‘Boom‐and‐busted’ dynamics of phytoplankton–virus interactions explain the paradox of the plankton

Summary Rapid virus proliferation can exert a powerful control on phytoplankton host populations, playing a significant role in marine biogeochemistry and ecology. We explore how marine lytic viruses impact phytoplankton succession, affecting host and nonhost populations. Using an in silico food web we conducted simulation experiments under a range of different abiotic and biotic conditions, exploring virus–host–grazer interactions and manipulating competition, allometry, motility and cyst cycles. Virus‐host and predator–prey interactions, and interactions with competitors, generate bloom dynamics with a pronounced ‘boom‐and‐busted’ dynamic (BBeD) which leads to the suppression of otherwise potentially successful phytoplankton species. The BBeD is less pronounced at low nutrient loading through distancing of phytoplankton hosts, while high sediment loading and high nonhost biomass decrease the abundance of viruses through adsorption. Larger hosts are inherently more distanced, but motility increases virus attack, while cyst cycles promote spatial and temporal distancing. Virus control of phytoplankton bloom development appears more important than virus‐induced termination of those blooms. This affects plankton succession – not only the growth of species infected by the virus, but also those that compete for the same resources and are collectively subjected to common grazer control. The role of viruses in structuring plankton communities via BBeDs can thus provide an explanation for the paradox of the plankton.


Fig. S1
The average cell-cell distance for cells of different size at different biomass abundance.        infections enabled for both A1 and A2, and A1 having a 1mo cyst cycle. Panel (b) is the same as (a), but with no cyst cycle; A1 and A2 are thus identical. Panel (c) has no virus but retains a cyst cycle for A1; here A3 rapidly becomes extinct, and A1 also outcompetes A2. Panel (d) has neither virus nor cyst cycles; A3 becomes extinct and A1 is identical to A2. Note that in the absence of viruses (panels (c) and especially in (d)) the dynamics are classic "boom-and-bust" with a regular predator-prey cycle.
With viruses (panels (a) and (b)), cycles of phytoplankton growth display "boom-and-

METHODS S1
Equations describing the virus model and the phytoplankton are described in full detail for a single virus-host couple in Flynn et al., (2021); the following gives a discursive overview of the virus-phytoplankton components, noting that here we now had two virus-host couples.
See Fig.1b for a schematic of the model.
The virus-host model comprised state variables for: • inorganic nutrient (DIN, as ammonium), • host phytoplankton (A1, A2) of a stated equivalent spherical diameter (ESD), maximum growth rate (µmax) and motility (either not motile or with motility allometrically scaled as 3  ESD s -1 ; Flynn & Mitra, 2016) • virus (V1, V2) associated with hosts A1 and A2 respectively, as free particles • infected A1 and A2 hosts (A1V1, A2V2) • fragments of burst A1V1 and A2V2 In addition, the model included (as per Flynn et al., 2021): • an implicit bacterial activity that converted (decayed) all N associated with cell fragments and detritus, and also adhered viral particles, back to DIN.
• suspended inert particles which affected virus-host encounters by adsorbing viruses.
• mixing within a water column of a stated mixing depth which acts in a fashion akin to a chemostat dilution, bringing in nutrient particles from outside of the mixed layer, and washing out a proportion of all materials in the mixed layer.
To the enlarged model of Flynn et al. (2021), as per above, we also added: • cyst stages for A1; into this stage variable was removed a small fraction of A1, with excystment being triggered every 1 or 2 lunar months (1 or 3  29.5d).
• an additional phytoplankton (A3) which was described physiologically in exactly the same way as A1 and A2, except that µmax was at 90% of that set for A1 and A2.

Flynn et al. (2022) Boom & Busted Dynamics
Page 9 of 10 specific encounter rates with no prey discrimination as the default setting. This zooplankton submodel was otherwise as described in chapter 5 of Flynn (2018).
Regenerated nutrient from zooplankton activity directly entered the DIN pool, while faecal material was degraded in the same way that debris was degraded in the original virus model (Flynn et al., 2021).
All state variables were described in units of mgN m -3 .
All particulate components were also associated with an equivalent spherical diameter (ESD), and thence with a particle mass calculated from an allometric equation of Flynn et al.

Functional equations
Functionally, the processes are described as follows: A1,A2,A3 and A1V1, A2V2 phytoplankton population growth = where burst size was itself a function of the nutrient status of the host and host ESD, and latent period is a function of host growth rate (see Flynn et al., 2021).