Meta-Analysis on Criteria and Forecasting Models for Potato Late Blight Pathosystem: Assessing Robustness and Temporal Consistency

Abstract

Climate change, along with the pathogens adaptive potential, challenges the robustness of criteria, forecasting models, and decision support systems for late blight (Phytophthora infestans) control, the most destructive disease affecting potato crops worldwide. Under PRISMA criteria, this meta-analysis examined the criteria and forecasting models in potato late blight over the last 106 years in 25 countries. The evaluation groups a total of 271 trials in which 59 different models were used. The criteria and the forecasting models were categorized by three generation types (G1 to G3) based on their statistical methodology, and by three mechanism types based on their internal structure (Semi-Mechanistic, SM; Non-Mechanistic, NM; Mechanistic, M). For each one of these groups, the accuracy, fungicide reduction capacity, and temporal consistency were evaluated. The results indicated that Mechanistic models (integrate pathogen biological variables) outperform Non-Mechanistic models (only consider environmental variables). Therefore, the integration of pathogen life cycle dynamics in the context of climate variability is crucial to developing robust forecasting models. This study highlights the limitations of Non-Mechanistic models and underscores the need for forecasting models to be developed under criteria of ecological realism of plant-pathogen interaction and pathogens adaptive potential under climate change scenarios.

1. Introduction

Severe global food insecurity has increased significantly from 122 million people in 2022 to 152 million in 2023 [1]. Approximately 7.1 million people (56% of the total population) were projected to face high levels of acute food insecurity between April and July 2024, including 2.3 million people in “emergency” and 79,000 people in “catastrophe” [2]. Some of the causes of the recent increase in food insecurity are due to the disruption of urbanization in the rural–urban continuum [1], armed conflicts [2], and climate change [1,2,3].

Climate change is considered the most important threat to future agricultural systems [3,4]. Global warming, changes in rainfall patterns, and climate variability could directly and indirectly influence threats to crops worldwide. Many economically important plant pathogens are present worldwide under varying environmental conditions. Alterations in the spatial distribution of pathogens and their host plants, temporal occurrence, incidence, and severity of diseases have been reported in different crops and were demonstrated [3,4,5,6]. Consequently, robust assessments of climate change risk in terms of pathogen adaptive capacities are difficult to predict [7]. Increasing atmospheric CO₂ concentrations will influence pathogenic fungi [3] by affecting their aggressiveness and increasing the reproduction and growth of some of them [8]. Warmer temperatures will also generate stronger winds, which could favor the transport of higher concentrations of spores in the air over long distances [9,10]. With drier environments in southern Europe, more irrigation will be needed, which translates into increased canopy wetness and therefore the development of disease outbreaks [5].

Among the fungal diseases of Solanum tuberosum (L.), late blight, caused by the oomycete Phytophthora infestans (Mont.) de Bary, is considered the most important disease affecting the potato crop, capable of causing total crop loss if not addressed [11,12,13,14]. In the last century, breeding programs focused on introducing resistance genes in potatoes against late blight. These strategies continued from the 1960s to the present; however, it has become evident that even multiple R genes could be rapidly overcome by the pathogen [15,16]. Current research targets the development of cultivars with significant levels of non-race-specific resistance, using biofungicides or models to forecast the appearance of early symptoms or disease behavior throughout the growing season [12,13,14]. However, most potato production in Europe is still concentrated on blight-susceptible varieties [17].

The climatic conditions appropriate to the occurrence of potato late blight are a minimum and maximum temperature, preferably between 7.2 and 26.6 °C, respectively, and a long period of high air humidity (above 75%) and cloudy or foggy weather [18]. P. infestans develops the disease over a wide temperature and humidity range, and it behaves as a polycyclic disease in the field, producing a disease progress curve, which varies with the weather [19] and has secondary cycles that interfere with the rate of development. Traditionally, meteorological information was used to build forecasting models that return disease risk values in the field and provide farmers with warnings for preventive spraying [20,21,22,23,24].

Criteria and forecasting models in the Solanum tuberosum and P. infestans pathosystem were researched for over 106 years [20,25]. Empirical models (climate rules-based) [20,21,22,23,24] and mechanistic models (process-based) [26,27,28,29,30,31] were used to simulate late blight risk. Some of these models were developed to simulate the risk of this disease under climate change scenarios [3,4,31]. Empirical forecasting systems often derive from the early research developed by Löhnis and Everdingen (1926), Beaumont (1947), Grainger (1953), Smith (1956), Wallin (1962), Hyre (1962), and Schrödter and Ullrich (1966) [20,21,22,23,24,32]. Specifically, Krause combined the methods of Wallin and Hyre to develop Blitecast [18]: the first decision support system (DSS) based on the accumulation of late blight risk units considering hourly temperature and humidity conditions. This model was tested in different countries by adjusting weather conditions to local conditions [25,27,28,33,34,35,36,37,38,39,40,41,42,43] and served to develop other empirical forecasting models. Currently, a wide variety of empirical models exist [12,14,25,27,28,29,30,34,35,36,37,38,41,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59], and some of them were improved using algorithms [14,58] and neural networks [59]. In the first mechanistic simulations of potato crop disease risk, varietal resistance as a biological parameter distinct from climatic conditions was included [12,13,14,27,28,29,34,35,38,40,41,42,43,45,47,49,50,53,54,56,60,61]. Some researchers often considered infection risk [57,62] and other disease risk parameters, such as the length of the latent period [57,63]. Other mechanistic models included the successive stages of the infection cycle [26,27,28,29,30,31,32,57,62,63,64,65,66,67,68], such as the SEIR (Susceptible, Exposed, Infectious, and Removed) approach used for BLIGHTSIM [31]. Other models considered spore release, spore survival, and spore airborne transport [12,13,14,55,57]. The most recent studies considered AUDPC (Area Under the Disease Progress Curve) as a measure of disease progress throughout the crop cycle. The AUDPC of the forecasting model and the AUDPC of the control treatment allowed the obtainment of a comparative measure (RAUDPC, Relative Area Under the Disease Progress Curve) of the effectiveness of the forecasting models [12,26,27,37,40,47,49,50,54,62]. These parameters have often been considered in isolation as independent variables to be combined in statistical prediction models. Therefore, the risk of late blight across the full crop cycle was not routinely simulated in previous studies.

Despite multiple studies conducted over the past 106 years related to the control and prediction of potato late blight, there is no quantitative review of scientific publications to identify patterns and/or trends or detailed conclusions that influence the effectiveness. Understanding the population dynamics of crop pests plays a fundamental role in implementing integrated pest management strategies. It is even more important to establish successful strategies against pathogenic diseases over time, especially resilient strategies to the changing climate [28]. Meta-analysis approaches have the power to synthesize dispersed information and offer it in a condensed and reviewed form, can reveal contradictions between individual studies, and improve the precision of estimates by allowing the assessment of the variability in the literature [69]. The objectives of this meta-analysis were to analyze the historical performance of criteria and forecasting models for the Solanum tuberosum-P. infestans pathosystem in terms of their accuracy in the forecast and monitoring of disease, their effectiveness in fungicide reduction, as well as their comparative consistency over time.

2. Materials and Methods

2.1. Study Design and Review Protocol

This research was carried out following the well-established PRISMA guidelines [70], which describe how to collect and analyze data from published studies. The PRISMA statement includes a three-phase flowchart that serves as an invaluable tool to guide researchers in the collection and analysis of data, reviews, and meta-analyses. The three phases of the structured systematic search (Identification, Screening, and Included) are presented below and schematized in Figure 1.

2.1.1. Identification Phase

A structured, systematic search of scientific articles in four databases was conducted: FAO AGRIS, ProQuestT, Scopus, and WoS. In databases, a series of keywords was used to track research conducted with forecasting models, and then another series of searches was conducted to track works that integrated the relationship between the pathosystem, forecasting models, and climate change. The search criteria used, the keywords, and the number of research articles extracted in these first searches in each database are shown in

Table 1. Structured systematic research in each database.

Keywords	Database
	FAO AGRIS	ProQuest a,b	Scopus a,c	WoS a
“solanum AND tuberosum AND phytophthora AND infestans AND predictive AND model”	3	73	3	1
“solanum AND tuberosum AND phytophthora AND infestans AND disease AND forecasting”	51	55	24	9
“solanum AND tuberosum AND phytophthora AND infestans AND decision AND support AND system”	25	198	22	8
“solanum AND tuberosum AND phytophthora AND infestans AND predictive AND model AND climate AND change”	0	42	1	0
“solanum AND tuberosum AND phytophthora AND infestans AND disease AND forecasting AND climate AND change”	0	36	3	1
“solanum AND tuberosum AND phytophthora AND infestans AND decision AND support AND system AND climate AND change”	0	119	1	0
	Total			675

^a: in scientific journals; ^b: only peer-reviewed articles; ^c: article title, abstract, and keywords. The last search was conducted on 17 February 2024.

. During the identification process, no research on the research topic addressed in the databases was found before 1993. However, it was known that there was literature before that year. Therefore, a prospective search for research before 1993 was conducted, resulting in 13 studies that met the search criteria. In addition, from 1993 to 2025, 16 more studies were discovered through cross-references that were not included in the databases. These studies were also included in this research study. Only articles published in scientific journals were considered.

2.1.2. Screening Phase

For the selection of research articles, Mendeley software (Elsevier) was used. Duplications resulting from the presence of the same research in different databases were considered, decreasing the number from 675 investigations to 238.

In the screening phase, three exclusion criteria (E. C.) were established for the eligibility of the research. For the first exclusion criterion (E. C. 1), only articles with quantitative research were considered. For the second exclusion criterion (E. C. 2), those investigations that did not focus on forecasting models in agrosystems and those that focused on forecasting models for other pathosystems different from Solanum tuberosum-P. infestans pathosystem were discarded. With the third exclusion criterion (E. C. 3), only those studies that obtained concrete numerical values of accuracy or fungicide reduction for their criteria or forecasting models were selected, and those studies whose data were already integrated in previous studies were discarded. These exclusion criteria and the total number of investigations are shown in the last part of Screening in Figure 1.

2.1.3. Included Phase

At the end of the included phase of the systematic review, 28 investigations were extracted. These investigations were added to the 13 and 16 (n = 29) obtained from the prospective search and cross-reference review, respectively. Finally, 57 studies for metric extraction were selected. The PRISMA flowchart was used to describe the complete procedure for obtaining the research subjects (Figure 1).

2.2. Classification and Structuring of Data

The selected articles (n = 57) were read and processed to extract specific accuracy and fungicide reduction data. Most studies tested different criteria or forecasting models, and it was necessary to structure the database on the specific model being tested. This classification also considered the year of publication of research, the author, the geographical area (country, region, and bioregion), the time of research (initial year and final year), the potato variety tested, the type of varietal resistance, the type of crop development, and the degree of incidence of P. infestans throughout the potato cycle when it was possible. Specific data on accuracy and fungicide reduction were extracted and included for meta-analysis, considering the described classification. In case of accuracy, some authors presented the data extracted from criteria or forecasting models directly [14,18,20,30,32,42,46,48,51,52,57,58,59,60,72,73,74,75,76]. For other researchers, the accuracy was calculated using the provided data; in some cases, it was calculated from data provided in data tables published [24,31,38,41,53,56,61,77]. For other investigations, the accuracy was calculated from the AUDPC (Area Under the Disease Progress) value, first transformed into RAUDPC (Relative Area Under the Disease Progress) following the methodology described by [27,43,78]. The following equation was then applied to obtain the percentage reduction in cumulative disease with the prognostic model compared to the control:

$$DSS Effectiveness \left(RAUDPC\right)=100-RAUDPC$$

This calculation of effectiveness allows obtaining a representative value that represents the effectiveness of the criteria or forecasting models used previously [12,26,27,29,35,37,40,47,50,54,62,66]. Lastly, some studies that tested the first criterion or empirical models based on environmental rules [13,28] counted the correct forecast days of the total number of days of the crop cycle to define forecast skill.

In the case of fungicide reduction, some data were published directly [32,40,61,73,79], and others [12,25,27,28,29,30,33,34,35,36,37,39,43,44,45,47,49,50,54,62,63,65,66,68], according to the following equation, were calculated:

$$\% Fungicide reduction= {\displaystyle \frac{Routine treatment-Predictive Model treatment}{Routine tratment}} \times 100$$

In trials where treatment with forecasting models was superior to routine treatment, a value of 0% was awarded for fungicide reduction. For accuracy, given the way it is calculated according to the literature, we did not find values that needed winzorization.

Finally, two additional categories were added to the previous classification: Generation and Mechanism. This classification allowed the metrics to be grouped for subsequent calculations. Generation was classified from G1 to G3 based on the methodologies used in the forecasting models. The first generation (G1) describes the first investigations in which basic arithmetic or empirical rules based on environmental data were used to generate forecasts, for example, the Dutch rules [20] or the Beaumont periods [21]. The second generation (G2) is based on the year of publication of the Negative Prognosis model [32], which, in addition to changing the approach of the first generation, used complex mathematical and statistical models to predict disease behavior. Furthermore, G2 included the models with a high degree of computerization that also integrate farmer decisions into their predictive criteria. The third generation (G3) began with the publication in 2007 of Baker and Kirk [52], where neural networks were used for forecasting models. G3 also included research with methodologies based on complex algorithms and artificial intelligence models for making forecasts. It is important to note that generational classification does not exclude recent studies that have based their tests on models or predictive criteria from previous decades. Therefore, it is common to find research published in recent years that is classified within previous generations because they use methodological approaches and predictive criteria belonging to those generations.

Mechanism classification refers to the types of variables that predictive models combine for their forecasts. For the mechanism, the previous classification established by Narouei-Khandan et al. [31] was considered. Also, considering the diversity of variables found in the literature, the Semi-Mechanistic (SM) category was included. In this way, Non-Mechanistic models (NM) only used climatological variables for prediction; Semi-Mechanistic studies (SM) integrated varietal resistance into the forecast; and Mechanistic criteria (M) integrated the climatological variables, biological variables of the host, and biological variables of the pathogen itself. The classification based on Generation and Mechanism is included in

Table 2. Classification of selected forecasting models by Generation and Mechanism class.

Number	Reference	Model or Criteria Used for Prognosis	Generation Class	Mechanism Class
1	[20,38,46,63,76]	Dutch rules	G1	NM
2	[21,38,46,72,77]	Beaumont periods	G1	NM
3	[13,23,28,38,58]	Smith period	G1	NM
4	[24,38]	Hyre’s model	G1	NM
5	[24]	Cook’s moving graphs	G1	NM
6	[13,24,38]	Wallin	G1	NM
7	[32]	Negative Prognose	G2	NM
8	[25,27,28,33,34,35,36,37,38,39,40,41,42,43]	Blitecast	G2	NM
9	[73]	BWI index	G2	NM
10	[26]	Computational Simulation	G2	M
11	[45]	PHYTEB (SIMPHYT I and II)	G2	NM
12	[40]	Blitecast Computational	G2	SM
13	[27]	Blitecast-Modified	G2	M
14	[27]	Tom-Cast	G2	NM
15	[27]	Sim-Cast	G2	SM
16	[46]	Bhattacharya method	G2	NM
17	[46]	Cumulative blight severity value	G1	NM
18	[46]	Jhulsacast	G2	NM
19	[34]	PhytoPRE	G2	SM
20	[47]	Dutch rules ME	G1	SM
21	[47]	NegFry	G2	SM
22	[60]	Naumova Mod	G2	NM
23	[43]	Sim-Cast Mod	G2	SM
24	[43]	Rainfall Thresholds	G1	NM
25	[49]	Førsund rules	G2	NM
26	[49]	NEGFRY-P	G2	SM
27	[49]	NEGFørsund rules	G2	SM
28	[28]	Sparks	G2	M
29	[29]	ProPhy	G2	M
30	[29]	Plant-Plus	G2	M
31	[30]	Bio-PhytoPRE	G2	M
32	[51]	Binary model	G1	NM
33	[52]	Determinacy analysis	G2	NM
34	[52]	Logistic regression	G2	NM
35	[52]	Discriminant analysis	G2	NM
36	[52,59]	Neural network	G3	NM
37	[53]	SIMBLIGHT1	G2	SM
38	[38]	Winstel	G1	NM
39	[41]	SIMPHYT I	G2	NM
40	[41]	SIMPHYT I (US)	G2	SM
41	[41]	Noblight	G2	NM
42	[56]	NWN07	G3	NM
43	[56]	THOM	G3	NM
44	[61]	VNIIFBlight	G2	SM
45	[62]	BlightPro	G3	M
46	[79]	Linear regression	G2	NM
47	[79]	Pace regression	G2	NM
48	[79]	BLITE-SVR	G2	NM
49	[74]	INDO-BLIGHTCAST	G2	NM
50	[68]	IPM 2.0	G3	M
51	[42]	Index	G2	NM
52	[31]	BLIGHTSIM	G3	M
53	[63]	Blight Management	G2	M
54	[63]	Dutch rules (MIR)	G2	M
55	[57]	Nærstad	G2	M
56	[57]	HOSPO90	G1	NM
57	[58]	Hutton Criteria	G1	NM
58	[58]	Algorithm	G3	NM
59	[14]	ML Algorithms	G3	NM

G1: first generation of forecasting models; G2: second generation of forecasting models; G3: third generation of forecasting models; NM: Non-Mechanistic models; SM: Semi-Mechanistic models; M: mechanistic models. Model name ordered based on appearance in the literature. Note: The specific name given by the authors to the criteria or forecasting models used was respected.

.

2.3. Bibliometric Analysis

The bibliometric analysis was performed using R Studio software version 4.4.2 [80]. A suite of packages was employed for data management, visualization, and statistical testing. These included readxl version 1.4.5 and writexl version 1.5.1 for Excel file handling [81,82]; dplyr version 1.1.4 and tidyr version 1.3.1 for data cleaning and transformation [83,84]; ggplot2 version 3.5.2 and patchwork version 1.3.0 for visualization [85,86]; and sf version 1.0.19, rnaturalearth version 1.0.1, and rnaturalearthdata version 1.0.0 for spatial representation of model locations [87,88,89].

Publication bias was assessed using both visual inspection of funnel plots and formal statistical tests. Egger’s regression test was applied to evaluate funnel plot asymmetry [90]. In addition, Duval and Tweedie’s trim-and-fill method [91] was used to estimate the number and potential influence of missing studies on the pooled effect size. This approach identifies asymmetry in the distribution of effect sizes and imputes hypothetical “missing” studies to produce an adjusted estimate that accounts for possible publication bias. Because several studies did not report sample sizes or standard errors, the within-study variance (vᵢ) was approximated as inversely proportional to study duration (time_years), following the assumption that longer monitoring periods provide more stable estimates. These analyses were performed using the metafor package version 4.8.0 [92] in RStudio software version 4.4.2 [80].

Furthermore, to assess the robustness of the pooled estimates, influence diagnostics and leave-one-out sensitivity analyses were performed for the precision and fungicide reduction outcomes. At each iteration, one study was sequentially removed, and the model was re-estimated to assess changes in the pooled effect size (Δb) and inter-study variance (Δτ²). This procedure allowed us to identify potentially influential studies and assess their impact on the overall results. Analyses were performed using the R package metafor version 4.8.0 [92]. The results of the leave-one-out sensitivity analysis have been included in the Supplementary Material, Table S1.

In terms of descriptive statistical analysis, model metrics (accuracy and fungicide reduction) were compared by generation (G1, G2, G3) and mechanism (NM, SM, M). Bonferroni-adjusted pairwise comparisons to assess significant differences between groups. For consistency of the accuracy and fungicide reduction metrics for each model over time, the mean was calculated for each model that had at least 3 numerical data points, and the data points were compared with respect to this mean and the standard deviation of the data.

A random-effects meta-analysis was conducted to estimate the overall mean effect for both outcomes (accuracy and fungicide reduction). The random-effects model assumes that the true effects vary across studies due to real differences in experimental conditions and model characteristics rather than sampling error alone [69].

Finally, a multilevel meta-regression was performed. We compared several random effects structures (with dependence between all variables, with the independent variables, and a hybrid structure that generated a cluster: Study × Model × Mechanism/EffectID). We adopted the hybrid structure as our primary objective because it (i) captures dependence within and between studies within a study, and (ii) enables robust variance estimation inference with a greater number of effective clusters. The models were fitted using REML (metafor:rma), with fixed moderators: generation, bioclimatic region, study duration, and resistance (standardized). To avoid confusion between the fixed effect and the dependence structure, only the mechanism was included in the cluster. Because many studies did not report standard errors, we used proxy variances scaled by the duration of the study.

All visualizations were created in high resolution for publication, and all data cleaning steps and code used in the analysis are available upon request for replication and transparency purposes.

3. Results

3.1. Overview of Research

This section presents a general overview of the research articles included in this meta-analysis, focusing on their temporal and geographical distribution, as well as the most frequently tested models. The systematic review covers 106 years of research in forecasting models of the Solanum tuberosum-P. infestans pathosystem, in which 57 articles were reviewed. Considering all 57 articles, 271 trials were analyzed since 1926. G1 and G3 included fewer trials, with 48 and 85, respectively, while G2 included 138 trials. In the same article, we find trials with models belonging to several generations, normally with contemporaneous and past generations, because the criteria or the forecasting models have been adapted over time to the meteorological conditions of the geographical area. Figure 2 provides an overview of the research reviewed, considering the generation type and total number of trials extracted from the research.

As shown in Figure 2, from 1926 to 1966, for a period of 40 years, models based only on empirical calculations (climate rules-based) (G1) were tested, with the trend changing in 1966 when the first models based on Negative Prognose and complex statistics began to be developed [32]. This second generation (G2) rapidly surpassed those of the first generation and was implemented to a greater extent in the following decades. As can be seen from the slope of the blue line, from 1966 to 2007, with 41 years of development of criteria and forecasting models, the number of tests carried out practically tripled with respect to the first generation. In 2007, complex algorithms and artificial intelligence were introduced in the implementation of predictive models (G3) [59]. In just 16 years, the number of tests with third-generation models was already more than half that of the previous generation, consolidating models based on artificial intelligence and complex algorithms as a trend and an opportunity to improve the performance of forecasting models.

The selected articles were conducted in 25 different countries. Figure 3 illustrates the countries involved, along with the total time each country spent conducting its trials. The countries with the highest number of research studies with model adjustment for the prediction of potato late blight were the United States of America, India, the United Kingdom, and Ireland (with more than 30 trials).

The most tested models by country are shown in

Table 3. Summary of the criteria and forecasting models by country reported in the literature.

Country	Model or Criteria
Algeria	Neural network
Brazil	Blitecast, ProPhy, Sim-Cast, NegFry, Wallin
Canada	BWI, VNIIFBlight
China	Binary model
Cuba	Naumova Mod, Rain Threshold
Czechia	NegFry, Noblight, Index
Ecuador	BLIGHTSIM, Rainfall Thresholds
Germany	Negative Prognose, PHYTEB (SIMPHYT I and II), SIMBLIGHT1
India	Beaumont periods, Bhattacharya method, Blitecast, Cook’s moving graphs, Cumulative blight severity value, Dutch rules, Førsund rules, Hyre’s model, INDO-BLIGHTCAST, Jhulsacast, Negative Prognose, NegFry, Sim-Cast, Smith period, Wallin, Winstel
Ireland	Blight Management, Dutch rules, Dutch rules ME, Dutch rules (MIR), IPM 2.0, NegFry, PHYTEB (SIMPHYT I and II), Plant-Plus, ProPhy
Japan	Blitecast, PhytoPRE, Sim-Cast
Lithuania	VNIIFBlight
Mexico	Blitecast, Blitecast-Modified, Sim-Cast, Sim-Cast Mod, Tom-Cast
Netherlands	Dutch rules, IPM 2.0, Sim-Cast, VNIIFBlight
Norway	Førsund rules, HOSPO90, Nærstad, NEGFørsund rules, NegFry-P
Peru	Rainfall Thresholds
Poland	NegFry, VNIIFBlight
Russia	VNIIFBlight
Slovakia	Index, NegFry, Noblight
South Korea	Blitecast, BLITE-SVR, Cook’s moving graphs, Linear regression, Pace regression
Spain	ML Algorithms, Negative Prognose, NegFry, Smith period, Wallin, Winstel
Switzerland	Bio-PhytoPRE
Ukraine	VNIIFBlight
United Kingdom	Algorithm, Beaumont periods, Blitecast, Dutch rules, Hutton Criteria, Negative Prognose, Negfry, Smith period, Sparks
USA	Binary model, Blitecast, BlightPro, Computational Blitecast, Computational Simulation, Cook’s moving graphs, Determinacy analysis, Discriminant analysis, Hyre’s model, Logistic regression, Neural network, Noblight, NWN07, SIMBLIGHT1, SIMPHYT I, SIMPHYT I (US), THOM, Wallin

. The United States of America (18), India (16), the United Kingdom (9), and Ireland (9) tested the most different types of criteria and forecasting models. In the rest of the countries, between 1 and 6 models were found. The most tested were Blitecast, in 10 countries (Brazil, India, Ireland, Japan, Mexico, Netherlands, South Korea, Spain, United Kingdom, and United States of America); NegFry, in 10 countries (Brazil, Czechia, India, Ireland, Mexico, Norway, Poland, Slovakia, Spain, and United Kingdom); and Wallin criteria in 6 countries (Brazil, India, Spain, United Kingdom, USA, and Mexico).

Throughout the meta-analysis, an evolution in the complexity of potato late blight criteria or forecasting models was revealed. Initially, NM (Non-Mechanistic models) were used. However, in recent decades, models were adapted to regional conditions, and in some cases, they integrate various technologies, computational testing, and even combine several previously established models. Fundamental models such as the Smith period [13,23,28,38,58] and Wallin [13,24,38] established the empirical foundation for early climate rules-based systems. These formulations were integrated into the Blitecast model [18], developed in the USA in the 1970s, which standardizes the use of temperature and humidity thresholds to anticipate P. infestans outbreaks. Blitecast served as the basis for the construction of derivative models, such as Blitecast-Modified [27], Blitecast Computational [40], and Sim-Cast [27], tested in a wide variety of countries (Table 3). More recent variants, but also derivatives of Blitecast, such as Sim-Cast Mod [43], Tom-Cast [27], and BLITE-SVR [79], introduced mathematical improvements or integrated machine-learning methods, such as support vector regression. At the same time, the NegFry model emerged from the fusion of the German Negative Prognosis and blight units developed by Fry et al. 1983 [47], improving its predictive capacity by incorporating biological risk factors such as inoculum pressure and variety resistance. NegFry’s influence expanded widely, giving rise to modified systems such as NegFry-P or NEGFørsund rules [49]. Its structure also shaped hybrid systems such as Bio-PhytoPRE [30] and PhytoPRE [34], which combine classical decision rules with biological monitoring and risk modeling.

Other criteria followed similar refinement trajectories. For example, the Hutton Criteria are a reinterpretation of traditional Smith periods, shifting from daily to hourly weather data [58], and the PHYTEB system in Germany evolved into SIMPHYT I and II and subsequently SIMBLIGHT1, reflecting progressive modular integration and constant regional recalibration [41,45,53]. Similarly, the Cook’s Moving Graph approach inspired models such as the Bhattacharya method in India [46] and provided logic to other Non-Mechanistic models (NM) that are used in other countries (Table 3).

Models such as VNIIFBlight (Russia), Naumova Mod (Cuba), and INDO-BLIGHTCAST (India) [60,61,74] also showed a differentiation based on regional rules for potato late blight forecasting. Furthermore, integrative DSSs such as Plant-Plus [29], IPM 2.0 [68], and more recent machine learning (ML)-based algorithms [14] are examples of a trend toward hybridization, combining Non-Mechanistic criteria (NM), climatological models, and artificial intelligence. This evolution reveals the dynamic interplay between model inheritance, environmental adaptation, and methodological innovation in the design of decision support systems for potato late blight management.

3.2. Bibliometric Results

Egger’s regression test showed no significant evidence of publication bias (accuracy: p = 0.26; fungicide reduction: p = 0.23). However, Duval and Tweedie’s Trim and Fill method suggested the potential absence of 13 studies on the left side of the funnel for accuracy and 6 for fungicide reduction. After imputing these hypothetical studies, the pooled estimate for accuracy became slightly lower and reached statistical significance (estimate = −6.82, p = 0.042), while the effect for fungicide reduction remained non-significant (estimate = −3.76, p = 0.17).

Visual inspection of the funnel plots (Figure 4) revealed a moderate asymmetry for accuracy, with a relative scarcity of studies reporting low or negative outcomes and larger standard errors on the left side of the funnel, consistent with mild publication bias or selective reporting. In contrast, the distribution for fungicide reduction appeared more symmetrical, indicating a more balanced representation of study results across the precision range. Egger’s regression test components are available in Table S2.

Overall, these findings suggest that the published literature may slightly overestimate model accuracy—reflecting potential over-optimism in reporting—but the evidence for bias in fungicide-reduction outcomes remains weak.

3.2.1. Data Distribution of Accuracy and Fungicide Reduction of Forecasting Models

The performance of the criteria and models extracted from the meta-analysis was analyzed in terms of accuracy and fungicide reduction. Figure 5 shows the box plot with the complete distribution of the accuracy and fungicide reduction global data. In addition to examining the variability in the reported values for each parameter, this analysis allowed for evaluating the consistency as a potential key parameter for decision-making. The overall mean accuracy effect was 68.75%, indicating relatively high overall forecast performance of the forecasting models. The standard deviation (29.21%) also indicated a wide dispersion of accuracy values, with lower accuracies below 50%, suggesting poor performance from some forecasting models. accuracies above 80% indicate that some forecasting models have achieved high forecast efficiency. For fungicide reduction, the overall mean was 39.22%, indicating that practically only one in four fungicide sprays was reduced. The standard deviation (24.47%) was also high, suggesting that some forecasting models had even worse fungicide reduction effects. However, others exceeded 50% in fungicide reduction, suggesting an important improvement. This indicates that some criteria and forecasting models have achieved better forecast efficiency, and in this sense, there is still a very wide window of opportunity to achieve significant values in the accuracy or fungicide reduction of forecasting models and therefore improve the prognosis of the dynamics of the disease and the sustainability of the potato crop.

3.2.2. Accuracy of Criteria and Models According to Generation and Mechanism Classification

To unify the criteria and improve the presentation/understanding of results, forecasting models by three generations and three mechanisms were categorized. This comparative analysis examined whether methodological or structural advances lead to greater forecast accuracy. The results showed an increase in accuracy, both with the progress of generation and with the complexity of the mechanisms (Figure 6). The average accuracy according to generation type was 48.90%, 71.91%, and 81.46% for G1, G2, and G3, respectively. The average accuracy according to the mechanism was 63.48%, 77.90%, and 82.10% for Non-Mechanistic (NM), Semi-Mechanistic (SM), and Mechanistic (M), respectively.

The results of the Bonferroni test showed significant differences between first generation (G1) and second generation (G2), and between first generation (G1) and third generation (G3) for the accuracy data. The same for the mechanism. We observed significant differences between Non-Mechanistic (NM) models and Semi-Mechanistic (SM) and between Non-Mechanistic (NM) models and Mechanistic (M) with the accuracy metric. Significant differences between G2 and G3 and between the SM and M mechanisms were not detected (Figure 6). p-values for pairwise comparisons are available in Table S3.

3.2.3. Fungicide Reduction of Models According to Generation and Mechanism Classification

This section shows the influence of forecasting model generation and of mechanism complexity on fungicide reduction. These findings are important for understanding how forecasting tools contribute to sustainable agriculture. The percentage of fungicide reduction shows a different pattern (Figure 7) compared to accuracy data. From the first generation to the last generation, there was an increase in fungicide reduction. However, in G2, it decreased compared to G1. Furthermore, the increase in predictive variables in the forecasting models suggested a slight increase in fungicide reduction. The average fungicide reduction, according to generation, was 42.54%, 32.90%, and 50.36% for G1, G2, and G3, respectively. The average fungicide reduction, according to the mechanism, was 35.27%, 39.93%, and 41.95% for NM, SM, and M, respectively.

The significant differences for fungicide reduction by generation and mechanism type were performed using the Bonferroni test. Regarding the mechanism, no significant differences between the three groups were found, although a slight increase in fungicide reduction was observed with increasing complexity of the predictive models. However, for generations, the results of the Bonferroni test indicated significant differences between the second generation (G2) and third generation (G3) with respect to the fungicide reduction metric (p-value <0.001). p-values for pairwise comparisons are available in Table S4.

3.2.4. Meta-Analytical Results

The random-effects model included 57 effect sizes for both accuracy and fungicide reduction outcomes. A high degree of heterogeneity was detected (I² = 84.7% and 82.4%, respectively; Q test, p < 0.0001), confirming that true differences among studies were substantial. The pooled mean effect was non-significant for both accuracy (estimate = −1.32; p = 0.73; 95% CI [−8.72, 6.09]) and fungicide reduction (estimate = −0.45; p = 0.87; 95% CI [−5.76, 4.86]), indicating that no overall direction of effect can be inferred when aggregating across all models. The other components of the random effects method were included in Table S5. This high heterogeneity highlights the need to explore moderators such as the generation of the model, the mechanism, the bioregion, the crop resistance traits, and other ecological variables of the pathosystem.

The multilevel meta-regression showed that between-study heterogeneity was moderate to high for both outcomes (accuracy and fungicide reduction), but with distinct variance structures. For model accuracy, heterogeneity was mainly attributed to the higher-level clustering (study × model × mechanism), which explained most of the total variance (I² total = 55%; I² cluster = 49%; I² effect = 6%) (Figure S1). In contrast, fungicide reduction outcomes exhibited lower overall heterogeneity (I² total = 34%) and a more balanced variance distribution between cluster (19%) and within-cluster (15%) levels.

This pattern indicates that predictive accuracy varies primarily across studies and model configurations, while fungicide-reduction results are influenced by both contextual and intra-study factors, reflecting a more complex interplay of experimental design and local conditions. These findings support the use of a hybrid random-effects structure to appropriately capture the nested dependence in the dataset and highlight the need for recalibration efforts that account for model- and context-specific sources of heterogeneity.

The distribution of residual heterogeneity across hierarchical levels was assessed. Variance partitioning was performed using the estimated variance components (σ²) from hybrid meta-regression models (study × model × mechanism as cluster). The results indicated a clear contrast between accuracy and fungicide reduction outcomes.

3.3. Analysis of the Consistency of Criteria and Forecasting Models over Time

The performance of the most frequently tested models was evaluated over time. Some models (n = 26) were tested less than three times or in fewer geographic regions; therefore, their consistency could not be studied. However, 33 criteria or forecasting models (grouped in 25 general categories) present 3 or more trials over time. Concretely, the criteria or model was Algorithm, Beaumont periods, Binary model, BlightPro, Blitecast (including Blitecast Computational, Blitecast-Modified, and Noblight), Cook’s moving graphs, Dutch rules (including Dutch rules (MIR) and Dutch rules ME), Førsund rules, HOSPO90, Hyre’s model, Jhulsacast (including INDO-BLIGHTCAST), IPM 2.0, Nærstad, Negative Prognose, NegFry (including NegFry-P), Neural network, PHYTEB (SIMPHYT I and II), PhytoPRE, ProPhy, Rainfall Thresholds, SIMBLIGHT1, Sim-Cast (including Sim-Cast Mod), Smith period, VNIIFBlight, and Wallin.

These models were analyzed in greater detail in Figure 8 and Figure 9 with respect to the comparative accuracy and fungicide reduction historical performance. The results showed that the highest concentration of research was found since 1966, with the expansion of the forecasting models of the second generation (G2). The historical criteria, like the Beaumont period, the Smith period, or the Wallin period, were used in previous decades, and they continue to be used, but less so. Other models like NegFry, PHYTEB, and ProPhy had varying consistency over the first decades, with higher presence in recent research, although without improving their performance a lot.

In the accuracy consistency assessment (Figure 8), a general pattern was observed in which more recently developed criteria or predictive models (with a broader time range) tend to have higher mean accuracy values. Categorization by mechanism provides additional information: Mechanistic Models (M), which integrate environmental variables along with biological parameters of the pathogen and cultivar, account for most of the highest accuracy values, mainly located at the top of the graph. Examples such as BlightPro, PHYTEB (SIMPHYT I and II), and Rainfall Thresholds exceed 85% mean accuracy, with low variability between trials, indicating robust and consistent performance in recent contexts.

Semi-Mechanistic criteria or models (SM), which combine environmental variables with cultivar characteristics, showed more heterogeneous behavior. Some, such as SIMBLIGHT1 or Binary Model, achieve accuracy comparable to Mechanistic models (>75%), while others, such as Blitecast, showed high dispersion and moderate mean accuracy.

Non-Mechanistic (NM) models, based exclusively on environmental variables, tend to be associated with older periods and lower accuracies (<65%), although there are notable exceptions such as ProPhy, which achieves high values. Intra-model variability was especially significant in NegFry and Blitecast, highlighting their dependence on constant recalibration and the agroclimatic context.

In the fungicide reduction consistency assessment (Figure 9), there was no direct relationship between the mechanism and the magnitude of reduction. Dutch rules (SM/M and G3) stand out with the highest mean reduction (>70%) and low dispersion, demonstrating that a historical model with important recalibrations (Dutch rules ME and Dutch rules -MIR-) can be highly effective in reducing applications in certain contexts. Among the Mechanistic models (M), IPM 2.0 and PHYTEB (SIMPHYT I and II) showed mean reductions of 40–60%, although with wide variability between the studies. Semi-Mechanistic models (SM) showed the most diverse range: VNIIFBlight reaches values >50%, while Blitecast and Førsund rules fluctuate between almost zero reductions and >70% depending on the application environment. Some high-precision Mechanistic (M) and Semi-Mechanistic models (SM), such as BlightPro and ProPhy, had low reductions (<30%), indicating a conservative approach, primarily focused on disease control rather than on optimizing fungicide use. Note that no comparative data are shown for Group G1. This does not imply an absence of studies within this group, but rather that, for Figure 9, only models reporting three or more specific data points on fungicide reduction were included (as explained in the Methodology section). Consequently, some G1 models seem not to have reached that threshold of three.

4. Discussion

In this meta-analysis, spanning more than 100 years, 59 criteria or forecasting models were obtained, classified according to their statistical methodology (generation) and their internal structure for predicting disease behavior (Table 2). The models described in the bibliometric assessment were tested under the meteorological conditions of 25 countries, over different time periods, resulting in 271 research trials. Not all trials reported specific accuracy and/or fungicide reduction values, and in some studies. This was particularly noticeable in the early literature. These were more focused on controlling the disease than reducing inputs, a goal that has become more recent in line with the sustainability demands of government and nongovernment institutions [93,94].

In contrast, these values were impossible to calculate following the established methodology due to the poor information reported. This resulted in large variability in sample sizes for the established categories (Figure 6 and Figure 7). Nevertheless, the reported trials provide significant analytical value, as each published accuracy and fungicide reduction value required several years of research, providing a broad statistical view of the current situation.

In some cases, several forecasting models were tested (such as in the USA, India, the United Kingdom, and Ireland), while in others, only one was tested (Table 3). The fact that a specific criterion or forecasting model has different trials in different geographical areas over the last years allowed for an analysis of the consistency over time. These forecasting models or criteria were Algorithm, Beaumont periods, Binary model, BlightPro, Blitecast (including Blitecast Computational, Blitecast-Modified, and Noblight), Cook’s moving graphs, Dutch rules (including Dutch rules (MIR) and Dutch rules ME), Førsund rules, HOSPO90, Hyre’s model, Jhulsacast (including INDO-BLIGHTCAST), IPM 2.0, Nærstad, Negative Prognose, NegFry (including NegFry-P), Neural network, PHYTEB (SIMPHYT I and II), PhytoPRE, ProPhy, Rainfall Thresholds, SIMBLIGHT1, Sim-Cast (including Sim-Cast Mod), Smith period, VNIIFBlight, and Wallin. It is important to highlight that some models categorized as distinct are evolutions or adaptations of preexisting frameworks, as detailed above for the construction of Figure 8 and Figure 9. These hybrid or derivative models often combine features from multiple approaches or are computational reinterpretations of field-tested models. Greater transparency and traceability in the construction of predictive tools must be part of their implementation to ensure success in disease control and sustainability goals.

The results of this meta-analysis provided evidence that predictive models of P. infestans vary significantly in their accuracy and ability to reduce fungicide use depending on their underlying structure. Mechanistic models incorporating biological variables from the pathogen’s life cycle tended to outperform Non-Mechanistic models in means accuracy and mean fungicide reduction, although it is important to recognize their limitations.

The consistency analysis for accuracy and fungicide reduction presented in Figure 8 and Figure 9 showed that accuracy increases in more recent models with a higher level of integration of variables, especially those related to the pathogen’s biology. An example of this is the case of Dutch rules [20,38,46,47,63,76]: A model that was initially Non-Mechanistic (NM) but recalibrated with biological details (SM/M) resulted in the greatest observed reduction, demonstrating that optimizing input management could also depend on these recalibrations and transformations.

Semi-Mechanistic (SM) models presented intermediate and highly context-dependent results, indicating that their practical effectiveness can vary significantly depending on calibration and local conditions. The variability observed in various models within each generation and mechanism confirms that final performance is influenced by factors such as climate, inoculum pressure, and agronomic practices, directly impacting the model’s conceptual architecture.

In terms of practical application, this suggests that the choice of model should consider both its predictive robustness and its expected impact on fungicide reduction, always prioritizing prior local validation. Furthermore, it opens the door to exploring hybrid models that combine high precision in disease control with efficiency in fungicide reduction.

Few models simulated the entire disease cycle, from spore release to host colonization. Only Narouei-Khandan et al. [31] and Hjelkrem et al. [57] proposed similar methodologies that approach the development of the phenophases of P. infestans throughout the crop. The BLIGHTSIM model of Narouei-Khandan et al. [31] takes susceptible (S), latent (L), infectious (I), and removed (R) stages in a compartmental model with hourly temperature and relative humidity as driving variables. The Nærstad model of Hjelkrem et al. [57] includes the structure of the underlying processes in the disease development, including spore production, spore release, spore survival, and infection of P. infestans. This reveals a crucial opportunity for improvement. Considering the biological cycle of the pathogen throughout the entire crop cycle in forecasting tools could increase their ecological realism and help farmers better respond to the risks of P. infestans and other emerging diseases.

In line with these mechanistic adaptations is research with aerobiological monitoring [9,12,13,55], which includes the dynamics of spores related to climatic variables throughout the crop cycle. Therefore, these studies represent an important advance in the integration of the biological variables of the pathogen. Furthermore, Meno et al. [14] used third-generation (G3) models with complex algorithms and artificial intelligence that achieved notable advances in the accuracy of the models and in the fungicide reduction in Northwest Spain.

In contrast, Non-Mechanistic models (NM), although historically fundamental and easier to implement, showed more variable performance over time. Blitecast (one of the most widely used forecasting models) demonstrated high efficacy in early evaluations [18], but required local calibration for different climatic conditions [25,27,28,33,34,35,36,37,38,39,40,41,42,43]. Our results reveal that fungicide applications are less optimized, and model accuracy often decreases if initial calibration is not performed.

Climate change complicates the robustness of forecasting models, as consistently pointed out in the literature [3,4,31,95,96]. Climate-driven changes in pathogen behavior, such as earlier emergence, increased severity, or changes in spore survival, cannot be integrated into Non-Mechanistic (NM) models. The predictive criteria developed to date have not incorporated the adaptability of pathogens or their life cycle plasticity. This is very limiting for the transferability of the results across locations and time, as some authors have pointed out [95,96]. The meta-analysis suggests that models that incorporate varietal resistance and their interaction with climatic conditions offer additional predictive power (Figure 6 and Figure 7). Semi-Mechanistic models incorporating resistance levels of potato cultivars better showed disease monitoring in fluctuating environments, especially with AUDPC or RAUDPC [47,53,61]. This factor is considered one of the most relevant strengths in the application of models in climate change scenarios [50]. Host–pathogen interactions can become more dynamic, and the variability in final potato production directly depends on the host response to the pathogen [97]. In this sense, BLIGHTSIM demonstrated better adaptation to changing environmental conditions because it developed a Mechanistic model with an hourly time step to simulate late blight under fluctuating environmental conditions [31].

Future environmental variability offers opportunities for pathogen adaptation [96]. In the potato crop, P. infestans, and Alternaria spp. (Cooke) Wint., Ralstonia solanacearum Smith, among others, stand out as the most frequent. Overall, the results of this study support a transition from basic climate rules to biology-based forecasting systems that can explain the change in pathogen adaptive potential in response to climate change. Recalibration alone may not be sufficient in the long term if models do not incorporate the adaptive mechanisms of both the pathogen and its host. As weather patterns change and pathogens evolve, robust forecasting must be based on an understanding of the ecological dynamics of pathogens. This represents not only a scientific challenge but also a strategic opportunity to align disease prognostication with the principles of agroecological resilience and precision agriculture.

In recent decades, studies on pathogen genetics have increased, particularly due to the knowledge of the development of new pathogen reproductive strategies [97] as well as the increase in the aggressiveness of some strains [98]. Genetics has proven to be a powerful tool for building knowledge about the behavior of different crop diseases [27,33,67,68,99]. Current genomic techniques present a window of opportunity to focus research on the integration of pathogen life cycles into forecasting models. Integrating pathogen life cycles, varietal resistance, and climatic variability into forecasting models represents a critical step towards forecasting systems that remain robust under ongoing global change.

5. Conclusions

This meta-analysis showed the historical evolution and limitations of some forecasting models applied/adapted in different geographical areas for potato late blight. Although accuracy improved with more advanced generations (G2 and G3) and mechanistic approaches, this progress did not result in a decrease in fungicide use. Furthermore, the decline in performance of some models over time (Wallin, Smith period, Blitecast, Sim-Cast) revealed an urgent need for systematic recalibration, especially in scenarios of high climate variability.

These findings suggest that future criteria and forecasting models must go beyond climatological rules. Incorporating dynamic biological variables, both host and pathogen, is key to successful potato late blight prediction. Models that simulate the biological aspects of the pathogen life cycle and account for varietal resistance and inoculum pressure show greater promise in adapting to climate change scenarios. Therefore, the transition toward integrative, ecologically grounded models represents not only a technical challenge, but there is also a strategic need to ensure more resilient, sustainable, and precise plant disease management.