glen e. p. ropella wrote circa 11-10-24 11:11 AM: > Scaling, why is animal size so important? > By Knut Schmidt-Nielsen
I checked out a copy of this one, and in Chapter 11, we find these gems: "The rate of oxygen consumption in mammals, relative to body size, decreases with increasing body size." "... the decreased relative need for oxygen and blood flow in the large animal is not achieved through a relatively smaller heart or stroke volume, but through a decrease in heart rate." So, as far as I've found West et al merely imply the derivation of hear beats from heart rate. There is data for heart rate. But the explanation of the heart rate data (above) relies on common knowledge I don't have or assumptions that are/were considered reasonable. I'm still looking for an explicit derivation of the heart beat invariant, which I would hope includes an analysis of variance. > Life History Invariants > Some Explorations of Symmetry in Evolutionary Ecology > Eric L. Charnov I also checked out a copy of this. And we see a hint at the confirmation bias in this quote: "Allometries can of course be multiplied or divided by each other to make up new allometries." I ran some _naive_ numbers on heart beats per lifetime (hble) in relation to heart rate (hr) and life expectancy (le) for humans (H), cows (C), and dogs (D). If I ass/u/me hr and le are independent (I know that's a false assumption, but since cov(hr,le) <= sqrt(v_hr*v_le), I think it's close enough) and my arithmetic is somewhere near correct, then it seems to me that the variance (v) in the inputs: v^H_hr: 81, v^H_le: 49 v^C_hr: 56, v^C_le: 6 v^D_hr: 49, v^D_le: 5.6 explodes when you combine them to get the "invariant" (m := mean): m^H_hble: 2.96e9, v^H_hble: 4.5e8, > 3s m^C_hble: 5.8e8, v^C_hble: 1.2e16, > 8s m^D_hble: 1.1e9, v^D_hble: 1.6e17, > 1s s := standard deviation. West et al states hble ~= 1.5e9, which is just over 1 s for dogs, but over 3s for humans and over 8s for cows. With numbers like that, I doubt Charnov's claim to be able to derive one allometry from another. But even if I accept that, my doubt is compounded in the derivation of the invariants, no matter how much magic is installed in the "approximation". I'm coming around to believe (parts of) the argument made here: The Illusion of Invariant Quantities in Life Histories http://www.sciencemag.org/content/309/5738/1236.abstract Anyway, I'm still looking for heart beat data and a published derivation. I welcome hits from the clue stick. -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
