All you have to do is listen to politicians around the world, and you will realize that many people, regardless of their background, agree that mathematics is useful for solving all sorts of real-world problems. We often hear about maths helping us build robots or increase profits, but maths applies to every field, especially ones where we need to make a decision. It helps us identify an option that achieves the best outcomes (optmisation) given a simplified representation of the complex problem (a mathematical model).
Sometimes maths improves decision-making, but other times it helps by unifying groups of people who contentiously disagree. Translating everyone’s ideas into maths (1) brings legitimacy and transparency to the problem but also (2) gets people talking more constructively.
But we can’t just sit down and solve a complicated maths problem every time we need to make a decision. Night would fall, and you’d still be calculating what you should eat for breakfast.
Modelling can cost you much more than your morning eggs.
If you are hiring out a complex modeling task it could easily exceed $100,000 in just a few months and if the project blows out it can likely get well into the millions). Modellers are not cheap. So one must ask why are we modelling?
Clearly, there is a cost to mathematical modelling, in either time (if you are doing the math problem yourself) or in money spent on labour (if you are hiring someone to do it for you). So when should you use a model and what model should you use?
In our new paper, we run through this question for fisheries management. We argue that modelling is not free and that we have to think about the expected benefits we could achieve by modelling, weighed against the cost of doing the maths.
Caption: Relative modelling cost ranges from Fisheries Queensland and Commonwealth Scientific and Industrial Research Organization, relative to median single-species stock assessment modelling costs. Single-species models include surplus production models all the way through to more complex, spatial, age-structured models. Ecosystem models include Models of Intermediate Complexity for Ecosystem assessment (MICE) and one of the world’s most complex ecosystem modelling frameworks (Atlantis). The cost is for modeller labour associated with data processing, model construction, analysis, and reporting.
Specifically, we looked at the cost of developing, deploying, analysing and communicating the results from ecosystem modelling vs simple single-species models taught in ecology 101. Complicated ecosystem models can be over 40 times the cost of simple single-species ones, but the simplest ecosystem models can cost less than the most complex single-species models.
Ultimately, which model to use will depend on model purpose, and we walk through how to think about costs and benefits in the paper, including a worked example. Feel free to have a read, and let me know what you think in the comments section below.
Caption: Examples of models considered in the paper.
Mathemagical Conservation 