Figure 1.
An overview of the four models postulated.
Table 1.
Symbols that pertain throughout the paper.
Figure 2.
A diagrammatic representation of models presented in this paper.
Diagram summarizing the expected proportions of hosts penetrated (or not) by genotypes A and/or B, and infected (or not) by genotypes A and/or B of a micro-parasite. The diagram is conditional on realizations of ξ, λA and λB. In a real population of insects, there will be heterogeneity in these parameters, which will distort the proportionalities in the figure. Hence, the panel illustrates only the aspect of dependence, given penetration and infection chances, and it does not represent the effects of heterogeneity. Panel A gives an overview of the all possible outcomes – in terms of penetration and infection – after challenge of hosts with virions of genotypes A and B. Hosts can be penetrated or not, and if hosts have been penetrated, they can be infected. These outcomes hold for all four models presented here. Panel B corresponds to Models 1 and 2, where only infecting genotypes are genetically represented in the viral progeny. The expected fractions of alive larvae (no fill), penetrated by virions of genotype A only or penetrated by both genotypes and infected by A (vertically dashed), penetrated by genotype B only or penetrated by both genotypes and infected by B (horizontally dashed), and penetrated by both genotypes and infected by both genotypes (horizontally and vertically dashed) are illustrated. Panel C corresponds to Models 3 and 4, where all penetrating genotypes are genetically represented in the viral progeny, conditional upon the host being infected by (at least) one virion. The expected fractions of alive larvae (no fill), penetrated by genotype A only and infected by A (vertically dashed), penetrated by genotype B only and infected by B (horizontally dashed), and penetrated and infected by both genotypes or penetrated by both genotypes and infected by genotype A or penetrated by both genotypes and infected by genotype B (horizontally and vertically dashed). Note that In Models 1 and 2 (Panel B) the fraction of non-infected hosts conditional upon ξ is greater than the fraction non-penetrated, whereas in Models 3 and 4 (Panel C) that fraction exactly equals the fraction non-penetrated. Panel D represents the original, single-phase IAH model, where penetration of the host automatically leads to infection. The equations indicate the cumulative probabilities underlying boxes (e.g., is the sum of boxes 1,2,4 and 5).
Figure 3.
Dose response for AcMNPV infection of S. exigua L5.
On the x-axis is the log10 of the virus dose (OBs per ml) droplet fed to larvae. The proportion of hosts dying is on the y-axis. The different symbols represent different replicates, which covered different ranges in dose. The line represents the IAH dose response relationship by non-linear regression (mortality = 1 - exp(-p· OB concentration), SPSS 15.0), rendering p = 2.205×10−7.
Figure 4.
Ratio of genotype A to genotype B in infected hosts.
The log-transformed genotype ratio (A:B) is given for S. exigua L5 larvae at different inoculum OB concentrations, as indicated in the upper left-hand corner of each panel. On the x-axis is the log10 of the genotype ratio (A:B), and on the y-axis frequency. Host survival (S) decreased with inoculum OB concentration, from S = 0.72 (105 OBs per ml) to S = 0.03 (108 OBs per ml). The number of hosts per dose are 14 (105 and 106 OBs per ml), 12 (107 OBs per ml) and 8 (108 OBs per ml).
Table 2.
Frequency of mixed-genotype infection at different doses.
Figure 5.
Fitted models and experimental data.
Fitted Models 1–4 compared with experimental data. In all panels, the log of the dose is on the x-axis and frequency on the y-axis. Dose mortality responses are given in the left-hand panels (A–D). Here, diamonds are the experimental data and the lines model predictions. Relationships between dose and rate of mixed-genotype infection in cadavers are presented in the right hand panels (E–H). Again, markers denote experimental data while lines denote model predictions: red circles and the red solid line denote mixed infection with genotypes A and B, green triangles and the green dotted line denote infections with genotype A only, and blue squares and the fine dotted blue line denote infections with genotypes B only. Horizontally adjacent panels pertain to the same model, as indicated in the left hand panel (e.g., panels A and E correspond to model 1). Model 2 gives the best description of the data (see Table 3).
Figure 6.
The predicted distribution of host susceptibility.
The distribution of host susceptibility predicted by model 2 with fitted parameters: p = 0.0059, α = 0.335, β = 143 (Table 3). Host susceptibility is characterized by the overall probability of disease causation for a single ODV, pξ, which is the product of the per virion chances of successful penetration, p, and the probability of successful infection given successful penetration, ξ. The shape of the cumulative distribution of pξ is the same as that of the beta distribution for ξ, but the domain of the former is limited to (0, p], and the distribution is accordingly shifted to the left compared to the beta distribution for ξ which has (0,1] as its domain. A logarithmic scale is used for the abscissa to represent the broad range of susceptibility in the host population, which is reflected in shallow dose response and is – as shown in this paper – intrinsically associated with a high incidence of mixed genotypes in cadavers.
Table 3.
AIC and estimated parameter table.
Figure 7.
The effects of heterogeneity in host susceptibility.
We assume a host population that is composed of 1, 2, 4 or 6 classes of individuals, varying in their susceptibility to a virus. The number of classes is given in the legend, and applies to all three panels. (E.g. A value of ‘1’ indicates the infection probabilities are the same for all hosts, so in this instance the host population is homogeneous. ‘6’ indicates that there are six host classes with different susceptibilities to the virus) The following infection probabilities were assumed: 1 class, 10−4.5; 2 classes, 10−4, 10−5; 4 classes, 10−3, 10−4; 10−5, 10−6; 6 classes, 10−2, 10−3, 10−4; 10−5, 10−6, 10−7. The geometric mean infection probability is 10−4.5 in all four cases. A virus population composed of two genotypes in a 1∶1 mixture, and no differences in infection probability for these genotypes, was assumed. In Panel A, the dose response relationship is illustrated. On the x-axis is the log of dose, and on the y-axis mortality. Note that as more host classes are introduced, the dose response relationship becomes shallower. In Panel B is the frequency of mixed-genotype infection, which follows a similar trend with dose. Panel C is the relationship between host mortality (x-axis) and the frequency of mixed-genotype infection (y-axis). The solid line is a 1∶1 relationship between mortality and the frequency of mixed-genotype infection. As a more heterogeneity is introduced in the host population, the frequency of mixed-genotype infection becomes higher and eventually approaches the 1∶1 line (both micro-parasite genotypes are established in all hosts at any level of mortality).