1) Measurement of Evolutionary Activity, Teleology, and Life / by Bedau and Packard

2) A comparison of Evolutionary Activity in Artificial Evolving Systems and in the Biosphere / by Bedau, Snyder, Brown and Packard
 

The first article is a half-metaphysical, half-scientific article that discusses a way to define evolution, and even life itself. On the way it also revives the old idea of teleology (the idea that things happen with a purpose, not because of an event-sequence).

There is an attempt made to grasp the intuitive concept of evolution by defining a mathematical measure of it – a system shows more evolution if it has more “evolutionary activity” going on.

The article describes a extensive method of measuring evolutionary activity in artificial models (it uses two artificial models, “Tropic Bugs” and “Strategic Bugs”) as follows:
We attach a counter to every gene in every individual in the system. The counter starts from zero and increases every time the gene is used, as long as the gene exists (including in children). If the gene is mutated, or is extinct, it’s counter disappears with it.

Now, the article looks at the 3D graph who’s X-scale is the time scale, and who’s Y-scale is U, the level of the above counter, and each spot (t, u) gets the value of the amount of counters that have the value u at time t.

When a new useful gene or group of genes is introduced into the system, we get an “activity wave”, caused by the continued use of these genes over time. This wave will remain, until the genes are extinct.

Now the article defines “Evolutionary Activity” (at time t) as the volume of new waves introduced (over a certain threshold that comes to dismiss waves caused by genes that are not persistent in the system).

The article shows a graph showing the evolutionary activity in the Bugs model, and the activity waves are indeed apparent.

Then the article goes on to discuss appliance of this technique to other evolutionary system such as the Biosphere (the “Real World”). It is easy to see why this technique isn’t readily applicable – it’s hard to attach counters to real genes. Instead the article suggests counting new “features” in the species-families fossil record. The article also suggests applying these methods to other computational models such as learning algorithms, interacting strings, genetic algorithms and such, although it doesn’t discuss how to apply them.

On the philosophical side, the article argues the teleology can indeed live together with the idea that is the infrastructure on which science exists – that of causality. The article suggests that these are the two faces of the same phenomena – on microscopic scale, things happen BECAUSE of previous happenings and settings. However, on the macroscopic scale (i.e. on the evolutionary time scale), things happen FOR A PURPOSE (e.g. ears appeared in evolution, SO their owners could hear).

The article also suggests this measurement as a measurement of life, arguing that in a certain system, the volume of its evolutionary activity defines life.

My comments: The measure given for evolutionary activity is indeed a novel idea, and gives our intuitive sense of evolution, a numeric meaning. However, its drawback is that it will be very difficult to apply it to systems that we do not have complete control of – such as the Biosphere. On the other hand, the attempt to find a semantic method to allow teleology to co-exist with science seems a little far-fetched. Also, introducing a numeric measurement of life, without first defining it, is not completely scientifically sound.
 

The 2nd article attempt to implement some of the ideas described above, namely applying an objective, mathematical criterion to measuring evolutionary activity, both in artificial systems, and in the Biosphere.

A mathematical measure is applied to two different artificial models (the Evita model and the Bugs model), as well as to the biosphere history as recorded in fossil data. However, the measure used here is slightly different than the one described in the previous article, mainly so it can be applicable to the two very different sets of data - data collected from artificial systems, and the fossil record data.
 
The article defines the following measures:
1)  “Evolutionary activity” of a certain component at time t, as the total time that component existed, until time t. If the component doesn’t exist at time t, it’s evolutionary activity is define as nil.
2) “Cumulative evolutionary activity” at time t, is the sum of the evolutionary activity of all the components that existed at time t.
3) The “Diversity” at time t, is the number of components that existed at that time.
4) The “mean cumulative evolutionary activity” is just the cumulative activity divided by the diversity.

A component is defined as one individual in the artificial models (i.e. one bug in the Bugs model), and one species family if the fossil record data.

The arbitrariness of the selection of an artificial model was handled by measuring the model itself and comparing it to the measurements of its neutral counterpart. A neutral counterpart of a model, acts exactly the same, except for not rewarding an individual for it’s behavior – decisions about dying or multiplying are made at random, without concern of the individual components’s internal energy level etc. This allows us to see the effects of the evolutionary activity itself, regardless of the “noise” inserted by the nature of the specific artificial model.

Conclusions from applying these measures:
Fossil Data: cumulative activity is on the rise almost throughout geological history – in a superlinear fashion. The mean activity however had linearly risen till about 250M years ago, and since then it’s more or less constant. This in because in the past 250M years, the rise in cumulative activity has been accounted for by similar rise in the diversity.

Artificial Models: In the first 20,000 or so steps, rise in cumulative activity and diversity was found, as the population was growing. After that stage, the population as well as it’s diversity stayed more or less stable, while the cumulative activity and thus the mean cumulative activity continued to vary in a wave-like fashion.

Neutral Artificial models: In the first 20,000 stages the population was growing, and so was the diversity and cumulative activity. Once the population seized to grow, all the measures became almost completely stable – with out the variance found in the non-neutral artificial models.

My comments: This article makes progress in attempting to define evolution in terms of mathematical equations that can actually be measured both in the biosphere and in artificial models. This enables us to learn more about the coarse of evolution in our world, as well as to evaluate how close (or how far) are our artificial models in mimicking this evolutionary pattern. However, it is my opinion that the measurements as presented in the article are not completely scientifically sound. The appliance of the same measures to two scales so different – families of species (even not individual species) over a time scale of hundreds of millions of years, and to individual virtual creatures over a time scale of tens of thousands of computer cycles – assumes the (unproved assumption) that evolutionary activity shows a “scalable” pattern, similar to Mendelson’s fractals. In addition, the failure of the artificial models presented to show a pattern of evolutionary activity similar to that of the biosphere can indeed be accounted to choice of models that are over-simplified even in comparison with other existing artificial models.