Von Bertalanffy model for fish growthVon Bertalanffy model for fish growth
Aim: To derive a semi-mechanistic mathematical model for growth based on an isometric morphological relationship
(i.e. a constant body plan over time)
Objectives:
1. Motivate problem using example of changes in weight of fish
2. Derivation of the model
3. Solution of a Bernoulli differential equation
4. Reinterpreting the mathematical solution in context
Jacob (Jacques) Bernoulli
Born: 27 Dec 1654 in Basel, SwitzerlandDied: 16 Aug 1705 in Basel, Switzerland
1696: solved class of differential equations now bearing his name
Karl Ludwig von Bertalanffy
Born: 19 Sep 1901 in Atzgerdorf, AustriaDied: 12 Jun 1972 in Aztgerdorf, Austria
Today’s heroesToday’s heroes
1938: formulated the model we study today
Bernoulli Equation – Extract from F.S.Bernoulli Equation – Extract from F.S.
Bernoulli is pretty famousBernoulli is pretty famous
The probability distributionused for Coin Tossing etc.
…the key building block of the Binomial distribution (will study next term)
Bernoulli is pretty famousBernoulli is pretty famous
A crater on the moon
Bernoulli is pretty famousBernoulli is pretty famous
A “leminscate”(i.e. a figure 8)
Bernoulli is pretty famousBernoulli is pretty famous
A number ofGerman andAustrian streets
But really the focus today: a guppy fishBut really the focus today: a guppy fish
Growth of fishGrowth of fish
Bernoulli Equation – Extract from F.S.Bernoulli Equation – Extract from F.S.
Integrating Factors – Extract from F.S.Integrating Factors – Extract from F.S.
Growth of fishGrowth of fish
Growth of fishGrowth of fish