A case study: The CBB and Arabica coffee

In this simple example, we consider the CBB that attacks coffee berries. We assume that, at the time scale considered, there is no visible effect on plant growth.

H. hampei (Ferrari) is a pest known as CBB, belonging to the order Coleoptera, family Curculionidae, and subfamily Scolytinae [48]. This small beetle originates from Central Africa and is present in all coffee-producing countries of the world.

A CBB hatches from an egg in the seed of a coffee berry. When the fertilized females leave the fruit, they colonize another one and start their own colony (Fig. ​(Fig.3).3). The factors triggering the exit from the fruit are the age of the insect and the climate (temperature, humidity, and rain). CBB is attracted to by red (ripe) fruits and green fruits (if they are large enough). The insect is more attracted by red than green fruits; however, if the number of attractive fruits is small, then CBB will colonize overripe fruits or fruits that have fallen to the ground. The average life span of a female CBB is nearby 45 d [49].

Fruits are grouped into 3 distinct categories. “Very attractive fruits” (VAp) are ripe fruits, from the moment they turn red. “Attractive fruits” (Ap) are well-developed green fruits. This category includes green fruits larger than 5 mm, with seeds capable of hosting the CBB, to fruits that turn yellow. “Ground fruits” (G) are all fruits fallen to the ground, whatever the former category they belonged to. In the proposed model, each of the above fruit categories has an attraction factor that influences whether CBB chooses to colonize a fruit or not.

Population monitoring is based on the grouping of different individuals within a population having the same oviposition day. Male CBBs are not considered in monitoring of populations as they do not play any role in the epidemic propagation (they represent only 110 of the individuals in a colony and are not disseminated). As already mentioned, population dynamics depend on temperature, relative humidity, and precipitation.

The cohorts of the model are built by crossing the groups of individuals and the categories of fruits where these individuals live.

On each simulation step, the results of new attacks are grouped into 2 categories: population data and fruit data. The population data contain information about each population group for a given day. It contains the date when this group left its original fruit to colonize other fruits, the number of flying CBB, the number of dead CBB, and so on. The fruit data include the fruit categories presented above. In addition, they are divided into 2 subgroups, healthy and colonized fruit. The result is a cohort of fruit categories attacked by a quantity of CBB hatched on a given day.

In the Sumatra region of Indonesia, Arabica coffee trees produce coffee berries throughout the year. With the presence of rainfall throughout the year and an average daytime temperature between 22 and 30 °C, the equatorial climate provides the necessary conditions for the trees to flower. A plant growth model is created as a reduced model to simulate fruiting only. We designed a cohort fruit model inspired by the GreenLab cohort assumption: Fruits with the same parameters (chronological age, physiological age, and sink power) are merged into the same cohort. An automaton is created that build fruit cohorts on the basis of the obseved numbers of berries harvested. Then, the model estimates the age of the fruits according to the harvest frequencies and the climatic data.

Human intervention is represented here as a simple harvest model. This model simulates harvesting of red berries at dates that correspond to observed data, which is useful for validation by comparing simulated data to actual data.

When CBB attacks a fruit on the tree, the inner seed is damaged, but the fruit continues to develop and the biomass is still distributed. We therefore consider that the feedback on the plant is negligible. Thus, in this case, the interaction focuses on the state of the fruits (attacked or healthy).

Interaction between the 2 models is achieved by converting the numbers of attacked fruits provided by the CBB model into the cohorts of the plant model An additional state variable ISS is created in MIMIC: the status of the cohort. This additional data is Boolean, indicating whether the cohort is colonized by the CBB.

To validate the functioning of the interface, we used climatic, fruiting, and attack data on 2 coffee trees in Indonesia for almost a year [50]. The observations were not made daily but separated by slightly irregular periods of time (about 20 d between each observation). This implies a daily operation of the model and an estimated chronological age of the initial populations. The solution chosen was to consider maturation occured exactly between 2 observations. A CBB colony is established at the start of the simulation and begins its development. The number of colonized fruits is initialized by the observed data. Because there is no data for fruit on the ground, this category was discarded from the simulation.

The study case and simulation results are presented below, after detailing the overall implementation aspects.