- Top of page
- The model and the evolutionary stable strategy
- Supporting Information
Plant viruses are a major threat to agricultural production, especially in less developed countries (Waterworth & Hadidi 1998; Rybicki & Pietersen 1999; Fereres, Thresh & Irwin 2000). Despite efforts to manage plant virus diseases, some viral disease problems are in fact continuing to emerge (Rybicki & Pietersen 1999; Varma & Malathi 2003). This is exemplified in particular by an escalation in disease epidemics caused by whitefly-transmitted geminiviruses (family Geminiviridae, genus Begomovirus). Several, seemingly new, diseases and many virus strains with altered pathogenicity have been reported over the past couple of decades (Brown 1990; Polston & Anderson 1997; Padidam, Sawyer & Farquet 1999; Mansoor et al. 2003a,b; Varma & Malathi 2003). The reason for the emergence of new strains is considered to be related to more rapid evolutionary changes of the virus brought about by increased vector and virus population sizes, more polyphagous vector populations and the potential for rapid genetic change in geminiviruses (Padidam, Sawyer & Farquet 1999; Varma & Malathi 2003; García-Arenal & McDonald 2003; García-Arenal, Fraile & Malpica 2003; Seal, van den Bosch & Jeger 2006).
Few direct means of control exist for most viral plant diseases. The available disease management options include the organization of agricultural practice, cultural control such as sanitation programmes, control of the vector population and use of host cultivars that support lower vector and virus populations. Vector population control has, however, often been difficult (Satapathy 1998; Perring, Gruenhagaen & Farrar 1999). Sanitation, in the form of roguing, and the use of resistant cultivars has in many cases been effective (Holt & Chancellor 1996; Holt, Colvin & Muniyappa 1999; Jeger et al. 2004). Much effort has been put into programmes to breed for resistance to begomoviruses and their whitefly vector Bemisia tabaci (Thresh, Otim-Nape & Lennings 1994; Bellotti & Arias 2001; Morales 2001; Lapidot & Friedmann 2002; Rubio et al. 2003). Any disease management effort will, however, put a selection pressure on the virus population to adapt to the new circumstances (Roossinck 1997). Given the rapid evolutionary changes in viruses it is no surprise that disease control that is initially effective is sometimes quickly rendered ineffective as a result of the adaptation of the virus (Roossinck 1997; Harrison 2002; McDonald & Linde 2002; García-Arenal & McDonald 2003; Mansoor et al. 2003b).
We restricted our study to one evolving virus trait, the multiplication rate of the virus within an infected cell. It should be stressed that our conclusions are only valid for the evolution of this trait. The within-cell multiplication rate varies widely between virus strains (Barker & Harrison 1986; Gray, Smith & Altman 1993; Jimenez-Martinez & Bosque-Perez 2004) and therefore was a useful starting point for our study. We used the within-cell virus multiplication to model the virus dynamics at the tissue level. Relationships between within-plant virus dynamics and population level parameters of acquisition, inoculation and roguing were used in accordance with data from experimental studies (Gill 1969; Foxe & Rochow 1975; Barker & Harrison 1986; Rubio et al. 2003; Jimenez-Martinez & Bosque-Perez 2004).
Although our model is of a generic nature, we used the specific system of whitefly-transmitted geminiviruses (begomoviruses) infecting tomato as our key example. Both experimental and modelling approaches have been used to study the epidemiology of tomato diseases (Holt, Colvin & Muniyappa 1999; Moriones & Navas-Castillo 2000). Holt, Colvin & Muniyappa (1999), studying tomato begomovirus diseases in India, reported that disease spread will occur for very low vector populations, and hence varietal resistance will be an important component of disease management. The breeding of begomovirus disease-resistant tomato cultivars is presently the subject of much research (Michelson, Zamir & Czosenk 1994; Vidavsky & Czosnek 1998; Lapidot et al. 2001; Pietersen & Smith 2002; Maruthi et al. 2003a,b; Gomez et al. 2004). These breeding programmes have been based on the introgression of resistance from accessions of wild Lycopersicon species (mainly L. peruvianum, L. chilense, L. pimpinellifolium and L. hirsutum) to cultivated tomato. Some of the types of resistance reported in this study can be found in the breeding lines of tomato breeding programmes, although it is not always easy to separate the various components of resistance.
- Top of page
- The model and the evolutionary stable strategy
- Supporting Information
When a resistant cultivar is introduced, the virus is not yet evolved to be adapted to the new situation. Our findings (Figs 4–6a,b) correspond with those of other modelling studies (Holt & Chancellor 1996; Holt, Colvin & Muniyappa 1999; Jeger et al. 2004). The effect of symptom-reducing resistance on the dynamics of a viral plant disease has not previously been modelled. The density of healthy plants slightly decreases with increasing levels of symptom-reducing resistance, which is understandable as the mortality/roguing rate decreases with increasing symptom-reducing resistance in the crop. We conclude that results obtained when the virus is allowed to evolve are thus not a result of a model specification that contradicts other models.
When the virus has had time to adapt to the use of host resistance, two broad categories of virus responses to resistance can be distinguished. The first type, including (i) inoculation resistance and (ii) acquisition resistance, does not put a selection pressure on the virus to evolve towards a higher virus multiplication rate. The second type, including (iii) virus titre-reducing and (iv) symptom-reducing resistance, does put a selection pressure on the virus to evolve towards higher virus multiplication rates.
The cultivars from this second group are not durable in the sense that they put selection on the virus that might reduce the effectiveness of the resistance. Whether symptom-reducing resistant cultivars and virus titre-reducing cultivars have a contribution to make is, however, dependent not only on this selection pressure but also on additional factors. The symptom-reducing resistant cultivar might still have a positive effect on yield even when the virus has evolved the new ESS simply because the symptom-reducing resistance provides a sufficient amount of additional damage reduction. Furthermore it could be that the ESS virus multiplication rate is outside the attainable range for the virus under consideration. Finally the time it takes the virus to evolve towards the new ESS virus multiplication rate may be so long to make it of little importance.
We are thus not proposing that symptom-reducing and virus titre-reducing cultivars do not have a contribution to make to the management of virus diseases, but rather that there are potential problems that need to be considered to maximize their durability and minimize their effects on viral populations. The breeding of inoculation resistant and acquisition resistant cultivars does not pose the same potential problems.
The model used in this paper is simple; several model extensions and other evolving virus traits have to be investigated before general conclusions can be drawn. Our model, however, does allow for several extensions without any change in the conclusions.
were constructed using the parameter values given in the figure legends. We have done the same calculations for a wide variety of parameter values around the values used (plus and minus 100%) and found that although quantitative differences occur, the qualitative trends do not change.
The plant–virus–vector population model does not include a latent period for the plant nor a latent period for the virus in the vector. These model extensions are discussed by Jeger et al. (1998
) and Madden, Jeger & van den Bosch (2000
). It is easily seen that the ESS value of the virus multiplication rate, k
, is still the value maximizing the basic reproductive number, implying that the trends in Figs 4–6
do not change when introducing these model extensions.
We assumed that the inoculation rate, α, is independent of virus titre and, because virus titre is related to virus multiplication rate, equation 3
, to k
. This is probably the least supported assumption about the relation between virus titre and population model parameters we have used. It is, however, possible to relax this assumption without any change in the results and conclusions. One might argue that the inoculation rate is related to virus titre as:
and introducing the resistance parameters we have:
Substituting this expression into the basic reproductive number and calculating the ESS value of the virus multiplication rate k, we find that kESS can be calculated from:
This equation can only be solved numerically. We have calculated Figs 4–6 using this expression and found no qualitative differences, although quantitative differences do occur.
We have thus investigated a number of models. In future, special attention needs to be given to other virus traits that are under selection pressure. Furthermore, assumptions on model structure need to be investigated for their effect on model outcome. For example, we use a mass action assumption for the transmission of viruses between plants and virions between cells. This assumption has been criticized (Cuddington & Beisner 2005) for its widespread use and research is needed either to justify its use in the present context, or the consequences of relaxing this assumption on model output must be quantified.
As Rubio et al. (2003) state, the lack of good methodologies for the evaluation of components of plant resistance is a limiting factor to the breeding for resistance. Further, the lack of consistent terminology related to resistance may be hindering the dissociation of resistance components in breeding programmes (Lapidot & Friedmann 2002). We hope that our definitions, as expressed in equations 6–9, help to categorize resistance components and develop methods to distinguish these.
In breeding programmes visual assessment of symptoms is often used to select plants for further breeding. This method will inevitably cause a bias towards the breeding of symptom-reducing or titre-reducing resistant lines. Plants expressing inoculation resistance or acquisition resistance will not be recognized because they will develop symptoms once infected. Further, in the evaluation of the usefulness of cultivars it is necessary to know which mixtures of resistance mechanisms are operating in the cultivar and their extent. Such information is a prerequisite to evaluating whether the evolution of the virus towards a higher virus multiplication rate will render the resistance of the cultivar ineffective.
Rubio et al. (2003) provide a major step towards a methodology to analyse the various types of resistance operating. They concentrated on unravelling the virus titre reduction and symptom-reducing resistance mechanisms. In combination with the methods used by Lapidot et al. (2001), which estimate acquisition and inoculation resistance, it should be possible to develop a methodology to separate these four types of resistance.
Besides the use of the model in distinguishing different types of resistance, our work can also help to develop hypotheses that can be tested experimentally. From the work presented in this paper we hypothesize that:
cultivars expressing resistance through virus titre reduction or through symptom reduction can eventually lead to the evolution of virus strains that build up higher virus titres in the plant compared with the cultivar they are derived from;
cultivars that reduce acquisition or inoculation, such as cultivars with leaf trichomes, etc., will not lead to the evolution of virus strains that build up a higher virus titre in the plant.
The key message from our work is that resistance to viral plant diseases can be expressed through several mechanisms. Each of these resistance mechanisms exerts its own characteristic selection pressure on the virus. There has been inadequate recognition of this by virologists and by breeders for virus resistance, but is, as we have shown in this paper, of key importance to the evolutionary response of the virus to the resistant cultivar. Methods need to be developed by practitioners to distinguish the different types of plant resistance, and to determine the combination of resistance mechanisms operating in a cultivar. Breeding for virus resistance can then be directed to deliver cultivars that put a minimal selection pressure on the virus to evolve more harmful strains. This paper provides the first step in disentangling the resistance components and their implications for virus evolution.
The ecological and epidemiological interactions included in the model allowed us to translate the mechanisms at the level of the within-plant virus dynamics to the epidemiological level. By so doing we have been able to quantify how the four types of resistance select or do not select virus strains with higher within-plant multiplication rates. The use of ecological theory and evolutionary stable strategy calculations has thus resulted in insight into the practical aspects that virologists and plant breeders will need to consider to improve programmes aimed at breeding for resistance. At present, few researchers determine the parameters through which resistance is expressed, and no adequate test of the hypotheses above is available. We hope that this paper inspires researchers to obtain experimental data with which to test the hypotheses.