Hi Martin, On Mon, Dec 17, 2012 at 3:17 PM, Martin Meiss <[email protected]> wrote:
> While there similarities between river branching systems and various > biological branching systems, there is no meaningful level of analysis at > which the can be said to be the same. Branching systems can be > characterized by number of orders of branching (and there are various ways > of counting orders), diameter ratios between parent branches and daughter > branches, diameter of daughter branches as a function of branching angle, > distances between branching points, number of anastomoses, etc. Biological > branching systems represent engineering solutions to problems of optimizing > mechanical strength, gas exchange, fluid dynamics (energy efficiency), > redundancy (e.g., finding alternative routes in case of blockages), > mechanical flexibility, repair mechanisms, and more. Even trees (in the > botanical sense) show vast diversity in the details of their branching > systems: pines vs. maples vs. strangler figs vs. rose bushes. Then there > is the diversity of branching systems in animals: airways, nerves, axons > and dendrites, arteries, veins, capillary beds, and more. > > Given this diversity, is it reasonable to refer to branchings systems as "a > pattern"? > Yes. Absolutely yes. All the differences you point out are quantitative differences. In some cases, they're biologically important; in other cases, not. But there's a reason we can refer to all these things as "branching systems" -- their strong qualitative similarity. It's branching, not stripes, spots or something else. Now, there could well be several ways to get branching, but this just adds another layer to our classification. What many contemporary biologists don't realize is that qualitative is more important than quantitative. Think of it this way. Suppose you have a dataset that exhibits cycles. You have one dynamical model of the system that produces cycles of the wrong amplitude and frequency and another that produces a flat line. The second model may give a larger R^2, but the first model is the better one. It has captured something important about the data (the fact that it cycles) that the second model completely missed. It's a bit ironic that my example comes from math (qualitative dynamics). The old anatomists would have understood. So, likely, would some contemporary developmental biologists. Jane Shevtsov -- ------------- Jane Shevtsov, Ph.D. Mathematical Biology Curriculum Writer, UCLA co-founder, www.worldbeyondborders.org “Those who say it cannot be done should not interfere with those who are doing it.” --attributed to Robert Heinlein, George Bernard Shaw and others
