Model Maps Safe Waiting Times for Fungicide in Brazil’s Green Coconuts

Brazil produces more than two billion coconuts every year, and a large share of that harvest is drunk fresh as coconut water or eaten as soft pulp. Yet the crop has no officially registered fungicides for its most damaging foliar diseases, so growers turn to products authorised for other species under agronomic prescription. One of the most widely used is cyproconazole, a triazole fungicide injected directly into the trunk to combat verrucosis and the leaf blight complex. Because the coconut palm fruits continuously, producing a new bunch roughly every month, a systemic chemical injected into the vascular system reaches fruits of every developmental stage at once. That biology creates an awkward regulatory problem: no pre-harvest interval, the waiting period between the last application and harvest, has ever been established for cyproconazole in coconut, either in Brazil or internationally.

A new modelling study published in Environmental Science and Pollution Research tackles this food-safety gap head-on. Lourival Costa Paraíba of Embrapa Meio Ambiente coupled a Level IV fugacity model, a fully dynamic thermodynamic framework for tracking a chemical’s movement between compartments, with Gompertz growth functions that let the coconut’s water and pulp compartments expand as the fruit matures. He then propagated uncertainty through the model using Monte Carlo simulation with 2,000 realisations and screened the sensitivity of the outputs with a Morris elementary-effects analysis. The result is a probabilistic harvest-safety matrix covering three doses, three application frequencies, and fruits harvested between five and eight months of age, offered as screening-level decision support until field residue trials can validate the predictions.

The fugacity approach works by describing the escaping tendency of a chemical from each compartment. Concentration in a compartment equals fugacity multiplied by a fugacity capacity, which depends on properties such as Henry’s law constant for the coconut water and the pulp–water partition coefficient for the lipid-rich pulp. Because the classical assumption of fixed compartment size is a poor fit for a growing fruit, the model ties those capacities to Gompertz sigmoidal growth curves calibrated against published Brazilian data: pulp mass approaching 100 grams and water volume approaching 400 millilitres at eight months. A logistic sub-model, fitted with a coefficient of determination of 0.94, tracks the pulp’s lipid fraction as it climbs from roughly 2 percent in young fruit to about 30 percent at maturity.

That lipid accumulation matters enormously for a compound like cyproconazole, whose octanol–water partition coefficient of 2.90 makes it moderately lipophilic. The modelled fraction of the chemical retained in the pulp rises from 0.943 in three-month fruit to 0.980 in eight-month fruit, meaning older coconuts sequester the fungicide more effectively. This dynamic partitioning, the study argues, has no parallel in static single-compartment residue models and represents a methodological advance for lipophilic pesticides in lipid-accumulating tropical fruits. It also means the worst-case harvest month corresponds to picking shortly after an injection, before the inter-application decay interval has done its work.

Two parameters dominate the model’s uncertainty, and the Morris screening confirmed it quantitatively. The transport efficiency of endotherapy, the fraction of an injected dose that actually reaches a given fruit, has never been measured in the field. In the absence of data, the study calibrated it conservatively: a single 2.0-gram application is assumed to produce an initial pulp concentration exactly equal to the maximum residue limit of 0.1 milligrams per kilogram in an eight-month-old fruit, the most protective reference point available. The degradation rate constant was drawn from the Pesticide Properties Database, which reports a plant-tissue half-life of 11.5 days nominally, ranging from 3.5 to 16.0 days across field crop trials. The Morris analysis found these two parameters each roughly an order of magnitude more influential than the next-ranked candidate, justifying their exclusive propagation in the Monte Carlo analysis.

The probabilistic results draw a sharper picture than a deterministic model alone. At the lowest dose of 1.0 gram, the probability of exceeding the residue limit stayed at or below 0.024 across every frequency and fruit age, placing that dose firmly in the safe category, with bimonthly and quarterly schedules below 0.01. At 1.5 grams, risk became markedly age-dependent: monthly application was classified as not recommended for five-month fruit, with an exceedance probability of 0.249, but fell to moderate risk from six months onward, while bimonthly and quarterly schedules became safe by seven to eight months. At 2.0 grams, monthly application was not recommended at any fruit age tested, with probabilities ranging from 0.312 to 0.602, and even the slower schedules carried moderate risk for older fruit only.

Perhaps the study’s most striking lesson is that several scenarios appearing safe under point estimates are not safe once uncertainty is propagated. The 1.5-gram monthly schedule, for example, shows a deterministic peak concentration of 0.091 milligrams per kilogram, just under the limit, yet carries a Monte Carlo exceedance probability of 0.249, a risk the single number alone never communicates. The author therefore recommends that the probabilistic matrix, not the deterministic one, guide screening-level decisions, and explicitly flags that five of the 36 scenarios classified as safe under a probability threshold of 0.05 would be reclassified as moderate risk under a stricter threshold of 0.01. The classification bands themselves are model-based risk-communication conventions, not regulatory limits; the only regulatory value used is the residue limit itself.

The modelling choices reflect the agronomic reality of continuous fruiting. Rather than simulating a single isolated application, the model generates an indefinite endotherapy schedule, so that by the far end of the 24-month simulation window a monthly programme has accumulated roughly 30 injections, each contributing residual mass that decays with first-order kinetics. Because first-order decay is linear, the superposition principle lets the total pulp concentration at harvest be summed across all previous applications. Ignoring that accumulation, the study notes, would drastically underestimate residues in older fruit, a well-documented shortcoming of single-application pre-harvest interval models. The resulting sawtooth concentration curves show substantial decay between injections, since the monthly interval spans roughly 2.6 half-lives.

Independent field data lend circumstantial support to the model’s conservatism. Monitoring studies have detected cyproconazole and other triazoles in Brazilian coconut water and pulp at levels below European Union limits, and dissipation studies of the structurally related difenoconazole in date palm fruit report half-lives of just 2.0 to 2.2 days, shorter than the range adopted here. Hotter tropical conditions would likely accelerate degradation further, pushing real residues below modelled values. Still, the author is careful to frame the work as a screening exercise, not a validated predictor: no cyproconazole residue measurements from actual coconut endotherapy trials exist, and factors from cultivar differences to tree health and application precision fall outside the model. Field trials measuring residues across multiple dose levels are identified as the single highest-priority experimental need. Until then, the harvest-safety matrix offers regulators and growers a transparent, probabilistic starting point for a crop that has, until now, had none.

Subject of Research: Probabilistic estimation of pre-harvest intervals for the fungicide cyproconazole in green coconut production using a Level IV fugacity model and Monte Carlo analysis

Article Title: Probabilistic pre-harvest intervals for cyproconazole in green coconut production in Brazil: a Level IV fugacity model with Monte Carlo analysis

Article References: Paraíba, L. C. (2026). Probabilistic pre-harvest intervals for cyproconazole in green coconut production in Brazil: a Level IV fugacity model with Monte Carlo analysis. Environmental Science and Pollution Research, 33(30), 15378-15391. https://doi.org/10.1007/s11356-026-38178-w

Image Credits: AI Generated

DOI: 10.1007/s11356-026-38178-w

Keywords: cyproconazole, green coconut, pre-harvest interval, fugacity model, Monte Carlo simulation, pesticide residues, endotherapy, food safety, triazole fungicides, Brazil, Gompertz growth, sensitivity analysis