Role of evolution by natural selection in population dynamics

Using a Monte Carlo approach we study the role of inheritance and natural selection in the dynamics of populations. We show that a population subject to inheritance has a much better chance of survival in a given condition than a population where new generations do not inherit genomes of their parents. The dependence of the survival chance on such factors as selection pressure, fecundity, or carrying capacity of the system is much stronger when selection and inheritance are present. We demonstrate, in accordance with biological observations, that in certain conditions evolution can save a population which would perish without it.

Figure 1

Number of individuals in a population vs time (in Monte Carlo steps) with and without evolution and with identical initial conditions. Selection pressure $s=2$, carrying capacity $K=900$, and fecundity $B=30$.

Figure 2

The most probable time to extinction $t_{ext}$ vs carrying capacity $K$ on a log-log scale. $B=30$, and $s=1.67$.

Figure 3

Survival chance $\left(\text{SC}\right)$, vs carrying capacity $K$ for populations with and without evolution. Simulation time $2000\text{MCS}$. Same values of $B$ and $s$ as in Fig. 2.

Figure 4

(a) Distribution of the most probable time to extinction for 1000 independent runs, each till $2000\text{MCS}$ with evolution. Same values of $B$ and $s$ as in Fig. 2, 3. (b) The same as in (a), but without evolution.

Figure 5

The most probable time to extinction as a function of selection for dynamics with and without evolution. $K=900$, $B=30$.

Figure 6

Survival chance vs selection for dynamics with and without evolution. Same values of $K$ and $B$ as in Fig. 5.

Figure 7

Averaged over all population value of the trait $z$ vs selection for the cases with and without evolution. Same values of $K$ and $B$ as in Fig. 5.

Figure 8

(a) Distribution of the most probable time to extinction for 1000 independent runs. Two values of selection. Same values of $K$ and $B$ as in Fig. 5. Case with evolution. (b) The same as in (a), but without evolution.

Figure 9

Most probable time to extinction vs fecundity $B$ for the cases with and without evolution. $K=900$, $s=1.67$.

Figure 10

Chance of survival vs fecundity $B$ for the cases with and without evolution, $K=900$, $s=1.67$