Dr Rachel Norman Dr Rachel Norman University of Stirling University of Stirling 10 10 th th June 2010. June 2010. Why Multi scale modelling of biological systems is important.
Dr Rachel Norman University of Stirling 10 th June 2010.
Jan 21, 2016
Why Multi scale modelling of biological systems is important. Dr Rachel Norman University of Stirling 10 th June 2010. My background. Rabies in ethiopian wolves Louping ill in red grouse Fish parasites. Why is changing scale important?. Arises in a large number of systems - PowerPoint PPT Presentation
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Dr Rachel NormanDr Rachel Norman
University of StirlingUniversity of Stirling
1010thth June 2010. June 2010.
Why Multi scale modelling of biological systems is important.
My background
•Rabies in ethiopian wolves
•Louping ill in red grouse
•Fish parasites
Why is changing scale Why is changing scale important?important?
Arises in a large number of systemsArises in a large number of systems
• Physical: From individuals to populations- Physical: From individuals to populations- cells, enzymes, people, animals…cells, enzymes, people, animals…
• Spatial: From local to global- bee hives, Spatial: From local to global- bee hives, villages, farms….villages, farms….
• Temporal: From short term to evolutionary Temporal: From short term to evolutionary time scales – transient dynamics vs time scales – transient dynamics vs equilibrium, present time vs evolutionary equilibrium, present time vs evolutionary time…time…
Individuals to populations: Examples
Population growth
Epidemiology
Immunology
Population growth
Exponential growth
rXXbabXaXdt
dX )(
Exponential growth
0
200
400
600
800
1000
1200
1400
1600
0 0.2 0.4 0.6 0.8 1 1.2
time
X
r=-0.2 r=0 r=0.15 r=0.25
Saturated growth
Assume birth decreases or death increases linearly with density
XsXrdt
dX)(
Logistic Growth
0
20
40
60
80
100
120
140
160
0 1 2 3 4 5 6 7
Time
X(t
)
Other possibilities
))1(1( KXrX tt
KXrX tt 1exp
trXK exp1
tt
XKXK
2
11
ctt
XKXK
2
1
1
ctt
XKXK
2
1
1
•Name (ref)
•Quadratic [6]
•Ricker [7]
•Skellam [8]
•Beverton Holt [9]
•Hassell [10]
•Maynard-Smith-Slatkin [11]
Brannstrom and Sumpter (Proc Roy soc, 272, 2065-2072. 2005)
Built model based on distribution of individuals amongst discrete resource sites.
Changed rules about competition.
Some models, for example the quadratic model cannot be derived this way.
Why not?
Questions
Why can’t you get the quadratic model?
What is the best form of a population growth model under different assumptions about the way individuals interact?
Epidemiology
Example :1 simple SIR model
Susceptible Infected Immune
births
deaths
Transmission Term f(S,I)
• Transmission rate per susceptible– contact*prob(infection)*prop infected =
c*p*I/N
• Density dependent transmission– Contact rate = constant * N– Transmission =
• Frequency dependent transmission– Contact rate = constant– Transmission =
SI
N
SI
Other forms
Hochberg (JTB, 153, 301-321, 1991)
Fenton, Fairbairn, Norman and Hudson (JAE, 71, 893-905, 2002)
Fitted experimental data on insect parasites to this transmission rate and compared with others in the literature.
baIS
Turner, Begon and Bowers (Proc Roy soc, 270, 105-112, 2003)
Cellular Automata
Defined contacts locally for density and frequency dependent transmission.
Look at what happens globally.
They found that they got frequency dependent transmission globally in both cases.
Questions:
Does that mean that you cannot get density dependent transmission from an IBM?
What is the “correct” form of the transmission form under different assumptions about interaction?
Immunology
Fenton and Perkins (Parasitology, 137, 1027-1038, 2010)
IIPefdt
dI
PIfrPdt
dP
)(
)(
Questions
Are these the right assumptions to make about interaction terms?
Can we derive better functions for this?
Conclusion
There are many systems where we make population level assumptions about interaction terms.
How do we write down rules about how be observe that individuals behave and derive the population level terms?
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