11 Tips for finding novel insights
Here are some of my top tips for finding novel insights.
11.1 Find analogues and push them to the extreme
Analogues are a great place to find inspiration for models. There are numerous examples. I already gave you one for Bayesian hierarchical models (students in schools is like quadrats in sites). If we treat animal movement like particle movement we can use diffusion theories to model animal movement. If we treat a spreading behaviour or invasive species like a disease, we can use epidemiological SIR models to describe its spread. If we treat species interactions like colliding gas particles, we can borrow statistical mechanics to find regularities at the community level. The appeal of an analogue is that it lets you stand on decades of theory built up in another field, and carry all of that machinery straight across into your new situation.
In most cases analogues don’t work when we push them too far. But you have to try to find those cases where they do work.
11.2 Add non-linearity
Adding non-linearity, where it can be justified, is a reliable way to find interesting insights. The thing is, human brains just aren’t very good at thinking non-linearly. Just look at how bad people are in general at understanding exponential growth and compounding interest rates. It takes training in math and science to build an intuition of exponential functions.
So when you add non-linearities in your model, you are often setting up to find non-intuitive results.
11.3 Go more granular on equations that are non-linear
In simple terms, Jensen’s inequality tells us when the function of a mean isn’t the same as the mean of the function. For example, when \(f(X)\) is a bending curve, in general
\[E[f(X)] \neq f(E[X])\]
Jensen showed that the direction of that inequality depends on the way the curve bends:
- If \(f\) is convex (bending up): \(E[f(X)] \geq f(E[X])\)
- If \(f\) is concave (bending down/flattening out): \(E[f(X)] \leq f(E[X])\)
You can use this inequality to find non-intuitive results.
A practical example: imagine we are using mean annual temperature to model a physiological rate. The rate is a non-linear function of temperature. You’ll get a different result if you calculate the rate from the mean annual temperature versus if you (more accurately) calculate the rate from daily temperatures and then take the average of those rates to get a yearly value.
Another way to employ this is to add stochasticity into your model. Once again, when we combine stochasticity with non-linear functions we often get an answer that differs from the mean of the original distribution.
11.4 Going beyond structural conventions
A ripe ground for new insights is to extend your sensitivity analysis to compare different model structures. Use some of those structures that are conventional in your discipline but also try alternative structures. Alternative structures can often be equally defensible but may reveal surprising insights.
A great example is fisheries modelling, which has stuck with convention of using a particular pair of models to describe the relationship between the size of the spawning population and the number of new recruits to the next generation (Beverton-Holt or Ricker models). Broadly, these models describe a curve with an increasing trend that flattens out. However, a simple structural change to use a ‘hockey stick’ model results in big differences for sustainability targets (Cattoni et al. 2024). The hockey stick also describes a similar curve to the Beverton-Holt model, and in fact typically fits data equally as well. But its predictions for sustainable fishing are very different. So Cattoni et al. (2024) challenged a structural convention to uncover an important insight.
I’ll end on this quote from Pip Williams’s book The Dictionary of Lost Words:
Our thinking was limited by convention, the most subtle but oppressive dictator.