PiscesLogoSmallerStill Seasonally adjusted von Bertalanffy

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Because organisms generally grow seasonally, a good description of the pattern of growth of an organism that lives for a number of years requires a seasonal adjustment to the growth rate. The seasonal growth equation used by Growth II is an extension of the von Bertalanffy growth equation derived by Somer (1988). This has the form:





where K is the growth rate and L, is the asymptotic length (or size) at which growth is zero and t0 is time at which the organism would have zero length (size) and





C is a parameter that measures the size of the seasonal variation in growth. When C = 0, the equation has no seasonal variation and is the same as the von Bertalanffy. When C =1 or (-1) growth becomes zero during the winter or other low growth season. If C is > 1 or < -1 then the organism will shrink during the non-growth season. The parameter ts is the time between t = 0 and the start of a growth oscillation. For visualization, it helps to define ts + 0.5 = WP, which expresses, as a fraction of the year, the period when growth is slowest. WP represents Winter Point.


This equation cannot describe long periods of zero growth, however, it often gives an adequate description of seasonal growth, and the parameter C can be used to compare the degree of seasonal growth shown by different species.


It is important to note that Growth II expects age (time) to be expressed in years or fractions of years. Thus, age 3 months is 0.25 years. 


Tutorial and examples of seasonal growth fitting.