As more and more consumers turn away from meat, especially that of mammals, they do, however, turn to fish. Consequently, there is increasing pressure on fish stocks in the wild, but a growing opportunity for fish culturists to improve fish rearing facilities. When I was still a student of Fisheries Science in 1967 and lectures I attended dealt with fish stock assessments, catch per unit effort, fish populations, age structures, longevities and survival rates of fishes, time and again Ludwig Von Bertalanffy was mentioned and equations he had developed were quoted and written with chalk on the blackboard (yes, chalk and blackboard in those days). But why were Von Bertalanffy’s calculations so useful and why are they still part of the backbone of fisheries assessments of fish stocks today?
Ludwig von Bertalanffy was born near Vienna in 1901 and although his parents got divorced when he was ten, he did enjoy a good home education until then, when he became a grammar school student. He had the famous anti-Darwinist Paul Kammerer as his neighbour and soon began to apply his mathematical interests to biology and the living world. He is now often regarded as the founder of General Systems Theory, which has inputs from thermodynamics, cybernetics and biology. At the University of Vienna his fields of expertise could be called Theoretical Biology and Philosophy and in 1937 he got a Rockefeller scholarship to work in the USA. When he failed to secure immigrant status, he returned to Vienna in 1938 and joined the Nazi-party. After the war he found living in Austria difficult, moved to the University of London in 1948 and from there two years later to appointments at various American and Canadian universities. He died in 1972 in Buffalo, New York.
In his biological research, Von Bertalanffy was interested in psychology, psychiatry, development and growth phenomena and concluded that thermodynamic principles worked well in closed systems, but not in open systems like those comprising living organisms. He came up with a simple growth equation for biological organisms that models mean length of animals in relation to age: L(a) = L∞ [1 – exp (-k(a – a0))], where a is age, k is the growth coefficient, a0 is the value used to calculate size when age is zero and L∞ is asymptotic size (which means the rate of growth continually decreases as an individual ages but never completely stops). The equation above is the solution of the linear differential equation: dL/da = k(L∞ – L) and applicable to organisms that do not cease to grow when adult (unlike, for instance humans, which actually shrink when reaching old age), but keep growing albeit at increasingly slower and smaller rates as they age. Fish are some of these animals and since it is important for fisheries biologists to know at what age (or body length) individuals of a species become reproductive and therefore should not be ‘harvested’ until old enough to have reproduced at least once, it’s obvious that much emphasis has been placed on Von Bertalanffy’s growth curve that relates age to body lengths.
To make this relationship ‘work’, it is crucial to know how old a fish is at any given length. Helping fisheries scientists in this matter are age-rings on the scales of fish (not unlike those that one uses to age trees). The problem is that not all fishes live in climatic zones in which there are distinct seasonal changes that result in age rings on the scales and secondly not all fish species even have scales. In my research with the Polish scientist R. Traczyk, we worked with Antarctic icefish that have no scales and live in constantly ice-cold water. In such cases one uses daily increments of extremely narrow CaCO3 layers, visible in sectioned ear-stones of the fish examined under the microscope. The layers provide an accurate estimation of the fish’s age that can be correlated with the fish’s total body length. What is then still left to discover is at what age and body length these fish spawn. For that to find out, fish have to be trawled near spawning grounds and females must be measured and examined as to whether they still have mature eggs in their ovaries or had already spawned. Once all the essential data are in, one can use the Von Bertalanffy growth curve to make recommendations to the fishing industry at what size it is ‘safe’ to harvest and market a species without depleting the population of younger and still immature specimens. Although Von Bertalanffy’s work doesn’t save all fish from being ‘fished’, it does help to ascertain that there are still enough youngsters around to maintain the population.
© Dr V.B. Meyer-Rochow and http://www.bioforthebiobuff.wordpress.com, 2021.
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