ING models: how they work and how they are constructed

1. ING models:how they work and how they are constructed Individual based Neural network Genetic algoritm by Espen Strand and Geir Huse

2. ING models - Presentation layout: • Representation of individuals • Attribute and strategy vector, super-individual • The genetic algorithm in ING models • Structure, initiation, selection vs. variability, reproduction • Model constraints (avoiding Darwinian monsters) • Fitness in ING models • The neural network • Network architecture, types of input, stimuli transformation • One example of an ING model

3. Strategy vector (length n) 3.2 1.3 -0.3 2.7 -4.1 2.3 0.1 1.0 …. n 1.6 kg 590 days 34g fat female 303 eggs Attribute vector The individuals • All individuals are numerically described by a unique strategy vector (easy think of it as genes): • All individuals’ states are described in the attribute vector:

4. 500 ind 590 days 34g fat female 303 eggs Attribute vector Super-individuals • There is, depending on model complexity, an upper practical limit to how many individuals that can be simulated • In models where the number or biomass of individuals are important and very high, a way around this problem is to treat each individual as a super-individual • A super-individual simply has a number added to its attribute vector telling how many (identical) individuals it represents

5. The genetic algorithm (GA) • A GA is an algorithm that mimics evolution by natural selection. So - what is required to make evolution possible? • A population of individuals • Genetic variability among individuals • A genotype – phenotype relationship • Individual variation in phenotypic success (fitness) • Inheritability of genotypes from one generation to the next • Introduction of new genetic variance (at least in the long run) • How is this implemented in a GA?

6. A population of individuals • Genetic variability among individuals • A genotype – phenotype relationship • Individual variation in fitness • Inheritability of genotypes from one generation to the next • Introduction of new genetic variance 1 2 3 … … N Implementing a GA - I Strategy vector (length n) Population (size N)

7. A population of individuals • Genetic variability among individuals • A genotype – phenotype relationship • Individual variation in fitness • Inheritability of genotypes from one generation to the next • Introduction of new genetic variance Neural network Input 1 Input 2 Input 3 Input 4 Input 5 1 Behaviour 3.2 1.3 -0.3 2.7 -4.1 2.3 0.1 1.0 -2.1 0.5 Depth 2 Strategy vector Linking behaviour to GA • This link is the cornerstone of an ING-model

8. A population of individuals • Genetic variability among individuals • A genotype – phenotype relationship • Individual variation in fitness • Inheritability of genotypes from one generation to the next • Introduction of new genetic variance 500 ind 90 days 34g fat female 303 eggs 0.4 ind 90 days 0.4g fat female 3 eggs Implementing a GA - III Attribute vector

9. A population of individuals • Genetic variability among individuals • A genotype – phenotype relationship • Individual variation in fitness • Inheritability of genotypes from one generation to the next • Introduction of new genetic variance Implementing a GA - IV + = or Strategy vectors

10. About fitness (or: who gets to reproduce?) • There are two distinctly different ways to incorporate fitness in an ING-model • By using a fitness measure (applied fitness) • sort all individuals in the population according to the fitness measure and only let the fit ones reproduce. A fitness measure is imposed on the population. Replace the old generation with the new one. No chance of extinction. No population dynamics. • By simulating the individuals’ entire life-span including mortality, gonad development, foraging, metabolic expenditure, etc… (emergent fitness) • individuals will reproduce off-spring according to how well they adapted they are to the environment. Fitness becomes an emergent property of the model. The off-spring is added to the population as juveniles and do not replace existing individuals. Emergent population dynamics. Population may go extinct.

11. Model constraints • Environment • Physiology • Temperature dependent effects • Stomach limitation • Prey size limitations • Behavioural limitations • …. (this list really never ends)

12. GA overview

13. Artificial Neural Network • The basic idea of an ANN was to make an algorithm that mimicked how a brain makes decisions based stimuli A real network of neurons An artificial neural network (ANN) From www.greenspine.ca/media/neuron_culture_800px.jpg

14. Artificial Neural Network - Architecture • An ANN is constructed of: • Input • Input nodes • Input connection weights • Hidden nodes • Hidden node bias • Output connection weights • Output node(s)

15. Artificial Neural Network – Input node • An input node receive a specific input and scales it linearly to a value between 0 and 1

16. Artificial Neural Network – Hidden node • The hidden node sums all input connection weights (CW) multiplied with the input node value

17. HiddenNodejT HiddenNodej Artificial Neural Network – Transformation • After obtaining the value HiddenNodej the value is transformed non-linearly. Most often a sigmoid function is used. A bias is also often included.

18. Artificial Neural Network – Output • The output node sums the transformed hidden node values multiplied with the output connection weights

19. Artificial Neural Network – Behaviour • The value calculated by the output node(s) is used to determine behaviour. This can be done in several ways: • Use value directly (e.g. output = swimming speed) • Use it to determine incremental step in behaviour (e.g. NewDepth = OldDepth + output) • Transform it (sigmoid) and multiply with some maximum range(e.g. NewDepth = MaxDepth*outputT)

20. ING-models: Pros and cons • Cons • No guarantee that the optimal solution is found • Need to run replicate simulations • Can be difficult to “decode” the adapted neural network ANN = black box? • Pros • Can incorporate very high levels of complexity: • Stochasticity, Intra- and Inter-specific competition • Can be used to study emergent patterns on different levels simultaneously: • Population dynamics, state-dependent behaviour • Can avoid using a measure of fitness by making fitness an emergent property of the model.

21. Example: A model of a planktivours fishStrand, E., Huse,G., Giske, J. (2002) • Time resolution • Simulates 1 day every month (and scales it to the entire month) • Each day is divided into 5 minutes time-steps • Run for several hundred generations • Behaviour and life-history strategy • Depth position • Energy allocation • Spawning strategy • Emergent fitness • Main focus • Differences in juvenile and adult behaviour • Effects from stochastic juvenile survival on life-history and behaviour

22. Example: A model of a planktivours fish

23. Vertical migration From Baliño and Aksnes (1991)

24. Energy allocation Data from Hamre (1999)

25. Spawning behaviour

26. The End