Transcript Lysbilde 1

ING models:
how they work and how they are
constructed
Individual based Neural network Genetic algoritm
by
Espen Strand and Geir Huse
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
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:
Strategy vector (length n)
3.2 1.3 -0.3 2.7 -4.1 2.3 0.1 1.0 ….
1.6 kg
590 days 34g fat
n
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
Attribute vector
500 ind 590 days 34g fat
female 303 eggs
The genetic algorithm (GA)
•
A GA is an algorithm that mimics evolution by natural selection.
So - what is required to make evolution possible?
1.
2.
3.
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•
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?
Implementing a GA - I
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2.
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2
Strategy vector (length n)
3
…
N
…
Population (size N)
1
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
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
Linking behaviour to GA
•This link is the cornerstone of an
ING-model
1.
2.
3.
4.
5.
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
Neural network
Input 1
1
Input 2
Depth
Input 3
Behaviour
Input 4
Input 5
2
3.2 1.3 -0.3 2.7 -4.1 2.3 0.1 1.0 -2.1 0.5
Strategy vector
Implementing a GA - III
1.
2.
3.
4.
5.
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
Attribute vector
500 ind 90 days
0.4 ind
34g fat
90 days 0.4g fat
female 303 eggs
female 3 eggs
Implementing a GA - IV
1.
2.
3.
4.
5.
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+
=
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
or
Strategy vectors
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.
Model constraints
• Environment
• Physiology
– Temperature dependent effects
– Stomach limitation
– Prey size limitations
– Behavioural limitations
– …. (this list really never ends)
GA overview
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
From www.greenspine.ca/media/neuron_culture_800px.jpg
An artificial neural network (ANN)
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)
Artificial Neural Network – Input node
• An input node receive a specific input and scales it
linearly to a value between 0 and 1
input i  input i min
InputNodei 
input i max  input i min
Artificial Neural Network – Hidden node
• The hidden node sums all input connection weights
(CW) multiplied with the input node value
1
HiddenNode j   ( InputNodei  CWij )
i
Artificial Neural Network – Transformation
• After obtaining the value HiddenNodej the value is transformed nonlinearly. Most often a sigmoid function is used. A bias is also often
included.
1 e
(  HiddenNodej bias j )
1.0
HiddenNodejT
HiddenNode jT 
1
0.8
0.6
0.4
0.2
0.0
-10
-5
0
5
HiddenNodej
10
Artificial Neural Network – Output
• The output node sums the transformed hidden node
values multiplied with the output connection weights
1
OutputNodek   ( HiddenNodeiT  CWjk )
j
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)
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.
Example: A model of a planktivours fish
Strand, 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
Example: A model of a planktivours fish
Vertical migration
From Baliño and Aksnes (1991)
Energy allocation
Data from Hamre
(1999)
Spawning behaviour
The End