reproduction leads to higher population fitness: as simple as...
TRANSCRIPT
Reproduction leads to higher population fitness:
as simple as that
Tommaso Brotto
Universitá degli Studi di Milano Prof. Sergio Caracciolo
Laboratoire de Physique Statistique - ENS Prof. Jorge Kurchan
Biological processes are complex!
Biological processes are complex!
Biological processes are complex!
Biological processes are complex!
Do we really need to take everything into account?
Reproduce = create offsprings with same traits
Mutate = change traits
What is really essential?
A cell can:
Reproduce = create offsprings with same traits
Mutate = change traits
What is really essential?
A cell can:
Traits:τ = mutation time
λ = fitness (ability to generate offsprings)
τ follows p(τ)
λ follows q(λ)
λmax
p(τ)
τ
λ
q(λ)
Create N cells, with random τ, λ
τ follows p(τ)
λ follows q(λ)
λmax
p(τ)
τ
λ
q(λ)τ and λ are
not correlated
Create N cells, with random τ, λ
τ, λ
τ, λ
τ, λ
Reproduction, with rate λ
Each time step, each cell:
τ, λ
τ, λ
τ, λ
τ, λ τ', λ'
Reproduction, with rate λ
Mutation,with rate 1/τ
Each time step, each cell:
τ, λ
τ, λ
τ, λ
τ, λ τ', λ'
Reproduction, with rate λ
Mutation,with rate 1/τ
To preserve N, kill randomly
Each time step, each cell:
First phase:
Randomness
What happens: sketch
First phase:
Randomness
p(τ)
q(λ)
What happens: sketch
First phase:
Randomness
Second phase: Condensation
What happens: sketch
First phase:
Randomness
Second phase: Condensation
What happens: sketch
First phase:
Randomness
Second phase: Condensation
What happens: sketch
First phase:
Randomness
Second phase: Condensation
Third phase:
Takeovers
What happens: sketch
First phase:
Randomness
Second phase: Condensation
Third phase:
Takeovers
What happens: sketch
First phase:
Randomness
Second phase: Condensation
Third phase:
Takeovers
What happens: sketch
Effect due to reproduction(collective)
Cells become fitter but also more stable:
lower 1/τ – λ
τ
λ
Effect due to reproduction(collective)
Cells become fitter but also more stable:
lower 1/τ – λ
λ
τ
Effect due to reproduction(collective)
Cells become fitter but also more stable:
lower 1/τ – λ
λ
τ
p(τ)
q(λ)
Effect due to reproduction(collective)
Cells become fitter but also more stable:
lower 1/τ – λ
λ
τ
Effect due to reproduction(collective)
Cells become fitter but also more stable:
lower 1/τ – λ
λ
τ
Effect due to reproduction(collective)
Cells become fitter but also more stable:
lower 1/τ – λ
λ
τ
Effect due to reproduction(collective)
Cells become fitter but also more stable:
lower 1/τ – λ
λ
τ
The model works for well-mixed, fully-connected environment
What about space?
(e.g. chemostat)
Process in two dimensions: Petri Dish
Free space: reproduce/mutate
No free space: mutate only
The model
Selection only while reproduction is active
Longer times to reach condensation
Free space: reproduce/mutate
The model
Results:
No free space: mutate only
time
Selection only while reproduction is active
Longer times to reach condensation
time
Selection only while reproduction is active
Longer times to reach condensation
time
Selection only while reproduction is active
Longer times to reach condensation
And much more...
Thank you.