Open Mike: Cornell OBI Conference Chapter Five – Basener on limits of chaos – Conclusion
|July 25, 2013||Posted by News under Mathematics, Cornell Conference|
To facilitate discussion, we are publishing the abstracts of the 24 papers from the Cornell Conference on the Origin of Biological Information here at Uncommon Descent, with cumulative links to previous papers at the bottom of each page.
Here is the Conclusion for William F. Basener’s* “Limits of Chaos and Progress in Evolutionary Dynamics”:
Our first conclusion is that chaos and nonlinear dynamical systems contribute nothing to the ongoing increase in complexity or evolutionary fitness of biological systems. Statements such as that quoted earlier from Novak [1, p.9], suggesting that complexity of life results from nonlinear chaotic systems, are contrary to mathematics.
Second, the evolutionary process driven by mutation-selection, in both mathematical models and directly observed behavior, is that of a system going to an equilibrium and staying there. It seems the discussion of evolution in biology is that of an ongoing process but the study of mathematical models of evolution is that of equilibrium dynamics. There is nothing inherent in the fitness-driven mathematical system that leads to ongoing progress; to the contrary, mathematical systems, both those which are specific models such as the quasispecies equation and very general classes of models, have limits on the amount of increase in fitness that occurs. This is really well-known, as speciation is believed to occur only when driven by geographical isolation [12, p.275].
We have determined certain means of evolutionary progress to be impossible, and some of these means, for example the idea that chaos can lead to extreme evolutionary progress, have in the past been used as hypothetical possibilities for evolutionary dynamics. This leads us to ask what is left?
The space of all possible genotypes, while a compact space (assuming we disallow genotypes of unbounded length), is still enormous. The potential fitness, while bounded, is still extremely high. We can imagine this space as an enormous dimensional space, and imagine every viable species as a point in this space. We can image a line segment connecting every pair of viable genotypes if there is a reasonable probability that mutation from one to the other, as suggested in Figure 2. The result is an enormous network amenable to analysis by mathematical Fig. 2. A large network with sparsely connected groups. The question we pose is whether the genotype network is connected like this, or if there are many disconnected islands. This image shows a partial map of the internet based on the January 15, 2005 data found on opte.org. Each line is drawn between two nodes, representing two IP addresses. The length of each line are indicates the delay between its endpoint nodes.
The quasispecies equation provides the local equilibrium dynamics in this space, and there is no mathematical reason to expect generally other than the equilibrium state naturally from the system; stability is what we observe experimentally and from well-supported equations. In the genotype network described above, each quasispecies lives within a group of highly interconnected points, called a community or clique in social network theory. If environmental conditions change, the quasispecies shifts within this group. In most cases, if the environment shifts to far (or at least too quickly) then the quasispecies is pushed to the edge of its local group, to points with low fitness, and then goes extinct. This decrease in fitness near the boundary of a local group can be observed in selective breeding; if too many desired properties in an animal or vegetation are attempted to be optimized through selective breeding, the simultaneous optimization becomes difficult and the species becomes less fit as a whole.
A question for evolution is to determine the structure of this genotype network. Are there bridges between groups of interconnected genotypes? How can we tell? What is the density of the network? How populated must a group be in order to support a quasispecies? Can the dimension of a local group be inferred, for example as the number of properties of a species that can be simultaneously optimized through selective breeding?
*Rochester Institute of Technology School of Mathematical Sciences Rochester, NY, 14623, USA
Note: All conference papers here.
See also: Origin of Biological Information conference: Its goals
Open Mike: Origin of Biological Information conference: Origin of life studies flatlined
Open Mike: Cornell OBI Conference— Can you answer these conundrums about information?
Open Mike: Cornell OBI Conference—Is a new definition of information needed for biology? (Chapter 2)
Open Mike: Cornell OBI Conference—New definition of information proposed: Universal Information (Chapter 2)
Open Mike: Cornell OBI Conference—Chapter Three, Dembski, Ewert, and Marks on the true cost of a successful search
Open Mike: Cornell OBI Conference—Chapter Three on the true cost of a successful search—Conservation of information
Open Mike: Cornell OBI Conference—Chapter Four: Pragmatic Information
Open Mike: Cornell OBI Conference—Chapter Four, Pragmatic information: Conclusion
Open Mike: Cornell OBI Conference Chapter Five Abstract