Biological evolution
The concept of biological evolution was introduced by the French naturalist Jean-Baptiste de Lamarck more than two centuries ago Lamarck, 1802 . The term evolution itself was not yet used at his time, but the word Biologie in French was invented by Lamarck. According to him, the various currently living species are neither static nor independent entities. They are the result of many small modifications occurred in ancient species, accumulated during very long times. Furthermore, species living...
Chaos
In the example of equations 2.1 and 2.2 , the dynamic variable x t vanishes at the end. Other systems would converge to other stationary states. For instance, by keeping the constant K in the right-hand side of equation 2.1 , instead of zero, the solution would change to x t K x0 e-t T. The fast, exponential rate of convergence, however, is the same. The final state K is called the attractor. Other linear or nonlinear systems could converge to more complicated attractors, for instance a cycle...
Conclusions
In this chapter, we have introduced a lot of subtle concepts originally used in the study of critical phenomena and phase transitions, a branch of Statistical Physics. In particular, the ubiquitous appearance of power-laws, instead of exponential decays, describing the behaviour of various quantities as functions of both distance and time. We have also shown that this behaviour is not restricted to these physical studies, it appears also in many other systems outside Physics, in particular...
Preface
Physicists pretend not only to know everything, but also to know everything better. This applies in particular to computational statistical physicists like US. Thus many of our colleagues have applied their computer simulation techniques to fields outside of physics, and have published sometimes in biological, economic or sociological journals, and publication flow in the opposite direction has also started. If one sets plates, knifes, and forks onto a dinner table, one has to put in human...
Penna model asexual
The Penna model Penna, 1995 , invented in September 1994 by a computational physicist at age 30, is by far the most widespread way to simulate ageing. It implements the mutation accumulation theory and was the first model to give the Gompertz law. With model we denote a description of individual elements and their interactions, as is customary in physics other sciences may denote any mathematical formula, like equation 3.1 , as a model. It uses bit-strings, that means chains of zeroes and ones,...
Differential equations
Let us assume that in one region two languages are spoken, like English and French in Montreal Canada , with fractions x and 1 x of the total population speaking mainly the first or the second language. Then Abrams and Strogatz 2003 assume dx di 1 x xas x 1 x a 1 s 5.1 with a free exponent a gt 1 to be fitted on experimental data, and a status variable s with 0 s 1 indicating how advantageous it is to use the first of the two lan- Abrams-Strogatz model at a 1.31 and s 1 2 for various Initial...
The edge of chaos
Equation 2.3 is incomplete when the Lyapunov exponent X vanishes. Indeed, the linear form on its right-hand side is only the first term of a series like XA y An . In Section 2.2, we treated only the cases where this first term dominates, the others were omitted, and the dynamic systems were classified as regular X lt 0 or chaotic X gt 0 . At the edge of chaos X 0 , however, those possible nonlinear terms cannot be omitted anymore. Systems evolving in time with zero Lyapunov exponent are said to...
Phenotype K
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 5 10 15 20 25 30 35 Time in units of 10,000 steps Figure 4.10. Upper part Phenotype distribution of the whole population for X 0.5, which after equilibration remains oscillating between the curve represented by filled circles and the one represented by filled triangles. Lower part Temporal behaviour of the selective females density for three different values of the competition level, X 1 upper curve , X 0.5 middle curve and X 0 0.9 0.8 0.7 0.6 0.5 0.4 0.3...
A simple evolutionary model
Let's consider the evolution of individuals which die and breed at the same rate, keeping nearly constant the population which fluctuates around Pq 1000 individuals. First, each of them produces one offspring, with the help of a sexual partner, doubling the population for a while. Then, half of the population is killed, on average, according to a selection rule described later, restoring the original number Pq. Let's first describe the breeding process. Sexual reproduction is adopted with...
Scaling
For systems in thermodynamic equilibrium, universality was understood after the so-called renormalisation group theory, invented by Kenneth Wilson and based on earlier works by Leo Kadanoff, Michael Fisher, Ben Widom and others. The first is awarded with the Nobel prize, and all four won the Boltzmann medal, the most important award within Statistical Physics. Below, there is an intuitive view of the corresponding concepts, the fundamental ingredient being the presence of long-range...
Penna model sexual
Hundreds of million years ago Mother Nature invented sex by copying Holland's genetic algorithm Children get half of their genome from the father and the other half from the mother. Genetic algorithms assume that mixing the lines of two different versions of a program could make it more efficient. Similarly, one could program sexual reproduction by still giving everyone one string of 32 bits, and the child gets on half of the positions the paternal bits and on the other half of the positions...
Additional remarks
According to some religions and Section 2.9, all humans are offspring of Adam and Eve. Simulations of the Penna model, as well as older theories, confirm this assertion, as reviewed by de Oliveira, de Oliveira and Stauffer 1999 . However, the female and the male ancestor of all living humans according to the simulations in general never met each other, if one does not start the simulation with only one pair. Initially all N individuals are equal, without any mutations. Then accidentally some...
Retirement demography
As Chapter 3 discussed, ageing is part of life. Who supports us in retirement We may have beautiful rights written down in present laws, supported by accumulations of our payments into pension funds or by our savings in various forms. But one must not forget that also by the year 2030 retired people will be consuming mostly only those goods and services which are produced at about that time by working people. If more money is available than things one can buy, inflation eats up the excess...