Study sites and data collection

In this study, field observations were carried out in a total of 41 fields in Ibaraki Prefecture, Japan from 1997 to 2009 (total of 425 visual observations; Fig 1, Table 1 and S1 Table). In Ibaraki Prefecture, many of the buried seeds were reported to germinate within a year [32]. In this area, wheat is usually sown in November and harvested in June, and delayed sowing from November to December has been considered to help eliminate the emerged A. fatua seedlings before wheat seeding, reducing the population density during the cropping season [23]. We selected wheat or barley fields where A. fatua colonized and conducted continuous annual visual observations. Surveys were conducted in May when A. fatua is in the flowering stage and easily observable, and is taller than wheat and barley. Coverage was classified into four levels as follows: 0 = “absent” (zero A. fatua found, degree of coverage 0%.), 1 = “low” (coverage less than 20%.), 2 = “medium” (coverage 20%–50%), and 3 = “high” (coverage more than 50%.). We also observed field and crop conditions and recorded the following. 1) farmland use comprised six categories: “wheat,” “barley,” “other crop (e.g. potato, vegetables, and, green manure crops),” “paddy rice,” “fallow with spring management (mainly tillage),” and “fallow without spring management.” Spring management was determined by investigations of soil conditions, weed size, and weed composition (S1 Table). Fields showing traces of tillage within a month, a small weed size and few winter weeds were classified as “fallow with spring management.” When no evidence of the above was found, the field was classified as “fallow without spring management.” 2) Delay in wheat sowing (binary) was determined by lower than expected growth. 3) Evidence of irrigation the previous summer (binary) was determined by observations of irrigation ditches, soil moisture, and weed composition.

Fig 1

Locations of the 41 study sites in Ibaraki Prefecture, Japan.

Points were converted into 1-km² grid data.

Table 1

Geographical location (latitudes, longitudes, and address), observation year, and mean temperature (± standard deviation) of the 41 study sites during the winter wheat growing season (Dec–Apr).

Site ID	Lat (°N)	Lon (°E)	Years	Mean Tmp (Dec-Apr)	Address
1	36.23	140.04	1998–2009	7.19±0.67	Kuramochi, Akeno
2	36.23	140.04	1998–2009	7.19±0.67	Kuramochi, Akeno
3	36.23	140.04	1998–2009	7.44±0.68	Kuramochi, Akeno
4	36.23	140.04	1998–2009	7.19±0.67	Kuramochi, Akeno
5	36.23	140.04	2000–2009	7.33±0.69	Kuramochi, Akeno
6	36.19	139.78	1998–2009	6.91±0.61	Inamiya, Sowa
7	36.19	139.77	2005–2008	6.74±0.69	Inamiya, Sowa
8	36.17	139.78	1997–2008	6.89±0.59	Yagihashi, Sowa
9	36.11	140.11	1999–2009	6.90±0.66	Shibasaki, Tsukuba
10	36.11	140.11	1999–2006	6.68±0.60	Shibasaki, Tsukuba
11	36.10	140.12	1998–2009	6.89±0.63	Shibasaki, Tsukuba
12	36.10	140.11	1999–2008	6.78±0.63	Shibasaki, Tsukuba
13	36.10	140.12	1999–2009	6.87±0.66	Shibasaki, Tsukuba
14	36.10	139.80	1998–2009	7.01±0.61	Shimokohasi, Sakai
15	36.10	139.80	1998–2009	7.01±0.61	Shimokohasi, Sakai
16	36.10	139.80	1998–2009	7.01±0.61	Shimokohasi, Sakai
17	36.10	140.12	1998–2006	6.79±0.58	Konta, Tsukuba
18	36.07	140.02	1999–2009	6.57±0.65	Takasuka, Tsukuba
19	36.06	139.99	1997–2009	6.66±0.60	Nakatsuma, Mitsukaido
20	36.06	139.99	1998–2009	6.65±0.63	Nakatsuma, Mitsukaido
21	36.06	140.10	1998–2009	6.78±0.63	Teshirogi, Tsukuba
22	36.06	140.14	1998–2006	6.65±0.57	Umezono, Tsukuba
23	36.06	140.01	1998–2009	6.62±0.63	Nakakawasaki, Mitsukaido
24	36.06	140.01	1998–2009	6.68±0.63	Nakakawasaki, Mitsukaido
25	36.06	140.09	1998–2002	6.78±0.50	Teshirogi, Tsukuba
26	36.05	140.01	1998–2005	6.64±0.52	Kawasaki, Mitsukaido
27	36.05	140.15	1998–2009	6.77±0.63	Shimosasagi, Tsukuba
28	36.05	140.01	1998–2004	6.67±0.56	Higashi, Mitsukaido
29	36.04	139.99	1999–2009	6.73±0.65	Oyamato, Mitsukaido
30	36.03	140.04	1999–2003	6.57±0.62	Dai, Yawara
31	36.03	140.03	1999–2008	6.60±0.62	Fukuoka, Yawara
32	36.03	140.03	1999–2008	6.60±0.62	Fukuoka, Yawara
33	36.02	140.03	1999–2008	6.65±0.62	Fukuoka, Yawara
34	36.00	139.91	1997–2009	6.88±0.59	Yahagi, Iwai
35	35.99	140.10	1998–2007	6.67±0.63	Kukizaki, Tsukuba
36	35.99	140.10	1999–2008	6.58±0.62	Kukizaki, Tsukuba
37	35.99	140.10	1998–2008	6.60±0.60	Kukizaki, Tsukuba
38	35.99	140.10	1998–2007	6.75±0.63	Kamiiwasaki, Tsukuba
39	35.97	140.10	1998–2009	6.82±0.62	Shimoiwasaki, Tsukuba
40	35.96	140.13	1999–2003	6.76±0.61	Shironaka, Ushiku
41	35.90	140.32	1998–2009	6.67±0.63	Minamiota, Shintone

We also examined temperature, which is reported to affect the emergence of A. fatua [33,34]. To determine the effect of differences in temperature among fields and years, temperature data were obtained at a resolution of 1 km² from Agro-Meteorological Grid Square Data, NARO (https://amu.rd.naro.go.jp/) [35,36]. Average temperatures during the growth period of A. fatua (December–April) were calculated for each field and observation year.

Modeling

We used transition matrix models that describe the changes in weed states from one time step to the next [12,37] to project the coverage level of A. fatua. The coverage level of A. fatua in a given year depends on that in the previous year via the seed bank. A transition matrix model is applicable in such situations where a discrete state changes from year to year. In this study, the transition probability is assumed to depend on the management practices adopted and temperature. x_ts denotes a vector of management factors and temperature in year t at site s, and the transition matrix is expressed as follows:

Here, p_ji denotes the transition probability from level i to level j, and the subscripts 0, 1, 2, and 3 indicate respective levels of coverage. The sum of each column is 1. For the explanatory variables, x, we considered farmland use (6-level categorical variable), summer irrigation (binary variable), delayed sowing (binary variable), and temperature (continuous variable). The state probability vector for the four coverage levels, q_ts, is given by the product of the transition matrix and the state probability vector for the coverage levels in the previous year, q_ts = P_tsq_t-1,s. The equilibrium state probabilities as t → +∞ are given by the right eigenvector associated with the dominant eigenvalue (λ = 1) of P_ts.

To estimate the transition probability matrix and effects of the different weed management strategies on the transition probabilities of A. fatua in crop fields, we fitted mixed ordinal logistic models [38] to the observed coverage levels. These models are formulated as a set of threshold regression models on transition probabilities:

p_0i(x_ts) = f_0|1(i, x_ts),

p_1i(x_ts) = f_1|2(i, x_ts)—f_0|1(i, x_ts),

p_2i(x_ts) = f_2|3(i, x_ts)–f_1|2(i, x_ts),

p_3i(x_ts) = 1—f_2|3(i, x_ts),

where f_j|j+1(i, x_ts) is a function of the threshold probability between coverage levels j and j+1 depending on the previous year’s coverage level i and explanatory variables x_ts. The threshold function is given by a mixed logistic regression model:

f_j|j+1(i, x_ts) = Logit(β_j|j+1 –(α_i + βx_ts + ε_s)).

Here, β_j|j+1 denotes threshold coefficients of coverage levels j and j+1, which increases in the order β_0|1 < β_1|2 < β_2|3, and α_i denotes ordered factors determining the dependence on the previous year’s coverage level i, with baseline i = 0 (α₀ = 0 < α₁ < α₂ < α₃ or α₃ < α₂ < α₁ < 0 = α₀). x_ts and β are vectors of explanatory variables and the corresponding regression coefficients, respectively, and ε_s is a site-level random effect with Gaussian prior ε_s ~ Normal (0, σ²).

The observed coverage level, Y_ts = j, conditional on the state of the previous year, Y_t-1,s = i, follows a multinomial distribution with probability vector p_.i = (p_0i(x_ts), p_1i(x_ts), p_2i(x_ts), p_3i(x_ts)). Model fitting was performed using the marginal maximum likelihood method with the clmm2 function of the ordinal package [39] in R software version 3.5.1 [40]. The best model was selected using downward model selection with the Akaike information criterion (AIC) [41] and was used for the projection.

Simulation of the effects of management strategies

To compare the effects of each management strategy and its repetition, we simulated temporal changes in the state probabilities of A. fatua coverage levels under different management scenarios using the best model. The management scenarios were as follows: repeated wheat cultivation, rotation of wheat and five other farmland uses, wheat with summer irrigation, and rotation of wheat with and wheat without summer irrigation. The initial level of A. fatua coverage was set at 0 or 3. The temporal changes across 20 years were then simulated. In all simulations, the random effect was fixed at zero to exclude the effects of differences among sites and to allow the average effects of each site to be determined.

We also calculated equilibrium state oscillation under different cycle options. When two different farmland uses are rotated from year to year, the probabilities of coverage levels oscillate between two states at equilibrium [42]. Given the transition matrices corresponding to two farmland use, P₁ and P₂, the probabilities of equilibrium coverage levels are given by eigenvectors of the two matrix products (P₂P₁) and (P₁P₂), respectively.

Ethics statement

All field works (visual observations) were conducted on public roads and no permission was required under law in Japan. All information of site locations is coarse enough to protect landowners' privacy.

Effects of each IWM strategy

The results of the transition matrix model obtained using accumulated coarse monitoring data demonstrated the contribution of each IWM strategy on A. fatua coverage and the effects of its repetition. The model projected that farmland use has a remarkable effect on coverage level of A. fatua, which tended to increase in “wheat” and “barley” fields, whereas fields planted with “paddy rice” and “other crops” drastically decreased the effect of coverage in the previous year. Barley is reported to be more competitive than wheat [25,43]; however, the results of this study suggest no differences in suppressing A. fatua. Selection of a cycle that incorporates other crops, paddy rice, or fallowing rather than wheat or barley is therefore recommended.

The “fallow” cycle option also had a strong effect on A. fatua coverage, although it increased the risk of increasing coverage compared with that of “paddy rice” and “other crops.” These findings suggest that the colonization risk of A. fatua is lower in cropped fields (other than those containing winter cereal) compared with fallow fields. Both the “fallow with spring management” and “fallow without spring management” options, which differed in terms of tillage, contributed to a decrease in A. fatua coverage; however, the effect was larger under “fallow with spring management.” This suggests that tillage during the booting to flowering stages is effective in breaking the life cycle of A. fatua and eliminating it. Mature weeds including A. fatua were sometimes able to survive spring tillage; thus, to prevent seed setting and dispersal, a management strategy that involves removing mature plants is important.

Fallowing could also help suppress A. fatua, although it risks increasing the invasion of other weed species. For example, in this study, weed species such as Capsella bursa-pastoris and Equisetum arvense were observed in place of A. fatua. C. bursa-pastoris is a common weed in vegetable fields in Japan [44], and E. arvense is known to cause damage to various types of agricultural fields [45]. Understanding the risk of invasion from other species and appropriate management is therefore important when considering fallowing as an IWM strategy.

Effect of irrigation in wheat fields

It was previously reported that wet soil conditions contribute to the decay of buried seeds [27,28]. The results of this study suggest that “summer irrigation” could effectively suppress A. fatua abundance in wheat fields. In Honshu, rotation of paddy rice and wheat is a major cropping system, a decrease in A. fatua damage has been reported for fields using this system [30]. The results of our model were also in line with this.

Although summer irrigation of wheat fields is effective, paddy rice rotation rather than continuous wheat was able to more rapidly and more effectively eliminate A. fatua coverage. This is thought to reflect the effect of summer irrigation on the seed bank, whereas paddy rice reduces both the seed bank and breaks the life cycle of A. fatua via spring tillage and irrigation.

In this study, the effects of delayed sowing and temperature were not included in the model because they were found to be weaker than those of the remaining variables. Previous studies have suggested the effectiveness of removing A. fatua seedlings by delayed sowing [23], and the effects of warm temperatures on A. fatua emergence have also been pointed out [34]. In the present study, negative effects of delayed sowing and positive effects of temperature were detected. Thus, although both effects were relatively small compared with farmland use and summer irrigation, our results do not contradict the results of previous studies.

Number of years required for A. fatua control

Crop rotation using other crops or fallowing is another effective method of weed control in wheat fields [20,21]. For example, planting barley instead of wheat is considered effective because it is more competitive [25], whereas winter fallow with tillage is thought to remove emerging A. fatua before seed maturation, helping to deplete the seed bank. Although the number of years required for crop rotation or fallowing have been unclear in spite of its importance, the results of our simulations provide information about it.

Simulations of repeated management revealed that farmland use in the form of rotation with “paddy rice” and “other crops” contributed to rapid A. fatua control in 1 year, even under the highest level of coverage (level 3). These findings suggest that changing farmland use only once can effectively eliminate A. fatua in fields where an outbreak has occurred. The remaining management options established a trend within 3 years and reached convergence in less than 10 years. These results suggest that our model can accurately estimate the effects of various management strategies and their cycles and can be used to aid decision-making on which strategies to select and how long to continue them.