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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
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.
In addition, we had to acquire data, which would be used to provide parameters for the model: fish catch, average weight & etc. He have stumbled upon another interesting problem. Unfortunately, the scientific community still lacks data about fish specie abundance in the ocean. We have made a crude, yet necessary assumption: the fish species with the highest population in the RAM Database (see Calculating biomass) are the most abundant ones. This "fish top" was used to for calculating various weighted averages.
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.
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 mostly produced 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.
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.
The next step was to “combine” the individual specie-specific time series into one, which would become our biomass data.
Browse the data
Ever wondered what is the average weight of a fish? This and many more surreal things inside. An introduction is included in case you get lost or want more information.
Calculating total fish biomass
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Cicero (not really)
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.
Parameter tuning
We changed the parameters in our model until its predictions closely replicated the real world fish biomass data.
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.
