7 minute read

There is no direction or intent in evolution. However, an idea that evolution has a goal towards some sense of perfection seems quite prevalent on the society. This perfection is often related to be more human-like: given enough time, monkeys and apes do not necessarily have to evolve to a more human like species. There is no purpose in evolution except facing the current threats through adaptation (or removal of less adapted diversity). So monkeys and apes will increase brain size if they need better tools for harnessing their surroundings, will favour bipedalism if the raised viewpoint and releasing the upper members from locomotion related tasks will provide an advantage, etc. Of course, this is the positive side, when the accumulated diversity assures some degree of fitness on a changing environment. The other possibility is that the species already drew all the evolutionary cards and has no other way to cope with current threats. In this case, populations will decrease in number and eventually will go extinct.

A broader interpretation of the idea that evolution is a kind of a force that drives species towards a more human like organism could be that evolution aims to perfection. In a strict sense, it is true: at each time, evolution does balance fitness with environment and provides the means to be perfect. However, this is always ephemeral, lasting only until the environment changes again. There is no long term perfection goal, there is only a lack of purpose in evolution.

With that in mind I tried to make a toy model in JS. It might provide some insights about some processes but it was aimed to be simple, not an exhaustive and detailed simulation of life. The main actor is the circle. It embeds the idea of perfection due to the simplicity of the representation: each point around the perimeter have the same distance to the centre. A single parameter controls the roughness of the circle by randomly adjusting the radius. It ranges from 1, a perfect circle, to 0 where every other point has a random value of radius, rendering it more star-shaped. Each shape, from the perfect circle to the rough one, has 20 points (small black dots) on the perimeter.

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You can press the refresh button on the image above to generate new configurations. You will see that the circle remains a stable shape as expected but the remaining shapes will assume different configuration by chance, being more noticeable as the roughness value increases.

First simulation

As said, the simulation is quite simple. It consists of a defined area were the actors move randomly, following a Brownian motion on the 2D space. All actors have the same base radius, velocity and longevity (500 iterations) and a maximum of 100 actors are allowed simultaneously. When a actor is born, it cannot reproduce until it reaches maturity after 100 iterations. At every iteration the position of the actors is checked. If the centres of a pair of actors, let’s say A and B, are at a distance equal to two times the radius, then a collision is detected. In this case, a possible reproduction event is checked: the distance of the centre of A (female) to each of the black dots of B (male) is calculated. The number of dots that are at a smaller distance than the radius of the actor at the moment of collision gives the number of offspring. The female cannot reproduce again for 100 iterations if she produces offspring. In the simulation, reproducing actors are green and non-reproducing are red.

To keep it simple, the offspring roughness is the average of the parents value. There is no discreet hereditary unit like a gene. Thus, the inheritance of the shape is quite different from real life, but still defined by the parents. One of the consequences of this is that there will be a trend to average the values and the most extreme values will tend to disappear as parents are removed. The other difference is that there is no external selective pressure. The simulation has a neutral environment and none of the shapes produced is being preferred. Still, if one shape tends to produce more offspring, then it might fix the roughness value towards there own values. The spikes might provide an advantage to produce more offspring but because their configuration is random, the offspring inherits the value but not the shape as shown in the image above.

The first simulation starts with half of the actors as a perfect circle and the other half as the star-shaped with roughness set to 1. There are 100 actors that start in random positions and are set to a random age to decrease the synchronization of born/death events. The histogram on the right shows the relative proportion of the roughness value at each iteration.

When the simulation is reset, different configurations of the actors emerge by chance. This initial configuration becomes decisive for the final result. Different random configurations produce a trend towards different values. If you let the simulation for some time, the histogram will peak at some value. After resetting you will see that the value might substantially change for the new simulation. This simple simulation of life already show some hints that there is no direction. The random mating will generate a pattern that depends on the local arrangement of the actors. If all perfect circles are grouped together, then they will tend to have offspring with very low values of roughness.

Second simulation

In this second simulation I have modified some of the parameters. The longevity is set to 200 iterations so the the female only reproduces once. To compare the effect on perfect circles and star-shaped circles (roughness set to 1) I have forced a hand-made natural selection… On the left all actors are fully star-shaped and on the right are perfect circles. Since there is no diversity of shapes, and because of the inheritance by averaging parents value and there is no mechanism for generating diversity, all children will have the same value as the parents.

When the simulation is started, three numbers appear at the bottom of each simulator square. The n is the current number of actors, the extinction is the number of extinction events for each population (the simulation is automatically restarted after an extinction event), and the average number of offspring per reproduction (since females only reproduce once, this value will be equal to offspring per female).

This simulation shows the effect of the shape in the number of offspring and how it can this affect the longevity of the population. Once the rate of reproduction is not sufficient, the population cannot be maintained and becomes extinct. There are other factors beside the shape that might affect the final result. The initial position of two actors in the simulator can have an effect on the final outcome but this is minimized by the random distribution of the actors in both simulations and the successive simulations after extinctions.

The simulated population on the left will become extinct far less often than the right one. With the conditions set in the simulation, the perfect circle has a smaller number of offspring which makes the population unsustainable. Due to the shorter longevity, the circles do not have time to wonder around, so the successful search for a partner depends much more on the proximity. This effect, however, is purely demographic in the simulation. An adverse environment could escalate the effect, by removing more individuals.

Some final remarks

These simple simulations do not prove much about direction in evolution but might provide some insights about the processes acting. More complex simulations, perhaps with a non-uniform environment, a more defined behaviour and a realist inheritance mechanism would provide further insights. There are many more things acting simultaneously in real life that might guide evolution to different directions. When looking backwards from the current state of an organism, the evolutionary path it underwent seems very logical, however we often forget all the failed evolutionary experiments that were needed. These were perfect at some time, but change or chance might have rendered them unsuitable.

The other purpose of this simulation was more technical: to use a canvas html object to display an animation. The simulation of simple mechanisms of life provided a good experiment field. The code of the simulations is available here and here.

If you did enjoy the simulation and have some comments or found some errors please send me a message on any of the contacts available.