Modeling sardine and anchovy population dynamics

5 
 
Index 
1. Introduction ........................................................................................................................... 11 
2. Materials and Methods ......................................................................................................... 15 
2.1 Study area ....................................................................................................................... 15 
2.2 Background of sardine biology and fishery ................................................................. 17 
2.2.1 Characteristics ........................................................................................................ 17 
2.2.2 Reproduction .......................................................................................................... 17 
2.2.3 Migrations ............................................................................................................... 18 
2.2.4 Feeding .................................................................................................................... 19 
2.2.5 Fishery..................................................................................................................... 19 
2.2.6 Predation ................................................................................................................. 19 
2.3 Background of anchovy biology and fishery ............................................................... 19 
2.3.1 Characteristics ........................................................................................................ 19 
2.3.2 Reproduction .......................................................................................................... 20 
2.3.3 Migrations ............................................................................................................... 21 
2.3.4 Feeding .................................................................................................................... 22 
2.3.5 Fishery..................................................................................................................... 22 
2.3.6 Predation ................................................................................................................. 22 
2.4 Time series ..................................................................................................................... 22 
2.4.1 Sardine biomass time series ................................................................................... 22 
2.4.2 Sardine landings time series .................................................................................. 23 
2.4.3 Sardine fishing mortality time series .................................................................... 24 
2.4.4 Water Temperature times series ............................................................................ 25 
2.4.5 Phosphate load time series ..................................................................................... 25 
2.4.6 Mackerel time series .............................................................................................. 26 
2.4.7 Anchovy time series ............................................................................................... 27 
2.4.8 Anchovy landings time series ................................................................................ 27 
2.4.9 Anchovy fishing mortality time series .................................................................. 28 
2.5 Conceptual models of the ecosystem............................................................................ 29

Index 
6 
 
2.6 Type of population dynamics simulation models ........................................................ 30 
2.6.1 Logistic models ...................................................................................................... 30 
2.6.2 Logistic model qualitative analysis ....................................................................... 30 
2.6.3 Modeling fishery .................................................................................................... 31 
2.6.4 Modeling temperature ............................................................................................ 31 
2.6.5 Modeling predation ................................................................................................ 32 
2.6.6 Modeling nutrients load ......................................................................................... 32 
2.6.7 Modeling competition ............................................................................................ 33 
2.7 Models fitting ................................................................................................................. 34 
2.7.1 Models Prediction .................................................................................................. 34 
2.7.2 Comparing models output with VPA data ............................................................ 34 
2.7.3 Finding the best fitting parameter set .................................................................... 34 
2.7.4 Code script debug ................................................................................................... 35 
2.7.5 Model sensitivity analysis...................................................................................... 35 
2.8 Goodness of model evaluation ...................................................................................... 35 
2.8.1 Root of sum of squared errors of prediction (RSSE) ........................................... 36 
2.8.2 Nash-Sutcliffe efficiency ....................................................................................... 36 
2.8.3 Akaike information criterion corrected for finite sample size ( AICc) ............... 36 
2.9 Models scenarios ............................................................................................................ 37 
3. Introduction ........................................................................................................................... 39 
3.1 Sardine model I: Logistic growth model and fishing mortality .................................. 39 
3.2 Sardine model II: Logistic growth model, fishing mortality and phosphate load 
(linear dependency)................................................................................................................... 41 
3.2.1 Exponential dependency ........................................................................................ 42 
3.3 Sardine model III: Logistic growth model, fishing mortality, phosphate load and 
predation .................................................................................................................................... 42 
3.4 Sardine model IV: Logistic growth model, fishing mortality, phosphate load, 
predation and water temperature .............................................................................................. 44 
3.5 Model V: Logistic growth model, fishing mortality, phosphate load, predation, water 
temperature and competition .................................................................................................... 46

Index 
7 
 
3.6 Sardine - other models ................................................................................................... 48 
3.6.1 Fishing mortality and predation ............................................................................ 48 
3.6.2 Fishing mortality and temperature ........................................................................ 49 
3.6.3 Fishing mortality, Po river phosphate load, and temperature .............................. 50 
3.6.4 Fishing mortality, Po river phosphate load, competition (Lotka-Volterra) and 
temperature ............................................................................................................................ 52 
3.6.5 Po river phosphate load.......................................................................................... 53 
3.6.6 Po river phosphate load and predation .................................................................. 54 
3.6.7 Predation ................................................................................................................. 56 
3.6.8 Competition and Po river phosphate load ............................................................. 57 
3.7 Sardine goodness of model evaluation summary......................................................... 59 
3.8 Sardine biomass prediction for the period 2011-2020................................................. 59 
3.8.1 Scenario A .............................................................................................................. 60 
3.8.2 Scenario B ............................................................................................................... 61 
3.8.3 Scenario C ............................................................................................................... 62 
3.8.4 Scenario D .............................................................................................................. 62 
3.8.5 Scenario E ............................................................................................................... 63 
3.8.6 Summary table ........................................................................................................ 64 
3.9 Anchovy model I: Logistic growth model and fishing mortality ............................... 65 
3.10 Anchovy model II: Logistic growth model, fishery and competition .................... 66 
3.11 Anchovy model III: Logistic growth model, fishing mortality, phosphate load and 
competition ................................................................................................................................ 68 
3.12 Anchovy model IV: Logistic growth model, fishing mortality, phosphate load, 
water temperature and competition .......................................................................................... 69 
3.13 Anchovy - other models ............................................................................................ 71 
3.13.1 Anchovy model V: Logistic growth model, fishing mortality, Po river flow, 
water temperature and competition ..................................................................................... 71 
3.13.2 Model VI: logistic growth model, fishing mortality and phosphate load ........... 73 
3.13.3 Anchovy model VII: Logistic growth model, fishing mortality and water 
temperature ............................................................................................................................ 74 
3.13.4 Anchovy model VIII: Logistic growth model, fishing mortality and predation. 75

Index 
8 
 
3.14 Anchovy goodness of model evaluation summary .................................................. 77 
3.15 Anchovy biomass prediction for the period 2011-2020 .......................................... 78 
3.15.1 Scenario A .............................................................................................................. 78 
3.15.2 Scenario B ............................................................................................................... 79 
3.15.3 Scenario C ............................................................................................................... 80 
3.15.4 Scenario D .............................................................................................................. 81 
3.15.5 Scenario E ............................................................................................................... 82 
3.15.6 Summary table ........................................................................................................ 83 
4. Discussion ............................................................................................................................. 85 
4.1 Sardine discussion.......................................................................................................... 85 
4.2 Anchovy discussion ....................................................................................................... 87 
4.3 Future developments ..................................................................................................... 89 
5. Conclusions ........................................................................................................................... 91 
6. Appendix A: Matlab model code ......................................................................................... 93 
6.1 Sardine script file ........................................................................................................... 93 
6.1.1 Function handle logistic script file ........................................................................ 95 
6.1.2 Function handle RSSE script file .......................................................................... 96 
6.2 Anchovy script file......................................................................................................... 96 
6.2.1 Function handle logistic script file ........................................................................ 98 
6.2.2 Function handle RSSE script file .......................................................................... 99 
7. Appendix B Tables of used data ........................................................................................ 101 
7.1 Table 1: Sardine biomass ............................................................................................ 101 
7.2 Table 2: Anchovy biomass .......................................................................................... 102 
7.3 Table 3: Po river phosphates load ............................................................................... 103 
7.4 Table 4: Mackerels CPUE ........................................................................................... 105 
7.5 Table 5: Sardine fishing mortality .............................................................................. 106 
7.6 Table 6: Anchovy fishing mortality ............................................................................ 107 
7.7 Table7: Water temperature in Trieste Porto Lido ...................................................... 109