Asexual Penna model

Model description

An implementation of a biological aging model in Fortran 2008 as first introduced by T.J.P. Penna [1, 2]. This program follows the original model with some important changes.

Age-dependent Verhulst factor

In the original description [1], the Verhulst factor is constant with the age of the individuals. In other variants, the Verhulst factor is disabled for newborn individuals and active throughout their lives. Here, we let the Verhulst factor freely vary with the age of the individuals.

$$V_a = 1 - w_a\frac{N(t)}{N_{max}},$$

where $V_a$ is the Verhulst factor at age $a$, $w_a$ is the Verhulst weight at age $a$, $N(t)$ is the population size at time $t$, and $N_{max}$ is the carrying capacity. The Verhulst weight is a real number in the interval [0, 1].

We note the unity term in $V_a$. Oliveira [2] defined the age-independent Verhulst factor to be $V = N(t)/N_{max}$. In their implementation of the model, individuals die if some real number $r \in (0, 1)$ is less than the $V$. In our case, they die if $r$ is greater than $V$. As such, both definitions of the Verhulst factor are equivalent given that the implementation of death corresponds with whatever definition we use. Here, we consider the following definition for the age-independent Verhulst factor from which the age-dependent one is derived.

$$V = 1 - \frac{N(t)}{N_{max}}$$

Now looking at $w_a$ (which we call as the Verhulst weight), if we let $w_a = 0$, $V_a$ is equal to 1 at age $a$. Since $r$ cannot be greater than 1, individuals at this age cannot randomly die due to the Verhulst factor. On the other hand, if $w_a = 1$, $V_a$ becomes the original Verhulst factor.

Varying the Verhulst factor can be useful in, say, modelling survivability. By letting $w_a$ increase with age, individuals are more likely to survive as they grow older. Conversely, young individuals are more likely to die due to being fragile and less adept in their environment.

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Installation

Prerequisite

• Python <=3.11
• A Fortran 2008 compliant compiler
  • e.g. Intel Fortran Compiler 2024.2.0 and GFortran 13

Installing the required Python libraries

This project requires the Python library FoBiS.py to build the Fortran code.

Currently, FoBiS.py can be installed using pip:

pip install FoBiS.py

To my knowledge, it is also available on Anaconda but only the older versions. Alternatively you can install FoBiS.py manually. Refer to the Wiki page of this project.

Building the Penna model program

Once you have downloaded or cloned the project, run the build script build.py in the project directory. It has several options to build the project but for most cases, you might want to do a release build. That is to say, run the follow commands:

cd asexual-penna-model     # Go to the project directory
python build.py --type release --clean

The output executable penna.out can be found in bin/ in the project directory.

For information about the other build types, run the script with the --help option.

python build.py --help

NOTE :

The build script assumes that you use gfortran. Due to limited time (and money), I was not able to implement options for other compilers. So if you use other Fortran compilers such as ifx, you will have to edit the build script.

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Usage

Running the executable in the bin/ directory runs the Penna model program with the default parameters indicated in bin/model.cfg.

For more information, run the Penna model program with the --help option.

bin/penna.out --help

WIP

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Reference

1. Thadeu Penna. "A Bit-String Model for Biological Aging". In: Journal of Statistical Physics 78 (Mar. 1995). DOI: 10.1007/BF02180147.
2. S. Oliveira. "Evolution, ageing and speciation: Monte Carlo simulations of biological systems", In: Brazilian Journal of Physics 34.3B (2004), pp. 1066-1076.