Team:St Andrews/Modelling
From 2012.igem.org
The mathematics of ω-3
Modelling the impact of alternative Omega-3 production on the global fish population
Our Model 101
![](https://static.igem.org/mediawiki/2012/f/f0/ModSquadLogo_100.png)
We sought to model fish population depletion. We succeeded. The result: unless we work together on a global scale and make drastic changes to our fishing habits, only a fraction of the total fish population that existed in 1950 will be present in our oceans by 2100. The work of our team in the laboratory - the creation of Omega-3 using E.coli - could be exactly the measure necessary to save our oceans.
Our approach: we took one of a multitude of different possible approaches to population modelling and our project can be broken down into approximately four different stages:
We performed meta-analysis to obtain information about the variation of total fish biomass in our oceans over time. We scaled our result to Villy Christensen’s (University of British Columbia) prediction of total fish biomass for 1950. We, thus, created a time series of total fish biomass in our oceans between 1950 and 2006. We believe our time series to be one of the first of its kind and certainly one of the first to be generated, largely, from real world data.
We hypothesised a differential equation model which we believe incorporates the key features responsible for fish population growth and decline. Our final model takes into account recruitment of fish into the adult fish population, death of adult fish due to fishing and death of adult fish due to natural causes.
Fish biomass data – collection and manipulation
Motivation
In order to model the future of the global fish population, we chose a differential equation modelling approach. Such an approach, however,does rely on precise parameter definition – and, as a result, we spent considerable time refining these parameters. In particular, this “tuning” was done by taking a set of observed data (in our case, fish biomass throughout the last 60 years) and changing these parameters until our model’s predictions resembled the data as closely as possible. Being able to precisely predict past biomass values, ensured that we had some grounding for making future estimates.
Unfortunately the global fish biomass data, the cornerstone of the tuning process, was not something which was readily available. A “total fish biomass” time series did not, to our knowledge, exist. We had to create it ourselves.
RAM database
After further investigation, we found that there were many cases in which biomass data was available for specific species in specific regions – this data being produced mostly for the sake of commercial stock assessment. RAM Legacy Stock Assessment Database is a “compilation of stock assessment results for commercially exploited marine populations from around the world”. We believe that it is the most complete compilation of Stock Assessment Results to this date. Another advantage of the RAM Database, compared to other databases (NOAA, ICES & etc.), is that it combines data from different regional agencies, thus ensuring good global coverage. Effectively, the RAM Database includes data from all known to us sources; therefore we decided to use it for our further work.
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RAM Database coverage
Ricard D, Minto C, Jensen OP, Baum JK (in press) . 2011. Examining the knowledge base and status of commercially exploited marine species with the RAM Legacy Stock Assessment Database. Fish and Fisheries doi: 10.1111/j.1467-2979.2011.00435.x.
Data manipulation
The data presented in RAM, in some cases, was not entirely homogeneous. For example, the Spawning Stock Biomass (total weight of those fish that have reached the breeding age) – the data figure we were interested in - was often presented in different measures. These measures ranged from weight in tonnes/kg/pounds to the biomass of the annually produced eggs and non-specified measures. We had to omit the datasets, which were not directly convertible to tonnes.
Calculating total fish biomass
These three graphs show the amount of papers published each year containing certain search queries, as well as the number of times these papers were cited. All graphs show positive tendencies: the competition is becoming more wide-spread and more iGEM-related papers are being published and recognized. The search queries were chosen to show which part of iGEM is usually cited: the iGEM competition, the Registry of Standard Parts, or both. The data shows that only around half of papers will cite both elements. It should be noted that some outlying data points were ignored as they are obvious mis-searches.
Mathematical model
We hypothesised a differential equation model which we believe incorporates the key features responsible for fish population growth and decline. Our final model takes into account recruitment of fish into the adult fish population, death of adult fish due to fishing and death of adult fish due to natural causes.
$\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Biomass(this year) - Biomass(last year) = Recruits added over year - (Catch over year + Natural death over year)
Biomass(this year) - Biomass(last year) = Biomass(this year) - Biomass(last year)
Parameter tuning
Model predictions
Content that our model could predict fish biomass in the past and present, we enabled our model to forecast future fish biomass. We discuss how alternative sources of omega three could influence this outcome.