# Generic crop rotation pattern-matching algorithm revealed dominant rotational systems for France

Ugo Javourez, Baptiste Girault, Philippe Martin, Marie-Sophie Dedieu, Olivier Therond

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## To cite this version:

Ugo Javourez, Baptiste Girault, Philippe Martin, Marie-Sophie Dedieu, Olivier Therond. Generic crop rotation pattern-matching algorithm revealed dominant rotational systems for France. 2025. [hal-05242682](https://hal.science/hal-05242682v1)

HAL Id: hal-05242682

https://hal.science/hal-05242682v1

Preprint submitted on 5 Sep 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Generic crop rotation pattern-matching algorithm revealed dominant rotational systems for France

Javourez Ugo<fnref n="1" />*, Girault Baptiste<fnref n="2" />, Martin Philippe<fnref n="2" />, Dedieu Marie-Sophie<fnref n="3" />, Therond Olivier<fnref n="1" />

## Abstract

Crop rotations remain poorly documented at large spatial scale, despite their central role in agroecosystem sustainability. We present a generic pattern-matching algorithm to infer crop rotations from annual crop sequence datasets, such as those derived from the European Land Parcel Identification System, with minimal crop aggregation. This method identifies field-level rotations, quantifies their flexibility, and enables spatially-explicit assessment of dominant crop and grasslands rotational systems at various spatial and thematic levels. Applied to mainland France, the approach identified crop rotations on 90% of arable area, with four-year rotations –typically including two to three years of flexible crops– being the most common. Nationally, the top 20 rotations accounted for 30% of arable land, while the top 52 covered 50%. At the agricultural district scale, we distinguished 25 dominant rotational systems grouped into eight categories, including (i) maize grain monocropping, (ii) maize grain – winter wheat rotations, (iii) sunflower – winter wheat rotations, (iv) grass-based systems, (v) maize silage – winter wheat rotations, (vi) winter wheat – barley – rapeseed rotations, (vii) root crop-based rotations, and (viii) specialized production. At national scale, organic rotations were longer and more flexible than conventional ones. Rotations of larger farms were longer and temporally more diverse than smaller ones, but showed lower spatial diversity. This scalable, data-driven approach offers new insights into crop rotation patterns and their spatial variability. It can support the large-scale assessment of agroecosystems with quantitative evidences on dominant rotations, but also help at tracking and characterizing localized rotational innovations.

## Keywords

Cropping patterns, Temporal crop diversity, Crop sequences, Crop rotations, Cropping systems,

Organic farming, Rotation flexibility

## Highlights

* Method to identify and characterize field-level flexible crop rotations

* Rotations identified on 90% of total mainland France arable land

* 52 rotational patterns alone covered 50% of national-scale arable area

* Spatial heterogeneities of rotational systems grouped into 25 clusters

* Rotation length and flexibility indicators supporting farming system assessments

<footnote n="1">¹ Université de Lorraine, INRAE, LAE, F-68000 Colmar, France</footnote>

<footnote n="2">² Université Paris-Saclay, INRAE, AgroParisTech, UMR SADAPT, 91120 Palaiseau, France</footnote>

<footnote n="3">³ INRAE, US ODR, Castanet-Tolosan F-31326, France</footnote>

<footnote>* Corresponding author: ugo.javourez@inrae.fr</footnote>
# 1. Introduction

Crop rotations are key drivers of farming system sustainability, resilience and climate change adaptation (Dury et al., 2012; Kollas et al., 2015). They shape the spatiotemporal arrangement and diversity of crops across plot, farm, and landscape scales (Castellazzi et al., 2008), thereby influencing yields (Dardonville et al., 2022), input needs -such a pesticide use (Guinet et al., 2023)- and the provision of ecosystem services (Bohan et al., 2021; Duru et al., 2015). Transitioning to longer and more diversified rotations offers multiple benefits: reduced soil erosion, sustained soil fertility and water retention, enhanced biodiversity via improved food and habitat resources, improved nutrient cycling, and disrupted pest and disease cycles (Keichinger et al., 2025; Kollas et al., 2015). Notably, reintroducing legume species and leys into cropping systems offers a promising way to provide a balanced set of ecosystem services while potentially reducing negative agronomic impacts (Cadel et al., 2023; Martin et al., 2020; Nemecek et al., 2008). For example, adding temporal grasslands or ley pastures into rotations can lower the need for mineral fertilizers in following crops, improve soil structure, and enhance biological pest control (Meiss et al., 2010; Zhao et al., 2022). However, the adoption of such strategies remains limited due to constraints in machinery, technical expertise, and perceived economic risk (Dury et al., 2012; Meynard et al., 2018; Steinmann and Dobers, 2013).

Quantitative evidences on actual crop rotation implemented by farmers, and what dominant patterns emerge at landscape or regional scales (e.g., rotation type, length, flexibility, etc.), remains scarce (Reumaux et al., 2023). However, spatially explicit rotation data are essential for diagnosing and assessing cropping systems, and for designing policy interventions based on localized evidences (Bohan et al., 2021). At the local scale, crop rotations are commonly estimated via expert knowledge, field surveys or farmer interviews (Xiao et al., 2014). Yet, these methods are difficult to scale for regional or national analysis, such as evaluating ecosystem services from agriculture (Tibi and Therond, 2024) or estimating cropland carbon storage potential (Launay et al., 2021). Large-scale assessments often rely on simplified crop rotation simulations due to computational and data limitations (Barbieri et al., 2017), still requiring robust methods to identify representative rotations (Schönhart et al., 2011). Critically, the selection and spatial allocation of simulated rotations substantially influences assessment outcomes, shaping both conclusions and policy recommendations (Sahajpal et al., 2014; Sharp et al., 2021).

Access to field-level crop sequences is a prerequisite for identifying crop rotations. Following the use of survey data on land use (e.g., TERUTI-LUCAS; Ballot et al., 2023; Xiao et al., 2014), advances in remote sensing and dedicated geographic information systems have made it possible to obtain annual records of crops grown on arable land over consecutive years (crop sequences) in several regions, including the European Union, Great-Britain and China (Blickensdörfer et al., 2022; Upcott et al., 2023). For example, multi-annual datasets derived from the European Land Parcel Identification System (LPIS) have been used to document crop sequences for nearly 8.5 million French agricultural plots continuously since 2015 (Levavasseur et al., 2016), covering approximately 94% of the country's agricultural area (Dedieu et al., 2024; Girault and Martin, 2024).

However, the intrinsic diversity of crop sequences presents a major challenge (Stein and Steinmann, 2018). Theoretically, up to 100⁴ unique crop sequences can be observed over four years in a system involving 100 different crops (Sahajpal et al., 2014). This diversity reflects the influence of unpredictable, context-specific factors on annual cropping decisions -such as weather, market conditions, and contractual constraints (Bohan et al., 2021; Sharp et al., 2021; Upcott et al., 2023). Even when rotations are planned, they are rarely fixed (i.e., a strict, recurring crop order). Adjustments and substitutions are common, leading to flexible -even non-cyclical- rotations of variable length (Castellazzi et al., 2008).
Previous efforts to characterize crop rotations at large scales typically addressed this diversity by simplifying crop sequences: grouping crops into broad categories (often 10-20 types), limiting the temporal scope to less than 4-5 years, or narrowing spatial coverage (Upcott et al., 2023). Rotation identification methods fall into two main categories: indirect and direct. Indirect methods apply statistical techniques -such as Markov models or clustering- to generate synthetic, yet territorially representative, crop rotations. These are then assessed with agronomic expertise (Dupuis et al., 2022; Mignolet et al., 2007; Nowak et al., 2022; Sharp et al., 2021). In some cases, analysis of the crop sequence structure, using frequency and diversity metrics, is performed (Ballot et al., 2023; Burchfield et al., 2024; Reumaux et al., 2023; Stein and Steinmann, 2018). Shorter crop sequences are eventually assumed to be cyclical by default (Mairura et al., 2022; Plourde et al., 2013). Direct methods, in contrast, search for recurring patterns within individual crop sequences and assess their representativeness post hoc (Leenhardt et al., 2012; Steinmann and Dobers, 2013; Upcott et al., 2023). While these approaches preserve the initial spatial resolution, like field scale, they face challenges in algorithmic convergence, as strict crop rotations are generally rare.

We present here a novel, generic, and tunable method to identify crop rotation patterns from field-level crop sequence datasets, explicitly accounting for their flexibility. Using mainland France as a case study, we demonstrate its ability to characterize cropping systems through rotation patterns and support large-scale assessments. First, we identify dominant crop rotations at the national level and reveal subnational specialization at the agricultural district scale. Second, we analyze how crop rotations attributes –such as length, flexibility, and types– vary across cropping systems (organic vs. non-organic) and farm sizes. Given access to crop sequence data, this approach is readily applicable to other regions and scales, offering analytical insights beyond the current case study. It supports both macro-level analyses, such as identifying dominant rotations across broad areas, and micro-level investigations, such as tracking the adoption of innovation practices or the integration of specific crops into localized rotational systems.

# 2. Materials and method

## 2.1. Flexible crop rotation pattern-matching algorithm

We developed a novel method for identifying and classifying crop rotations, extending the rule-based approach from Leenhardt et al., (2012). The methods targets cyclical crop rotations of fixed length, following the classification by Castellazzi et al., (2008). It requires two inputs: a crop sequence dataset and a crop codes nomenclature. The crop sequence dataset contains, for a given geographical area the ordered list of *N* successive crop names/codes recorded on each agricultural plot (hereafter referred to as *field*). These temporally ordered lists of length *N* are referred to as *observed sequences*. Prior to rotation identification, the dataset undergoes specific pretreatments.

### 2.1.1. Crop sequence pretreatment

Observed crop sequences are initially described with the native crop classification of the source data, which may be unsuitable for agronomic analysis. For example, the post-2014 French LPIS datasets use a nomenclature of more than 300 crop codes, originally designed for the Common Agricultural Policy (CAP) subsidies estimation, potentially leading to artificially high sequence diversity. A crop codes simplification table can be used to aggregate these native codes to a coarser, goal-oriented resolution, enhancing the detection of recurring patterns in simplified sequences. Aggregation can be based on agronomical similarity, for example. Previous studies typically used a simplified classification prioritizing major crops and grouping minor ones into broader classes (e.g., grouping all cereals except soft wheat and barley under “other cereals”), leading to 10-20 types (benchmark in the **Supplementary Materials; SM**). In our case study, we applied a refined nomenclature of 41 crop codes, enabling more
detailed agronomic assessment (Table 1). Only fully characterized sequences -those without missing values nor ambiguous “diverse” entries-, without perennial crops, were retained for the rotation identification step (see Section 2.2.2.).

<table><caption>Table 1: Crop codes nomenclature</caption><thead><tr><th>Crop code</th><th>Full name</th><th>Crop category</th></tr></thead><tbody><tr><td>ORH</td><td>Winter barley</td><td rowspan="10">Cereals</td></tr><tr><td>ORP</td><td>Spring barley</td></tr><tr><td>RIZ</td><td>Rice</td></tr><tr><td>SGH</td><td>Winter ray</td></tr><tr><td>SGP</td><td>Spring ray</td></tr><tr><td>SOG</td><td>Sorghum</td></tr><tr><td>TTH</td><td>Winter triticale</td></tr><tr><td>TTP</td><td>Spring triticale</td></tr><tr><td>AVH</td><td>Winter oat</td></tr><tr><td>AVP</td><td>Spring oat</td></tr><tr><td>BDH</td><td>Winter durum wheat</td><td rowspan="4">Oilseeds</td></tr><tr><td>BDP</td><td>Spring durum wheat</td></tr><tr><td>BTH</td><td>Winter (common) wheat</td></tr><tr><td>BTP</td><td>Spring (common) wheat</td></tr><tr><td>cer2nd</td><td>Other cereals</td><td></td></tr><tr><td>CZH</td><td>Winter rapeseed</td><td></td></tr><tr><td>CZP</td><td>Spring rapeseed</td><td></td></tr><tr><td>TRN</td><td>Sunflower</td><td></td></tr><tr><td>olea</td><td>Other oilseeds</td><td></td></tr><tr><td>prairieA</td><td>Legume leys</td><td>Legume leys</td></tr><tr><td>gel</td><td>Fallow land</td><td>Grass</td></tr><tr><td>prairie</td><td>Grass</td><td></td></tr><tr><td>foua</td><td>Fodder roots</td><td>Root crops</td></tr><tr><td>PdT</td><td>Potato</td><td></td></tr><tr><td>BTN</td><td>Sugar beet</td><td></td></tr><tr><td>CHV</td><td>Hemp</td><td>Other</td></tr><tr><td>LIF</td><td>Fiber flax</td><td></td></tr><tr><td>legfl</td><td>Horticulture</td><td></td></tr><tr><td>aindus</td><td>Other industrial crops</td><td></td></tr><tr><td>MIE</td><td>Maize silage</td><td>Maize</td></tr><tr><td>MIS</td><td>Maize grain</td><td></td></tr><tr><td>lupH</td><td>Winter lupin</td><td rowspan="5">Pulses</td></tr><tr><td>lupP</td><td>Spring lupin</td></tr><tr><td>poisH</td><td>Winter pea</td></tr><tr><td>poisP</td><td>Spring pea</td></tr><tr><td>SOJ</td><td>Soybean</td></tr><tr><td>FVL</td><td>Field bean</td><td></td></tr><tr><td>leggr</td><td>Other pulses</td><td></td></tr><tr><td>div</td><td>Diverse</td><td>NA – discarded as part of pretreatments for crop</td></tr><tr><td>cann</td><td>Sugarcane</td><td></td></tr></tbody></table>
<table><thead><tr><th>perenne</th><th>Perennial crops</th><th>rotations analysis in mainland France</th></tr></thead></table>

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Mapping of 352 native LPIS crop codes with the proposed 41 crop codes nomenclature is provided in the **Supporting Data** (Javourez, 2025).

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### 2.1.2. Pattern matching algorithm

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Rotation identification is performed by systematically detecting and classifying recurrent patterns within each observed crop sequence. A pattern ($P_n$) is defined as a subsequence of $n$ consecutive crops that repeats -either fully or partly- within an observed crop sequence of fixed length $N$. Repetitions may be separated by crops not included in the pattern, referred to as non-P. Patterns may include repeated instances of the same crop and are not restricted in diversity. For example, in the observed sequence A_B_B_D_A_B_B_A ($N$ = 8; with each letter representing a distinct crop), the recurrent pattern $P_n$ = A-B-B appears twice. Here, non-P = {D}, as crop D separates the two repetitions. For each unique observed sequence, all possible patterns $P_n$, where $n$ ranges from 1 to $n_{max}$, are initially considered. $n_{max}$ is the maximum pattern length evaluated.

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A pattern is retained as a matching pattern only if it covers a minimum length threshold percentage (%seqmin) of the observed sequence. For a sequence of length $N=8$, setting %seqmin to 60% means a pattern must cover at least 5 years (5/8 = 62.5% ≥ 60%). When computing the sequence coverage (%seq), potential truncation at the beginning or end of the observed sequences is accounted for. In the previous example, pattern A-B-B is observed twice. The presence of crop A at the end may indicate a third repetition, or at least does not preclude it. Therefore, A_B_B is considered to cover 7 of 8 years, yielding %seq = 88%, and is classified as a matching pattern. This tolerance allows to capture flexibility in crop rotations: patterns need not to fully or exactly cover the sequence; a share of non-P crops is permitted as long as coverage exceeds %seqmin.

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The %seqmin threshold is tunable but must be strictly greater than $n_{max}/N$ to ensure that matching patterns occur at least twice (including possibly truncated repetitions) within the sequence. As a default, we recommend setting $n_{max}$ to no more than $N/2$. For instance, in 8-year crop sequences limiting pattern length to a maximum of four years allows for at least two full repetitions to be theoretically observable (limits in **Section 4.1**). Multiple matching patterns (e.g., of two and four years) may be identified for a single crop sequence, but only one is retained based on a hierarchical selection procedure. First, patterns with the highest length sequence coverage (%seq) are prioritized. In case of ties, the shorter-length matching pattern is selected. If ties persist, the pattern appearing later in the sequence -i.e., more recently in time- is favored.

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Each sequence with a selected pattern is classified using a custom notation: *$P_n$_f_{non-P}$_%seq$ where $P_n$ is the selected pattern, non-P the list of flexible (f) crops between its repetitions, and %seq its coverage. These are referred to as *classified sequences*. To harmonize the classification, a circularity check is applied: patterns that are circular permutations of each other (e.g., A-B-C, B-C-A, C-A-B) are renamed to a common canonical form (e.g., A-B-C, for being the first occurrence). Similarly, the associated non-P lists are standardized within each unique pattern. Revisiting the sequence A_B_B_D_A_B_B_A (with %seqmin=60% and $n_{max}=4$), eight matching patterns are identified: (i) A-B_f_{B-D, B}_62%, (ii) A-B-B_f_{D}_88%, (iii) D-A-B_f_{B, B-A}_62%, (iv) A-B-B-D_f_{A-B-B}_62%, (v) B-B-D-A_f_{B-B-A}_62%, (vi) B-D-A-B_f_{B-A}_75%, (vii) D-A-B-B_f_{A}_88%, and (viii) A-B-B-A_f_{B-B-D}_62%. Patterns (ii) and (vii) both reach the highest sequence coverage (88%). Pattern (ii) is selected due to its shorter length (three vs. four years). Not all sequences yield matching patterns, even when they contain repeated crops. For example, sequences such as A_B_C_D_E_B_A_D and A_A_A_A_B_B_B_B do not satisfy the matching criteria under the above algorithm settings.

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### 2.1.3. Selection of dominant crop rotations

Following terminology harmonization, the diversity of classified *P<sub>n</sub>*_{f_{\{non-P\}};%seq} objects can remain substantially high, depending on the sequence length (*N*), algorithm settings, and the characteristics of the studied area (e.g., spatial extent, crop diversity, etc.). At this stage, each unique selected patterns *P<sub>n</sub>* is treated as a potential crop rotation. This is justified by the algorithm's focus on identifying patterns based on their recurring propensity. However, these patterns are not necessarily observed as fully covering any observed sequence (i.e., %seq < 100%) and may not be strictly repeated in practice. Therefore, they remain potential until further evidences support their agronomic feasibility and representativity.

The broader the area over which a potential rotation was selected as a matching pattern, the more likely it appeared under varying conditions (e.g., with different flexible crops or temporal arrangements), gaining support as a representative crop rotation of the studied area. Since each classified sequence is linked to a single selected pattern *P<sub>n</sub>*, the cumulated area coverage of each potential rotation can be ranked. This ranking enables the identification of dominant crop rotations. The threshold for defining representativity is subjective and should align with the study's objectives. For instance, dominant rotations may be defined as the selected patterns *P<sub>n</sub>* either covering at least a minimum share of the total arable land, belonging to a predefined maximum number of rotations, or collectively summing over a target cumulative area coverage (Sahajpal et al., 2014). Crop rotations further refer to selected patterns (*P<sub>n</sub>*), that meet the predefined thresholds for representativity, while flexible crops (non-P) and sequence coverage (%seq) are treated separately, as flexibility attributes.

### 2.1.4. The case of near-monocropping

Length-one crop rotations (*P*<sub>1</sub>), as identified by the pattern-matching algorithm, include both strict and near-monocropping. Merging these categories when analyzing rotational systems can lead to agronomic inconsistencies and misinterpretations. For example, near-monocropping of winter wheat -occurring 5-6 times over 8 years- is relatively common in France, whereas strict monocropping is rare. Here, strict and near-monocropping practices are distinguished by combining length-one patterns with their sequence coverage, noted as *P*<sub>1;%seq</sub>, when ranking potential crop rotations. For other patterns (*P*<sub>n</sub>, with *n*≠1), only *P*<sub>n</sub> was considered (see **section 2.1.3**). Examples of near-monocropping identified using the algorithm include the sequences A_A_A_A_B_B_A and A_B_A_C_A_D_A_A. These are classified as A_f_{\{B-B\}}_75% and A_f_{\{B, C, D\}}_62%, respectively, and the resulting crop rotations are denoted A_75 and A_62. However, as defined, a near-monocropping identified as dominant across the study area -e.g., A_75- remains implicit and cannot be directly simulated by soil-crop models. Although not mobilized in the case study, we propose an approach to reconstruct artificial, explicit *N*-year crop rotations representative of each near-monocropping, enabling simulation. This reconstruction relies on identifying the most frequent flexible crops (non-P) associated with a given near-monocropping and inserting them between repeated sequences of the dominant crop (of typical length), following study area-level statistics (see SM).

### 2.1.5. The case of grass-crop mixed patterns

An additional treatment targets non-classified sequences involving temporary grassland-based rotations (i.e., including grass and legume leys). The objective is to identify extended rotational patterns (*n*>n<sub>max</sub>) that include consecutive years of temporary grassland and other crops. Non-classified sequences containing at least 100-%seq<sub>min</sub> consecutive years of grass codes (from the grass category; see **Table 1**) are retained. For *N*=8 and %seq<sub>min</sub> = 60%, this corresponds to sequences with 3-4 years of consecutive grassland. The algorithm then searches within the remaining (non-grass) portion of each sequence for any previously identified matching patterns *P*<sub>n</sub> from earlier treatments described above. If a match is found, the same hierarchical selection rules are applied. The sequence is then
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reclassified with the associated pattern grass-grass-...-grass-$P_n$. Circular permutations check and terminology harmonization are applied as previously described. This approach likely results in classifying fields undergoing conversion between permanent grassland and arable land as grass-crop mixed rotations (see **Section 4.1**).

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## 2.2. Mainland France simulation plan and treatments

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### 2.2.1. Data sources

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We used the 2015-2022 crop sequence dataset developed by Girault and Martin, (2024), derived from public French LPIS data (IGN, 2025) with method detailed in Levavasseur et al., (2016). This dataset documents approximately 14 million elementary plots, resulting from spatial intersection of eight annual LPIS layers, covering 28.2 million hectares (Mha) across the agricultural area of mainland France, including Corsica. Only plots larger than 0.5 hectares were retained, a standard threshold to reduce noise from spatial intersection processes (Levavasseur et al., 2016). After filtering, the dataset includes 8,413,741 plots, hereafter considered as *agricultural fields*, totaling 27.2 Mha (3.5% area loss). This public crop sequence dataset was joined with a restricted-access French LPIS dataset available to researchers, which adds field-level information such as organic farming and farmer identifiers for the same 2015-2022 period (see **SM**).

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To enable spatial analysis, we discretized mainland France into the 433 historical agricultural districts -established in 1946- provided and used by the French agricultural statistics agency (Agreste, 2017). Their spatial extent varies considerably: filtered crop sequence areas per district range from 0.8 kha to 569.1 kha, with a mean of 62.9 kha and a median of 36.4 kha (excluding the *Paris* district with no agricultural land). District assignment was performed via zip code matching between the crop sequence dataset and the reference district table.

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### 2.2.2. Algorithm implementation

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The flexible crop rotation pattern-matching algorithm was applied to the prefiltered and enriched crop sequence dataset for mainland France, using agricultural districts as the reference spatial units. While the zoning does not influence algorithm outputs, it provides a consistent framework for analysis, interpretation and visualization. As the dataset spans $N=8$ years (2015-2022), the maximum rotation length was set to $n_{max} = 4$ years, with a minimum sequence coverage threshold of %$seq_{min} = 60\%$. It means that matching patterns must cover at least 5 out of the 8 years. A four-year pattern is then considered as a match if it is fully observed at least once within the 8-year period, and either the beginning or end of the pattern is observed on at least one additional year.

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The about 300 native LPIS crop codes were simplified into a 41-code nomenclature, grouped into 9 crop categories (**Table 1**). Agricultural fields (i.e., prefiltered crop sequences) were considered *permanent grassland* if they hosted grass crops continuously across the full 2015-2022 period. Under this definition, permanent grassland accounted for 8.8 Mha or 32.4% of prefiltered area. Crop sequences excluded during pretreatments represented 2.6 Mha (9.5%). It included approximately 0.6 Mha (2.1%) of sequences containing at least one perennial crop (e.g., orchards, vineyards) and 2.0 Mha (7.4%) with sequences either incomplete (e.g., missing year) or containing at least one "diverse" code. The remaining 15.8 Mha (58.1%) were classified as *arable land* and constitutes the analysis dataset (4,806,679 fields). The algorithm and the scripts used for the French case study are available, see the **Research data statement**.

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### 2.2.3. Spatial, farm and rotation analysis

The characterization of rotational systems across France followed the clustering approach of Xiao et al., (2014), with minor adaptations. Agricultural districts were grouped based on the similarity of their dominant crop rotation distributions. First, districts dominated by non-arable land were excluded.
Two filtering conditions were applied: (i) a minimum of 20% arable land (as a share of prefiltered area), or (ii) at least 1,000 ha of arable land if arable land was below 50%. This removed 98 districts, which together accounted for only 2.2% of total arable land in mainland France (approx. 0.35 Mha). Next, all crop rotations covering at least 1% of the arable land in any of the 335 remaining districts were retained. For each district, the shares of arable land occupied by these rotations (ranging from 0 to 1) served as active clustering variables (available in the **Supporting Data**; Javourez, 2025). As supplementary variables, we included the average 2015-2022 agricultural land cover per district, expressed using the 41 crop-code nomenclature (Table 1). A principal component analysis (PCA) was first performed on the active variables. The top components explaining 95% of cumulative variance were retained for hierarchical clustering, using Ward's method. The workflow was implemented with the FactoMineR package (Lê et al., 2008). The number of PCA dimensions and clusters was manually defined through iterative testing to ensure meaningful spatial differentiation of rotational systems and robust cluster interpretation. Lowering the variance threshold below 95% led to an overrepresentation of grassland-dominated districts in small, poorly interpretable clusters, due to the strong influence of the first grass-related PCA dimension.

Cluster analysis included summary statistics of dominant crop rotations within each cluster, along with *v*-values for both active and supplementary variables. The *v*-value measures the standardized deviation of a cluster's mean from the overall population mean, and is accompanied by a *p*-value indicating statistical significance. Typical districts representing each cluster were selected among the five closest to the cluster centroid.

To compare conventional vs. organic rotations, fields were classified as *organic* only if continuously declared under organic management throughout the 2015-2022 period. This yielded 0.44 Mha of organic arable sequences (2.8% of total arable land), compared to 1.68 Mha (10.6%) recorded as organic in 2022. To evaluate crop rotations at the farm level, agricultural districts related to permanent grasslands or specialized southwestern France production systems were excluded (Clusters 11, 12, 24, 25; see **Section 3.2.**). Among the remaining 278 districts, only farms with at least 20% of their total agricultural area as arable land were included. This selection yielded 175,560 farms (~56% of total farms) accounting for 14 Mha, or ~89% of the total arable land. Farms were then categorized into five size groups based on total prefiltered agricultural area: <20 ha, 20-50 ha, 50-100 ha, 100-200 ha, and >200 ha, consistent with the French agricultural census classification. A separate group for larger farms was not included, as only 16 of the selected farms exceeded 1,000 ha.

Temporal crop diversity on arable land was assessed using the Inverse Simpson Index, following Dedieu et al., (2024). This index reflects the effective number of distinct crops in a sequence, weighted by their relative abundance (true diversity of order 2; Keichinger et al., 2025). For 8-year crop sequences, the index ranges from 1 (strict monocropping) to 8 (eight different crops each observed once). Field-level indices were calculated at both the 41 crop-code level (*inv_sim*) and the 9 crop-category level (*inv_sim_cat*), the latter reflecting functional or taxonomic diversity. Here, the spatial diversity of arable land was not directly calculated, but it intrinsically related with its temporal diversity (Bohan et al., 2021). For all classified sequences, rotation length (*n*) and sequence coverage (%seq) were recorded. Aggregated indicators for larger spatial or thematic groups were calculated as area-weighted averages.

# 3. Results

## 3.1. French arable land described by a few yet flexible crop rotations

Field-level crop rotations were identified on 14.1 Mha, accounting for ~90% of the 15.8 Mha of arable land in mainland France. This high identification rate was largely achieved by considering
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flexibilities in crop rotations. Strict monocropping and strict rotations together represented only 9% of arable land, indicating that most fields follow a general rotational structure while allowing for temporary deviations. Over the eight-year observation period, 17% of the arable land exhibited one year of flexibility, 29% showed two, and 31% three. These proportions highlight the role of the sequence coverage threshold in capturing rotational patterns. The most frequent configurations were four-year rotations with two or three flexible years, covering 4.6 Mha (29%), suggesting an overall rotational diversity at field scale. These may include longer underlying cycles not fully detected with the current settings. Integrating the grass-crop mixed treatment (see **Section 2.1.5.**) extended the identification of rotations to an additional 2% of arable land (0.33 Mha). However, such grass-crop mixed rotations were characterized with a high uniqueness (median surface area of 3.9 ha), mostly because of their longer length (area-weighted average of 7.22 years). Hence, this additional treatment yielded limited additional analytical insights.

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At the national scale, the area-weighted temporal crop diversity index (inv_sim) for near-monocropping averaged 1.66. This increased to 2.7, 3.1, and 3.3 for two-, three-, and four-year flexible rotations, respectively. A similar trend was observed at the crop category level, although both two- and three-year rotations shared the same diversity (inv_sim_cat = 2.1). This indicates a predominant use of two crop categories -typically cereals and oilseeds-, and a limited number of crops in these flexible rotations. Notably, crop diversity tends to increase as both rotation's length and flexibility increase (see SM). The 10.4% of arable land with unclassified crop sequences showed notably higher diversity, averaging five different crops over eight years (inv_sim = 4.2). This further supports the method's effectiveness in capturing prevalent patterns, with the remaining areas likely reflecting complex, more diversified or transitional cropping systems.

A relatively small number of rotational patterns dominates the national landscape (Figure 1). The 20 most common patterns cover 30% (4.7 Mha) of total arable land area, while the top 52 account for 50%. Thus, using a 41-crop-code nomenclature, 52 distinct crop rotations are enough to describe half of France's arable surfaces. Beyond the 110th ranked rotation, each represent less than 0.1% of the total: their representativity drops. Many rotations differ only slightly -often by the substitution or addition of a single crop from the same family or season. These are referred to here as *derivatives*. A notable example is the winter wheat - winter barley - winter rapeseed rotation (w-b-r), alone identified on 624,000 ha. W-b-r derivatives frequently involve additional winter wheat, either consecutively or in alternation. Collectively, the w-b-r and its derivatives represent the most widespread rotational group, identified on over 10% of arable land (1.7 Mha). On average, w-b-r rotations include one flexible year within an eight-year span (area-weighted sequence coverage ~88%), while derivatives trend toward two (Figure 1). Other dominant systems include flexible alternation of winter wheat with maize silage, winter oilseeds, or maize grain. Among these, winter wheat - rapeseed rotations were more flexible (2.2 years on average) than winter wheat - sunflower (1.7 years). Strict monocropping (inv_sim = 1.0) covered approximately 2% of arable land (320,000 ha), primarily maize grain (MIS; 220,000 ha) and maize silage (MIE; 60,000 ha), which together represented 87% of this category. The remainder strict monocropping included legume leys (as the pluriannual crop alfalfa), horticulture, and industrial crops (e.g., hop, spice, lavender).
<figure><img src="image_3.png" /><figcaption>357 **Figure 1: Dominant crop rotations for mainland France**</figcaption></figure>

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Only crop rotations identified on more than 30 kha are displayed here. Derivates around similar rotational patterns were manually grouped together, and classified by descending coverage of national-scale arable land. The color scale represents the area-weighted average of field-level sequence coverage %seq per rotation (88% means the rotation presented one year of flexibility over 8 years; see Section 2.1.2.). Crop codes correspondence is described in Table 1 (w. for winter, s. for spring).

**Supporting data** is provided in Javourez, (2025).
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<figure><img src="image_4.png" /><figcaption>Figure 2: Field-level crop diversity and rotations indicators for mainland France arable land</figcaption></figure>

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Field-level indicators were averaged at the agricultural district level (area-weighting). Diversity indicators (top) include all arable land crop sequences, while rotation indicators (bottom) only include arable land where crop rotations were identified. Light grey agriculture districts are those presenting a total arable land area below threshold (see Section 2.2.3.); these are mostly covered by permanent grassland or perennial crops (e.g., orchards, vineyards). The time scope is 2015-2022 (8 years).

**Supporting data** is provided in Javourez, (2025).

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## 3.2. Spatial typology of French rotational systems

The analysis at the agricultural district level revealed distinct regional patterns in crop rotations (Figures 2 and 3). Despite wide variation in agricultural orientation -arable land covered a median of 59% of the prefiltered area (interquartile range: 27%-79%)- rotation identification rates remained consistent (median: 89%; interquartile range: 86%-92%; see SM). Across the 335 arable land-dominated districts used for clustering (see Section 2.2.3), the top 10 dominant rotational patterns accounted for an average of 43% of arable land (median: 41%; interquartile range: 34%-50%), indicating that a limited number of rotations can also describe district-level rotational systems. However, these representative rotations varied across clusters: capturing the first 50% of arable land in each district required 758 distinct rotations -compared to only 52 at the national level. Of these, only 372 appeared on at least 1% of the arable land in any of the 335 selected districts.

Clustering based on dominant rotation patterns grouped districts into 25 clusters, organized into eight broader groups (letters in Figure 3). Group A was defined by maize grain specialization, with clusters varying in the degree of strict versus near-monocropping (Figure 4), and in associated crops. For instance, Cluster 2 typically involved 2-3 years of consecutive maize grain followed by horticulture, pulses or potatoes (covering ~10% of arable land; Table 2). In Cluster 5, typical break crops rather included winter wheat and temporary grassland, and diverse locally specific rotations such as pulses (x3) followed by sunflower were observed. This highlights how districts can also be characterized by typical rotational practices beyond the dominating patterns. Cluster 1 exhibited the highest levels of strict maize grain monocropping and the lowest temporal crop diversity nationally (Figure 2, Table 2). Group B included Clusters 6 and 7, characterized by the two-year maize grain - winter wheat rotations and their derivatives. Cluster 6 showed strong correlations with winter and spring durum wheat, respectively covering 10% and 1.3% of agricultural area on average, approximately 100 times more than in other districts. Durum wheat was also prevalent in Cluster 10 (16% of agricultural area), where it typically rotated with sunflower in a two-year rotation (~20% of arable land). Cluster 10, along with Clusters 8 and 9, featured dominant sunflower - winter wheat rotations (Group C).

Group D encompassed districts with extensive permanent grasslands (covering 55-70% of total agricultural area), with arable land dominated by semi-continuous grasslands systems. Typical rotations included 2-3 years of temporary grassland, often with legume leys, maize silage, barley, or triticale. The high share of grass explained the low crop diversity and short rotation lengths observed (Figure 2; Table 2). Group E also included permanent and semi-continuous grasslands systems but was distinguished by prevalent two-year maize silage - winter wheat rotations and their derivatives. Maize silage near-monocropping was notably frequent in Cluster 13 (~10% on average), while Cluster 14 showed higher rotational diversity, with cereal-oilseed rotations (e.g., *w*-*b*-*r* and derivatives) alongside temporary grass - cereal - maize silage rotations. Group F, the largest (28.1% of national arable land), was centered around the *w*-*b*-*r* rotations and their derivatives. Clusters differed mainly in the weight of winter wheat and the integration of flexible crops integrated into the baseline *w*-*b*-*r* scheme. For instance, Cluster 19 exhibited the lowest crop diversity in the group (Table 2), with three dominant rotations (*w*-*b*-*r*, *w*-*w*-*b*-*r* and *w*-*w*-*r*) covering over 40% of arable land (Figure 4). Conversely, Cluster 16 -the largest in the group- showed the highest diversity, notably combining spring barley within *w*-*b*-*r* derivatives.

Group G consisted of districts dominated by root crop-based rotations in northern France (Figure 3). Clusters varied in the type of root crops and associated crops. Cluster 22 featured sugar beet - winter wheat alternance, while Cluster 20 involved typical four-year rotations with sugar beet and spring barley and exhibited one of the highest crop diversity levels (Figure 2; Table 2). Cluster 21 was associated with potato production, with typical alternation of sugar beet and potato every other year
with winter wheat (Figure 4). Rotations combining wheat, root crops, horticulture (~5% of agricultural area), and pulses were also common, contributing to some of the highest crop category diversities nationally. Cluster 23 was marked by four-year rotations involving flax and winter wheat along with maize silage, barley, potato or sugar beet. The prevalence of such flax-based rotational systems made the Pays de Caux district stand out with some of the longest rotation lengths and highest crop category diversity (Figure 2). Group H included southeastern France districts with near-monocropping of regional crops such as rice, sainfoin, and durum wheat (Cluster 24), as well as highly specialized systems like lavender monocropping (Cluster 25). These districts also had the highest levels of continuous organic farming (~10% of agricultural area). Further details on the rotational systems per cluster are provided in the SM.

<figure><img src="image_5.png" /><figcaption>Figure 3: Clustering French agricultural districts by typical crop rotational systems</figcaption></figure>

Quantitative data and description are provided in Table 2 and Figure 4. w.: winter.
<figure><img src="image_6.png" /><figcaption>Figure 4: Distribution of dominant crop rotations for 25 clusters of the French agricultural districts</figcaption></figure>

Top-ten rotations per cluster. Boxplots show the intra-cluster inter-districts variability while black dots show the area-weighted mean at the cluster level (here, n represents the number of agricultural districts in a cluster). Blue tones indicate that a rotation is significantly representative of the cluster (higher intra-cluster average compared to total districts average) while red tones indicate that a rotation is significantly underrepresented in this cluster (see Section 2.2.3.). Colored squares, cluster numbers, and group letters, correspond to the legend used in Figure 3. Crop codes are described in Table 1. Supporting data is provided in Javourez, (2025).
<table><caption>Table 2: Key indicators for the 25 typical French rotational systems</caption><thead><tr><th>n°</th><th>Cluster name</th><th>Area (%tot)</th><th>District count</th><th>Top-10 rotations (%area)</th><th>Rotation length n</th><th>%seq</th><th>inv sim</th><th>inv sim cat</th><th>Typical districts</th></tr></thead><tbody><tr><td>1</td><td>Dominant maize grain strict monocropping</td><td>1.0%</td><td>9</td><td>76%</td><td>1.50</td><td>87%</td><td>1.58 (0.10)</td><td>1.48 (0.07)</td><td>Pays de Gosse</td></tr><tr><td>2</td><td>Dominant maize grain near-monocropping with roots and pulses</td><td>0.6%</td><td>4</td><td>76%</td><td>1.74</td><td>83%</td><td>1.74 (0.09)</td><td>1.68 (0.08)</td><td>Landes du Médoc; Hardt</td></tr><tr><td>3</td><td>Dominant maize grain near-monocropping with sunflower and soybean</td><td>1.0%</td><td>9</td><td>59%</td><td>1.90</td><td>82%</td><td>2.03 (0.20)</td><td>1.79 (0.17)</td><td>Bas Armagnac</td></tr><tr><td>4</td><td>Dominant maize grain near-monocropping with winter wheat</td><td>1.3%</td><td>8</td><td>57%</td><td>2.47</td><td>80%</td><td>2.30 (0.20)</td><td>2.03 (0.13)</td><td>Coteaux en bordure des Dombes; Vallée de la Garonne</td></tr><tr><td>5</td><td>Cohabitation of maize grain near-monocropping with perennial and grasslands</td><td>0.4%</td><td>7</td><td>36%</td><td>2.27</td><td>78%</td><td>2.42 (0.17)</td><td>1.95 (0.11)</td><td>Vallée de la Dordogne</td></tr><tr><td>6</td><td>Dominant maize grain – durum wheat rotations</td><td>0.5%</td><td>4</td><td>31%</td><td>2.90</td><td>76%</td><td>3.01 (0.08)</td><td>2.28 (0.11)</td><td>Marais Poitevin</td></tr><tr><td>7</td><td>Dominant maize grain – winter wheat rotations</td><td>2.5%</td><td>17</td><td>36%</td><td>2.83</td><td>78%</td><td>2.71 (0.18)</td><td>2.17 (0.12)</td><td>Vallée de la Sarthe</td></tr><tr><td>8</td><td>Flexible sunflower – winter wheat rotations with barley and rapeseed flexibility</td><td>11.2%</td><td>35</td><td>24%</td><td>2.95</td><td>75%</td><td>3.07 (0.17)</td><td>2.22 (0.10)</td><td>Bergeac; Saintonge agricole</td></tr><tr><td>9</td><td>Dominant sunflower – winter wheat rotations</td><td>2.9%</td><td>10</td><td>35%</td><td>2.86</td><td>76%</td><td>3.09 (0.15)</td><td>2.39 (0.08)</td><td>Coteaux Sud Garonne</td></tr><tr><td>10</td><td>Dominant sunflower – durum wheat rotations</td><td>1.6%</td><td>2</td><td>38%</td><td>2.84</td><td>76%</td><td>3.15 (0.13)</td><td>2.29 (0.02)</td><td>Lauragais</td></tr><tr><td>11</td><td>Mixed grass-cereal rotational systems</td><td>5.9%</td><td>33</td><td>40%</td><td>2.53</td><td>75%</td><td>2.51 (0.21)</td><td>2.09 (0.09)</td><td>Monts du Jarez; Segala</td></tr><tr><td>12</td><td>Dominant semi-continuous grassland systems</td><td>0.9%</td><td>6</td><td>55%</td><td>2.05</td><td>75%</td><td>2.16 (0.25)</td><td>1.91 (0.15)</td><td>Plateaux moyens du Jura</td></tr><tr><td>13</td><td>Cohabitation of dominant maize silage rotational systems with grasslands</td><td>6.3%</td><td>15</td><td>49%</td><td>2.62</td><td>79%</td><td>2.55 (0.26)</td><td>2.09 (0.09)</td><td>Région de Fougères; Avranchin</td></tr><tr><td>14</td><td>Mixed winter wheat – maize silage with rapeseed and grass-based rotations</td><td>12.1%</td><td>30</td><td>33%</td><td>2.85</td><td>76%</td><td>2.85 (0.22)</td><td>2.22 (0.11)</td><td>Bocage; Plaine du Forez</td></tr><tr><td>15</td><td>Flexible winter wheat – rapeseed – barley rotational systems with maize grain flexibility</td><td>6.4%</td><td>23</td><td>31%</td><td>3.23</td><td>75%</td><td>3.19 (0.15)</td><td>2.17 (0.17)</td><td>Vallées de la Marne et du Morin; Brie humide</td></tr><tr><td>16</td><td>Mixed winter wheat – rapeseed – barley rotational systems</td><td>13.7%</td><td>30</td><td>30%</td><td>3.22</td><td>74%</td><td>3.36 (0.19)</td><td>2.03 (0.12)</td><td>Barrois vallée; Plateaux de Bourgogne</td></tr></tbody></table>
<table><thead><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td></td><td>with spring barley flexibility</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>17</td><td>Flexible winter wheat - barley - rapeseed rotational systems</td><td>5.7%</td><td>14</td><td>45%</td><td>3.12</td><td>78%</td><td>3.11 (0.19)</td><td>2.10 (0.11)</td><td>Plaine Grayloise; Pays Sancerrois</td></tr><tr><td>18</td><td>Specialized winter wheat - barley - rapeseed rotations</td><td>0.8%</td><td>5</td><td>48%</td><td>3.20</td><td>76%</td><td>3.43 (0.10)</td><td>1.93 (0.13)</td><td>Pays d'Othe; Tonnerois</td></tr><tr><td>19</td><td>Dominant winter wheat-based rotational systems</td><td>1.5%</td><td>6</td><td>64%</td><td>3.26</td><td>80%</td><td>2.89 (0.11)</td><td>2.02 (0.09)</td><td>Plateau d'Evreux</td></tr><tr><td>20</td><td>Sugar beet - spring barley rotational systems</td><td>4.6%</td><td>6</td><td>29%</td><td>3.44</td><td>73%</td><td>3.60 (0.15)</td><td>2.21 (0.20)</td><td>Champagne Crayeuse</td></tr><tr><td>21</td><td>Root crops - winter wheat rotational systems</td><td>4.7%</td><td>17</td><td>40%</td><td>3.31</td><td>75%</td><td>3.13 (0.19)</td><td>2.44 (0.11)</td><td>Pays Aire; Ponthieu</td></tr><tr><td>22</td><td>Sugar beet between winter wheats rotational systems</td><td>5.3%</td><td>11</td><td>47%</td><td>3.25</td><td>76%</td><td>3.02 (0.06)</td><td>2.29 (0.07)</td><td>Noyonnais</td></tr><tr><td>23</td><td>Diversified winter-wheat based rotational systems with flax, rapeseed, sugar beet and maize silage</td><td>4.9%</td><td>16</td><td>36%</td><td>3.22</td><td>75%</td><td>3.00 (0.15)</td><td>2.35 (0.17)</td><td>Roumois; Plaine de Caen et de Falaise</td></tr><tr><td>24</td><td>Specialized Southern-East France near-monocropping</td><td>1.6%</td><td>16</td><td>31%</td><td>2.73</td><td>73%</td><td>2.74 (0.19)</td><td>2.16 (0.19)</td><td>Val de Durance; Garrigues</td></tr><tr><td>25</td><td>Specialized Southern-East France industrial crops</td><td>0.2%</td><td>2</td><td>53%</td><td>1.93</td><td>78%</td><td>2.22 (0.09)</td><td>1.94 (0.08)</td><td>Plateau de Forcalquier</td></tr></tbody></table>

Area (%tot): share of national arable land area by each cluster. Top-10 rotations (%area): share of arable land within the cluster covered by the top 10 rotations (black dots in **Figure 4**). Other indicators were described in **Section 2.2.3**. For these, area-weighted averages were calculated at the agricultural district level. Values represent intra-cluster means (standard deviations) across districts. Cluster numbers correspond to those in **Figures 3 and 4**. A detailed description per district is available in the **SM**.

### 3.3. Organic farming shows greater crop diversity and flexibility in rotations

On land under continuous organic farming (0.44 Mha), crop rotation identification dropped to ~76% nationally. Over one-quarter of organic arable land was occupied by semi-continuous grass- or legume ley-based systems, contributing to the relatively short area-weighted rotation length observed in organic systems (**Figure 5**). The most common organic rotations combined temporary grassland and legume leys -at least two consecutive years- followed by cereals (~16,000 ha), or, occasionally maize silage (~3,000 ha). Excluding grass and legume leys, the leading organic rotation was pulses - winter wheat, though it covered only ~4,000 ha nationwide. Other typical organic rotations included soybean - winter wheat, sunflower - winter wheat, and continuous horticulture (mostly vegetables), each observed on ~2,000 ha.

Grass appeared at least once in 8-year sequences across 21% (~3.4 Mha) of total arable land, but across 41% of organic arable land. Interestingly, cropping systems involving grass showed no significant difference in diversity or rotational structure between organic and conventional management. Semi-continuous grasslands represented 1.2 Mha, mostly interrupted with maize silage (0.41 Mha), winter wheat (0.33 Mha), or winter triticale (0.21 Mha). Grass was most often embedded in flexible four-year rotations involving 2-3 years of temporary grassland followed by cereals, maize or legume leys., or in non-classified sequences (**Figure 5**). The dominance of semi-continuous grasslands explains why
systems with grass showed lower crop-level diversity (inv_sim = 2.63) compared to those without (3.08), while exhibiting higher diversity at the category level (inv_sim_cat of 2.24 vs 2.15). Grass generally played a central role in rotations rather than being integrated as flexible crops into other systems. Nevertheless, it was occasionally found in semi-continuous legume leys and maize - winter wheat alternations (~65 kha each).

<figure><img src="image_7.png" /><figcaption>Figure 5: Contrasted rotational features of cropping systems with grass or pulses</figcaption></figure>

*: Inverse Simpson Index (inv_sim), area-weighted average per modality.

In contrast, systems without grass showed clear differences between organic and conventional practices. In organic systems, strict -inflexible- rotations were nearly absent (~8,500 kha), and approximately 90% of arable land without grass exhibited at least two years of flexibility. Notably, nearly 30% lacked any identifiable rotational background (Figure 5). These organic grass-free systems had significantly higher diversity than their conventional counterparts (inv_sim: 3.56 vs. 3.07; inv_sim_cat: 2.40 vs. 2.14).

The greater length and flexibility of organic rotations were also linked to the widespread use of pulses, present on 50% of organic arable land but only 17% under conventional management (Figure 5). Pulses presence led to higher crop diversity (inv_sim: 3.59 vs 2.85; inv_sim_cat: 2.50 vs 2.09) for both organic and conventional systems. The observed lower diversity in organic pulse-less systems, relative to their conventional counterparts, is primarily attributed to the fact that ~50% of organic pulse-less surfaces consist of semi-continuous grasslands or legume leys, which are treated as near-monocropping in the diversity index used here. About 75% of organic areas with pulses were under flexible four-year rotations or more complex cropping systems, and ~35% of this area remained unclassified. Few individual organic rotations involving pulses exceeded 1,000 ha, reflecting high rotational variability.
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The use of pulses as break crops in semi-continuous organic grassland and legume leys was the most common. In conventional systems, they were mainly found as flexible crops in w-b-r rotations and derivatives, winter wheat – maize or winter wheat – root crops alternations, and occasionally in near-monocropping of maize grain or winter wheat. The most common pulse-centered conventional rotations included: winter wheat – spring pea – winter wheat – rapeseed (~36,000 ha), winter wheat – soybean (~24,000 ha), winter wheat (x2) – barley – spring pea (~19,000 ha and 14,000 ha, respectively, for winter and spring barley), and winter wheat (x2) – spring pea (~14,000 ha).

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### 3.4. Larger farms exhibit greater rotational diversity but lower spatial diversity

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Across the 175,560 selected farms -covering approximately 89% (14 Mha) of total arable land-larger farms exhibited more diverse and longer crop rotations on average (Figure 6). These farms also tended to display higher temporal diversity, although the diversity at crop-category level (inv_sim_cat) plateaued around 2.2 for farms with over 100 ha of agricultural area. Farms from size groups 100-200 ha and >200 ha accounted for 41% of the selected farms, but comprised 76% (10.6 Mha) of their arable land. The greater number and diversity of crop rotations observed on larger farms can be attributed to their broader crop portfolios: on average they cultivated 11-12 different crops over the eight years (from the 41-crop-code nomenclature), compared to ~8 crops for 20-50 ha farms and ~5 for farms <20 ha (Figure 6). While more crops generally led to more rotation options, their average rotation length was relatively similar, tending towards three years for larger farms. Rotation flexibility was also similar across all farm sizes, averaging around two years variation within the eight-year period.

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Yet, larger farms tended to have fewer distinct rotations and crops per unit area compared to smaller farms (Figure 6). This indicates that, in larger farms, individual rotations -or crops- were observed over larger surface areas, and crops were more often within the same rotations. This suggests a decline in spatial crop diversity with increasing farm size. Nationally, the mean area occupied by a single rotation was 3.1 ha in farms <20 ha (interquartile range: 1.5-3.8 ha), 6.7 ha in farms of 50-100 ha (IQR: 4.1-7.6 ha), and 13.7 ha in farms >200 ha (IQR: 8.5-16.1 ha).

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Small farms (<20 ha) displayed the most variable rotational patterns. Approximately 30% of their arable land was under near-monocropping systems, while over 40% was managed with rotations of four years (28%) or with no matching pattern (15%). In 67% of these small farms, a single crop rotation accounted for half of their arable land, compared to just 15% and 6% for the 50-100 ha and >200 ha farm groups, respectively. Despite this dominance of few individual rotations on small farms, no single rotation was adopted by more than 10% of them, indicating a high overall diversity of cropping systems. The most commonly implemented patterns among small farms were semi-continuous grasslands and maize grain monocropping. Other rotations adopted by more than 1,000 farms in this group included winter wheat alternated with either maize grain or sunflower. Notably, clusters associated with maize grain monocropping (Group A, Figure 3) had the highest concentration of small farms, representing up to ~40% of all farms for Cluster 1 (see SM).

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Semi-continuous grassland emerged as the most widespread rotation type across all farm size groups. Its prevalence largely explains the lower crop diversity and shorter average rotation lengths observed on farms that included permanent grasslands in their agricultural area, compared to those without (Figure 6). One third of farms with permanent grasslands also managed semi-continuous grasslands. Although permanent grasslands covered only 5-25% of the agricultural area at the district level, they were present on 77% of the 175,560 selected farms.

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Beyond semi-continuous grasslands, the most widespread rotations across all farm sizes were winter wheat – maize silage alternation (~16% of selected farms), the w-b-r and its derivatives (~14%), winter wheat – maize grain alternation (~14%), and near-monocropping of winter wheat (~13%). In total, 28
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distinct rotations were implemented by over 10,000 farms, and 223 rotations were found in more than 1,000 farms. The *w-b-r* rotation, its derivatives, and winter wheat near-monocropping became increasingly dominant in farms larger than 100 ha. These rotations were present on over 60% of the farms in Group F districts, with dominant *w-b-r* rotational systems (Figure 3).

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<figure><img src="image_8.png" /><figcaption>Figure 6: Farm-level crop diversity and rotations indicators for French arable land</figcaption></figure>

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The farms selection procedure is described in the **Section 2.2.3**. Vertical ridgeline plots display the distribution of farm-level indicators within each farm size group, under two modalities (subpopulation shown; averages as dotted lines). *N rotations*: number of distinct crop rotations identified on a farm. *N crops*: number of unique crops cultivated over the eight years per farm (41 crop codes nomenclature in **Table 1**). Both indicators were also divided by the arable land area of the farm (/ ha). *inv_sim* and *inv_sim_cat* are indicators of temporal crop sequence diversity at two levels of crop aggregation (see **Section 2.2.3**), calculated here as area-weighted averages at the farm level. *Rotation length* and sequence coverage (%seq) are also farm-level area-weighted indicators describing rotation characteristics. Stacked bar plots illustrate the composition of arable land in terms of rotation types, as in **Figure 5**, for each farm size group.

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# 4. Discussions

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## 4.1. Strength and limits of the flexible pattern-matching algorithm

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The proposed field-level identification and classification procedure for flexible crop rotations enables multi-scale and cross-thematic analysis of cropping and farming systems through the lens of crop rotations. Our national-scale case study in mainland France demonstrates only a subset of the analytical potential. Understanding the method's key features, adjustable parameters, and limitations is essential before broadening its scope of application.

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First, the procedure does not capture all rotation types and flexibilities. It targets dominant patterns, simplifying inherently more complex annual cropping decisions. For instance, non-cyclical rotations, of variable length, are not addressed. Moreover, “flexible rotation” was usually referring to the eventual substitution of a crop by another within a baseline rotational scheme (Castellazzi et al., 2008), while “flexible rotation” here referred to the sporadic introduction of crops between two occurrences of the rotation. Accordingly, our approach can be seen as a groundwork for broader consideration and characterization of flexibilities in rotations.

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To achieve simplification, the selection process favors shorter rotations. Prioritizing longer matching patterns was discarded as it led to over-selection of rotations with the maximum length ($n = n_{max}$), which are more diverse hence individually less representative. Similarly, allowing identification of patterns longer than $N/2$ (half the observed period) also resulted in selection towards longer, less flexible, and less common rotations, as it required adjusting the sequence coverage threshold (%seq$_{min}$) depending on matching pattern length. Indeed, eight-year crop sequences would always match with a five-year rotation, if still allowing three flexible years (corresponding to a %seq$_{min}$ of 62% here).

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The maximum rotation length ($n_{max}$) strongly influences the results, and was here capped at four due to the eight-year observation window. For example, most rotations involving flax fibers were classified as four-year rotations (mean length: 3.88 years, area-weighted). However, flax fibers were typically observed once during this period (mean occurrence: 1.20, area-weighted), indicating a true return period of six to seven years on the same field. Relying solely on the identified four-year rotation pattern would therefore underestimate this return period. Since the method also retains flexibility characteristics, these can be mobilized post-hoc to reconstruct longer, more representative flax fiber rotations, suitable for application such as soil-crop modeling. Notably, rotations involving flax fibers covered, on average, 72% of the eight-year period (area-weighted), implying the presence of at least two flexible years. By identifying the most common flexible crops inserted into these rotations -using study-area-level statistics- it becomes possible to reconstruct artificial but representative six-year rotations that match the observed flax return period. This approach parallels the method used to derive explicit rotations representative of near-monocropping practices (see Section 2.1.4.).

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The approach was designed to identify steady-state rotations, not temporal changes or land cover transitions. Longer time series, while improving confidence in rotation identification, might also achieve lower overall identification rates as rotational systems shifting would gain more weight (Debaeke et al., 2022; Mignolet et al., 2007). No specific treatment was implemented to identify transition between arable land, permanent grasslands, perennial crop production, or other land cover. For instance, a sequence such as A_A_A_grass_grass_grass_grass_grass was classified as semi-continuous grassland (prairie_62), although it could indicate a transition from arable land to permanent grassland. Identifying such grassland-to-cropland conversions would require context-specific agronomic thresholds and co-variables (Xiao et al., 2015), which are beyond the scope of this study. The decision to treat grass -and legume leys- as other crops shaped the interpretation of crop diversity and rotation indicators. Approximately 7% of arable land was classified as semi-continuous

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grassland (Figure 1) and treated as near-monocropping (one-year rotations). Consequently, indicators for these areas were as low as those for monocropping systems such as maize grain. Agronomically-informed diversity indicators would be better suited to reflect impacts of cropping systems on actual biodiversity or other areas of protections, though such indicators would necessarily remain context-specific (e.g., adapted to local pedoclimatic conditions; Keichinger et al., 2025). Here, diversity should be interpreted in light of the chosen crop aggregation level, as a single crop code may obscure underlying land cover diversity (Reumaux et al., 2023; van der Velde et al., 2024).

## 4.2. Appropriate scale of rotation analysis

This study also raises the question of the appropriate scale for crop rotation analysis. Nationally dominant rotations were geographically associated with clusters of districts sharing similar production orientations and high arable land coverage (e.g., France's 78 w-b-r-dominated districts; see Table 2), but lacked representativeness elsewhere. The relevant scale may depend on the study's thematic focus (e.g., watershed, administrative region), but our method imposes no strict lower spatial limit, as long as representative near-monocropping practices can be reconstructed -typically requiring a minimum of ~1,000 ha. Conversely, our method could help define what a relevant scale might be by identifying shared rotation patterns from field-level data and using them to rezone agricultural districts accordingly -making zoning an output rather than an input. While the farm-level results presented here (Section 3.4.) were derived at national scale, different insights could emerge at intermediate (meso or territorial) scales. Such scales may better capture trade-offs between farm structure (e.g., dominant farm sizes), within-farm cropping and rotational systems, and the resulting inter-farms landscape-level crop diversity, with both spatial and temporal patterns.

Future comparison of dominant rotations and their proportions using this method versus others (e.g., CropRota; Schönhart et al., 2011) or local expert knowledge could enhance interpretation. Such comparisons may also guide the classification of the unmatched crop sequences, for example by determining whether these reflect highly flexible or longer rotations not captured, independent annual cropping decisions, or artifacts from shifting field boundaries over time, among other possibilities. Annual updates from the LPIS dataset allow for routine monitoring of crop rotations and could be used to test the robustness of the results across time periods (e.g., by excluding early years). A major challenge, beyond parcel filiation through time, lies in the evolving LPIS crop code nomenclature -for example, the post-2022 changes in the French LPIS.

## 4.3. From rotational analysis to impact assessment and policy design

Our method can be integrated into simulation-based assessment frameworks, as illustrated by Launay et al., (2021), who used a crop model to evaluate the carbon footprint of French cropping systems. However, it will require selecting which rotations to simulate over the investigated study area. To extend simulation coverage, a similarity metric could be used to assign fields with un-simulated rotations or unmatched patterns to the most similar rotation selected for simulation. Not mobilized here, we explored such distance-based allocation by integrating custom Hamming distance metrics to our method, with further details in the SM.

Improved knowledge of crop rotations enhances our ability to deeply characterize farming systems (Mignolet et al., 2004). Identifying which crop rotations are implemented, and where, is essential for designing, tracking, and evaluating agricultural policies, including the effectiveness of incentives or interventions promoting sustainable practices. Our approach supports the characterization of baseline rotations, monitoring their evolution at different temporal milestones. For instance, it could be used to strengthen the role of crop rotations in future EU CAP frameworks by enabling quantitative monitoring of rotational patterns, which are currently assessed mainly by crop frequency and
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maximum consecutive occurrences (van der Velde et al., 2024). Quantifying and localizing crop rotations also provide a grounded evidences for training, advisory services, and policy making across thematic areas (e.g., organic farming, mixed crop-livestock systems) and spatial scales. For instance, it can help disseminate how and under which conditions -currently minor- crops could be inserted into existing cropping systems, and foster transition of practices. Such systematic rotational systems innovation tracking is directly enabled by our approach, and entirely tunable by designing a crop code nomenclature tailored to emphasize specific minor crops, as opposed to the dominant-crop oriented nomenclature proposed here (Table 1). Other application examples include unravelling the relation between rotational practices and intercrop management. Albeit necessary to assess carbon storage, erosion, or water issues, French LPIS do not provide intercrop management data. Jointure with remote sensing data may offer opportunities for this need.

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Beyond identifying “which” and “where”, understanding “why” and “how” specific rotations are adopted into different farming systems -e.g., if intentional or conjectural- remains crucial. Future research should explore the drivers of rotational flexibility and the role of specific flexible crops, potentially using decision-rule frameworks at the farm level to classify not only by observation but also by farmer intent (Dury et al., 2013). Unraveling the drivers of rotation adoption can be achieved by linking this rotation analysis to farming structure datasets covering e.g., livestock, yield, management practices, pedoclimatic variables and market conditions (Burchfield et al., 2024; Chongtham et al., 2017; Pott et al., 2023).

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## 5. Conclusion

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We proposed a novel generic pattern-matching algorithm to identify and classify crop rotations from field-level annual crop sequences, enabling the quantitative assessment of rotations characteristics, such as composition, length, and flexibility, across spatial scales. Applied to the 15.8 million hectares of arable land in mainland France from 2015 to 2022, our approach revealed that national-level cropping systems are structured around a limited yet flexible and regionally distinct set of crop rotations. A spatial typology at the agricultural district level identified 25 distinct zones with typical rotational systems. At the national scale, organic farming systems exhibited greater crop diversity and rotational flexibility than conventional systems. On average, larger farms implemented longer and more diverse rotations than smaller farms, but over larger areas, resulting in lower spatial diversity. The proposed method is adaptable to various regions and objectives, providing a robust tool for the diagnosis and assessment of cropping and farming systems. It may equip agricultural stakeholders at multiple levels with a mean to characterize these agricultural systems and better target improvement strategies. It also lays the groundwork for large-scale simulations that accurately represent field-level practices, while allowing localized focus on innovative or specific rotational systems. Future research should integrate rotation-level data with farm management, biophysical, and socioeconomic data to uncover the drivers of rotation adoption with their respective flexibilities, as well as anticipating their evolution in a changing world.

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## 6. Data statement

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Supporting data is available at https://doi.org/10.57745/XJ13KO, and the code use to generate and analyze the data for the case study is available at https://forge.inrae.fr/ugo.javourez/crop-rotations-pattern-matching-algorithm.
7. CRediT author statement

**Javourez Ugo**: Conceptualization, Methodology, Software, Formal analysis, Investigation, Data curation, Writing – Original draft, Visualization. **Girault Baptiste**: Conceptualization, Methodology, Writing – Review & Editing. **Martin Philippe**: Conceptualization, Methodology, Writing – Review & Editing. **Dedieu Marie-Sophie**: Conceptualization, Resources, Writing – Review & Editing. **Therond Olivier**: Conceptualization, Methodology, Writing – Review & Editing, Supervision, Funding acquisition

8. Funding sources

This work is part of the project SLAM-B of the exploratory research program FairCarboN and received government funding managed by the Agence Nationale de la Recherche under the France 2030 program, reference ANR-22-PEXF-0003. It was also supported by the European Union (EU) under the Horizon Europe program (HORIZON-MISS-2023-CLIMA-01-01 topic) project TRANSFORM (grant agreement 101155748).

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