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 1 of 8

The context of our work “Competitive Exclusion Principle” (CEP): the number of competing coexisting species is limited by the number of available resources. 1 of 8

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 of 8

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 1 of 8

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 1 of 8

Modeling ecological competition 2 of 8

Modeling ecological competition Since the ’70s, the main mathematical tool used to model competitive ecosystems has been MacArthur’s consumer-resource model . 2 of 8

Modeling ecological competition Since the ’70s, the main mathematical tool used to model competitive ecosystems has been MacArthur’s consumer-resource model . species S 1 α σ i species S 2 resource R 1 . . . . . . . . . species S p resource R p . . . species S m > p 2 of 8

Modeling ecological competition Since the ’70s, the main mathematical tool used to model competitive ecosystems has been MacArthur’s consumer-resource model . species S 1 α σ i species S 2 resource R 1 . . . . . . . . . species S n ≤ p resource R p . . . species S m > p 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). 2 of 8

Our work 3 of 8

Our work In the literature of consumer-resource models α σ i are always considered as fixed parameters that do not change over time. 3 of 8

Our work In the literature of consumer-resource models α σ i are always considered as fixed parameters that do not change over time. Problem � In many experiments diauxic shifts have been observed (Monod 1949)! Cell concentration ( g / l ) 1.00 0.50 0.10 0.05 0.01 0 2 4 6 8 10 12 Time ( hours ) Growth of Klebsiella oxytoca on glucose and lactose. Data taken from Kompala et al. 1986, figure 11. 3 of 8

Our work In the literature of consumer-resource models α σ i 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. 3 of 8

Our work In the literature of consumer-resource models α σ i 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 . 3 of 8

What we have found 4 of 8

What we have found Using adaptive metabolic strategies allows us to explain many experimentally observed phenomena, that span from the single species to the whole community! 4 of 8

What we have found Using adaptive metabolic strategies allows us to explain many experimentally observed phenomena, that span from the single species to the whole community! 1/5) With one species and two resources, the model reproduces diauxic shifts: 4 of 8

What we have found Using adaptive metabolic strategies allows us to explain many experimentally observed phenomena, that span from the single species to the whole community! 1/5) With one species and two resources, the model reproduces diauxic shifts: 4 of 8

What we have found Using adaptive metabolic strategies allows us to explain many experimentally observed 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. 4 of 8

What we have found 2/5) When multiple species and resources are considered, the model naturally violates the Competitive Exclusion Principle: 5 of 8

What we have found 2/5) When multiple species and resources are considered, the model naturally violates the Competitive Exclusion Principle: 10 1 10 0 10 - 1 10 - 2 10 - 3 10 - 4 10 - 5 10 - 6 0 50 100 150 200 Fixed metabolic strategies 5 of 8

What we have found 2/5) When multiple species and resources are considered, the model naturally violates the Competitive Exclusion Principle: 10 1 10 0 10 - 1 10 - 2 10 - 3 10 - 4 10 - 5 10 - 6 0 50 100 150 200 Adaptive metabolic strategies 5 of 8

What we have found 3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive α σ i leads to more stable communities: 6 of 8

What we have found 3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive α σ i leads to more stable communities: 10 0 10 - 3 10 - 6 10 - 9 0 100 200 300 400 500 Fixed metabolic strategies, τ in = τ out = 20 6 of 8

What we have found 3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive α σ i leads to more stable communities: 10 1 10 0 10 - 1 10 - 2 10 - 3 10 - 4 10 - 5 10 - 6 0 100 200 300 400 500 Adaptive metabolic strategies, τ in = τ out = 20 6 of 8

What we have found 3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive α σ i leads to more stable communities: 10 1 10 - 1 10 - 3 10 - 5 10 - 7 10 - 9 0 100 200 300 400 500 Fixed metabolic strategies, τ in = 20, τ out = 5 6 of 8

What we have found 3/5) When environmental conditions are variable (i.e. the nutrient supply rates change in time) using adaptive α σ i leads to more stable communities: 10 1 10 0 10 - 1 10 - 2 10 - 3 10 - 4 10 - 5 10 - 6 0 100 200 300 400 500 Adaptive metabolic strategies, τ in = 20, τ out = 5 6 of 8

What we have found Adaptation velocity d is a crucial element of the model. 7 of 8

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 7 of 8

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 7 of 8

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: 10 1 10 0 10 - 1 10 - 2 10 - 3 10 - 4 10 - 5 10 - 6 0 100 200 300 400 500 7 of 8

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 7 of 8

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 of 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. 8 of 8

An idea �

An idea � 1 of 4

An idea � Adaptation velocity d is a crucial element of the model. 1 of 4

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? 1 of 4

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. 1 of 4