Introduction

While Team St Andrews' "Omega Squad" works to produce EPA Omega 3 Fatty Acids in the Laboratory; our "Mod Squad" motivates their endeavours, quantitatively. In particular, we seek to model the time evolution of human-available EPA and DHA Omega 3 Fatty Acids from the year 1950 and into the future. We will also investigate recent trends indicating increasing demand for these resources: due to population growth, as well as heightened awareness of the health benefits associated with a diet containing these Fatty Acids.

Our Model

Our Model relies on a number of assumptions:

Assumption 1: Humans obtain their necessary EPA and DHA Omega 3 Fatty Acids from fish, and fish alone. (Insert justification for this assump- tion)

Assumption 2: In addition to Assumption 1, only mature fish (insert clear definition of “mature”) can be considered a source of EPA and DHA. (Justification: current catch is composed mostly of mature fish (data to sup- port statement). This assumption also greatly simplifies our model: refer to Equation (4) later in this document)

Let $\omega(t)$ represent the DHA and EPA Omega 3 available for human consumption at time $t$ years (in tonnes). Further, let $B(t)$ represent total mature fish biomass in the world at time $t$ years (again, in tonnes) and $\omega_B(t)$ represent the average Omega 3 (DHA + EPA) content per tonne of mature fish biomass at $t$.

Then:

$\omega(t)=B(t) \cdot \omega_B(t)$ (1)

Assumption 3: The average Omega 3 content per tonne of mature fish biomass, $\omega_B(t)$, does not depend explicitly on time (an initial approximation that does not take into account the effects of, for example, climate change). Correspondingly, as a constant value, Omega 3 per tonne of biomass will be represented as $\omega_B$ throughout the rest of this document.

Differentiating (1) then yields:

$\frac{d\omega(t)}{dt}=\frac{dB(t)}{dt} \cdot \omega_B$ (2)

In addition,

$\omega_B = \sum_{all f} p_f \cdot \omega_f$ (3)

Where $p_f$ is the probability that you select a mature fish at random and it is of species $f$ and $\omega_f$ is the average Omega 3 content per tonne of biomass of that species.

Further:

$\frac{dB}{dt} = r \cdot B(t-\tau) \cdot e^{- \delta_J \, \tau} - (F + \delta) \cdot B(t)$ (4)

Introduction

While Team St Andrews' \Omega Squad" works to produce EPA Omega 3 Fatty Acids in the Laboratory; our \Mod Squad" motivates their endeav- ours, quantitatively. In particular, we seek to model the time evolution of human-available EPA and DHA Omega 3 Fatty Acids from the year 1950 and into the future. We will also investigate recent trends indicating in- creasing demand for these resources: due to population growth, as well as heightened awareness of the health bene�ts associated with a diet containing these Fatty Acids.

Data collection

When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$