Fraser River Sockeye Fisheries and Fisheries Management - Cohen ...

0 would mean that the forecast does not consistently over- or underestimate the returnfrom year to year.To find the central tendency in PEs across years, researchers routinely take the averageand also use the acronym MPE (in this case it stands for Mean Percent Error).We opted for using the median over the average (mean) PEs because the median avoidsthe undue influence of single aberrant years and still describes central tendency.Graphing MPE for each consecutive year can illustrate changes in systematic forecasterror though time. For example, forecasts may underestimate run strength during timeswhen stream productivity and/or marine survival are increasing then switch tooverestimating when these factors are decreasing. Furthermore, a MPE = 0 does notmean that the forecast is precise. There could still be substantial error in any one year;only, this error is cancelled by substantial error in the other direction for other years. Forprecision we must use another metric such as MAPE.What is MAPE?Median Absolute Percent Error (MAPE) is also a measure of central tendency withrespect to the differences between observed and predicted values. MAPE is derived byfirst calculating the absolute difference between forecast and return values (|forecastreturn - observed return| = absolute error or AE) for each year; second converting thosevalues into a percent relative to the observed value ([AE / observed return] ×100 = APE);and third taking the median across years (MAPE). For example, if we forecast 1.5million sockeye and 1 million return, the error in our forecast would be 50% higher thanthe actual return (absolute percent error or APE=50%). If we forecast 1 million sockeyeand 2 million return, our error in forecast would be 50% lower than the actual return(APE=50%). Thus, APE does not indicate direction of the difference (as does PE), butonly the magnitude expressed as a percent. APE also renders errors proportional toactual sockeye return size, making errors in large forecasts directly comparable to errorsin small forecasts. However, sometimes small absolute errors can result in large APEvalues, which can be misleading. For instance, if we forecast 30,000 for a run that isusually in the millions and 10,000 return then our APE will be (30,000-10,000)/10,000×100=200%. This value seems like a lot, but the forecast worked well inthat it warned managers that a very small run was coming (thousands instead of millions).Conversely, a forecast of 30 million when 10 million return results in the same APE, butthe consequences are much more dire (i.e., 20 million is a lot of lost fishing opportunity).For this reason we opted for using the median of APEs as we did for PEs to avoid thedisproportionate influence of very small returns.F-2