The Feeding Mode Probability Curve

It’s funny; I became a biologist, in part, because I didn’t like math. But the more I learned, the more I realized that biology is as much about mathematics and probabilities as it is about the biology.

Take trout length for example. If you were to survey trout in a lake that all hatched in the previous spring (i.e. they have all been developing and growing for roughly a year), you would find that trout length varies within a certain size range. If you measured each trout and plotted the total number of fish at each size, you would end up with a graph that looks like this:

The graph shape is what is referred to as a normal distribution or a probability curve. If you were to catch 100 of those trout and measured each one, odds are that most of them would be in the size range near the center of the distribution (i.e. 15-17 cm). A few trout might be bigger (17-19 cm) or smaller than the average (15-13 cm), and fewer still would be out at the tails of the graph – being quite a bit bigger (19-22 cm) or smaller than expected (10-13 cm). In other words, the probability of catching a near average sized trout is quite high, but the probability of catching a one year old trout that is quite a bit bigger or smaller is very low – but still possible.

This distribution not only applies to physical characteristics, it also applies to trout behavior. Under any given set of conditions, you would expect most trout to act a certain way. But there will always be a few trout that will act somewhat different from what is expected, and fewer still that act very different from what is expected. If we place the normal distribution on our trout feeding mode continuum from last week, we get a feeding mode probability curve; it looks like this:

As feeding opportunities or conditions change, the curve will shift left or right, with most trout feeding near the center of the curve. Under average conditions most trout will be feeding in the non-hatch mode, but there will still be a few fish feeding somewhat selectively or somewhat opportunistically, and possibly the occasional fish feeding in hyper-selective or opportunistic mode. If conditions change – say in the presence of a heavy hatch, the curve may shift farther to the right, and tighten up:

Here, most trout will be feeding selectively, a few trout may be feeding hyper-selective or somewhat selective, and the occasional fish may still be feeding somewhat opportunistically. The interesting thing is that not only does the trout feeding probability curve apply collectively to groups of trout exposed to similar conditions in the same water body; it also applies to individual fish.  This leads to what I call the fly selection probability curve (yes, more graphs are on the way…next week). 

When it comes to biology and animal behavior, things are rarely cut-and-dry. The best we can do is distill things down to a mathematical model that predicts behavior under a certain set of circumstances. As you move away from the peak of the probability curve, the odds on a specific event or behavior taking place becomes lower. It turns out that fly fishing and fly selection is also as much about mathematics and probabilities as it is about biology.