Evolution of Jilwutses

What motivates everyone (humans, animals, everything) is the survival of its own species. Examples of ways to survive are becoming stronger, and making more babies. On the long term, the way to achieve that is through evolution.

The following is an example of how evolution works with natural selection following a mutation.


The Gist
Let's create a fictional race of little animals called Jilwutz. These wild animals are about the size of a medium house cat. Times are tough, jilwutses are delicious, and predators are abundant. A female jilwutz can have a pretty large litter of baby jilwutses, but most of them are eaten before the age of procreation. In average, though, the global jilwutz population is rising steadily, but very slowly.

One day, a baby jilwutz is born with a mutation in its ears. This defect allows it to hear better than the other jilwutses. It is now one of the first to flee from predators, because it can hear them faster. This gives it a natural advantage over the other jilwutses, and a higher chance of survival.

If this mutation is not hereditary, the story ends here. If it is, this mutation can be passed to its descendants, all of which will have better chances of survival. Over time, the population of mutated jilwutses will become more populous than normal ones. Over even more time, only the mutated jilwutses will be left.

Natural selection wins. The jilwutz race is stronger.


A Mathematical Scenario
Let's define this fictional animal in more details. A jilwutz can live an average of two years, the first six months being still infertile. They have two estrous cycles per year, and thus, in average, let's say that they participate in 2.9 mating seasons, and that 54% of the females are impregnated during these and successfully give birth after a three weeks gestation. They have a litter of 1.4 baby jilwutses, on average.

Thus, on average (again), each female jilwutz will give birth to 2.2 babies during her life (54% impregnation  × 1.4 babies × 2.9 mating seasons). 1.1 of these are female, which will continue the tree of jilwutz life.The jilwutz population will grow by a factor of 1.1 every generation.

The mutated jilwutz is born. Being able to hear better, its life expectancy rises to two and a half years, so that it, and its descendants, participate in an average of 3.7 mating seasons (instead of 2.9). These mutated jilwutz females will bear an average of 2.8 babies in a lifetime.

In fact, because the normal jilwutses are easier to kill, their population will diminish faster and faster as the mutated population grows. The jilwutz population over time would perhaps look like this:

Many more layers of difficulties can be added. The mutation is assumed to be hereditary, but it doesn't mean it's passed to all children. It could, for example, have 25% chance of being passed  if only one parent have the mutation, and 80% chance if both have it. The effect could be dimmed if one parent doesn't have it.

But if the mutation catches on to enough jilwutses, over time, it will become the standard. Now, because the jilwutz population grows more rapidly, the predators have more food to eat, and their own population (at least in the area) will also rise, which will decrease the number of jilwutses again.

Everything stays the same...