Adaptive consumer-resource models LIPh lab winter workshop 2018 - - PowerPoint PPT Presentation

Adaptive consumer-resource models

LIPh lab winter workshop 2018

Leonardo Pacciani-Mori December 16th, 2018

The context of our work

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The context of our work

“Competitive Exclusion Principle” (CEP): the number of competing coexisting species is limited by the number of available resources.

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The context of our work

“Competitive Exclusion Principle” (CEP): the number of competing coexisting species is limited by the number of available resources. There are many known cases in nature where this principle is clearly violated:

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The context of our work

“Competitive Exclusion Principle” (CEP): the number of competing coexisting species is limited by the number of available resources. There are many known cases in nature where this principle is clearly violated:

1 Bacterial community culture experiments

From Goldford et al. 2018

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The context of our work

“Competitive Exclusion Principle” (CEP): the number of competing coexisting species is limited by the number of available resources. There are many known cases in nature where this principle is clearly violated:

1 Bacterial community culture experiments

From Goldford et al. 2018

2 Direct bacterial competition experiments

From Friedman et al. 2017

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Modeling ecological competition

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Modeling ecological competition

Since the ’70s, the main mathematical tool used to model competitive ecosystems has been MacArthur’s consumer-resource model.

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Modeling ecological competition

Since the ’70s, the main mathematical tool used to model competitive ecosystems has been MacArthur’s consumer-resource model. species Sm>p . . . species Sp . . . species S2 species S1 resource Rp . . . resource R1 . . . ασi

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Modeling ecological competition

Since the ’70s, the main mathematical tool used to model competitive ecosystems has been MacArthur’s consumer-resource model. species Sm>p . . . species Sn≤p . . . species S2 species S1 resource Rp . . . resource R1 . . . ασi

As it is, the model reproduces the CEP. In order to violate it, very special assumptions or parameter fine-tunings are necessary (Posfai et al. 2017).

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Our work

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Our work

In the literature of consumer-resource models ασi are always considered as fixed parameters that do not change over time.

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Our work

In the literature of consumer-resource models ασi are always considered as fixed parameters that do not change over time.

Problem

In many experiments diauxic shifts have been observed (Monod 1949)!

2 4 6 8 10 12 0.01 0.05 0.10 0.50 1.00 Time (hours) Cell concentration (g/l)

Growth of Klebsiella oxytoca on glucose and lactose. Data taken from Kompala et al. 1986, figure 11.

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Our work

In the literature of consumer-resource models ασi are always considered as fixed parameters that do not change over time.

Our work in one sentence

We have modified MacArthur’s consumer-resource model so that the metabolic strategies evolve over time.

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Our work

In the literature of consumer-resource models ασi are always considered as fixed parameters that do not change over time.

Our work in one sentence

We have modified MacArthur’s consumer-resource model so that the metabolic strategies evolve over time.

How?

Adaptive framework: each species changes its metabolic strategies in order to increase its own growth rate; adaptation velocity is measured by a parameter d.

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What we have found

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What we have found

Using adaptive metabolic strategies allows us to explain many experimentally

• bserved phenomena, that span from the single species to the whole community!

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What we have found

Using adaptive metabolic strategies allows us to explain many experimentally

• bserved phenomena, that span from the single species to the whole community!

1/5) With one species and two resources, the model reproduces diauxic shifts:

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What we have found

Using adaptive metabolic strategies allows us to explain many experimentally

• bserved phenomena, that span from the single species to the whole community!

1/5) With one species and two resources, the model reproduces diauxic shifts:

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What we have found

Using adaptive metabolic strategies allows us to explain many experimentally

• bserved phenomena, that span from the single species to the whole community!

1/5) With one species and two resources, the model reproduces diauxic shifts:

Notice

We can explain the existence of diauxic shifts with a completely general model, neglecting the particular molecular mechanisms of the species’ metabolism.

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What we have found

2/5) When multiple species and resources are considered, the model naturally violates the Competitive Exclusion Principle:

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What we have found

2/5) When multiple species and resources are considered, the model naturally violates the Competitive Exclusion Principle:

50 100 150 200 101 100 10-1 10-2 10-3 10-4 10-5 10-6

Fixed metabolic strategies

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What we have found

2/5) When multiple species and resources are considered, the model naturally violates the Competitive Exclusion Principle:

50 100 150 200 101 100 10-1 10-2 10-3 10-4 10-5 10-6

Adaptive metabolic strategies

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What we have found

3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive ασi leads to more stable communities:

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What we have found

3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive ασi leads to more stable communities:

100 200 300 400 500 100 10-3 10-6 10-9

Fixed metabolic strategies, τin = τout = 20

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What we have found

3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive ασi leads to more stable communities:

100 200 300 400 500 101 100 10-1 10-2 10-3 10-4 10-5 10-6

Adaptive metabolic strategies, τin = τout = 20

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What we have found

3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive ασi leads to more stable communities:

100 200 300 400 500 101 10-1 10-3 10-5 10-7 10-9

Fixed metabolic strategies, τin = 20, τout = 5

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What we have found

3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive ασi leads to more stable communities:

100 200 300 400 500 101 100 10-1 10-2 10-3 10-4 10-5 10-6

Adaptive metabolic strategies, τin = 20, τout = 5

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What we have found

Adaptation velocity d is a crucial element of the model.

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What we have found

Adaptation velocity d is a crucial element of the model. 4/5) If adaptation is sufficiently slow there can be extinction and the Competitive Exclusion Principle can be recovered:

20 species, 3 resources

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What we have found

Adaptation velocity d is a crucial element of the model. 5/5) If nutrient supply rates change in time, faster adaptation leads to less variable populations:

20 species, 4 resources

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What we have found

Adaptation velocity d is a crucial element of the model. 5/5) If nutrient supply rates change in time, faster adaptation leads to less variable populations:

100 200 300 400 500 101 100 10-1 10-2 10-3 10-4 10-5 10-6

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What we have found

Adaptation velocity d is a crucial element of the model. 5/5) If nutrient supply rates change in time, faster adaptation leads to less variable populations:

20 species, 4 resources

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References

Friedman, Jonathan et al. (2017). “Community structure follows simple assembly rules in microbial microcosms”. In: Nature Ecology and Evolution 1.5, pp. 1–7. Goldford, Joshua E. et al. (2018). “Emergent simplicity in microbial community assembly”. In: Science 361.6401, pp. 469–474. Kompala, Dhinakar S. et al. (1986). “Investigation of bacterial growth on mixed substrates: Experimental evaluation of cybernetic models”. In: Biotechnology and Bioengineering 28.7, pp. 1044–1055. Monod, Jacques (1949). “The Growth of Bacterial Cultures”. In: Annual Review

• f Microbiology 3.1, pp. 371–394.

Posfai, Anna et al. (2017). “Metabolic Trade-Offs Promote Diversity in a Model Ecosystem”. In: Physical Review Letters 118.2, p. 28103.

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An idea

An idea

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An idea

Adaptation velocity d is a crucial element of the model.

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An idea

Adaptation velocity d is a crucial element of the model.

Question

How could d be measured? What biological interpretation can we give it?

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An idea

Adaptation velocity d is a crucial element of the model.

Question

How could d be measured? What biological interpretation can we give it?

Possible answer?

I suspect that an interesting biological quantity in this sense could be the lag phase of a microbial community, that precedes exponential growth.

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An idea

Adaptation velocity d is a crucial element of the model.

Question

How could d be measured? What biological interpretation can we give it?

Possible answer?

I suspect that an interesting biological quantity in this sense could be the lag phase of a microbial community, that precedes exponential growth.

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An idea

Adaptation velocity d is a crucial element of the model.

Question

How could d be measured? What biological interpretation can we give it?

Possible answer?

I suspect that an interesting biological quantity in this sense could be the lag phase of a microbial community, that precedes exponential growth.

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An idea

In any microbiology textbook we can find that:

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An idea

In any microbiology textbook we can find that:

1 the lag phase can last from a few hours to several days 2 of 4

An idea

In any microbiology textbook we can find that:

1 the lag phase can last from a few hours to several days 2 during the lag phase bacteria adapt to the environmental conditions

(particularly if they have been incubated in a medium different from the

• ne where they are cultivated)

RNA, enzymes and other molecules are synthesized cells almost don’t divide, but grow in size and prepare for reproduction

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An idea

In any microbiology textbook we can find that:

1 the lag phase can last from a few hours to several days 2 during the lag phase bacteria adapt to the environmental conditions

(particularly if they have been incubated in a medium different from the

• ne where they are cultivated)

RNA, enzymes and other molecules are synthesized cells almost don’t divide, but grow in size and prepare for reproduction

Question

Can our adaptive consumer-resource model reproduce something similar? And if so, how is the lag phase related to d?

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An idea

From the thesis of a student of Prof. Squartini:

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An idea

From the thesis of a student of Prof. Squartini:

Figure: Growth of Escherichia coli in broth, 103 cells/ml

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An idea

From the thesis of a student of Prof. Squartini:

Figure: Growth of Agrobacterium tumefaciens in broth, 103 cells/ml

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An idea

From the thesis of a student of Prof. Squartini:

Figure: Growth of Rhizobium leguminosarum in broth, 103 cells/ml

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An idea

From the thesis of a student of Prof. Squartini:

Figure: Growth of Enterococcus mundtii in broth, 103 cells/ml

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An idea

From the thesis of a student of Prof. Squartini:

Figure: Growth of Enterococcus mundtii in broth, 103 cells/ml

Notice

They have used different mediums for different species!

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An idea

Consumer-resource model for one species and one resource:

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An idea

Consumer-resource model for one species and one resource:

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Figure: d = 0.5, resource supplied only initially

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An idea

Consumer-resource model for one species and one resource:

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Figure: d = 1, resource supplied only initially

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An idea

Consumer-resource model for one species and one resource:

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Figure: d = 10, resource supplied only initially

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An idea

Consumer-resource model for one species and one resource:

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Figure: d = 0.5, resource supply constantly

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An idea

Consumer-resource model for one species and one resource:

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Figure: d = 1, resource supply constantly

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An idea

Consumer-resource model for one species and one resource:

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Figure: d = 10, resource supply constantly

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An idea

Consumer-resource model for one species and one resource:

10 20 30 40 50 5 10 15 20

Figure: d = 10, resource supply constantly

My hope is to use these observations to design and perform some experiments in order to compare the model directly with data.

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An idea

Consumer-resource model for one species and one resource:

10 20 30 40 50 5 10 15 20

Figure: d = 10, resource supply constantly

Feel free to share your feedback with me!

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