Transcript Implementing behaviour and life history strategies in IBMs Geir Huse

Implementing behaviour
and life history strategies in
IBMs
by
Geir Huse
Department of Fisheries and Marine Biology,
University of Bergen, Norway
Lecture I, NORFA course
Talk outline
1 Introduction
2 Present concept for implementing adaptive
traits in IBMs
•Strategy vectors
•The genetic algorithm
•Artificial neural networks
3 Case study
•Morph evolution in sticklebacks
Why do we need behaviour in IBMs?
Life is a lot easier without it..
But
•Behaviours are abundantly present in the real world
•Behaviour can have strong impact on spatial and
population dynamics
•Implementing behaviour is a potential advantage of
IBMs compared with state variable approaches
Implementation of adaptive traits in IBMs:
1 By applying estimated parameter values for traits
2 Through “rules” thought to represent an evolved
strategy
3 Through evolved behaviours evaluated by an
objective criterion
Specififying individuals in IBMs:
Attribute vector:
(weight, age,position,fitness,….)
Chambers 1993
Strategy vector:
(parity, SAM, allocation of energy, behavioural
strategies,...)
Huse et al. (2002)
The genetic algorithm (Holland 1975)
”mum” ”dad” ”offspring”
0.56 0.86
0.56
6.78 5.01
6.78
5.15 -0.25
5.15
1.65 1.65
1.85
-0.21 0.50
0.50
8.91 7.56
7.56
-2.93 -1.05
-1.05
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Strategy vector or
”chromosome”
Mutation
Breakpoint
The GA
Initiate random
population
New
population
Reproduction
-produce new
strategy vectors
Generation
loop
Problem test
-update attribute
vector
-recombination
-mutation
Rank
individuals
Artificial neural networks can be used to
translate strategy vectors into behaviour
Input
Input 1

Input 2

.

.

.

Input n
Hidden
Output
Wih
•
•
Who
• Behaviour
•

Weights implemented on
strategy vector S
What is a good strategy vector?
Determine by a fitness measure:
•Net reproductive rate R0
•Instantaneous rate of increase r
These fitness measures are hampered by
many assumptions and are often difficult to
implement in IBMs
•Alternatively: use endogenous fitness
Do the GA find optimal solutions?
While optimality models always find the best
solution to problems,
How about adaptation models ...?
•Patch choice model
•A simple vertical migration scenario
In cases were the optimal solution can be
calculated, it tends to be found by the GA
Exploring adaptive radiation and
speciation in fish by individualbased models
(Huse & Hart in prep.)
(Gasterosteus aculeatus)
Background
Differentiation into limnetic and benthic is seen in
pairs of threespine stickleback found in several lakes
in British Columbia
Hypothesis: co-existence of morphs is governed by
habitat specific selection pressures on foraging, with
intermediate phenotypes suffering competitive
disadvantages (Schluter 1993)
Sympatric speciation? Invasions? ..
Objectives
Develop
individual-based
model
of
trophic
interactions between stickleback morphotypes
Study the effect of diffent prey types, competition,
spatial detail and invasions on speciation
Evaluate individual-based modelling as a tool in
studying speciation
The model: Feeding
Two separate prey populations:
•Limnetic prey: Daphnia 1-2 mm
•Benthic prey: Asellus 7 mm
Each fish gets 250 attempts per generation to get food
Prey encounter proportional to relative prey abundance
Outcome determined by individual morphotype using
Monte Carlo simulation
Random sorting of individuals per round of attempts
Prey is removed from population when eaten
Growth calculated by bioenergetics
The model: Adaptation
Strategy vector:
(body size, limnetic fidelity, mate selectivity, gill raker length)
11 different alleles [0,1] per locus
Individuals are diploid and recombinations are
performed as in meiosis
Phenotype calculated as the average of the two
homologues alleles
Fitness criterion: Net reproductive rate R0 = lx·mx
Offspring production in proportion to fitness
Simulations
Four different simulations are presented:
•1 Adaptation without competition
•2 Adaptation with competition
•3 Assortative mating without spatial detail
•4 Assortative mating and spatial detail
General results
Training decomposition:
•Individuals act ”silly” due to random initiation of
strategies
•Solved by gradually making tasks more difficult
Fecundity factor
1200
0.012
1000
0.01
800
0.008
600
0.006
400
0.004
200
0.002
0
0
50
100
Generation
150
0
200
Fecudity factor
Population abundance
Population size
1 Adaptation without competition:
Limnetic
Benthic
Both
1.0
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
Proportion
Proportion
Benthic
0.5
0.4
Limnetic
Both
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
25
28
31
34
37
40
43
Body size (mm)
Body size
46
49
52
55
0.07
0.15
0.22
0.29
0.36
0.44
0.51
0.58
Gill raker length (mm)
Gill raker size
Phenotypic differentiation due to different
prey sizes available
0.65
0.73
0.80
2 Adaptation with competition:
B-50%
B-75%
B-85%
Both
0.6
0.6
0.5
0.5
0.4
0.4
Proportion
Proportion
Both
0.3
L-75%
0.3
0.2
0.2
0.1
0.1
0.0
L-50%
0.0
25
28
31
34
37
40
43
46
49
52
Body size (mm)
Reduced benthic food
55
25
28
31
34
37
40
43
46
Body size (mm)
Reduced limnetic food
Phenotypic differentiation from competition
49
52
3 Assortative mating without spatial
detail
0.6
0.4
Frequency
Frequency
0.5
0.3
0.2
0.1
0
25
28
31
34
37
40
43
Body Size
Body size
46
49
52
55
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.07
0.22
0.36
0.51
0.65
Gill raker length
Gill raker length
No population divergence seen despite
increased competition and assortative mating
0.80
0.5
0.5
0.4
0.4
0.4
0.3
0.2
0.1
Frequency
0.5
Frequency
Frequency
4 Assortative mating and spatial detail
0.3
0.2
0.1
0
28
31
34
37
40
43
46
49
52
55
0
25
28
31
34
Body size (mm)
37
40
43
46
49
52
55
25
0.4
0.2
0.1
Frequency
0.4
Frequency
0.4
0.3
0.3
0.2
0.1
0
37
40
43
Body size (mm)
20
46
49
52
55
40
43
46
49
52
55
46
49
52
55
0.3
0.2
0.1
0
34
37
10
0.5
31
34
5
0.5
28
31
Body size (mm)
0.5
25
28
Body size (mm)
1
Frequency
0.2
0.1
0
25
0.3
0
25
28
31
34
37
40
43
Body size (mm)
50
46
49
52
55
25
28
31
34
37
40
43
Body size (mm)
100
Conclusions
The model predicts phenotypic differentiation to
different environmental states
The model predicts that sympatric speciation can
occur given that prey occur spatially distinct
Assortative mating is important in maintaining
differentiation and sympatric speciation
The methodology may help bridge the gap
between phenotypic and genotypic approaches to
life history evolution
ANN calculations
Summing over hidden node h
Nh   mi1Wih  Ii
Variable description
1
Transforming hidden node value
TN h 
1
(1  e ( Nh Bh ) )
2
Summing over output node o
O   nh 1Who  TNh
3
Transforming the output node
TO 
1
(1  e (O Bo ) )
4
Ii :
input data i,
Wih : the connection weight between
input data i and hidden node h
Nh : the sum of the weighted input
data of hidden node h
m:
the number of input nodes
connected to hidden node h
n:
the number of hidden nodes
TNh : the transformed node value
Bh : the bias
Who : the connection weight between
hidden node h and output node o
The patch choice model of Mangel
and Clark 1988 by ANN
(Huse, Strand & Giske 1999)
•The problem is to find the patch at each time
step that maximises the survival to the horizon
given the current state of the individual
SDP
ING
Average patch value
2.28 2.30±0.02
Survival
0.51 0.51±0.00
Patch choice similarity (%)
100.0 96.8±1.95
ING model predictions and optimal solutions
0
24
48
Hour
72
96
120
0
10
Depth (m)
20
30
40
50
60
70
Pp = 0,7 , Zb = 1,1
Pp = 1,5 , Zb = 0,9
Pp = 1,3 , Zb = 1,3
Pp = 0,6 , Zb = 0,5
Pp = 1,0 , Zb = 1,0
Figure 18:Pp=
Adapted
behaviour
in an ING model with a 5:30:1
The predator
density parameter (Pp) and zooplankton biomass
local
predator
ZbANN.
= local
zooplankton
parameter (Zb) values are shown for each day at the x-axis. The white line is the global optimum calculated by using the optimisation
abundance
model. Black
line is the adapted behaviour of M. muelleri inabundance
the ING model. M. muelleri clearly adapts to the stochastic environment
and reaches the global optimum solution.
Monte Carlo simulation:
Makes decision using probability and random
numbers
Example
IF random number < probability of getting prey
THEN prey is caught
Get next individual
Calculate prey
encounter rate and
feeding
Prey
availability
Monte Carlo
yes
no
Starve?
Feed?
simulations
yes
no
Calculate growth
and new larval size
Predator
field
Calculate encounter
rate with predators
and probability of
being captured
yes
Eaten?
no
Add to individuals
surviving to next
time step
Record predation
mortality
Record
starvation
mortality
Endogenous fitness
•Simulating ”survival of the fittest” within the
model domain
•Monte Carlo simulations
•Those who manage to fulfil the criteria for
reproduction in the best way are the fittest
•Survivors at any time are the fittest
•No knowledge of optimal strategy
