of the plant by dismantling its immune system, ending up in an exacerbation of the infec- tion symptoms. On the other hand, if the RNA satellite does not have sequence similarity with the host, it may trigger an acute activation of RNA silencing mechanisms, hindering the progression of the infection and leading to an attenuation of its symptoms (Hu et al., 2009). Additional examples of these phenomena are found in other plant families like satellite Tobacco mosaic virus, which worsens the symptoms of the helper virus (Dodds, 1998), or the tripartite virus CMV, whose association with a fourth non-essential satellite component modifies its virulence depending on the satellite component (Betancourt et al., 2011) or on the infected host (Betancourt et al., 2013). The role of satellites as virulence modifiers of their helper virus has an ecological importance in regulating both virus and host populations. Several authors explored the theoretical consequences in the ecology of the mimivirus-virophage interaction. The dynamics of virus and host population were altered considering a sequential infection —hyperparasitism— (Wodarz, 2013) or coin- fection (Taylor et al., 2014). In both cases, they focused on phenotypes that emerged assuming that the virophage negatively affected virus replication, which is not the general case for satellites.
Associations with satellites have an impact beyond virus virulence, especially in those cases that imply a long-term interaction between virus and satellite. Coevolution may led to an interdependency of the two associates. For example, natural isolates of the tombusvirus Groundnut rosette virus(GRV), are always accompanied with an RNA satellite which is the main cause of the symptoms in groundnut and is essential for aphid transmission (Murant, 1990): without the RNA satellite, GRV is still able to infect, but it cannot be transmitted by its vector. Symbiosis has been documented for at least two tombusviruses: Pea enation mo- saic virus(PEMV) and GRV. These viruses are unusual species of the genus Umbravirus which do not encode a capsid protein (Syller, 2003; Dall’Ara et al., 2016; Roossinck, 2005). They are encapsidated in trans by hijacking the capsid of a coinfecting virus that belongs to the family Luteoviridae. As pay off, they allow the entry into blocked tissues for their luteovirus partners, endowing them with a systemic movement in the plant host. The symbiosis observed between umbraviruses and enamoviruses has evolved towards the spe- ciation of PEMV into a bipartite virus whose fragments belong to two independent genetic backgrounds. Another illustration of this phenomenon is found in the family Geminiviri- dae. Virus-satellite associations are extremely abundant in geminivirus infections. These associations became permanent in the genus Begomovirus: a bipartite species constituted by an ancestral geminivirus and a satellite of nanovirus origin (ul Rehman and Fauquet, 2009; Mansoor et al., 2003). Theoretical works on virus associations showed a fast transi- tion from a mutualistic two-species to a single species dynamics, supporting the fact that mutualistic and symbiotic interactions are usually the prelude of speciation (Nee, 2000).
In order to overcome the cost of their replication, satellites should be beneficial to the helper virus, either by providing a rapid phenotypic change or an adaptive ecological re- sponse to certain environments. In a context of viral competition, an association with a satellite can quickly modify the outcome of the competition without the need of finding adaptive solutions in the form of genomic changes. Furthermore, ecological consequences of satellite associations are expected as a result of the changes in virus and host dynam- ics caused by the association. Altogether, we will explore theoretically in the following section the effects of a non-mandatory satellite-virus association in a context of viral com- petition. Our goal is to evaluate the likelihood of transient associations being a first step towards multipartitism, as it seems to have happened for PEMV and begomoviruses.
MODELLING THE ECOLOGICAL EFFECTS OF A SATELLITE IN A VIRAL COMPETITION 29
3.3 Modelling the ecological effects of a satellite in a viral competition
In this section we explore the ecological consequences of the introduction of a satellite that assists one of the two competing viruses.To this end, we devise an epidemiological model to examine the role of different parameters, in particular those related to how the in- teraction between virus and satellite modifies emergent phenotypes. We will first consider a model of virus competition that serves as a null model. Later, we will investigate how the introduction of a satellite that associates with one of the competing viruses modifies the dynamical outcome. Similarities and differences between both models are discussed in this section.
3.3.1 Model of viral competition
Consider a host (plant) which can be infected by two types of viruses. Healthy hosts appear at a constant rate g and decay at a rate d. The amount of susceptible hosts at time t is H(t) and that of hosts infected by either virus are X(t) and Y (t). The model does not explicitly consider free viral populations, just susceptible or infected hosts in the different states. The model works in the mean-field approximation, and therefore assumes that hosts interact homogeneously through averaged values. Each virus is characterized by the rate px,y at which it infects a susceptible host (in contact with an infected host of its class) and a parameter dx,y which quantifies the increase in mortality of the host due to the infected state. A scheme of the model including the parameters is depicted in Figure 3.4.
The equations that describe the dynamics for this system of two competing viruses are: ˙ H = g − dH − pxXH − pyY H (3.1) ˙ X = pxXH − (d + dx)X (3.2) ˙ Y = pyY H − (d + dy)Y (3.3)
As a consequence of the symmetry of eqs (3.2) and (3.3), there will always be a virus that, in the mean-field scenario, will displace the other —with the exception of a set of points of zero-measure. For consistency, all parameters are strictly positive.
H
X
Y
px py g d O O d+dx d+dy OFigure 3.4: Scheme of two virus competition.
Healthy hosts (plants), H, are seed at a constant rate g and die with basal rate d. Plants get infected by either virus with rate pi, being i ∈ {x, y} for virus x and y. Infected plants X and Y see their basal mortality increased in an amount diwhen infected.
30 ASSOCIATIONS IN THE VIRAL WORLD