The discovery of five RNA viral pathogens of the SCN (Bekal et al., 2011, 2014) creates the possibility of using such viruses as biocontrol agents. However, their transmission modes, virulence, and nematode pathogenicity are currently not well understood. Hypothetically, however, these viruses could become a useful tool in the management of SCN infestations in the field. The decade-long viability of SCN eggs in the soil (Schmitt et al., 2004) implies that developing and testing virus-based SCN biocontrol technologies will require at least a decade. Over this period, it is reasonable to expect that the virus and the nematode could both evolve in potentially unpredictable ways. Numerical simulations to model interactions between the virus, its SCN host, and the soybean plant would serve to provide insight into the long-term interactions within this ecosystem. This study documents the development of Soybean Cyst Nematode Simulation Framework (SCNSim), an agent-based simulation engine designed to explore the biocontrol outcomes of a range of hypothetical viruses interacting with the SCN.
The simulation recapitulates essential features of the SCN life-cycle as well as the potential pathogenicity due to a hypothetical virus. SCNSim uses published data on the SCN life cycle and takes into account an environmental (i.e., temperature) model as well as soybean planting and growth timelines (Schmitt et al., 2004; Niblack et al., 2006). The resulting simulation generates dynamical behavior that can be interpreted from the perspective of host–pathogen coevolution.
Modeling host–pathogen coevolution: theoretical and experimental investigations of biocontrol are generally motivated by the desire to contain infectious disease (Rock et al., 2014). In contrast, in this study, the desirable outcome is a viral pandemic in the nematodes and the resulting protection of the soybean plant. Such models capturing interspecies interactions at multiple trophic levels need to be complex enough to capture the adaptive arms race between the nematode host and the viral pathogen.
Similar to many microbial biocontrol agents, the basic system of equations modeling an epidemic-the Susceptible-Infected-Recovered (SIR) type models-must be sufficiently rich to provide insight into host-pathogen interaction (Brauer, 2008; Rock et al., 2014). Here S, I, and R represent compartmentalized portions of the total population and stand for susceptible, infected, and recovered host individuals, respectively. The dynamic system of equations is parameterized with terms for the rate of transmission
Pathogens, including viruses, acquire an adaptive tradeoff between fecundity and host resistance, commonly known as the trade-off theory. Exploitation of the host improves the pathogens transmissibility, but at the cost of the survival of the host and therefore reduce the duration of transmission. This adaptive tradeoff phenomenon is driven by the costs of resistance (energetic or otherwise) and risk of pathogenic infection (Galvani, 2003; Demas et al., 2012; Raberg˚ and Stjernman, 2012). The virulence–transmissibility tradeoff has been demonstrated empirically in malaria models where transmission and virulence are positively correlated until the benefit of increased transmission no longer outweighs the concomitant increase in host mortality (Mackinnon and Read, 2004b; Alizon et al., 2009; Raberg˚ and Stjernman, 2012). Another example is the canonical study of the myxoma virus in invasive European rabbit (Oryctolagus cuniculus) populations in Australia (Fenner and Ratcliffe, 1965). Within 2 years, the myxoma virus fatality cases caused by the most prevalent strains dropped from 90% to 99% to between 70% and 95% over 30 years. (Fenner and Ratcliffe, 1965; Kerr et al., 2012).
Following the SIR paradigm, a definition of fitness emerged called the basic reproductive ratio of the pathogen,
From a game-theoretic perspective, pathogens will evolve to maximize
On the other hand, agent-based models are a class of numerical models that represent hosts and pathogens as individual agents, capable of movement and interaction with each other and their host environment. Typically, agents in the agent-based model can be modeled as complex units with discontinuous behavior. While such models are more complex to build and require greater computational resources, they are finding increasing value in the modeling of infectious disease dynamics (Siettos and Russo, 2013).
The objective of this study was to use an agent-based model to investigate combinations of viral transmission and virulence in order to identify viral properties that resulted in the highest suppression of nematode populations, and whether these characteristics and their dynamical evolution over time would follow behaviors posited by existing ecological theories. In particular, it is hypothesized that the epizootic behavior of these SCN viruses would follow the adaptive virulence trade-off hypothesis which suggests that virulence is an unavoidable consequence of transmissibility. A successful viral biocontrol agent would evolve toward an intermediate or optimum virulence that balances the epizootic and trade-off characteristics of the virus (Alizon et al., 2009).
Construction of SCNSim: the SCNSim framework employed an object-oriented, discrete time simulation to model the evolution of nematodes and their viral pathogens as they interact with each other within a single soybean plant. The Nematode class was a state-based abstraction for the SCNs. Instances of the Nematode class (i.e., Nematode agents) recapitulated the SCN life cycle as they hatched, grew, mated and reproduced. Their survival and successful transition was predicated upon a Health parameter that was increased as they fed upon the plant and decreased as they progressed through their life cycle. Viral infections in the nematodes were instance properties parameterized by their intensity or viral load (
An outbreak of RNA virus on SCN was characterized by combinations of several scale-free virulence properties as described in Table 1. These properties coevolved with the SCN population. Each property was randomly varied at model initiation to create a population of viruses described by a normal distribution of the properties. Viruses were transmitted according to dynamic transmission rates (
Numerical properties of the viruses in the Soybean Cyst Nematode Simulation Framework SCNSim.
Definition | ||||
---|---|---|---|---|
Property | Symbol | Range | in vivo | in silico |
Viral Load |
|
0 1 | Amount of viral particles per host | Scalar multiplier to nematode health decrement |
Virulence |
|
|
Pathogen damage inflicted on host | Multiplier to Viral Load |
Transmissibility |
|
0 1 | Rate of infection of suscep-tible population | Proportion of viral load sexu-ally transmitted from infected male to a recipient female or from female to egg |
Prevalence |
|
0 1 | Disease prevalence in a population | Fraction of initial population infected |
Durability |
|
0 1 | Longevity of virus parti-cles. | The complement is an ampli-fying constant on increasing viral load. |
Mutation Rate |
|
0 1 | Proportion of progeny gen-eration with significant ge-netic variation | Probability of virus proper-ties undergoing mutation |
SCNSim simulated the random nature of viral evolution as well as direct the population kinetics of the infected SCN. During the simulation, the diversity of viruses increased according to a mutation rate (
The Nematode Agent: within the SCNSim framework, the Nematode agents recapitulated the different stages in the SCN life cycle (Fig. 1). SCNSim considered the initial SCN population densities per soybean plant, with each cyst capable of producing a uniformly distributed number of eggs between 300 and 500. The model assumed that each transition between the nematode stages was determined by the environment and the health of the Nematode agent. The major environmental constraints that dictated the periods of nematode growth are detailed in Table 2.
Environmental set points and nematode stages modeled in the Soybean Cyst Nematode Simulation Framework (SCNSim) based on figures in Schmitt et al. (2004).
Model compartment | Parameter description | Value |
---|---|---|
SCN life cycle laws | SCN eggs per cyst | 300-500a |
Minimum hatching temperature | 16° C | |
Maximum hatching temperature | 36° C | |
Cyst dormancy initialize temperature | < 20° C | |
Probability of hatching from egg sac | 0.2b | |
Probability of hatching from cyst | 0.002b | |
SCN life stages | Egg state | 1-5 d |
J1 state | 1-2 d | |
Unhatched J2 | 1-3000 d | |
Hatched J2 | 1-4 d | |
J3 | 3-4 d | |
J4 male | 5-6 d | |
J4 female | 3-4 d | |
Adult male | 1-21 d | |
Adult female | 2-60 d | |
Range of mating | 1-21 d | |
Gestation period | 3-5 d | |
Egg Sac | 1-3000 d | |
Cyst | 1-3000 d | |
Soybean growth | Minimum germinate temperature | 13 ° C |
Soybean germinate date | 115 days (about April 25) | |
Soybean harvest date | 240 days (about August 28) | |
Optimal soybean growth temperature | 27° C | |
SCN Parasitism | Minimum soybean age for parasitism | 20 days post germinationc |
Maximum soybean age for parasitism | 100 days post germinationc | |
Feed rate | 5% |
According to Biology and Management of Soybean Cyst Nematode 2nd ed., a female cyst growing in optimal conditions may produce up to 600 eggs. However, the averages found in fields has been reported to be much lower, ranging between 60 and 200, depending on the location (Koenning, 2004).
bIf hatching is allowed by environment; cSoybeans typically take 20 d to produce root exudates that attract SCN. After 100 d, soy-beans are usually within reproductive maturity and root development slows while a woody epidermis prevents new SCN from penetrating.
Nematode Health was measured on a scale of 0 to 100, where 0 corresponds to a dead nematode, and 100 to a completely healthy nematode. Starvation during the hatched J2 stage and infection caused nematodes to lose their health at varying rates depending on the length of the starvation period and the severity of the viral infection. On the other hand, it was assumed that parasitizing soybeans replenishes nematode health at a fixed rate. The health parameter quantified the probability with which the Nematodes transitioned to their next life stage. Repeated failure to develop caused an irreversible decrease in Health that would eventually cause the Nematode to die.
Any viral infection the male carried was transmitted to the female according to the probability of transmission. The total resulting viral load was then divided equally among the eggs.
SCN females transitioned from egg sacs to dormant, egg-containing cysts between growing seasons or if temperatures dropped below 20° C (Schmitt et al., 2004). Eventually, the cysts would release SCN juveniles in the following Spring when favorable conditions returned. This dormant cyst phase slowly degraded over 3000 days, given that the cysts remain viable for about 9 years (Schmitt et al., 2004). It was assumed that the metabolism in the dormant phase occured at a negligible rate and viruses do not mutate or cause damage.
As multiple Nematode agents advanced through their simulated life cycle, the simulation engine generated data for the means and standard deviations of the nematode population distribution including distributions across the simulated nematode stages as well as means and standard deviations of the dynamic virulence properties and means of environmental variables. Data generated in each run were stored in a database separately, along with the variables corresponding to the initialization of the simulation.
Assumptions: at the time of this writing, relatively little is known about the epidemiology of the SCN viruses, including their pathogenesis, transmission rates, mutation rates, and etiologies. Thus, broader definitions were needed to describe their in silico counterparts and the following simplifying assumptions were made: (1) Viruses were only pathogenic to SCN, i.e., no mutualism, symbiosis, commensalism or competition between viruses was assumed; (2) viruses began inflicting damage immediately after infection; (3) differences in success rates between horizontal and vertical transmission were ignored; (4) contact transmission of viruses was ignored; (5) spatial dimension was ignored, i.e., metapopulation dynamics did not influence the epizootic; (6) soybean immune responses against nematode parasitism were ignored, except for biomass reduction; (7) soil moisture did not impact the model, and (8) nematodes replenished their Health at 5% per feeding event as they fed on the soybean plant. Based on data available, an initial population of 10 cysts increased to 5000 within one growing season (Schmitt et al., 2004). To replicate this nematode growth rate in the absence of viral infection in the simulation model, the feeding rate was calibrated to 5%.
Simulation data generation: Each unique combination of the varying initial conditions for virus properties were simulated 10 times over a 5-year period of continuous soybean monoculture. Simulation data were generated to correspond to a frequency of 4-day sampling interval (Table 3). In the data, each unique combination of virus properties is referred to as a pathotype. The replicates were averaged for each combination at each time point. Data points where there was no SCN activity (days 1–99, and 256–365) were removed. Where appropriate, medians of each non-normally distributed variables were determined for each within-treatment crop year for expedited qualitative analyses. The simulation code is available at
Simulation parameters used in producing data on the Soybean Cyst Nematode Simulation SCNSim framework.
Simulation configuration | Sampling frequency | 4 days |
Iterations | 10 | |
Simulation duration | 5 years | |
Virus properties | Mutation rates ( |
0, 0.1, 0.2, 0.4, 0.6, 0.8 |
Virulence ( |
0.1, 0.5, 1, 1.5, 2, 2.5, 4 | |
Transmissibility ( |
0.5 | |
Infection rate ( |
0.2, 0.8 | |
Durability ( |
0.5 | |
Viral load ( |
0.5 |
Replication ratio: The basic reproduction ratio from the SIR models,
where each of the terms are initially at their maximum capacity and birth rates are not taken into consideration. Therefore, with the exception of the mortality rate terms
To determine a recovery ratio
Statistical analysis: Data were subjected to the Shapiro–Wilk test (Shapiro and Wilk, 1965) to test for heteroscedasticity. Since heteroscedasticity was significant in most of the variables observed, non-parametric tests were used for further analysis of variance (Kruskal and Wallis, 1952; Daniel, 1990), and permutation tests were used for multi-factorial analysis of variance (ANOVA) (Wheeler, 2010). Results from the virus treatment simulations were compared to a control simulation which assumed null viral infection rates. Statistical analyses were performed using R® Statistical Software (R Core Team, Vienna, Austria) (R Core Team, 2013).
A total of 31 variables and over a million records were used in the analysis. All data were subjected to scaled principle component analysis using the prcomp function in R®. Variables analyzed included population distribution across multiple nematode stages (J1, J2, J3, J4, J4 males, J4 females, males, females, nematodes mating, fertilized females, females with egg sacs, cysts, and average number of eggs per cyst), population mean and standard deviations of virus properties (virulence, transmissibility, viral load, durability), and epidemiological measures (number of deaths in nematodes due to viral infections as well as due to other factors such as starvation), average health of the nematode, and the propensity of the virus to mutate.
Variables ‘Nematodes’ and ‘Cyst’ were chosen to represent the SCN population, ‘Virulence’ and ‘Transmissibility’ were used to describe the viral epizoology, and ‘Fraction Infected’ and ‘Death by virus’ were used to describe disease impacts on SCN. Nematode mortality rates attributed to viruses,
The Soybean Cyst Nematode Simulation (SCNSim) framework. Envi-ronment, Nematode, Viral Infection and Soybean boxes represent classes in an object-oriented framework, with their respective properties listed within the boxes, and interactions between each other shown by solid arrows. The Nematode class is a simplified model of the life cycle of the nematode
To evaluate the extent of nematode suppression by SCN viruses, final mortality rates of SCN were compared across multiple factors. For all pathotypes of viruses where
Simulation on Inundative release of viruses: based on data collected on SCNSim simulations across multiple virus properties listed in Table 3, nematode mortality rates were broken down by infection prevalence, mutation rate and initial starting virulence as shown in Figure 2. As expected, the greater the starting prevalence
Overall, the
Moreover, the average mortality rates due to viruses for simulations with initial prevalence
This result agrees with the stochastic modeling study by Shea and Possingham (2000) which identified the notion that a high release strategy results in greater biocontrol. However, treatments within each
Nematode suppression across viral pathotypes: effects of viral virulence on SCN mortality when
Dynamic evolution of SCN viral pathogenicity: Figure 3 shows the time course evolution of mortality, prevalence, and viral transmissibility for the viral mutation rate of
At
The dynamic evolution of SCN viral pathogenicity modeled with SCNSim indicates that it is more important to select a virus strain with an intermediate starting virulence
Replication ratio–disease fitness: the replication ratio was used to compare the disease fitness across combinations of virulence factors. According to the tradeoff hypothesis, epizootics with high fitness are expected to have high
For the
Figure 4 shows that within the
On the other hand, above this virulence threshold, increasing mutation rates improves the fitness of the epizootic. At these higher
Correlation between virulence and transmissibility. Figure 5 shows the parametric relationships between
Furthermore, this study suggested a positive relationship between transmissibility and virulence, as opposed to an inverse relationship posited by Raberg˚ and Stjernman (2012).
However, as indicated by the time component, in some simulations, the relationship between transmissibility and virulence does not evolve monotonically. Figure 6 highlights three distinct trends found in Figure 5. For instance in
Although Raberg˚ and Stjernman (2012) reported an inverse relationship between virus virulence and transmissibility, the data generated from SCNSim revealed that at intermediate virus
Figure 5 also visibly supports the notion of optimal virulence: greatest nematode mortality is achieved by intermediate pathotypes, which lay on a diagonal of the grid. Within these intermediate pathotypes,
Soybean cyst nematode mortality across viral pathotypes. Each panel describes the mortality in the nematode population as a function of the mutation rate for a given initial virulence V0. Greater prevalence of the infection resulted in higher mortalities than the low release treatments.
SCN suppression over time at mutation rate of 0.4 across initial virulence
Replication ratio (
Four-dimensional scatter plot showing virus-caused nematode mortali- ties over time across treatments by mutation rates and virulences. Each panel in the grid layout denotes the evolution of transmissibility
Relationship between transmissibility and virulence across three distinct initial virulence values (
SCNSim represents the first attempt at capturing the evolutionary dynamics of host–pathogen interaction in the context of biocontrol of SCNs with viruses. A key advantage of SCNSim is that it is possible to model host morbidity through the stochastic events driven by the health parameter of the nematode and permits the modeling of diseases with small case fatalities (Mackinnon and Read, 2004b).
Because morbidity manifests at the individual nematode, this is a crucial advantage of agent-based models over the continuous, differential Susceptible-Infected-Recovered (SIR) models (Rock et al., 2014), where it is difficult to interpret model results where there are few discrete individuals. The SCNSim simulation supports the idea that the best biocontrol agents have intermediate values for initial virulence. It also illustrates that biocontrol agent performance also strongly depends upon the mutation rate, i.e., the adaptability or evolvability of the pathogen, which allows the pathogen to rapidly achieve an optimum under selection. Moreover, SCNSim highlights the fact that the virulence and transmissibility properties of a virus that maximize the reproductive fitness of a pathogen can be counterproductive to its use a biocontrol agent. Virulence levels below optimal will lead to avirulence, whereas higher virulences kill the nematode rapidly, reducing the opportunity for transmission. From a practical standpoint, the ideal virus-based biocontrol strategy for SCN would include (1) a design for optimally initial virulence, (2) adaptable viruses (3) delivery mechanisms to ensure sufficiently high disease prevalence to permit vertical transmission of the pathogen, and (4) multiple years of successive treatment, allowing the biocontrol agent to maximize nematode suppression over multiple years.