Download A probabilistic method for food web modeling

A probabilistic method
for food web modeling
Bayesian Networks – methodology,
challenges, and possibilities
Anna Åkesson, Linköping University, Sweden
2nd international symposium on Ecological Networks, Bristol, UK
A probabilistic method for
food web modeling
Motivation
• To efficiently predict extinction risk of species in
ecological networks
• Species function in complex networks – a single
species extinction can cause a cascade of secondary
extinctions
• There is the danger of simplification, and there is
complexity – can we find a middle ground approach?
Common methods
- Topological approach
• Advantages
• Requires only network
structure as input
• Possible to analyse very
large networks
• Drawbacks
• All nodes have identical
characteristics
• Secondary extinctions only
occur when all resources are
lost
Common methods
- Dynamical modeling
• Advantages
• Possible to capture indirect effects –
such as top-down effects
• Species can be given various
properties depending on, for
example, trophy level
• Drawbacks
• Requires extensive set of parameters
• Slightly different initial conditions
can produces different outcomes 
many replicates necessary
Bayesian Networks
- a graphical model
• Middle-ground approach: topological structure 
no extensive simulations, but with some of the
complexity used in dynamical models included
• Applications
• Probability of the presence of various diseases
• Modeling beliefs in bioinformatics (gene regulatory
networks, protein structure, gene expression analysis)
• Artificial Intelligence
Bayesian Networks
- structure
• Nodes – Bernoulli random
variables
• Links – directed arcs, representing
conditional dependencies among
variables
• Extinction probabilities - a
function of the state of a species
parent nodes (resources)
Bayesian Networks
- structure
Extinction probability of species i;
P(i|f) = π + (1-π) × f
P(D|A,C)=0.2
P(D|A,C)=0.6
P(D|A,C)=0.6
P(D|A,C)=1
where f is the fraction of resources lost
P(C|A,B)=0.2
P(C|A,B)=0.6
P(C|A,B)=0.6
P(C|A,B)=1
P(A)= π (0.2)
P(B)= π (0.2)
Bayesian Networks
- structure
Topological
Bayesian network
P(D|A,C)=0.2
P(D|A,C)=0.2
P(D|A,C)=0.2
P(D|A,C)=1
P(D|A,C)=0.2
P(D|A,C)=0.6
P(D|A,C)=0.6
P(D|A,C)=1
P(C|A,B)=0.2
P(C|A,B)=0.2
P(C|A,B)=0.2
P(C|A,B)=1
P(A)=0.2
P(B)=0.2
P(C|A,B)=0.2
P(C|A,B)=0.6
P(C|A,B)=0.6
P(C|A,B)=1
P(A)=0.2
P(B)=0.2
Bayesian Networks
- structure
Bayesian network
• Different baseline probability
of extinction
P(D|A,C)=0.4
P(D|A,C)=0.7
P(D|A,C)=0.7
P(D|A,C)=1
P(C|A,B)=0.3
P(C|A,B)=0.65
P(C|A,B)=0.65
P(C|A,B)=1
P(A)=0.2
P(B)=0.2
Bayesian Networks
- structure
Bayesian network
• Different baseline probability
of extinction
• Interaction strengths:
resources weighted for their
relative contribution (e.g.
proportion biomass flowing
from resource to consumer)
Bayesian Networks
- marginal probabilities
• Builds a table for each
species, specifying its
probability of extinction
 defining the Bayesian
network
P(D|A,C)=0.2
P(D|A,C)=0.6
P(D|A,C)=0.6
P(D|A,C)=1
P(C|A,B)=0.2
P(C|A,B)=0.6
P(C|A,B)=0.6
P(C|A,B)=1
• Need to combine all
possible states (tables) of all
species  solving the
Bayesian network
• Receives marginal
probabilities for every
species
P(A)=0.2
P(B)=0.2
Bayesian Networks
- testing the method
• Can we capture the secondary extinctions produced in
dynamical simulations?
• 100 networks built with the niche model
• Extinction scenarios simulated by the Allometric Trophic
Network (ATN) model  provide reference extinction
scenarios
• Computation of the likelihood that the Bayesian network
algorithms replicate ATN-simulated extinctions
Bayesian Networks
- performance
• Eklöf et al. (2013): Results
close to result of the ATN
model, however; secondary
extinctions where all of
the species resources are
extant cannot be predicted
 Can top-down effects be
implemented in a
Bayesian network?
Bayesian Networks
- attempts to improve the model
Calculate marginal
probabilities for
bottom-up controlled
network…
…and somehow
include bi-directional
forces, such as
pressure from predator
to prey?
Dynamic Bayesian Networks
- a possible solution?
• Extension of Bayesian networks – variables are related to each other
over adjacent time steps.
• Enables modeling of sequential data, e.g. temporal data
• Unfold the network in time to enable bi-directional forces
t
Dynamic Bayesian Networks
- a possible solution?
• Extension of Bayesian networks – variables are related to each other
over adjacent time steps.
• Enables modeling of sequential data, e.g. temporal data
• Unfold the network in time to enable bi-directional forces
t
t+1
Dynamic Bayesian Networks
- a possible solution?
• Extension of Bayesian networks – variables are related to each other
over adjacent time steps.
• Enables modeling of sequential data, e.g. temporal data
• Unfold the network in time to enable bi-directional forces
t
t+1
t+2
Conclusions
Bayesian networks
- combine the simplicity of the topological approach
with important features of dynamical models, without
an extensive set of parameters
- builds a bridge between theoretical biology and
conservation biology; includes results from
conservation-oriented research into algorithms for the
analysis of networks
Bayesian Networks
- practical usage
Take the network structure for some ecological system 
Use the IUCN Red List to assign baseline probabilities 
Calculate each species probability of going extinct; Pinpoint
species particularly threatened; Simulate primary extinctions
and consequences for the remaining system
Thank you for listening!
[email protected]