I take your points, Jane (though I may have some reservations about your curve-fitting example), but my point, backed up by my examples, is that branching systems represent MANY patterns. I think this is especially important when we consider anastomoses (cross-connections). When there are enough of them, we have a network (like capillary beds, or strangler-fig roots), not a topological tree, but I don't know of any good way of deciding where to draw the line.
Martin 2012/12/18 Jane Shevtsov <[email protected]> > 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 >
