Fig 1.
Schematic representation of insect vector behaviour in the context of varietal mixing and vector-borne pathogen transmission.
The field consists of two types of plants, A and B, each having three possible disease states: (1) Healthy (SA and SB), Latently infected (LA and LB), and Infectious (IA and IB). Upon dispersal, insect vectors settle on one of the six types of plants in proportion to their frequency. Virus-free vectors can acquire the virus from infectious plants at a rate that depends on the plant variety, while infectious vectors ultimately disperse the virus when they settle on a healthy plant, with an inoculation rate that also depends on the plant variety. Insect vectors experience the same dispersal and mortality rates regardless of virus-status. The schematic allows for regular roguing of infected plants, i.e., one of the principal means by which virus epidemics in host plants is managed.
Table 1.
Dynamics of virus transmission and vector interactions among plant compartments.
The table summarizes the events involved in virus spread and vector behaviour, detailing the flow of individuals between compartments, along with the corresponding rates of each event. Each event is categorized by its type, including inoculation, latency and roguing for plants of variety A or B; Acquisition, recovery, and insect mortality for infectious insect vectors that acquired the virus on either A plants (VA) or B plants (VB). The table summarises the interactions between healthy, latently infected, and infectious plant states, as well as the role of insect vectors in the transmission process. The inoculation rates and
are in plant per vector per day, and the acquisition rates
and
are in vectors per day. All other event rates in the table are expressed per day. The overall insect abundance, F, in the field, assumed constant.
Fig 2.
Illustration of a mixture and disease incidence dynamics for yield calculation.
Table 2.
Four cassava phytotypes for CMD and equivalent phytotypes for CBSD.
All phytotypes share the same detection probability, d = 1.
Table 3.
(a) is the median value from the posterior dispersal distribution in [36]. (b) The vector death rate was estimated between 0.06 and 0.18 [37]. The growth rate of vectors was estimated at 0.2 based on laboratory experiments. However, analysis of natural population curves revealed a slope of 0.0118, suggesting that mortality contributes approximately 0.1882 (i.e. 0.2–0.0118) to the overall growth rate [38]. Bayesian parameter estimation and hypothesis testing have shown that the available laboratory data does not support whitefly recovery from CMD (c), and that the whitefly median duration of infectiousness with CBSD is approximately 1 hr (d) is the median value from the posterior recovery distribution in [28,39]. (e) Cassava takes an average of 10-12 months to mature before harvest but, in some cases, cassava can take up to 24 months to reach full maturity [40]. (f) is a representative choice based on literature ranges [36].
Fig 3.
Desktop and mobile views of the simulation app tabs.
CropMix is organized into three tabs: (1) a Simulation tab where the user can set the input and observe the outputs; (2) a cultivar selection tab (“Select Cultivars”) where the user selects two varieties for analysis, each represented by a plant phytotype; (3) a settings tab (“About and parameters”) that provides an overview of the model and allows the user to edit intrinsic parameters.
Fig 4.
(A) CMD incidence dynamics under low insect pressure for three different roguing frequencies: no roguing, once a month, and once every two weeks.
In the absence of roguing, incidence rapidly rises to 100%, whereas the saturation level decreases as roguing becomes more frequent. (B) No mixtures can protect susceptible cassava from CMB: Optimal monocultures for diverse setups. When no roguing is performed or when roguing is less frequent than every month, the tolerant monoculture yields the best, no matter the insect burden. Conversely, with more frequent roguing, the susceptible monoculture yields the best. The resulting yields vary little with the insect burden. (a) The yields are calculated for and are slightly lower for
while the order of best yielding monocultures remains unchanged. (b) The yields are calculated for
and are slightly higher for
while the order of best yielding monocultures remains unchanged.
Table 4.
Optimal mixtures against CBSD for diverse setups.
The table presents: (i) the reference yield of SUSC grown alone, (ii) the optimal mixture of SUSC with RES and its yield, (iii) the optimal mixture of SUSC with TOL and its yield, and (iv) the optimal mixture of SUSC with DEC and its yield. The latter three optimal mixtures may be monocultures. When the optimal mixture consists solely of SUSC, as in the case of mixing with DEC, an additional row is unnecessary. (a) The yields are calculated for and are lower for
. The optimal mixture proportions may vary with reduced values of the roguing rate ρ until they stabilize to the same profile as when there is no roguing. (b) The yields are calculated for
and are higher for
than for
. For higher values of the roguing rate ρ, the best-yielding order remains unchanged: the SUSC monoculture remains optimal under low and medium insect burdens, while the SUSC–RES mixture remains optimal under high insect burden. In the latter case, the proportion of SUSC in the mixture increases with the roguing rate, reaching 100% as ρ approaches 1 (roguing every day). More generally, increasing the frequency of roguing increases the share of SUSC in mixtures Fig 6.
Fig 5.
A susceptible-resistant mixture (16.4% susceptible vs. 83.6% resistant) is yield-wise optimal under moderate whitefly pressure and brown streak disease.
This mixture produces a yield of 20.6 tons/ha for the resistant variety and 4.9 tons/ha for the susceptible variety. Notably, the susceptible cassava yield in the mixture outperforms that of a susceptible monoculture, despite the smaller proportion of susceptible cassava (16.4%) in the mixture. Disease incidence is significantly reduced in the mixture.
Fig 6.
Optimal proportion of susceptible (SUSC) in a mixture with resistant (RES) plants as a function of the number of days between roguing events (i.e., the inverse of the roguing rate) under different levels of insect pressure and CBSD.
Under a high roguing regime (), a SUSC monocrop is optimal regardless of insect pressure. As roguing becomes less frequent, the optimal SUSC proportion decreases under medium and high insect pressure, while remaining at 100% under low pressure. These proportions eventually reach their minimum values in the absence of roguing, as shown in Table 4: 16.4% for medium insect pressure and 0.0% for high insect pressure.
Fig 7.
Roguing increases the proportion of the susceptible cassava variety in the optimal mixture with the resistant variety under moderate insect pressure and brown streak disease.
When roguing is performed once a month, the optimal mixture contains 9.8% resistant plants, compared with 83.6% in the absence of roguing. Overall, the total yield with roguing in the optimal mixture (29.8 tons/ha) is slightly higher than in a susceptible monoculture (29.5 tons/ha), and both are significantly better than scenarios without roguing, due to reduced disease incidence.
Fig 8.
Roguing reintroduces the susceptible cassava variety in the optimal setup under high insect pressure and brown streak disease: a proportion of 65.3% resistant plants is optimal in a mixture with susceptible when roguing is performed once a month, while the resistant monoculture was optimal in the absence of roguing.
Fig 9.
Decoy plants can protect cassava from cassava brown streak ipomovirus under high whitefly pressure.
An optimal proportion of 82.9% decoy plants attracts enough whiteflies to significantly lower the disease incidence. This insures 4.1 tons/ha of cassava yield associated with the 17.1% of susceptible cassava in the mixture, while a monoculture of susceptible cassava achieves 3.1 tons/ha.
Fig 10.
Decoy plants can protect cassava from cassava brown streak ipomovirus under moderate whitefly pressure.
An optimal proportion of 61.4% decoy plants attracts enough whiteflies to significantly lower the disease incidence. This insures 9.5 tons/ha of cassava yield associated with the 38.6% of susceptible cassava in the mixture, while a monoculture of susceptible cassava achieves 3.1 tons/ha.
Fig 11.
Summary - Cassava yields in diverse growing scenarios without roguing in the presence of CMD (top) and CBSD (bottom).
Regardless of insect pressure, the incidence of CMD quickly rises to 100%, and the tolerant monoculture yields the best as it responds better to disease-induced yield loss. Susceptible varieties do not need resistance shielding from CBSD under low whitefly pressure, but as insect pressure increases, resistant varieties become more dominant. As a result, a mixture of susceptible and resistant varieties is optimal under moderate whitefly pressure, while a monoculture of resistant varieties is optimal under high whitefly pressure. In both cases, shielding susceptible cassava crops with decoying plants that attract whiteflies similarly is more effective than growing susceptible cassava alone, despite the significantly reduced proportion of cassava grown.