By Jillian Kunze
The coffee berry borer (CBB) is a worldwide pest with serious impacts on coffee production. “The female infiltrates the coffee bean, and once inside, starts to reproduce,” Amitabha Bose of the New Jersey Institute of Technology said. The CBB offspring eat away at the bean, eventually rendering it unusable for coffee production (see Figure 1).
Figure 1. A coffee berry with damage caused by coffee berry borers. Figure adapted from
Forestry Images photo by Whitney Cranshaw, Colorado State University,
Bugwood.org.
During a
minisymposium presentation at the
2023 SIAM Conference on Applications of Dynamical Systems, which took place this week in Portland, Ore., Bose presented a joint effort with Mariano Marcano and Paul Bayman (both of the University of Puerto Rico) to map the dynamics of CBB in order to find pest management strategies. This work was motivated by the increasing prevalence of CBBs across the globe — the pest now inhabits most regions of the world where coffee is grown. “The main issue in all of these regions is, how do you control CBBs?” Bose said.
Several factors complicate the management of this insect. Since the females are encapsulated inside of coffee beans, they cannot be targeted by natural predators. And pesticides are not desirable for coffee production. The main strategy at present is integrated pest management, which is culturally-based and effective but difficult and time-consuming. “Once we have a mathematical model, can we come up with culturally-based strategies that can effectively mitigate CBB proliferation and minimize labor?” Bose asked. The researchers aimed to find a strategy to eradicate the CBB population over the course of several years.
The mathematical model that Bose described includes five populations: three states for the coffee beans—uninfected, moderately infected (still usable), and severely infected (unusable)—as well as encapsulated and free CBBs. The model also incorporates parameters like the transition rates and carrying capacity per berry. The researchers specifically focused on coffee production in Puerto Rico, where there is only one growing season per year.
Using this model, Bose and his colleagues derived one-dimensional maps to track the CBB population dynamics from year to year. “We’ll evolve the dynamics from the start of the season to the harvesting time from some initial conditions,” he said. They start with a particular free CBB population at the beginning of the year and use single-season dynamics to get through the season. They then harvest a certain percentage of the beans at the harvest time, thereby removing whatever CBBs are encapsulated in those beans. Finally, the dynamics are linked from season to season.
Figure 2. One-dimensional maps for different harvesting percentages. Figure courtesy of Amitabha Bose.
This process produces a one-dimensional map with two stable fixed points as well as one unstable fixed point in between (see Figure 2). The stable points represent either eradication or total infestation of CBBs, while the unstable fixed point is the threshold between the CBB being completely removed or totally taking over. If the CBB population falls to the left of the unstable fixed point on the map, one can then estimate the number of years until eradication with that particular harvesting percentage.
“This is the reason to build a map,” Bose said. “You can start to investigate the parameters without dealing with dynamics by looking at fixed points.” He described one potential strategy of harvesting 90 percent of the beans for three years, then checking the position on the 80 percent map and potentially switching to that harvesting percentage. This tactic could help minimize labor after some number of years with high harvesting efforts. By controlling the rate of harvesting in this way, it may be possible to eradicate CBBs over the span of several years.
“I’d like to give a plug that we need to be aware of conditions in the field,” Bose concluded. Moving forward, he and his collaborators are currently investigating the effects of fungal application and may also apply the model to locations that have two growing seasons per year. Overall, while the season-to-season maps depend on many estimates, they are able to provide suggestions for harvesting percentages across multiple years. It is clear that getting rid of CBBs will not be possible in a single year — patience will be essential.
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Jillian Kunze is the associate editor of SIAM News. |