at i...

Aging is a fundamental aspect of living systems that undergo a progressive deterioration of physiological function with age and an increase of vulnerability to disease and death. Living systems, known as complex systems, require complexity in interactions among molecules, cells, organs, and individuals or regulatory mechanisms to perform a variety of activities for survival. On this basis, aging can be understood in terms of a progressive loss of complexity with age; this sug...