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

Height

Weight