reproduction leads to higher population fitness: as simple as...

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.