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# The network structure and eco-evolutionary dynamics of CRISPR-induced immune diversification

## Abstract

As a heritable sequence-specific adaptive immune system, CRISPR–Cas is a powerful force shaping strain diversity in host–virus systems. While the diversity of CRISPR alleles has been explored, the associated structure and dynamics of host–virus interactions have not. We explore the role of CRISPR in mediating the interplay between host–virus interaction structure and eco-evolutionary dynamics in a computational model and compare the results with three empirical datasets from natural systems. We show that the structure of the networks describing who infects whom and the degree to which strains are immune, are respectively modular (containing groups of hosts and viruses that interact strongly) and weighted-nested (specialist hosts are more susceptible to subsets of viruses that in turn also infect the more generalist hosts with many spacers matching many viruses). The dynamic interplay between these networks influences transitions between dynamical regimes of virus diversification and host control. The three empirical systems exhibit weighted-nested immunity networks, a pattern our theory shows is indicative of hosts able to suppress virus diversification. Previously missing from studies of microbial host–pathogen systems, the immunity network plays a key role in the coevolutionary dynamics.

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• ### Systematic analysis of putative phage-phage interactions on minimum-sized phage cocktails

Scientific Reports Open Access 14 February 2022

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## Data availability

Simulated and empirical network data are available in the dedicated GitHub repository associated with this paper at: https://github.com/Ecological-Complexity-Lab/CRISPR_networks.

## Code availability

The code for the simulations and their analysis is available in the dedicated GitHub repository associated with this paper at: https://github.com/Ecological-Complexity-Lab/CRISPR_networks.

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## Acknowledgements

We thank W. England and M. Pauly for data processing and collection and Q. He for guidance on the construction of the phylogenetic trees from the model outputs. R.W. acknowledges the support of the Cystic Fibrosis Foundation (no. CFF C2480) and an Allen Distinguished Investigator Award from the Allen Frontiers Institute. M.P. acknowledges the support of the University of Chicago. We are grateful for the access to the computer cluster of the Research Computing Center of the University of Chicago.

## Author information

Authors

### Contributions

S.P. conceptualized the study, carried out the formal analysis (networks and data analysis, model dynamics, visualizations) and wrote the original manuscript draft. S.A.A.-C. carried out the formal analysis (networks analysis, model simulation) and reviewed and edited the manuscript. T.W. was involved with the software, methodology and formal analysis (model dynamics). T.K. curated and analysed the data and reviewed and edited the manuscript. S.M. was involved with the software, methodology and funding acquisition, and reviewed and edited the manuscript. R.W. conceptualized the study, curated and analysed the data, acquired the funding, supervised the study and reviewed and edited the manuscript. M.P. conceptualized the study, carried out the formal analysis (model dynamics), acquired the funding and prepared the original manuscript draft.

### Corresponding authors

Correspondence to Rachel Whitaker or Mercedes Pascual.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Viral and host abundance and richness.

a, Host abundance. The 100 most abundant strains are colored, the rest are aggregated and shown in gray. b, Richness (i.e., number of unique strains) of hosts (blue) and viruses (red). The number of unique spacers (spacer richness) is depicted in brown. During VDRs the abundance of both hosts and viruses fluctuates. As a response to virus diversification, host richness eventually increases despite possible declines at the beginning of the VDR resulting from the initial viral attack.

### Extended Data Fig. 2 Host phylogenetic tree.

The tree is not inferred, but rather drawn based on exact genealogical data (which strain descends from which) collected during the simulation. Branch length indicates the lifetime of any given host strain. Hosts diversify and go extinct primarily during VDRs, resulting in strain replacement, but strains can also persist from one VDR to the next.

### Extended Data Fig. 3 Host and virus diversification and extinction.

Each host (panel a) or viral (panel b) strain is plotted with a line, starting at the time when the strain was generated and ending when the strain went extinct. During VDRs the rate of diversification of both viruses and hosts is higher than during HCRs. While viruses have relatively short persistence (shorter line lengths), hosts have long persistence and can persist during an entire VDR.

### Extended Data Fig. 4 Modules in the infection network.

A time series of the number of modules in the infection network for a single simulation. Modularity enables diversification since it allows the temporary coexistence of different groups of viruses.

### Extended Data Fig. 5 Host and virus rankings in the weighted nested immunity matrix as a function of age.

The plots show node strength (sum of the corresponding number of matches in the immunity network) of hosts (top) and viruses (bottom) against their age measured from the time of their birth, for two selected times before the start of an HCR (leY, t=231 and right, t=1720). Each data point represents a host (top) or virus (bottom) strain. On the different plots, selected groups of youngest and oldest strains are indicated. The oldest host strains occupy the lower rows (low node strength), and their rankings tend to decrease with age. This is because descendants of a given host inherit all of its spacers and add a new one, which always results in an increase in total matches (host node strength). Because they have acquired additional protection, they can grow in abundance and through resulting enhanced encounters and infections, the failure of existing spacers can add redundancy (more than one spacer to the same virus), further contributing to their ranking. The oldest viruses occupy the leftmost columns, with the highest column sums of matches to hosts, since longer lifetimes provide the opportunity for many encounters, and therefore for both the failure of existing spacers (which adds redundancy to a given entry) and the addition of new spacers (which distributes immunity throughout entries). A successful offspring will have mutated a protospacer that confers escape from a given match of the parent; thus, successful descendants exhibit one less match and are placed to the right. It is worth noting that there is considerable variation around the general trends with age, reflecting the complex interplay of the stochastic acquisition of spacers and protospacers with the abundance dynamics which affect both encounter and mutation rates.

### Extended Data Fig. 6 Order of extinctions.

We tested for ‘orderly’ extinctions in which extinction preferentially happens from the viruses to which hosts have most immunity to those that can infect many hosts. For any virus that went extinct we calculated an ‘immunity rank’. Specifically, for a given time step, we calculated the strength of all n virus nodes in the immunity network, s=(s1,s2, …,sj,…,sn), where sj is the node strength of virus j (i.e., the sum of the columns in Fig. 2g in the main text). Viruses with higher values of sj are those that are more to the left in Fig. 2g, and to which hosts have high immunity. We removed duplicate values in s (to avoid ties) and ordered it in ascending order to obtain s’. We then calculated the relative position of sj in s’. A rank of 1 means that the virus that went extinct was highly ranked (e.g., position 5 out of 5 values will render a rank of 1). 50% of viruses (median indicated by a vertical dashed line) had an extinction rank of 0.5.

### Extended Data Fig. 7 Viral escape via 1-matches.

A tripartite virus-protospacer-host network depicting escape routes for a single virus. Each host is connected to a single protospacer (colored boxes). The spacer composition of strains is shown. Escape occurs through matching colors.

### Extended Data Fig. 8 Reproductive numbers R0 and R1.

At the entrance into an HCR, the average of reproductive numbers $${{\rm{R}}}_{{\rm{j}}}^{0}$$ over all virus strains j (weighted by their respective abundances) (light blue line) is considerably below 1. After this initial stage, this mean measure hovers around 1 (horizontal dashed line) and exhibits considerably larger values towards the end of this period before the transition to a VDR. Growth based purely on hosts made available by a single escape mutation is shown here as the weighted-mean of $${{\rm{R}}}_{{\rm{j}}}^{1}$$ across viruses j (in pink). This quantity exhibits an increasing trend during the HCR, which also raises the potential $${{\rm{R}}}_{{\rm{pot}}}^{{\rm{j}}}$$, defined as the sum of $${{\rm{R}}}_{0}^{{\rm{j}}}$$ and $${{\rm{R}}}_{1}^{{\rm{j}}}$$ (not shown, for clarity).

### Extended Data Fig. 9 Modularity of empirical host-spacer networks.

Each row represents a different data set: Sulfolobus islandicus hosts from Yellowstone (Top). Pseudomonas aeruginosa hosts from Copenhagen (middle). S. islandicus hosts from the Mutnovsky Volcano in Russia, 2010 (bottom). Panels a, c and e, are host-spacer networks in which interactions within host-spacer modules are colored. Panels b, d and f, are distributions of the map equation (L) obtained from networks shuffled by randomly distributing interactions. Value of the observed L is depicted with a vertical dashed line.

### Extended Data Fig. 10 Regime definition.

Each point in the virus abundance time series in panel a is first converted to relative abundance (panel b) and then classified into a HCR (green) or VDR (purple). This classification is based on the second difference (panel d) (for comparison we also show the first difference in panel c). Momentary virus growth periods (marked with an arrow) are not classified as VDR. The final classification is shown using vertical lines. HCRs start with a purple line and VDRs with a green line.

## Supplementary information

### Supplementary Information

Supplementary Tables 1–4, Methods and Notes.

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Pilosof, S., Alcalá-Corona, S.A., Wang, T. et al. The network structure and eco-evolutionary dynamics of CRISPR-induced immune diversification. Nat Ecol Evol 4, 1650–1660 (2020). https://doi.org/10.1038/s41559-020-01312-z

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• DOI: https://doi.org/10.1038/s41559-020-01312-z

• ### Systematic analysis of putative phage-phage interactions on minimum-sized phage cocktails

• Felipe Molina
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• ### Competition and coevolution drive the evolution and the diversification of CRISPR immunity

• Martin Guillemet
• Hélène Chabas
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Nature Ecology & Evolution (2022)