Team:St Andrews/Modelling

From 2012.igem.org

(Difference between revisions)
Line 63: Line 63:
   <p><b>Assumption 1:</b> Humans obtain their necessary EPA and DHA Omega 3 Fatty Acids from fish, and fish alone. (Insert justification for this assump- tion)</p>
   <p><b>Assumption 1:</b> Humans obtain their necessary EPA and DHA Omega 3 Fatty Acids from fish, and fish alone. (Insert justification for this assump- tion)</p>
   <p><b>Assumption 2:</b> 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)</p>
   <p><b>Assumption 2:</b> 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)</p>
-
   <p>Let <i>ω(t)</i> represent the DHA and EPA Omega 3 available for human con- sumption at time <i>t</i> years (in tonnes). Further, let <i>B(t)</i> represent total ma- ture fish biomass in the world at time <i>t</i> years (again, in tonnes) and <i>ωB(t)</i> represent the average Omega 3 (DHA + EPA) content per tonne of mature fish biomass at <i>t</i>.</p>
+
   <p>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 $t$.</p>
   <p>Then:</p>
   <p>Then:</p>
   <p>$\omega(t)=B(t) \cdot \omega_B(t)$ (1)</p>
   <p>$\omega(t)=B(t) \cdot \omega_B(t)$ (1)</p>
   <p><b>Assumption 3:</b> 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.</p>
   <p><b>Assumption 3:</b> 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.</p>
   <p>Differentiating (1) then yields:</p>
   <p>Differentiating (1) then yields:</p>
-
   <p>$\frac{d\omega(t)}{dt}=\frac{dB(t)}{dt} \cdot \omega_B$</p>
+
   <p>$\frac{d\omega(t)}{dt}=\frac{dB(t)}{dt} \cdot \omega_B$ (2)</p>
 +
  <p>In addition,</p>
 +
  <p>$\omega_B = \sum_{all f} p_f \cdot \omega_f$ (3)</p>
 +
  <p>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.</p>
 +
  <p>Further:</p>
 +
  <p>$\frac{dB}{dt} = r \cdot B(t-\tau) \cdot e^{- \delta_J \, \tau} - (F + \delta) \cdot B(t)$</p>
 +
 
 +
 
 +
 
</section>  
</section>  

Revision as of 17:21, 12 July 2012

Resource: Omega 3

Past, Present and Future Supply and Demand


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


Introduction

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:

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


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 $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$

Back to top

University of St Andrews, 2012.

Contact us: igem2012@st-andrews.ac.uk, Twitter, Facebook

This iGEM team has been funded by the MSD Scottish Life Sciences Fund. The opinions expressed by this iGEM team are those of the team members and do not necessarily represent those of Merck Sharp & Dohme Limited, nor its Affiliates.