Kreiner et al. (2018) argue, 'The evolution of herbicide resistance in weed populations is a highly replicated example of adaptation surmounting the race against extinction, but the factors determining its rate and nature remain poorly understood' ( p. 611). Despite this great potential for exploring resistance evolution, this intriguing domain has been somewhat overlooked in mathematical biology, overshadowed by the prominence given to antibiotic resistance in bacteria and drug resistance in cancer. Even at academic conferences, the ratio of research dedicated to such topics is glaringly imbalanced. Conferences our group visits feature, for example, typically several sessions on cancer modelling, but I have only once met another participant modelling pesticide application and the evolution of resistance in cropping regions. Notwithstanding, understanding the ecological and evolutionary dynamics of herbicide resistance is more critical than ever. The increasing prevalence of herbicide-resistant weed species presents an undeniable challenge to our global food security - a challenge that grows along with our world population. Carrying out this project, I often wondered, 'So why is there so little participation in this topic?' It is in the pursuit of stoking this interest that our work takes root.
Intrigued by the multifaceted life cycle of perennial weeds and convinced we grow with our challenges, we conducted a theoretical study of the perennial Sorghum halepense, commonly known as Johnsongrass. While mathematical modelling has proven valuable in studying population dynamics and herbicide resistance evolution in weed populations, not even a handful of studies addressed the complex life cycle of perennial weed species. The majority of the existing weed models deal with annual species. Our goal was to achieve a good representation of the perennial life cycle (Fig. 1) and to include inherent features of Johnsongrass' reproduction that might impact herbicide resistance evolution. The path of science is not linear, and our project was no exception. After months of rigorous code optimisation and analysis, we pivoted from an individual-based simulation model to a population-based one. Ultimately, we obtained similar results with both frameworks and agreed to strive for simplicity. The advantages of an accessible model overpower the disadvantage of only reflecting the average weed. While attending a conference in March this year, inspiration hit me, and I created the first scientific illustration of my career. I drew the life-history stages to design a schematic illustration of Johnsongrass' life cycle (Fig. 1) and its representation in our model (Fig. 2). Here, the strength of our final model becomes apparent. We can outline the population dynamics in a simple flow chart supplemented by two schematic plots illustrating the density-dependent mortality and reproduction due to competition between the weed plants.
Our finalised model brought the life cycle of Johnsongrass to digital life, effectively predicting population dynamics and the evolution of herbicide resistance. However, crafting the model was only half the battle. The other half was a taxing task of guesstimation, especially without comprehensive data. German being my mother tongue, I like how the composite "guesstimation" literally describes what we often do as theoreticians. We do not have sufficient data, or our models do not aim to reflect a natural system but rather give us some general insights, so we choose parameters in a somewhat reasonable range. However, selecting parameter values becomes challenging in a model with many parameters detailing the complex life cycle of a perennial weed species. Lacking the possibility to carry out extensive field trials for our model parameterisation, we relied on published studies and experimental data. Expectedly, no field study ascertained all life-history traits that we included. Several traits show a wide variation between ecotypes and field trials, where the latter is likely caused by differences, for example, in climate, soil and cultivation practices. On some characteristics of Johnsongrass, even conflicting information exists in the literature. Facing this disparity in reported trait values, I spent much time and effort inferring biologically realistic values for all our model parameters. Having used mixed parameter sets from published weed population models for preliminary explorations of our model, I was very excited to get the first meaningful results. Yet, due to the extraordinarily high fecundity of Johnsongrass, the simulated weed populations were growing under recurrent herbicide applications even when fully susceptible towards the applied herbicides. Several additional hours of fine calibration, deep dives into the literature, and a little too much chocolate followed. To save future Johnsongrass modellers a lot of time and tears, we have added the detailed parameter derivation, including all relevant references, in our Supporting Information and the well-commented code on GitHub.
Overall the project was a bumpy ride, and I genuinely admire the positivity and irrepressible optimism of my co-author and supervisor, Chaitanya Gokhale. Searching for a compelling and recent modelling study of herbicide resistance evolution for our department journal club, I found what I was looking for. Another team had just published a population dynamical model of herbicide resistance in Johnsongrass, addressing similar questions as we did. Working on such a niche topic, I was unprepared for that and worried that all the work would be in vain, but Chaitanya just said, 'That is good news; that means there is much to explore!' With steadfast support from our colleagues and a constant supply of chocolate to keep us going, we developed our study further and other aspects. Ultimately, I am incredibly pleased to have taken this journey from applied mathematics to agriculture, underscoring the importance and urgency of deepening our understanding of herbicide resistance. We hope our work inspires more to join this exploration, marking another step towards safeguarding our global food security.