Differential heating and cooling rates in bigeye tuna (Thunnus obesus Lowe): a model of non-steady state heat exchange.

We analyzed water temperature, visceral cavity temperature and depth data from archival tags retrieved from bigeye tuna (Thunnus obesus) at liberty in the central Pacific for up to 57 days using a mathematical model of heat exchange. Our model took into account the transfer of heat between the portions of the myotomes comprising red muscle fibers adjacent to the spinal column and served by vascular counter current heat exchanges (henceforth referred to as ;red muscle') and the water, as well as between the red muscle and the temperature sensor of the archival tags in the visceral cavity. Our model successfully predicted the recorded visceral cavity temperatures during vertical excursions provided that the rate constants for heat transfer between the ambient water and the red muscle during cooling (k(low)) and those during heating (k(high)) were very dissimilar. Least-squares fitting of k(low) and k(high) for the entire period that the fish were at liberty yielded values generally in the ranges 0.02-0.04 min(-1) and 0.2-0.6 min(-1) (respectively), with an average ratio k(high)/k(low) of approximately 12. Our results confirmed those from previous studies showing that bigeye tuna have extensive physiological thermoregulatory abilities probably exerted through changes of blood flow patterns that controlled the efficiency of vascular countercurrent heat exchanges. There was a small but significant negative correlation between k(low) and size, whereas there was no correlation between k(high) and size. The maximum swimming speeds during vertical excursions (calculated from the pressure data) occurred midway during ascents and averaged approximately 2 FL s(-1) (where FL=fork length), although speeds as high approximately 4-7 FL s(-1) were also noted.