The goal of all scientific research is to increase our understanding of the natural world – to discover the truth about how the world works. Despite the general consensus on this objective there have been relatively few attempts to measure understanding and progress. In principle, understanding can be measured as the linear distance along the continuum between the size of the prediction error with minimum understanding (i.e. maximum prediction error) and the size of the prediction error with maximum understanding (i.e. minimum prediction error). This idea is conceptually simple but may be difficult to apply. Here, I outline practical approaches to estimating prediction error with minimum and maximum understanding and apply these approaches to estimate how much incorporating density dependent regulation into population models improves our understanding of animal and plant population fluctuations. I built simple density dependent models (Model DD) for 100 population time series containing at least 25 annual counts. The last ten years were held back to test model predictions and the remaining years used to build the model. I estimated the increase in our understanding as the linear distance of the observed prediction errors along the continuum between maximum and minimum prediction error.
1. Minimum prediction error (MinPE) = 0.
This assumes that true stochasticity doesn’t exist, i.e. that what we commonly call stochastic error is just the sum of the things that we don’t understand.
2. Maximum prediction error (MaxPE) = ABS (N t-1-N t).
This assumes that the minimum we would know about a population when predicting N t would be N t-1 and that population fluctuations are a simple random walk.
3. Model DD prediction error (DDPE) = ABS(N t (DD) – N t) where N t (DD) is the value for N t predicted by Model DD
4. Progress in Understanding (PU) = DDPE/(MaxPE – MinPE) = ABS(N t(DD) – N t) /ABS (N t-1-N t).
Preliminary results suggest that incorporating simple density dependence into population models improves our understanding of population fluctuations by, on average, 5-10% although there is wide variability across populations.