# Combining a field experiment and literature to model the regrowth probability of perennial storage organs fragmented by tillage: Case study of Cirsium arvense (L.) Scop

Solèmne Skorupinski, Hugues Busset, Jacques Caneill, Delphine Moreau, Brice Mosa, Eugène Motton, Nathalie Colbach

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Solèmne Skorupinski, Hugues Busset, Jacques Caneill, Delphine Moreau, Brice Mosa, et al. Combining a field experiment and literature to model the regrowth probability of perennial storage organs fragmented by tillage: Case study of Cirsium arvense (L.) Scop. Soil and Tillage Research, 2024, 244 (2), pp.106279. 10.1016/j.still.2024.106279. hal-04721747

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# Combining a field experiment and literature to model the regrowth probability of perennial storage organs fragmented by tillage: Case study of *Cirsium arvense* (L.) Scop

Solèmne Skorupinski<sup>a</sup>, Hugues Busset<sup>a</sup>, Jacques Caneill<sup>a</sup>, Delphine Moreau<sup>a</sup>, Brice Mosa<sup>b</sup>, Eugène Motton<sup>a</sup>, Nathalie Colbach<sup>a,*</sup>

## ARTICLE INFO

### Keywords:

Perennial weed

*Cirsium arvense* (L.)

Tillage tool

Fragmentation

Regeneration rate

Predictive model

Non-chemical weed management

## ABSTRACT

Management of perennial weeds has become increasingly difficult with the reduction of herbicide use. Creeping perennials accumulate reserves in specialized belowground organs from which they regenerate new plants after a disturbance. Through tool selection, tillage operations could be optimized to reduce perennial-weed reserves and limit regeneration. In the present study, the effect of five tools on the fragmentation of the creeping roots of *Cirsium arvense* (L.) Scop. (Canada thistle), a major perennial weed in arable crops, were analysed. A field trial was set up to measure the lengths of the root fragments left after tillage. Five tools were tested: mouldboard ploughing, rotary harrow, disc harrow, rigid-tine cultivator and goose-foot cultivator. Fragment-length distribution varied according to the tool: rotary harrow left the smallest (3.7 cm on average) and least variable fragment lengths, mouldboard ploughing the longest (12.7 cm) and most variable ones. The other tools produced intermediate-sized fragments (8–10 cm). Based on these results and literature, a model was proposed to predict perennial-weed regeneration probability from storage-organ fragments after one tillage run. The effects of six factors, which were agronomic (tillage tool), environmental (soil conditions and temperature) and biological (storage-organ fragment diameter, maximal belowground-shoot length and pre-tillage storage-organ distribution), were tested through a sensitivity analysis. According to the model, the probability of fragment regeneration success is lower for the rotary harrow than for the mouldboard plough. The most important drivers of fragment regeneration success were the biological traits: fragment diameter and maximal belowground-shoot length per unit fragment biomass. The present model should be complemented to predict the effect of tillage on perennial-weed regrowth and help improving non-chemical weed-management strategies. To achieve this, further research is needed on plant regrowth potential from storage organs and their architecture in the soil.

## 1. Introduction

Weeds are a major cause of yield loss in arable crops (Oerke, 2006). Herbicides are the most used weed-control technique but this practice must be reduced owing to its detrimental effects on the environment and human health (Haarstad and Ludvigsen, 2007). However, to date, there is no alternative in-crop curative technique as simple and efficient as herbicides. Herbicide-sparse weed control must therefore rely on a complex combination of partially effective mostly preventive cultural techniques (Liebman and Gallandt, 1997). Tillage operations are a key alternative lever for weed management but this practice also needs to be

reduced as it is costly, time-consuming and may degrade soils (Holland, 2004).

Herbicide-sparse and low-till fields have been reported to be increasingly infested by perennial weeds (Trichard et al., 2013; Salonen et al., 2023). Perennials, unlike annuals, accumulate reserves in storage organs that persist through the non-growing season and can regrow new plants by vegetative multiplication. This enables perennials to propagate rapidly and to regenerate following a disturbance that destroyed or damaged aboveground plant parts or storage organs. The most troublesome perennial weeds develop belowground storage organs (Håkansson, 1982) such as roots capable of adventitious sprouting (e.g.,

<footnote><sup>a</sup> Agroécologie, INRAE, Institut Agro, Univ. Bourgogne, Univ. Bourgogne Franche-Comté, Dijon F-21000, France</footnote>

<footnote><sup>b</sup> INRAE, U2E, Unité Expérimentale du domaine d'Epoisses, Bretenière F-21110, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: nathalie.colbach@inrae.fr (N. Colbach).</footnote>
Cirsium arvense (L.) Scop., Sonchus arvensis L.) or rhizomes (e.g., Elymus repens (L.) Gould) (Lacroix, 2020; Tørresen and Gerowitt, 2022). These organs are well protected from harsh environmental conditions (e.g., frost and drought), can grow deeper than tillage depth, spread rapidly and have a great regeneration capacity (Zimdahl, 2018). Even few-cm-long pieces of sprouting roots or rhizomes can regrow a new plant (Håkansson, 1982). These weeds are thus very hard to control without herbicides or intensive tillage (Mohler et al., 2021) and farmers often lack solutions.

To reduce perennial weeds in arable fields, the reserves in the storage organs must be depleted to hamper the regeneration and proliferation of new plants (Graglia et al., 2006). To this end, tillage (between harvest and sowing) is a key lever (Melander et al., 2012). Indeed, tillage 1) destroys aboveground plant parts, stopping carbon supply and therefore reserve accumulation 2) fragments and buries the storage organs located in the tilled layers, which triggers the regrowth of belowground adventitious shoots. To prevent new plants from regenerating, tillage-induced storage-organ fragments should be small and buried deeply (e.g., Anbari et al., 2011) so that the reserves are insufficient for the belowground shoots to reach soil surface and develop a new plant.

Field studies suggest that the choice of the tillage tool has an impact on the control of perennial weeds: perennial-weed infestation in the year (s) following tillage depends on tillage depth (Børresen and Njøs, 1994; Brandsæter et al., 2011), the tool's ability to invert the soil (Chandler et al., 1994; Pekrun and Claupein, 2004; Weigel et al., 2024) and, more rarely, on the type of share (e.g., duckfoot tine vs. disks in Aronsson et al., 2015). Some underlying mechanisms have already been investigated. The effect of tillage tools on soil conditions (notably structure) according to their mechanical actions and to their tillage depth has been studied for a long time (Hénin et al., 1969; Perdok and Kouwenhoven, 1994; Roger-Estrade et al., 2004). The movement of soil clods, seeds and plant debris during tillage in interaction with soil conditions has also been investigated and modelled (Cousens and Moss, 1990; Mead et al., 1998; Colbach et al., 2000, 2014; Roger-Estrade et al., 2001). In a few rare cases, perennial-weed regrowth from belowground storage organs has been investigated in sufficient detail to predict shoot elongation as a function of the biomass of storage-organ fragments (Torssell et al., 2015, 2016). However, little is known about how tillage fragments storage organs of perennials. Moreover, to our knowledge, no study has combined all the knowledge to determine how the choice of the tillage tool influences the regeneration of perennial weeds, depending on soil conditions and weed species.

Consequently, the objectives of this study were 1) to analyse the impact of several tillage tools on the length of the produced storage-organ fragments by means of a field experiment, 2) to propose a model (with knowledge from the present experiment and from literature) for predicting storage-organ fragment regeneration probability and 3) to use this model to evaluate the sensitivity of fragment regeneration probability (i.e., the proportion of storage-organ fragments that will give rise to, at least, one new emerged plant) to tillage, soil conditions and weed-species traits. We focused on *Cirsium arvense* (Canada thistle), a perennial species with creeping roots capable of adventitious sprouting, which is one of the most problematic weeds in both organic and conventional farming systems in Europe (Andert et al., 2023) and elsewhere (Skinner et al., 2000).

# 2. Materials and methods

## 2.1. Overview

The existing knowledge on the morphology and regenerative capacities of *Cirsium arvense* was synthesized to justify the methodological choices during the field experiment and the construction of the predictive model of tillage-induced-fragment regeneration probability. A field trial was conducted in Dijon in 2022–2023 to compare the effect of five contrasting tillage tools on the size of *C. arvense* root fragments. The

fragments were sampled in the soil after single passages by the five tools. They were identified according to the organ type and measured in length and diameter. By combining the results of this experiment and data from literature on the other processes involved, a model to predict the regeneration probability of perennial weeds from tilled fragments was built. A practical application in different scenarios and a sensitivity analysis were performed to identify and rank the factors with the greatest impact on the regeneration rate.

## 2.2. Morphology and functioning of thistle belowground system

### 2.2.1. Which part can multiply if fragmented?

*Cirsium arvense* is a perennial species which propagates via a complex belowground system (Fig. 1) consisting of: ① ordinary absorbent roots, ②③ creeping roots (also called sprouting, thickened or plagiotropic roots), ④ adventitious buds ⑤ belowground shoots (also called adventitious shoots) and ⑥ belowground part of emerged shoots (Sagar and Rawson, 1964). Only the creeping roots and, in some cases, the below-ground part of emerged shoots (sometimes mistakenly referred to as “rhizomes” (Donald, 1994)) are capable of vegetative multiplication.

To model the regeneration probability of *C. arvense* (and perennial weed species in general) from fragments of storage organs, it is essential to consider only the fragments that can regenerate a new plant (i.e., that are capable of vegetative multiplication). The main regenerative organs of *C. arvense* are the creeping roots ②③ in Fig. 1. These are easy to recognize because they bear many adventitious buds and their diameter is usually between 5 and 15 mm (Sagar and Rawson, 1964). They can grow new shoots as soon as they reach 1 mm in diameter (Hamdoun, 1972) so all creeping roots over 1 mm in diameter should be considered.

The belowground part of emerged shoots ⑥, recognizable by their scale leaves, can also produce further new shoots once their reserves are replenished by the aboveground part (see Magnusson et al., 1987). Replenishment starts after the aboveground shoot assimilates more carbon than needed by stems, leaves and absorbent roots (i.e., compensation point, see Nkurunziza and Streibig, 2011; Verwijst et al., 2018). Replenished belowground shoot parts (i.e., which are able to multiply) were reported to be thickened and akin to a taproot (Lund and Rostrup, 1901) but there is no precise morphological criterion to distinguish them from reserve-less belowground shoot parts ⑤.

Therefore, we considered that the thin (less than 5 mm in diameter), hollow and brittle belowground shoot fragments, without root branching nor adventitious buds were not able to regenerate a new plant (= reserve-less belowground shoots ⑤) and should not be included in the model. To conclude, only fragments of creeping roots over than 1 mm in diameter and the fragments of “thickened” belowground shoot parts ⑥ were considered as a potential regeneration source here.

### 2.2.2. How is the belowground system distributed across soil layers?

According to field observations, 25–50 % of the *C. arvense* root system is located above 25-cm depth (Nadeau and Vanden Born, 1989; Tiley, 2010) and can be fragmented by tillage. However, to our knowledge, only Frank et al. (2010) studied *C. arvense* root systems at a scale fine enough to allow a description of root distribution in tilled soil layers. They found a gradual increase in root frequency with soil depth until 50-cm depth which suggests that the impact of tillage on creeping-root fragmentation will depend on tillage depth and tillage-induced soil movements.

## 2.3. Description of tillage tools used

Five tillage tools (Table 1) were chosen according to their contrasting attributes and usual tillage depths to compare contrasted types of mechanical actions on the soil and cover a diverse range of farming operations. Overall, tillage depths varied from 6 to 25 cm; shares, discs and tines were compared; one tool (rotary harrow) was power take-off driven and one tool (mouldboard ploughing) induced a complete soil
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Diagram of a possible belowground system of *Cirsium arvense* with soil depth in purple. Each number corresponds to a type of organ. The organs that contain reserves and are able to regenerate if fragmented are in bold. The drawing, with the corresponding soil depth values, was extracted and adapted from (Tiley, 2010), itself extracted and adapted from Lund and Rostrup (1901) with permission of the Royal Danish Academy of Sciences and Letters. Tillage frequencies were added for general information only, from often tilled soil layers (in red) to untilled soil layers (in white).</figcaption></figure>

inversion.

## 2.4. Field trial

The field trial was carried out at the INRAE Dijon-Epoisses experimental station (Bretenière, France, 47.237881, 5.099605, 210 m, weather data in Fig. S1-S2 in supplementary material online) on a plot with a high density of *C. arvense*. The field had been managed for several years without pesticides and with regular tillage. The last tillage operations (superficial tillage with a goose-foot cultivator followed by a rotary harrow) was carried out in March 2022 and preceded an onion crop. The soil was a eutric cambisol (FAO classification) and average texture of the ploughed layer (0–30 cm) was 32 % clay, 61 % silt and 7 % sand. *C. arvense* was the only perennial species present.

All patches of *C. arvense* were geolocated with a GNSS (Global Navigation Satellite System) receiver (Trimble®). The field was divided into six strips: one for each tool plus one to remain untilled (Fig. S3 in supplementary material). The tilled strips were made wide enough to include at least two tool runs (i.e., twice the tool width) and were widened further when the patches of *C. arvense* were few or sparse. Two grass strips (initially present on the field) perpendicular to the tilled strips were used to discriminate three non-randomised blocks perpendicular to tillage runs. For practical reasons (tillage operations and *C. arvense* patch locations), it was impossible to set up a completely randomised design.

The mouldboard plough, the disc cultivator and the goose-foot cultivator were applied on 8 November 2022 and the rotary harrow and the rigid-tine cultivator (also called chisel) were applied on 30 January 2023. On each tillage date, three soil samples of approx. 250 mg were collected (0–10 cm depth) per tool and per block to assess soil moisture level. The samples were weighted before and after drying at 105 °C for 48 hours. Soil moisture level was 18 % (resp. 21 %) at first (resp. second) tillage date and there was no significant difference between tools nor blocks (Fig. S4 in supplementary material online), showing that soil moisture was likely to be homogeneous across all plots. Soil water potential was calculated from soil moisture level according to van Genuchten's (1980) equation (that had been fitted to data of INRAE Dijon-Epoisses experimental station in a previous study, Colbach et al., 2006) and was −0.26 MPa (resp. −0.13 MPa) at first (resp. second) tillage date.

Soil structure was described just after tillage in each tilled strip and in the untilled strip. Three-m-wide and 60-cm-deep observation pits were dug perpendicular to the tillage direction and the soil structure of the 0–30 cm layer was described using the method proposed by Manichon (1982), (1987) (see also Roger-Estrade et al., 2004). The soil structure was similar in each strip (90 % dominant CΔ structure, corresponding to a compacted soil). The soil profiles were also used to determine tillage depth (Table 1).

## 2.5. Fragment sampling

Within each tilled strip, three 50 × 50 cm quadrats per block were delimited, that is, nine quadrats per tool in total. The quadrats were placed where the patches of *C. arvense* had been geolocated beforehand (see 2.4) to ensure the presence of root fragments. The soil within the quadrat was excavated manually down to the tillage depth (depending on the tool, see Table 1), and *C. arvense* root fragments were extracted carefully. If a fragment broke during the extraction (which occurred very rarely), it was discarded. Fragments were put into plastic bags (one bag per quadrat) and stored in a cold chamber at 3°C in complete darkness until measurements.

## 2.6. Fragment measurements

After sampling, the bags were emptied one by one and the fragments were washed with clear water to facilitate inspection and measurements. The few fragments from other species were discarded. First, root-based fragments were distinguished from belowground-shoot-based fragments. Then, only fragments of creeping roots over 1 mm in diameter and fragments of thickened belowground shoot parts fragments were kept (see morphological criterion in 2.2.1 and examples of fragment in Fig. 2). If aboveground parts were still present, they were removed.

The length and diameter of each fragment were measured with a ruler and a digital caliper, respectively. Several diameter measurements (one every 5 or 10 cm depending on the length and shape of the fragment) were taken to calculate an average diameter. In branched fragments, the longest axis was identified and the other axes were measured separately. Finally, all the fragments were dried in a 105°C oven for 48 hours and weighed for biomass determination.
<caption>**Table 1**</caption>

Characteristics and working depths of the five tillage tools in the experiment of tillage effects on *Cirsium arvense* root-fragment lengths. The mechanical action of the tool on the soil is also described (synthesis from literature (Hénin et al., 1969; Perdok and Kouwenhoven, 1994)). Working depths were measured on vertical soil profiles after tillage in our experiment. (CC BY NC ND Solèmne Skorupinski).

<table><thead><tr><th>Tool name</th><th>Working depth (cm)</th><th>PTO<sup>a</sup>-driven</th><th>Soil inversion</th><th>Blade type</th><th>Picture</th></tr></thead><tbody><tr><td>Mouldboard plough</td><td>22-25</td><td>No</td><td>Yes</td><td>Share</td><td></td></tr><tr><td></td><td colspan="5">The soil is cut horizontally and vertically into furrows, which are twisted (around an axis parallel to tillage direction), and then fragment into slices sliding down onto the plough pan. Complete soil inversion (which no other tool does), with a deep burial of previously superficial soil, seeds, roots and other organic matter.</td></tr><tr><td>Disc cultivator</td><td>10-12</td><td>No</td><td>Yes</td><td>Disc</td><td></td></tr><tr><td></td><td colspan="5">The soil is cut vertically by the sharp edges of the discs, which pulverizes soil clods. Partial soil inversion due to the rotational movement and the concave shape of the discs.</td></tr><tr><td>Rigid-tine cultivator</td><td>13-15</td><td>No</td><td>No</td><td>Tine</td><td></td></tr><tr><td></td><td colspan="5">The soil is cut horizontally and vertically by the tines. Clods are fragmented during tine progress parallel to tractor movement. No noticeable soil inversion.</td></tr><tr><td>Goose-foot cultivator</td><td>6-8</td><td>No</td><td>No</td><td>Tine</td><td></td></tr><tr><td></td><td colspan="5">Same effects as for rigid-tine cultivator but the wider and flat-shaped shares also cut horizontally and spread soil clods.</td></tr><tr><td>Rotary harrow</td><td>6-8</td><td>Yes</td><td>No</td><td>Tine</td><td></td></tr><tr><td></td><td colspan="5">The soil is intensively cut and sheared by the vertical rotary movement of sharp blades. Clods are pulverized and projected more intensively than by unpowered tools. Important soil inversion (but less deeply than mouldboard ploughing).</td></tr></tbody></table>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

## 2.7. Statistical analyses

To analyse the effect of tillage tool on the fragmentation of *C. arvense* belowground organs, the length of the fragments that are able to regenerate (i.e., creeping-root and thickened-belowground-shoot-part fragments) were analysed. In branched fragments, only the length of the longest axis (see 2.6) was used, as the number of branches is not related to the effect of tillage but to the initial root system density at the sampling location. Hereafter, all fragments included in the analysis are referred to as "root fragments" for simplicity.

### 2.7.1. Comparing the effect of tillage tools on root-fragment length

A preliminary analysis showed that there was no correlation (at p = 0.05) between the length and the diameter of the fragments (see Fig. S5 in supplementary material online). Thus, the length of a fragment was analysed independently of its diameter. The distribution of the lengths of the root fragments was quantified by fitting a non-linear model (Weibull function) to the cumulated frequency of the observed lengths (Fig. 3), using the *nls()* function or R (R Core Team, 2023).

The Weibull function parameters were used to calculate the quantiles

of root fragment length distribution: q25 and q75, the first and last quartiles (Equation 2 in Fig. 3). In other words, 25 % (75 %) of the fragments were shorter than q25 (respectively q75).

To assess the impact of the tillage tool on the distribution of root fragment lengths and to check if the observed effect was independent of the tillage location in the plot (block), the quantiles of root fragment length distribution (q25 and q75) were analysed with a linear model as a function of tool and block, using the *lm* function of R (R Core Team, 2022) followed by an analysis of variance with the Anova function of R and type-III sum of squares.

Finally, a pairwise comparison of means using an LSD test (Fisher's least significant difference test, *LSD.test()*) function from the *agricolae* package in R) was carried out to compare fragment lengths by tool.

### 2.7.2. Decomposing the effect of tools according to their mechanical properties

With a perspective of predicting *C. arvense* root fragment length after tillage with new tools (i.e., other tools than the five used in the present experiment), the effect of the main tool characteristics were studied. The quantiles of root fragment lengths distribution (q25 and q75) were

<footnote>a Power take-off.</footnote>
<figure><img src="image_11.png" /><figcaption>Fig. 2. Pictures (CC BY NO ND) of Solémne Skorupinski of Cirsium arvense belowground-organ fragments sampled on the field: a) emerged but thin and reserve-less belowground shoot part attached to parent creeping-root, b) portion of a 2-cm-in-diameter creeping root with an adventitious bud, c) emerged and replenished belowground shoot part attached to parent creeping-root. The aboveground plant part was determined based on the absence of root branching, green colour and fibrous aspect.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 3. Cumulated frequency of root fragment lengths after one tillage run (example of mouldboard plough of block 1). Symbols: observed fragment lengths; continuous red line: fitted Weibull equation (eq. 1). Eq. 2 allows calculating percentiles (dotted blue lines) characterising the distribution.</figcaption></figure>

analysed as a function of tillage depth (cm), working mode (i.e., with or without power take-off drive) and blade type (share/disc/tine) as given in Table 1.

A linear regression model was fitted, using the *ols.step backward p()* function to successively eliminate factors that were not significant at *p* = 0.05. Partial *R*² were calculated to quantify the relative effect of factors on the variation of shoot length (Type-III Anova function of R).

## 2.8. A model to predict regeneration rate from perennial-weed fragments after tillage

The regeneration rate after tillage from storage-organ fragments was defined as the percentage of able-to-multiply fragments from which at least one belowground shoot will reach soil surface and establish a new photosynthesizing plant. To predict regeneration rates, the regeneration success of each fragment must be determined, which requires to estimate 1) the length of each fragment after tillage, 2) the maximum length that the belowground shoots of each fragment can reach and 3) the soil depth at which each fragment is buried. The first step was based on the
present experiment on *C. arvense*, the other two on literature.

### 2.8.1. Predicting storage-organ fragment length after tillage

To predict fragment length after tillage with a given tool, the results of the present field experiment on the fragmentation of *C. arvense* root system were used. The probability density function of fragment lengths was calculated for each tool by derivating the corresponding Weibull function (see Figs. 3 and 4).

### 2.8.2. Predicting maximal shoot length per fragment

The maximum length that a belowground shoot growing from a storage-organ fragment can reach depends on the fragment weight, and by extension, on its dry biomass (Torsell et al., 2015). Fragment dry biomass can be estimated from fragment length and diameter. To do so, we used the data from the present experiment: the dry biomasses of the unbranched creeping-root fragments of *C. arvense* were analysed as a function of their length and diameter with *lm* function of R.

No data was available in literature to predict maximum belowground shoot length from fragment biomass in *C. arvense*. Instead, data on *S. arvensis* was used, which is a creeping-root-perennial species similar to *C. arvense*. Torssell et al. (2015), (2016) modelled root fragment biomass depletion and allocation to the belowground shoots and fine roots, according to soil temperature and to the initial biomass of the root fragment (they adjusted the equations parameters for three fragment-size categories). Here, their equations were used to calculate, for each fragment, the maximum amount of biomass that can be allocated to the shoot depending on the initial fragment biomass and soil temperature (using their parameter values for "medium sized roots" as an average to easily take fragment of all sizes into account). The shoot biomasses were then converted to shoot lengths using *S. arvensis* shoot specific length (Torsell et al., 2016).

### 2.8.3. Predicting fragment burial depth

To our knowledge, there are no data regarding the burial depth of fragments of perennial storage organs in response to tillage. Instead, the results on seed movements during tillage were used (Cousens and Moss, 1990; Mead et al., 1998; Colbach et al., 2000, 2014; Roger-Estrade et al., 2001). These consist of a series of matrixes of the proportion of seeds (or root fragments in the present case) moved from a pre-tillage 1-cm-thick soil layer to a post-tillage 1-cm-thick soil layer for a given tillage tool and tillage depth as well as soil structure.

The tillage-induced fragment-movements matrixes must be applied to a matrix of the proportion of storage organs per 1-cm thick soil layers down to the deepest tillage layer. We used the work of Frank et al. (2010) who measured and modelled root frequency as a function of root depth for several species (including *C. arvense*) by measuring the presence of root DNA in soil cores in intervals of 5 and 10-cm depth.

<figure><img src="image_13.png" /><figcaption>**Fig. 4.** Probability density of *C. arvense* root fragment lengths (cm) as a function of tillage tool. Each curve is the derivate of the Weibull equation (Fig. 3) with the corresponding coefficients.</figcaption></figure>

## 2.9. Model application to evaluate the sensitivity of the weed regeneration rate to tillage, species characteristics and environment

### 2.9.1. Principle

To test our model, the sensitivity of the post-tillage storage-organ fragment regeneration probability of perennials to tillage, weed species characteristics and environment was evaluated. The regeneration probability was calculated for the two most contrasting tillage tools (mouldboard plough with a skim-coulter vs rotary harrow) with their usual tillage depth (25 and 8 cm, respectively), two soil structures (compacted vs uncompacted soil), two pre-tillage storage-organ distributions in tilled soil layers (uniform vs depth-increasing), two soil temperatures (10 vs 18°C), two fragment diameters (0.3 vs 0.6 cm) and two levels of shoot length per unit fragment biomass (the one calculated according to Torssell et al. 2015, 2016 vs half that value). The combination of these factors resulted in 64 scenarios (2 tools × 2 soil structures × 2 organ distributions × 2 soil temperatures × 2 fragment diameters × 2 shoot lengths per biomass unit), each simulating one thousand fragments.

### 2.9.2. Steps

First, one thousand fragment lengths were generated according to the fragment length distribution of the chosen tillage tool. Secondly, for a given fragment diameter, fragment lengths were converted to dry biomasses according to the relationship established from the data on fragment measurements of the present experiment. Then, maximal shoot lengths were calculated according to fragment dry biomasses for a given temperature with the equations of Torssell et al. (2015), (2016) according to the chosen level of shoot length per unit fragment biomass. In parallel, a burial depth was randomly drawn for each fragment according to a post-tillage-distribution matrix. The latter was obtained by applying the tool-and-soil-structure specific fragment-movement matrix to the pre-tillage perennial-organ distribution.

Finally, for each fragment, burial depth and maximal shoot length were compared to determine if the shoot could reach soil surface and develop a new plant (i.e., if the fragment could regenerate). If maximal shoot length exceeded burial depth by at least 1 cm, regeneration was considered successful for the fragment with exception for fragments located on soil surface (i.e., with burial depth = 0 cm). The latter are considered to be drying out and dying (personal observations and Sciegienka et al., 2011). Finally, the regeneration rate was the number of regenerated fragments out of the 1000 fragments initially generated.

### 2.9.3. Sensitivity analysis

To assess the impact of tillage, weed species characteristics and the environment on the probability that a fragment of perennial-weed storage organ regenerates successfully, the regeneration success response variable (yes/no) was analysed as a function of the factors of the tested scenarios: tillage tool, soil structure, pre-tillage storage-organ distribution, soil temperature, fragment diameter and shoot length per unit fragment biomass. A binary logistic regression was carried out with the `glm` function of R (R Core Team, 2023) using the family = *quasibinomial*(link = "logit") argument, followed by a Type-III Anova function with a p-value significance threshold of 0.05. Odd ratios were calculated to compare the relative odds of the regeneration success of fragments given exposure to the different variables of interest (here, the six factors of the scenarios). The more the odd ratio of a factor differs from 1 (higher or lower), the more the factor affects (respectively, increases or decreases) the regeneration probability of the fragments.

## 3. Results

### 3.1. Root fragment length depends on the tool

The non-linear Weibull equation was fitted satisfactorily to the frequencies of root fragment lengths for each tool (Fig. 3) with high R²
values (between 0.95 and 0.99). The analyses of variance on the quantiles of the distribution of root fragment lengths revealed that the block effect was never significant (at p = 0.05). As the soil moisture was shown to be similar in all plots and soil structure similar across all tilled strips (2.4), the experimental conditions (soil conditions and plant characteristics) can thus be considered sufficiently homogeneous across blocks so that the non-randomization of the tillage tools inside the blocks did not affect our results. The effect of the tillage tools was significant (at p = 0.05) and explained 49 % and 59 % of the variability in the first and third quartile values, respectively (see Fig. S6 in supplementary material online).

Across all tools, root fragment lengths varied mainly between 1 and 20 cm, with only 6 % of the fragments longer than 20 cm (Fig. 4). The most contrasting tools were the rotary harrow and the mouldboard plough (Table 2). The rotary harrow produced the shortest and least variable fragment lengths, while the mouldboard plough produced the longest and most variable fragment lengths (Fig. 4). Indeed, 75 % of the fragments produced by the rotary harrow were shorter than 4.3 cm (q25 in Table 2) while 75 % of the fragments produced by the mouldboard plough were longer than 7 cm (q25 in Table 2). The longest fragments produced by mouldboard ploughing were longer than 16.8 cm (q75 in Table 2) and some fragments exceeded 20 cm (Fig. 4). The distributions of root fragment lengths after the rigid-tine cultivator, goose-foot cultivator and disc cultivator were similar (Table 2) and intermediate between those of the rotary harrow and the mouldboard plough. In average, the shortest lengths varied between 4.3 and 5.5 cm and the longest lengths varied between 9.7 and 11.5 cm.

## 3.2. The link between root-fragment length and tillage-tool characteristics

When analysing the root-fragment length distribution as a function of tool characteristics, the results for the shortest (q25) and the longest (q75) fragments were similar. The main determinants of root fragment length distribution were the blade type (highest partial R² of 0.39 and 0.44 for q25 and q75, respectively, Table 3) and the working mode (0.42 and 0.38). Shares produced longer fragments than discs and tines. The difference in lengths between tines and discs was not significative. Power take-off driven tools produced shorter fragments than drawn tools.

Among the longest fragments, shares induced 6.4-cm longer fragments than the tines and 5.1-cm longer ones than discs. The difference was less pronounced (2.5 and 0.4 cm respectively) for the shortest fragments (all else being equal). In other words, for a given tillage depth and working mode, a tool with shares considerably increased the length of large fragments compared to discs and, even more, tines.

The conclusion was similar for working blade effect: compared with drawn tools, power-take-off-driven tools reduced the length of the longest fragments more than shorter ones. Therefore, the power take-off driven blade movements prevented especially the occurrence very long fragments.

### Table 2

Comparison of root fragment length distributions for each tool. Mean lengths of the shortest and longest fragments (given first and last quartiles values, q25 and q75 respectively, calculated with the Weibull equation with the corresponding coefficients for each tool, Fig. 3). Means followed by a common letter (A, B, or C) are not significantly different at p = 0.05 (pairwise comparison of means with a least-significant-difference test).

<table><thead><tr><th rowspan="2">Tillage tool</th><th colspan="2">Shortest fragments<br>q25 (cm)</th><th colspan="2">Longest fragments<br>q75 (cm)</th></tr><tr><th>Mean</th><th>Group</th><th>Mean</th><th>Group</th></tr></thead><tbody><tr><td>Rotary harrow</td><td>2.0</td><td>A</td><td>4.3</td><td>A</td></tr><tr><td>Rigid-tine cultivator</td><td>4.3</td><td>B</td><td>9.7</td><td>B</td></tr><tr><td>Goose-foot cultivator</td><td>4.8</td><td>B</td><td>10.9</td><td>B</td></tr><tr><td>Disc cultivator</td><td>5.5</td><td>BC</td><td>11.5</td><td>B</td></tr><tr><td>Mouldboard plough</td><td>7.0</td><td>C</td><td>16.8</td><td>C</td></tr></tbody></table>

### Table 3

Response of the quartiles of root fragment length distribution (q25 and q75) to the tillage tool characteristics. Regression coefficients and analysis of variance (type-III sum of squares) with partial R² indicating the proportion of variance explained by each factor. NS = not significant at p = 0.05. Estimates followed by a common letter (A, B, C or D) are not significantly different at p = 0.05.

<table><thead><tr><th rowspan="2">Factor</th><th colspan="3">Shortest fragments<br>q25 (cm)</th><th colspan="3">Longest fragments<br>q75 (cm)</th></tr><tr><th>Estimate</th><th>Group</th><th>Partial<br>R<sup>2</sup></th><th>Estimate</th><th>Group</th><th>Partial<br>R<sup>2</sup></th></tr></thead><tbody><tr><td>Intercept</td><td>4.552</td><td></td><td></td><td>10.451</td><td></td><td></td></tr><tr><td>Blade type</td><td></td><td></td><td>0.397</td><td></td><td></td><td>0.443</td></tr><tr><td>Share</td><td>2.463</td><td>A</td><td></td><td>6.387</td><td>A</td><td></td></tr><tr><td>Disc</td><td>0.408</td><td>B</td><td></td><td>1.291</td><td>B</td><td></td></tr><tr><td>Tine</td><td>0</td><td>B</td><td></td><td>0</td><td>B</td><td></td></tr><tr><td>Working<br>mode</td><td></td><td></td><td>0.423</td><td></td><td></td><td>0.377</td></tr><tr><td>PTO<sup>a</sup>-<br>driven</td><td>-2.609</td><td>C</td><td></td><td>-5.999</td><td>C</td><td></td></tr><tr><td>vs Drawn</td><td>0</td><td>D</td><td></td><td>0</td><td>D</td><td></td></tr><tr><td>Working<br>depth (cm)</td><td></td><td></td><td>NS</td><td></td><td></td><td>NS</td></tr><tr><td>Total</td><td></td><td></td><td>0.82</td><td></td><td></td><td>0.83</td></tr></tbody></table>

Finally, the tillage depth had no significant effect, meaning that root fragment lengths were the same for all tillage depths, all else being equal. However, the depth effect was hidden by the other two effects. Indeed, the blade types producing the longest and shortest fragments were also the tools tilling the most deeply (mouldboard ploughing) and most shallowly (tines), respectively. Similarly, the working mode producing the longest and shortest fragments were also those tilling the most (drawn-tools) and least deeply (PTO).

## 3.3. Model formalisation

The following sections describe the steps followed by the model to predict regeneration rates from fragments of perennial-species storage organs after tillage. The formalism of each step (●-● in Fig. 5) is presented and applied to the different driving factors chosen in 2.9.3 (tillage tool, soil structure, pre-tillage storage-organ distribution in tilled soil layers, soil temperature, fragment diameter and shoot length per unit fragment biomass).

### 3.3.1. The prediction of fragment regrowth potential

● Fragment lengths were randomly drawn in a probability density function depending on the tool used, based on the results of 3.1. The lengths simulated with the rotary harrow (respectively, mouldboard plough) were 3 cm (resp., 12 cm) in average and were poorly (resp., widely) dispersed, with a standard deviation of 1.1 cm (resp., 6.8 cm).

● Fragment dry biomass (mg) was analysed as a function of its lengths (cm) and diameter (cm) measured in our experiment. It significantly increased with fragment length and diameter (R² = 0.84, Fig. S4 in supplementary material online). Fragment biomass was four times higher if its length increased from 3 to 12 cm, and three times higher if its diameter increased from 0.3 to 0.6 cm.

● Maximal shoot length per fragment was calculated according to Torssell's (2016) equations as the shoot length reached when the fragment reserves were depleted (i.e., when the fragment biomass was zero). Maximal shoot length increased linearly with fragment dry biomass by a factor of about 0.16 for both tested soil temperatures (10 and 18 C°). With the half shoot potential, maximal shoot length was half as long for a same initial fragment biomass.

### 3.3.2. The prediction of fragment location in the tilled soil layers

● The depth-increasing pre-tillage storage-organ distributions were established based on the graphical results of Frank et al. (2010). These

<footnote>a Power take-off.</footnote>
# I. FRAGMENT POTENTIAL

1

Draw 1000 fragment lengths according to the tillage tool

<figure><img src="image_14.png" /></figure>

2

Convert fragment length to dry biomass according to fragment diameter

<figure><img src="image_15.png" /></figure>

3

Estimate fragment maximal shoot length according to soil temperature and shoot length per unit fragment biomass

<figure><img src="image_16.png" /></figure>

# II. FRAGMENT LOCATION

4

Determine pre-tillage storage-organ distribution in the soil-tilled layers according to two representations

<figure><img src="image_17.png" /></figure>

5

Extract tillage-induced-fragment-movement matrixes corresponding to the chosen tool and soil structure

<figure><img src="image_18.png" /></figure>

6

Draw a burial depth for each fragment according to the chosen final depth distribution (calculated from ④ × ⑤)

<figure><img src="image_19.png" /></figure>

# III. FRAGMENT REGENERATION SUCCESS AND REGENERATION RATE

7

Compare maximal shoot length and burial depth of each fragment to determine its regeneration success

<figure><img src="image_20.png" /></figure>

8

Calculate regeneration rate for each scenario

<figure><img src="image_21.png" /></figure>

<caption>**Fig. 5.** Model for the prediction of perennial-weed regeneration probability from storage-organ fragments after a single tillage operation. Illustration for a mouldboard plough and a rotary harrow.</caption>

<footnote n="1">¹Torssell et al. (2015, 2016), ²Frank et al. (2010), ³Roger-Estrade et al. (2001), ⁴Colbach et al. (2014)</footnote>
distributions had no storage organ from soil surface down to 3 cm, fol-
lowed by a linear increase of storage-organ frequency from 4 cm down
to tillage depth. For example, if the soil was tilled 8 cm deep, 21.5 % of
the tilled storage organs were located between 0 and 5-cm depth and
78.5 % were located between 5 and 8-cm depth. The uniform distribu-
tion was simply established based on an equal storage-organ frequency
in each 1-cm-thick soil tilled layer.

❷ Tillage-induced-fragment-movement matrices for each tool / tillage depth and soil structure were taken from the work of Roger-Estrade et al. (2001) for mouldboard ploughing and Colbach et al. (2014) for rotary harrowing. The fragments were buried deeper (i.e., down to 25-cm depth) with mouldboard ploughing than with rotary harrowing (i.e., down to 8-cm depth). The fragments were moved more uniformly in an uncompacted compared to a compacted soil, regardless of the initial position of the fragments in the soil. In a compact soil, the rotary harrow concentrated the fragments in the 5–7-cm soil layers while the mouldboard plough buried most fragments a few centimetres deeper than their initial position.

❸ Post-tillage-fragment distribution matrices were obtained by applying the fragment-movement matrices to the pre-tillage organ distributions and varied according to the combination of tillage tool × soil structure × storage-organ distribution. The majority of the fragments simulated with the rotary harrow in the compacted soil were buried 7.5 cm deep while those simulated in the uncompacted soil were buried uniformly from soil surface to 8-cm depth. The results were the same for both uniform and depth-increasing pre-tillage organ distribution scenarios. In the case of mouldboard ploughing, fragments were buried uniformly in the uncompacted soil, while more fragments were buried in the deepest tilled soil layers (i.e., 24–25-cm deep) in the compacted soil. This increase in the frequency of deeply buried fragments was greater for the depth-increasing pre-tillage organ distribution.

3.3.3. *The prediction of fragment regeneration success and total regeneration probability of fragments*

❷ The maximal shoot length and the burial depth of each simulated fragment were compared to determine the regeneration success. If maximal shoot length exceeded burial depth by at least 1 cm, fragment regeneration was successful.

❶ The number of regenerated fragments was counted for each scenario and divided by the total number of simulated fragments (= 1000) to get the regeneration probability of fragments. The results varied strongly between the scenarios, from 13 % to 94 % regeneration probability (see the result of each scenario in Fig. S5 in supplementary material online).

3.4. Sensitivity of the fragment regeneration success to tillage and fragment characteristics

The probability of a fragment regenerating successfully was analysed as a function of the six factors that varied in the tested scenarios. Fragment diameter was the most important factor (highest odd ratio, Fig. 6) and doubling the diameter from 0.3 to 0.6 cm resulted in a 32 % increase in fragment regeneration probability. Maximal shoot length per unit fragment biomass was the second most influential factor (odd ratio = 3.36); doubling the maximal shoot length per unit fragment biomass increased regeneration probability by nearly as much, i.e., 29 %.

The impact of the tillage tool and soil structure on regeneration probability was lower (lower odd ratios in Fig. 6). Tillage with a rotary harrow led to a 13 % decrease in fragment regeneration probability compared to mouldboard ploughing. Tillage in a compacted soil induced a 6 % decrease in regeneration probability compared to uncompacted soil.

Pre-tillage storage-organ distribution had little effect, with a 3-%-lower regeneration probability for the depth-increasing vs uniform distribution. The only non-significant factor was soil temperature, meaning that the belowground shoots regrowing from fragments had the same probability of reaching soil surface at 10 as at 18°C.

4. Discussion

**4.1. Novelty of our work**

4.1.1. Deciphering an important mechanism

The present article is the first scientific publication to propose an
experimental method for measuring the direct effect of tillage tools on
the fragmentation of storage organs of perennial-weed species, with

<figure><img src="image_22.png" /></figure>

**Fig. 6.** Probability that a fragment of perennial-weed storage-organ regenerates (i.e., reaches soil surface and establishes a new plant) according to fragment diameter, shoot length potential (i.e., shoot length per unit fragment biomass), soil structure, tillage tool, pre-tillage storage-organ distribution in the soil tilled layers and soil temperature. For each factor, odd ratio (OR), 5 % and 95 % confidence intervals values are shown. The factors are significant at p<0.0001 (*** ) or not significant at p = 0.05 (NS).
results on *C. arvense*, a very problematic creeping-root species. The analysis of the individual effects of tool characteristics makes it possible to generalize and extrapolate these results to other tools than those tested.

Studying the fragmentation mechanism is crucial for understanding and quantifying the effects of tillage tool choice on post-tillage perennial-weed regrowth. A few studies measured the in-field infestation of perennial weeds after tillage but these are field studies which are very context-dependant (by definition) and whose results are often variable (e.g., Ringselle et al., 2023). Moreover, most of these studies are multifactorial (e.g., combination of different tools, several tillage dates) so the individual effects of the involved factors cannot be disentangled (e.g., Melander et al., 2012). To our knowledge, only one field experiment from a technical report (Leblanc and Lefebvre, 2018) compared the effect of several tillage tools on the fragmentation of storage organs of two perennial species (*C. arvense* and *S. arvensis*) but their method and soil conditions were not sufficiently described.

### 4.1.2. An innovative approach toward mechanistic modelling

Our paper proposed an innovative modelling approach by combining the existing knowledge on perennial-weed biology and response to tillage. To our knowledge, our model is the first mechanistic model of perennial-weed regrowth in response to tillage. The model produced emerging knowledge as it quantified and ranked the effect of various factors (biological, agronomic and environmental) underlying the process of perennial-weed regeneration from storage-organ fragments. The model predictions will make it thus possible to compare the effectiveness of different perennial-weed-control strategies.

To date, only qualitative models based on expert opinion have been developed to estimate *C. arvense* infestations in response to tillage and other agricultural practices (e.g., IPSIM-Cirsium, Lacroix et al., 2021). While such models synthesize expert knowledge, they are based on subjective opinions and context-dependent feedback from the field. Unlike mechanistic models, they cannot be used in a large range of contrasting farming situations of easily adapted to other weed species.

## 4.2. Results of the field experiment are consistent with literature

Our results on the effects of tillage tools on *C. arvense* root fragmentation are consistent with previous observations of the effects of tillage tools on the soil (e.g. Perdok and Kouwenhoven, 1994). For instance, the high root-fragmentation by the rotary harrow was related to the power take-off driving the blades, which increased the number of cutting points. The very long fragments left by mouldboard ploughing can be explained by the large blocks of soil cut by the ploughshares (Kouwenhoven and Terpstra, 1972; Colbach et al., 2000; Roger-Estrade et al., 2001) inside which long root fragments remain undisturbed.

Moreover, our results are consistent with those of Leblanc and Lefebvre (2018), the only existing similar study: their rotary harrow and their rototiller (i.e., a power-take-off-driven tool with horizontal blades) also produced short fragments although their tools tilled deeper (19 and 28 cm, respectively) than ours. This supports our finding that tillage depth has no significant impact on root fragment length compared to blade type and working mode.

However, neither we nor Leblanc and Lefebvre (2018) tested enough tools to clearly decorrelate tillage depth from tool features. Indeed, tillage depth could modulate the effect of a given tool somewhat: a shallower tillage would mean shorter fragments originating from vertically-growing roots. But, tillage depth should not affect the fragment length of horizontally growing roots.

## 4.3. What did we learn from our predictive model?

### 4.3.1. The simulation results were mostly consistent with literature

Because of the novelty of our approach, it was somewhat difficult to find literature to check the consistency of our simulation results. But the

few existing studies confirm our findings. For instance, the better regeneration success of thick fragments observed in our simulations was also found in experiments (e.g. Sciegienka et al., 2011) and is consistent with the longer belowground shoots produced by heavier fragments in other experiments (Torsell et al., 2015), presumably because of a greater amount of reserves. The slight decrease in regeneration success in compacted vs. uncompacted soil was less than the one observed in field trials on seed-based seedlings (Colbach et al., 2006) but this is not surprising as seeds include few reserves for pre-emergent growth compared to fragments (e.g., seed weight was 2.3 mg in Colbach et al. 2006 while the smallest fragment of our experiment weighed 5.5 mg). Similarly, the absence of any soil temperature effect in our simulations is not surprising as previous experiments showed a negligible effect on fragment biomass loss (Torsell et al., 2016). However, shoot emergence could be faster in warmer soils as growth rates are driven (among others) by temperature.

The smaller fragments and the lower regeneration success after a rotary harrow than after mouldboard ploughing in our simulations are in line with Bergkvist's et al. (2017) field study which concluded that increased storage-organ fragmentation by tillage led to lower perennial-weed infestation. However, fragment size will probably only be influential inside a certain range (see Kolberg et al., 2018): above a certain length, there will always be enough reserves to emerge even from deeply buried fragments, and, conversely, below a certain length, there will never be enough reserves to emerge even from shallow fragments.

Other results were more surprising at first glance. For instance, the fragment regeneration probability after mouldboard ploughing was higher than after other tools, which seems inconsistent with the better perennial-weed control observed after mouldboard ploughing in fields (Weigel et al., 2024), particularly when increasing ploughing depth (Borresen and Njøs, 1994). However, our model only predicts regeneration probability of fragments, disregarding the number of fragments as well as the shoots emerging from unfragmented storage organs located below the tillage depth. The former depends on how much storage biomass is disturbed by tillage and therefore, on tillage depth, while the latter is yet poorly understood.

### 4.3.2. What consequences for perennial-weed management

The ranking and effects of factors identified by the model can already contribute to understand and reason perennial-weed management. According to the simulations, the biological traits driving maximal shoot elongation per unit fragment length are the most important determinants of fragment regeneration success. Among these traits, the potential of the plant to convert reserve biomass into belowground shoot biomass is species-specific and cannot be manipulated by the farmer. However, storage-organ thickness and reserve amount vary across seasons, and field reports confirm that tilling when the reserves in the storage organs are at their lowest works best for controlling weeds (Håkansson, 2003; Brandsæter et al., 2017), during post-winter regrowth and sexual reproduction.

Though the timing of tillage thus appears to be more influential than the choice of tillage tool, the latter should not be overlooked, especially if the field is tilled several times. During fallow, a deep and highly-fragmenting tool would trigger a maximum regrowth of belowground shoots from fragments, leaving fewer unemerged fragments and less undisturbed storage biomass. If a subsequent highly aggressive tillage kills the regrowing shoots before the cash crop is sown, less storage biomass remains to regrow and infest this crop, following a principle similar to false seeding used to manage annual weeds. If the second tool moreover tills deeply, the remaining "unsprouted" fragments would be buried deeper, with a lower regeneration probability.

Finally, as soil structure and temperature had negligible effects on fragment regeneration success, weather conditions and soil type do not need to be considered when choosing tillage timing and tools.
## 4.4. Limits of our model and how to go further

### 4.4.1. More knowledge is needed to predict accurately perennial regrowth probability from fragments

To better predict fragment regeneration probability, more knowledge is needed on perennial-weed biological traits. As fragment diameter was the most important factor driving fragment regeneration success in our simulations, the drivers of storage-organ thickness, which depend on several factors like soil type, plant age and field management (Lemieux et al., 1993), must be better known.

Fragment diameter is though only one of the determinants of fragment reserve amount and the relationship between fragment diameter, dry weight and reserve amount used here (Fig. 5) was based on roots collected for a single species and at a single site and date. However, the level of reserve per dry weight of storage organ varies with species (Arny, 1932) and population (Liew et al., 2013) as well as seasons (McAllister and Haderlie, 1985) and storage-organ age (Klimesová and Klimes, 1996).

Finally, it is essential to estimate the maximal shoot length per fragment biomass for several perennial-weed species. Here, we used a model based on S. arvensis (Torsell et al., 2015, 2016) but shoot lengths will probably differ for other species, even for similar ones like C. arvense, which differs from S. arvensis on anatomical (Bartušková et al., 2021) and phenological (Brandsaeter et al., 2010) aspects. In addition, Torssell's et al. (2015, 2016) model does not consider the competition effect when several shoots are growing from the same fragment, which could lead to a significant reduction in maximum shoot length per fragment (Skorupinski et al., 2024).

### 4.4.2. The effect of environmental conditions should be examined on a broader perspective

Soil structure and temperature had little or no effect on the fragment-regrowth-related processes studied in our analysis. However, we could not analyse the effect of soil structure on C. arvense root fragmentation in our field trial. Tillage in a compact clay soil, such as the one in our study (see 2.4) might increase fragmentation rate over a lighter soil, as the storage organs are trapped in soil clods. Moreover, the choice of tillage tool will modify soil structure. For instance, rotary harrowing will fragment soil clods more than any cultivator (Table 1), thus resulting in a finer soil structure. This structure (as well as moisture) certainly influences belowground shoot elongation, as has been well investigated and modelled for seed-based seedlings (Gardarin et al., 2012), but was not considered here. However, based on the Gardarin et al.'s 2012 trait-based analysis, soil structure should not really affect pre-emergent mortality of fragment based shoots as their large shoot diameter confers them a better emergence force (Sinha and Ghildyal, 1979; Gardarin et al., 2010).

Finally, the range of the tested temperatures (10 and 18°C) regarded fragment burial depth was perhaps too small to observe a significant effect on fragment regrowth probability. It would be worth testing lower temperature like those experienced during early spring and autumn tillage. Low temperature (e.g. around 5°C) would considerably slow down shoot elongation rate and thus increase the biomass lost through respiration. Moreover, shoot emergence would be delayed, and the timing of weed emergence vs. crop emergence is known to be a key factor of weed harmfulness (Fahad et al., 2015).

### 4.4.3. How to compare tillage tool effects on perennial-weed regrowth?

Our model predicts the regeneration probability of perennial storage-organ fragments after tillage as a function of tillage tool, in interaction with weed species traits and environmental conditions. It does not consider the number of fragments produced by the different tools. Logically, a little-fragmenting tool as the mouldboard plough would produce fewer fragments than the highly-fragmenting rotary tool. For instance, a given amount of storage organs would result in four times the amount of fragments after harrowing vs. mouldboard ploughing,

with the average fragment lengths of 3.3.1. This though disregards the fact that the deeper plough would dig up considerably more storage organs than the shallow harrow. For instance, with the depth-increasing storage-organ distribution, the shallow (8-cm deep) rotary harrow only fragments 7% of the storage-organ amount fragmented by the deep (25-cm deep) mouldboard plough. The architecture of storage organs of perennial weed species in the soil therefore needs to be investigated further, which could be inspired by the work of Miyazaki (2008) on Solanum carolinense L.

But combining the probability of fragment regeneration of our current model with a relative number of fragments depending on tillage depth and storage organ distribution is insufficient to compare tillage tools in terms of perennial-weed regrowth. Indeed, plants can also regrow from the undisturbed part of the storage organs and probably exceed those regrowing from fragments (Thomsen et al., 2013). A few studies measured the regrowth capacities of intact creeping-root systems after defoliation (e.g., Andersson et al., 2013) but 1) defoliation does not fully mimic tillage and 2) the relationship between the number of regenerated plants and the initial biomass of the storage organs remains unknown.

Finally, to design efficient tillage strategies for managing perennial weeds, the model also needs to consider the timing of the tillage operations (see 4.3.2) and the resulting shoot emergence, notably relatively to the weeds' life cycle, and include the resulting submodel in a broader cropping-system model predicting crop-weed interactions over the years (Colbach et al., 2021).

## 5. Conclusion

In the present study, we combined a field experiment on the effect of tillage tools on the fragmentation of perennial-weed storage organs with literature data to predict the regeneration probability of storage-organ fragments after tillage in interaction with weed species traits and environmental conditions. Our innovative approach allowed producing new knowledge on the factors and mechanisms behind the regeneration of perennials weeds. The experiment showed that the lengths of storage-organ fragments produced by tillage varied according to the tool used and its properties. Our predictive model, synthesizing knowledge from different disciplines, showed that these fragment lengths are important driver of perennial-plant regeneration success from fragments. This means the effects of tillage on perennial-weed regrowth is partly tool-dependent. The model also highlighted that the regrowth potential of the species, depending on weed biological traits, is the main driver of regeneration success and needs to be studied further. The present model should be combined with others or include in a broader cropping-system model to predict the effect of tillage tools on perennial-weed regrowth.

### CRediT authorship contribution statement

**Delphine Moreau:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Investigation, Conceptualization.
**Brice Mosa:** Resources, Methodology, Investigation, Conceptualization.
**Eugène Motton:** Investigation, Formal analysis.
**Nathalie Colbach:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization.
**Solèmne Skorupinski:** Writing – original draft, Supervision, Software, Methodology, Investigation, Formal analysis, Conceptualization.
**Hugues Busset:** Supervision, Methodology, Investigation, Conceptualization.
**Jacques Caneill:** Writing – review & editing, Methodology, Investigation, Conceptualization.

### Funding information

INRAE; the Office Français de la Biodiversité (OFB); French Ministries in charge of Ecology, Agriculture, Health and Research.
Declaration of Competing Interest

The authors declare the following financial interests/personal re-
lationships which may be considered as potential competing interests:
Nathalie Colbach reports financial support was provided by French
Biodiversity Office. Solemne Skorupinski reports financial support was
provided by French Government Ministry of National Education. If there
are other authors, they declare that they have no known competing
financial interests or personal relationships that could have appeared to
influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgements

This project was supported by INRAE and the Office Français de la Biodiversité (OFB) as part of the Ecophyto call on "Global approaches to limit the use of phytopharmaceuticals: Combining preventive and curative products in sectors, from farmers to consumers" launched by the French Ministries in charge of Ecology, Agriculture, Health and Research, and a Ph.D. grant for Solémne Skorupinski from the French Ministry of Research. The authors would like to thank Anna Busset, Pierre Lebreton, Nicolas Cavan as well as the staff of CA-SYS platform of INRAE Dijon, especially Philippe Chamoy, Pascal Farcy, Jeremy Gervais and Benjamin Pouilly for essential technical assistance.

**Appendix A. Supporting information**

Supplementary data associated with this article can be found in the
online version at doi:10.1016/j.still.2024.106279.

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