Modelling Host-Microbiome Interactions

methods and madness

Bob Week - Kiel University

Who am I

• Background: Mathematical evolution and ecology
• Was a postdoc with Brendan Bohannan 2022-2024
• Now a postdoc with Hinrich Schulenburg at Kiel University

Overview (two parts)

1. ACROSS HOST GENERATION DYNAMICS (host-microbiome feedback)

• Modelling host-microbiome evolution
• Extended inheritance frameworks
• Microbiome-mediated rescue
• Microbiome-extended quantitative genetics
  • A gap: microbiome inheritance ??
  • motivates…

2. WITHIN HOST GENERATION DYNAMICS (microbiomes structured by fixed hosts)

• Modelling microbiome community dynamics and transmission
• Metacommunity Framework
• Viscocity hypothesis

We live in a microbial world

Microbiomes mediate host trait variation

Microbiomes can be inherited

Can Microbiomes facilitate adaptation?

• Lewontins Conditions \(\uparrow\) for evolutionary adaptation

But microbiomes not like nuclear genes…

• Community assembly (microbial dispersal, within-host selection, etc …)

Extended inheritance account for microbiomes?

• Maternal Effects
• Indirect Genetic Effects
• Niche Construction
• Multilevel Selection

Maternal Effects

Definition:

influence of parent trait on offspring trait

Indirect Genetic Effects

Definition:

genotype of one individual influences trait of another individual

Niche Construction

Definition 1:

organism activity alters environment

Definition 2:

organism activity alters selection pressures

Two perspectives:

1. microbiome as environment

2. microbiome modifying environment

Multilevel Selection

• MLS1: Selection on “individuals” in groups (host-associated microbes)
  • within group selection for individuals
  • among group selection for individuals
• MLS2: Selection on “groups” (hosts)

Multilevel Selection 1 (on microbes)

Colonization-based selection:

covariance of microbe trait α with occurance within host relative to prevalence in environment (colonization w)

Proliferation-based selection:

covariance of microbe trait α with difference in abundance across host development stages (proliferation w)

Multilevel Selection 2 (on hosts)

Conclusion

PROS

• Maternal Effects ~ vertical parent-offspring inheritance
• Indirect Genetic Effects ~ horizontal social inheritance
• Niche Construction ~ horizontal environmental inheritance
• Multilevel Selection ~ quantify alignment of evolutionary interests

CONS

• Lack realism, need testing
• Assessment of microbiome-mediated adaptation requires synthesis
  • Designed for unique biology of host-microbiome systems

Working on it!

• Microbiome Mediated Rescue of Host Populations
• Quantitative Genetics of Microbiome Mediated Traits
• Multilevel Selection and Maintenance of Costly Mutualists
• Evolution of Microbiome Mediated Traits
  • Niche Construction

Working on it!

• Microbiome Mediated Rescue of Host Populations
• Quantitative Genetics of Microbiome Mediated Traits
• Multilevel Selection and Maintenance of Costly Mutualists
• Evolution of Microbiome Mediated Traits
  • Niche Construction

Microbiome Mediated Rescue of Host Populations

Quantitative Genetics of Microbiome Mediated Traits

Host Trait Variance Partitioning

\[P=G+M+E\]

• \(P\) … phenotypic variation
• \(G\) … explained by genetic var
• \(M\) … explained by microbiome var
• \(E\) … explained by other stuff

Microbiome Partitioning

\[M=M_L+M_N+M_V\]

• \(M_L\) … lineal microbes
• \(M_N\) … non-lineal microbes
• \(M_V\) … novel microbes

Predictions

• \(M_L\) ~ most adaptive potential
• \(M_N\) ~ less adaptive potential
• \(M_V\) ~ least adaptive potential

Limits of Current Quantitative Genetic Approach

• Variance partitioning general ✔️
• Classical adaptation predictions assume:
  • Mendelian inheritance
  • Many loci small effect
  • Random mating
  • etc …
• Need to understand microbiome inheritance process:
  • Transmission
  • Dynamics
  • Patterns

Part2: A Metacommunity Ecology Approach

Metacommunity Idea

• Dispersal among discrete patches
• Local interspecific interactions
• Habitat filtering

Host-Associated Microbiome Metacommunity

• Transmission between hosts
• Within host interactions
• Host control

Why we need new theory (a matter of scale)

• Extreme abundance asymmetry
  • local abundances astronomical compared to number of dispersers
• Transmission mediated by host structure
  • constrained by social contact and environmental proximity
• Discretely packaged transmission events
  • concentrated pulses instead of continuous flow
• Strong demographic buffering locally
  • transmission alters composition, not abundance
• Implications:
  • different dynamics ~ different patterns
  • microbiome diversity likely linked to host sociality…

A Model

\[dN_i^k=\left({\color{yellow}{r_i^k}}-{\color{red}{\sum_{j=1}^S\alpha_{ij}^kN_j^k}}\right)N_i^k\,dt + \sum_{\ell=1}^K{\color{magenta}{T_{\ell\leftrightarrow k}(dt,dN)}}% + %{\color{green}{\varepsilon_{\ell k}e_i}})N_{i\ell} % - \sum_{\ell=1}^K({\color{purple}{\psi_{k\ell}s_{k\ell}^i}} + % {\color{olive}{\varepsilon_{k\ell}e_{k\ell}^i}})N_{ik} +{\color{lime}{e_i^k\,N_i^k\,dE_i^k}} +{\color{skyblue}{\beta_i^k\sqrt{N_i^k}\,dD_i^k}}\]

• \(i=\) microbe species 1,…,S
• \(k=\) host individual 1,…,K
• \(N_i^k=\) abundance microbe \(i\) in host \(k\)

\(\color{yellow}{\circ}\) \(=\) habitat filtering / host selection

\(\color{red}{\circ}\) \(=\) competition / ecological network

\(\color{magenta}{\circ}\) \(=\) social contact

\(\color{lime}{\circ}\) = environmental stochasticity

\(\color{skyblue}{\circ}\) \(=\) demographic stochasticity

\({\color{lime}{E_i^k}},\,{\color{skyblue}{D_i^k}}\,=\) Brownian motions

Transmission

• \({\color{magenta}{T_{\ell\leftrightarrow k}}}\,=\) jump process
  • \(\Psi_{\ell k}\,=\) jump rate btwn hosts \(\ell,\,k\)
    • (social contact network)
  • size of jumps for \(N_i^\ell,\,N_i^k\) :
    • \(B_i^kC_i^k\)
    • \(B_i^k\sim\mathrm{Bern}(L(N_i^k))\)
    • \(C_i^k\sim\mathrm{Exp}(c)\)
    • \(c\,=\) chonk size parameter

Viscocity Hypothesis

• Idea:
  • mutulists move freely
    • lower viscocity
    • colonization is easier
  • pathogens face more resistance
    • higher viscocity
    • need more attempts to colonize
• Prediction:
  • pathogen diversity accumulates in clusters
  • mutualist diversity accumulates in bridges

(Extremely) Preliminary Results

Conclusion