ING models: how they work and how they are constructed

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ING modelshow they work and how they are
constructed

• Individual based Neural network Genetic algoritm
• by
• Espen Strand and Geir Huse

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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

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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

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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

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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?

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Implementing a GA - I
Strategy vector (length n)
Ind Sv(1) Sv(2) Sv(3) Sv() Sv(n)
1 2.3 -0.4 2.1 0.2
2 3.4 1.0 5.0 4.2
3 -1.4 2.1 -1.6 0.3

N 0.03 2.1 -2.6 -0.4
Population (size N)
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Linking behaviour to GA

• This link is the cornerstone of an ING-model

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Implementing a GA - III
Attribute vector
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Implementing a GA - IV

1. A population of individuals
2. Genetic variability among individuals
3. A genotype phenotype relationship
4. Individual variation in fitness
5. Inheritability of genotypes from one generation
   to the next
6. Introduction of new genetic variance

or
Strategy vectors
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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.

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Model constraints

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

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GA overview
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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
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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)

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Artificial Neural Network Input node

• An input node receive a specific input and scales
  it linearly to a value between 0 and 1

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Artificial Neural Network Hidden node

• The hidden node sums all input connection weights
  (CW) multiplied with the input node value

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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.

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Artificial Neural Network Output

• The output node sums the transformed hidden node
  values multiplied with the output connection
  weights

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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 MaxDepthoutputT)

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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.

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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

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Example A model of a planktivours fish
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Vertical migration
From Baliño and Aksnes (1991)
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Energy allocation
Data from Hamre (1999)
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Spawning behaviour
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The End