Bill, I agree with all that you said ... but one. You said:
What was the water clarity for the predation probability function of jpsdad's referenced study? I assume the experiment for the probability function was conducted in a tank or aquarium.
So, I would like to correct. The probability function I use is not from data collected from experiments conducted in tanks and/or aquariums. I inferred the probability function from data collected from field data of DOW's of multiple states. I have referenced this paper many times. Anyone interested can find it by googling "Go big or . . . don’t? A field-based diet evaluation of freshwater piscivore and prey fish size relationships". My probability function was inferred from their findings and is consistent with their findings. It is based on the assumption that the most frequently consumed prey size will be the prey that provides the maximum energy per pursuit.
Although the function pairs with their findings, I will be first to admit that it may be conservative. IOWs the probability of a successful pursuit could be higher than I model. What people will learn about me ... when they get to know me ... is that I am actually a very skeptical person. I frequently challenge my own thoughts about things. I always think I have more to learn and I am constantly amazed of how cock-sure so many others are and their unwillingness to listen, review, and converse about ideas that presently don't agree with. My understanding is moldable, my opinions are moldable, and what they moldable by are good arguments supported by reliable evidence. I am not hell bent on the probability function I use. But I am hell bent on this. LMB cannot consume prey that does not fit their gape (probability is zero) AND prey that just barely fits their gape is much more difficult to consume than prey that is smaller. My thoughts on this is that if people disagree with that ... they are just being unreasonable ... and they can't be reasoned with.
When I first pursued understanding probability of pursuit ... I did so by relating the potential for speed. I had learned that the viscosity of water inhibits the speed potential of organisms. Very small creatures are very limited for speed. So I worked up a theory based on this where the weight of the organism is proportional to its potential for the power(energy rate) required to overcome the friction of water and the friction of the water being proportional to the surface area of the organism. Simplistically, the power is proportional to L^3 while the surface area is proportional to L^2. Because speed would be proportional to power and inversely proportional to surface area resistance ... I could create a rudimentary function:
Speed is proportional to (L^3/L^2) or L
IOWs, the speed of an organism in water is proportional to its L. So, I just related these theoretical speeds of LMB to BG and found the limit at the gape of LMB is around a speed ratio of 4 (LMB 4 times faster than prey). Now keep in mind, this is totally tongue in cheek and even now I am not hell bent on saying that this should be the litmus test of probability of consumption but the linear probability relationship arising from this analysis when multiplied by the weight of the prey produced a curve like was found in the paper. This curve represented the consumption per successful pursuit. The energy per successful pursuit ... if one prefers. If one were to assume that the most frequently consumed prey is the one that provides the most energy per pursuit ... then the most frequently consumed prey would be 1/4 length BG. OK. The study of field samples does not agree with this.
The most frequently consumed BG are ~18.5% the length of LMB (<1/5 proportionately). But if I adjusted the probability function ... I could match theory with the field study. I use that probability function ... more or less ... tongue in cheek.
So let's assume alternatively, that my original speed analysis better represents the actual probability of success. I think many who claim that LMB need 1/4 to 1/3 length BG would better accept my behind the desk analysis (because it better supports their claim) than the field results in the study referenced above.
Here is what I finally decided. It doesn't matter what would maximize the energy per pursuit. What matters is the rate of consumption. What relative weight of prey is consumed on a daily basis ... this is what maintains a fish and helps it grow. Just looking at what maximizes the energy per pursuit ... this doesn't necessarily maximize energy consumed daily. To satiate with 1/4 length prey (the length optimized by my behind the desk theory) the population of 1/4 prey had to be dense enough to provide the encounter needed to provide the pursuits required to meet the satiation ration. So there is a prey density required ... below which ... the probability of successful pursuit ... would prevent consumption of the satiation ration. All that metric (the relative length/weight where energy per pursuit is maximizes) means is that this is the length/weight where the population density is minimized to meet the satiation ration. So we are comparing prey at equal populations when we define optimal sizes in this way.
If instead we compare prey at equal standing weights, a different picture emerges. Smaller prey at the same biomass density have a greater population and thus afford a greater number of encounters and a greater number of pursuits. Of those pursuits, a greater proportion of them are successful. So a fish will consume the satiation ration with less time spent foraging. Naturally, smaller prey are more abundant, and so it is clear to me that there should be no behavior of predators to avoid small prey that are easily consumed in preference for larger fish that provide more energy per pursuit.
In the end, I have come to reject Optimal Foraging Theory, even though it does seem to be apparent. Consuming prey in smaller sizes optimizes consumption but is it the LMB making choices and or having ingrained behaviors? I think not. All of this can be explained by probability of success and the natural populations of consumable forage. In so doing we can also falsify the notion that larger prey are needed to support LMB. This would only be true when the standing weights of smaller prey are too low to provide the needed consumption.
