Comparative Analysis of Statistical Tools To Identify Recruitment-Environment Relationships and Forecast Recruitment Strength Bernard A. Megrey Yong-Woo Lee S. Allen Macklin National Oceanic and Atmospheric Administration National Marine Fisheries Service Alaska Fisheries Science Center Seattle, WA USA

Overview Background and motivation Mechanics of testing procedures Results of application of 3 statistical tools to 2 data sets Concluding remarks and observations

Why Forecast Recruitment? Understand important bio-physical factors controlling the recruitment processes –The ultimate test of a model is its ability to predict Project future stock dynamics Evaluate management scenarios Provide reference points for fishery management Assist commercial fisheries decision making

The data we collect as it relates to recruitment variability and the factors that influence it probably will not change dramatically in the near future. “We should endeavor to treat the data differently in a statistical sense.” R.J.H Beverton 1989

What are the best statistical tools for estimating environment-recruitment relationships and forecasting future recruitment states? ? ? ? ? ? ?

Problems in Forecasting The complexity of recruitment forecasting often seems beyond the capabilities of traditional statistical analysis paradigms because…. Bio-physical relationships are inherently nonlinear Often there are limitations in theoretical development or standard models cannot deal with data pathologies Inability to meet required assumptions Time series of data are short Lack of degrees of freedom The need to partition already short time series into segments representing identified regimes

Objectives Test and compare several statistical methods to evaluate their ability –to identify recruitment-environment relationships –to forecast future recruitment In a real world setting we can never know the parameters and underlying relationships of actual data –simulate data with known properties and different levels of measurement error using Gulf of Alaska pollock Use methods on actual North Atlantic data –Norwegian spring spawn herring SB and R, Kola Line SST, and Index of NAO (Toresen and Ostvedt 2000) Environmental effects occur in birth year (i.e. no lags)

Simulated Data with Known Properties R = a·S·exp(-b·S+c·N+d·T+ ε ) R: Recruitment S: Spawning Biomass N: Wind Anomaly - No relationship T: Sea Surface Temperature ε : Measurement Error, N(0,σ 2 ), σ 2 was estimated from a Ricker fit to actual data. *** 3 Error levels: [no error] [½ σ 2 ] [σ 2 ] ^^

Summary of Simulated Data SBWindSST Relationship to Recruitment Nonlinear Ricker noneLinear Functional Relationship Exponential Nonlinear MeanLog Linear Probability Distribution GammaLognormalNormal

Herring Simulated

Tested Statistical Tools Recruitment on the absolute scale (billion fish) Nonlinear Regression (NLR) Generalized Additive Models (GAM) Artificial Neural Network (ANN) FISHERIES APPLICATIONS GAM Cury et al. 1995; Swartzman et al. 1995; Meyers et al. 1995; Jacobsen and MacCall 1995; Daskalov 1999 ANN Chen and Ware 1999

Neural Networks

General Additive Models

Comparisons Statistical Methods Parametric (NLR) vs. Non-parametric (GAM, ANN) Conventional (NLR) vs. Innovative (GAM, ANN) Model Free (GAM, ANN) vs. functional relationships specified a priori (NLR)

Time Series Partitioning 2 Data Segments Training segment used for parameter estimation Forecasting segment used for forecasting accuracy Simulated Data (n=42) Training segment (n=37) Forecasting segment (n=5) Herring Data (n=89) Training segment (n=79) Forecasting segment (n=10)

Simulated vs Predicted, for Error level = 0 R-square for TrainingMSE for Forecasting

Simulated Data Testing and Forecast Segment Comparison using MSE ERROR 2 ERROR 1 ERROR 0

Simulated Data ANN Relative Weight Comparison 3 variables 2 hidden neurons 10 parms 2 variables 2 hidden neurons 8 parms

Spurious Correlations We did see evidence of spurious correlations when analyzing the simulated data. The GAM model, Err = 2; R = SB + WIND + SST WIND was significant in NLR model, Err=3. When dealing with data with typical levels of variation, it is possible to conclude that unnecessary or irrelevant variables are significant. “Spurious correlations are the first enemy of recruitment biologists” Tyler (1992)

Herring Data Testing and Forecast Segment Comparison using MSE and R 2 ANN Relative Weight Comparison

GAM fit to Herring Data

Summary Need to be cautious when dealing with noisy data, because a wrong model or variable could be identified as influential to recruitment. We did see evidence of spurious correlations under very controlled data situations. It appears that ANNs forecast better than conventional parametric methods when data are noisy. Non-parametric methods (GAMs and ANNs) work well for suggesting functional relationships and forecasting future recruitment states –desirable property because real systems are highly non- linear and include complex interactions among the variables.

Summary (con’t) There is no one “best” method to address the environment- recruitment problem. ANNs are highly flexible and show promise for forecasting, thus using GAMs and ANNs together with more traditional methods should enhance analysis and forecasting. When considering estimation in conjunction with forecasting it is better to consider a balance between “best” models. Results underscore the need to build good conceptual models first, then guided by hypotheses regarding factors that control recruitment and their time and space scales of influence, judiciously apply a suite of statistical models to quality data sets. Data mining and “kitchen stew” correlation exercises are not appropriate.

Simulated Data

Norwegian Spring Spawn Herring