Evolution as Reproduction with Variability

In the presence of selection, agents in the regime under selection pressure die without producing offspring like themselves. To maintain population levels constant, in this case a new agent is born having the x and y characteristics randomly chosen from the distribution of such characteristics in the population at the time. The degree of selection pressure is modelled as the probability that an agent in the regime under selection pressure dies without producing an offspring like itself. Under low selection pressure an agent in that regime has some probability of producing agents more or less like themselves.

Step through a simulation by repeatedly clicking the Go button, or start and stop a continuously running simulation using the Go Until button. A record of all variants that have existed during a simulation can be obtained by turning on the Mark switch. In this case, variants will leave a white mark as an indication of their existence. To get rid of the record of variants, click "Reset mark." Bar diagrams display the x and y distributions of the agent population at any given time; mean x and y values of these distributions are continually updated to the right.

Directionality to change over time in the absence of selection pressure does not depend on a left wall effect. Start with a population of 100 or so agents at x = 0 and y = 0, and turn Mark on. Notice that the mean x value doesn't change over time but that there is a progressive increase in the number of variants that have existed over time until all possibilities have been tried. By itself, reproduction with variance moves progressively toward exploring all possibilities. You can check that while this doesn't depend on selection, it does depend on variability by repeating the observations with variability set to 0.

Its interesting to think about selection in this context. Return to the starting condition of a population of 100 or so agents at x = -16 and y = 0 and variability = 1, and now turn on selection with a vertical bar at x = 0 and selection pressure set to maximum. Agents explore all possibilities to the left of the selection regime but none of those to the right. From this perspective, selection can be thought of as a contraint on a tendency to explore that is inherent in reproduction with variance.

To observe adaptation, start with a population of agents at x = 0 and y = 0 and run the simulation until the population has become randomly distributed across the space of possibilities. Pause the simulation and create a selection regime using the vertical and horizontal bars. This might involve, for example, selecting against all agents with x values less than 0 or selecting against all agents that have either x or y values less than -3 or greater than 3. Restart the simulation and notice that the population quickly becomes restricted to locations outside the selective regime. That adaptation is a transient phenomenon, dependent on the interaction between random variation and a selective regime, can be illustrated by pausing the simulation again, removing the selection regime, and observing the return of the population to a random distribution across all possibilities.

The effects of selection pressures that change with time, and their dependence on the population at any given time, can also be explored to some degree with the simulation. Start, for example, with a population at x = -14 and let the simulation run until the population has expanded somewhat. Pause the model, create a selection regime that selects against agents with x values less than some value, and restart the model. Notice that the population adapts to the new selection regime, more slowly if there are no current members of the population outside the values selected against and more rapdily if there are. By progressively extending the selection regime, one can move the population progressively toward any given set of characteristics.

The constraint of selection can be overcome to varying degrees either by reducing selection pressure or by increasing variance. Try out various combinations to see what differences it makes.