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Study area and samplingSmall mammals (murid rodents and shrews) were captured using mouse-type snap traps in Tatarstan, Russian Federation (Fig. 1, Table S1). Area type (urban or rural), vegetation (forest or field) and distance from trapping points to the nearest human settlement were recorded. The distinction between forest and field was made based on the UN Food and Agriculture Organization’s criteria23,24. Each administrative division in the Tatarstan was defined to be urban or rural by the Federal Service of State Statistics of Russian Federation25. Based on these criteria, Kazan city and Naberezhnye Chelny city were classified as urban districts and Vysokogorsky district, Yelabuzhsky district, Laishevsky district, Mamadyshsky district, Nizhnekamsky district, Pestrechinsky district and Tukayevsky district were classified as rural districts. Small mammals were captured during the spring and fall periods of 2016 and 2017. Fifty traps were placed in a line every 5 m in one place. Traps were baited and left for one night. Animal suffering was minimized as snap traps cause rapid death in murid rodents and shrews. Each captured small mammal’s species, age, and sex were morphologically identified using a reference guide26, and the animals were then stored at − 20 °C until their brains were isolated.EthicsAll experiments were performed in compliance with relevant Russian and Japanese and institutional laws and guidelines and were approved by the Ministry of Health of the Russian Federation and the Animal Research Committee of Gifu University (Permit Nos. MU 3.1.1029-01, and 17060, respectively). Study was carried out in compliance with the ARRIVE guidelines (https://arriveguidelines.org).DNA extraction and PCRBrain tissue samples were prepared as described previously12. Brain samples stored at − 20 °C were transferred to a − 86 °C deep freezer. Each deep-frozen whole brain sample was homogenized in 1 ml of a 0.9% saline solution. Total DNA was extracted from the brain tissues of each small mammal using a Genomic DNA Purification Kit (Promega, Madison, WI, USA), following the manufacturer’s instructions. Nested PCR was performed with the Takara PCR Amplification Kit (Takara Bio Inc., Foster City, California, USA) according to the manufacturer’s instructions. The primer sets and PCR conditions used to detect the B1 gene from T. gondii were those described previously12.MappingSpatial referencing of the sampling sites was conducted using global positioning system navigation with a Garmin eTrex 10 device. Visualization of cartographic data and measurements of the distances from the trapping points to the nearest human settlements were performed using QGIS 3.12 software27. Geodetic coordinates were projected into planar rectangular coordinates in the Universal Transverse Mercator projection on the WGS-84 ellipsoid (Universal Transverse Mercator, zone 39N). The overview map of the European part of Russia was made in the Lambert Conformal Conic Projection. Map coordinates are represented as geodetic coordinates (WGS-84, degrees and minutes north latitude and east longitude). To visualize thematic objects (administrative boundaries, forests, agricultural lands, and water bodies), a set of vector data layers, NextGIS (Russia), was purchased from OpenStreetMap and contributors, 2021 (https://data.nextgis.com). Data license: ODbL.Dataset and statistical analysesMultivariate logistic regression was performed using the R statistical software package (version 3.6.3)28 to assess the trapping point area (urban or rural), vegetation (forest or field), small mammal species type (alien or non-alien species), age (0–2 months-old juveniles, 3–6 months-old adults or ≧ 6 months old), sex (male or female) and distance from trapping points to the nearest human settlements as risk factors for PCR positivity. According to previous reports2,13,16,17,18, four species, Mi. arvalis, A. flavicollis, A. agrarius, A. uralensis, and three species, My. glareolus, S. araneus and D. nitedula are considered alien and non-alien species, respectively. Quantitative data were replaced with 0 or 1 dummy variables, and age data were replaced by 0, 1 and 2 for juveniles, adults and elders, respectively. Multicollinearity of the explanatory variables was evaluated using Spearman’s coefficient29 calculated using dplyr, FSA and psych packages30,31,32. None of the Spearman’s coefficients were  > 0.6. To find the best fit model, a forward selection procedure was used. Predictive performance and model fitting were assessed using the area under the receiver operating characteristic (ROC) curve, area under the curve (AUC) and corrected Akaike’s information criterion (AICc) with Akaike weight (Wi). AICc and Wi were calculated using the MuMIN package33, and the AUC was calculated using the R pROC package34. P-values of  More

The micro-CT results from Arthrorhynchus agree perfectly with the previously known light microscope and transmission electron microscope images2. This emphasizes that microtomography is a good technique to visualize the type of fungal attachment to the host and especially the penetration of the cuticle, apart from the study of thallus in amber fossils17. As Jensen et al. (2019) demonstrated the presence of a haustorium in Arthrorhynchus using scanning electron microscopy, we are confident that the lack of penetration and haustorium in Rickia found by micro-CT is real. This is also in agreement with results from the scanning electron microscopical investigation of the attachment sites of R. gigas, which exhibits no indication of penetration and are very similar to those of R. wasmannii previously shown18.Despite the absence of a haustorium, and hence without any obvious means of obtaining nutrition, Rickia gigas is quite a successful fungus, being often abundant on several species of Afrotropical millipedes of the family Spirostreptidae10. It was originally described from Archispirostreptus gigas, and Tropostreptus (= ‘Spirostreptus’) hamatus20, and was subsequently reported from several other Tropostreptus species19.A further challenge for Laboulbeniales growing on millipedes is that infected millipedes, in some species even adults, may moult, shedding the exuviae with the fungus, as has been observed by us on an undescribed Rickia species on a millipede of the genus Spirobolus (family Spirobolidae).The question of how non-haustoriate Laboulbeniales obtain nutrients has been discussed by several authors18, including staining experiments using fungi of the non-haustoriate genus Laboulbenia on various beetles21. Whereas the surface of the main thallus was almost impenetrable to the dye applied (Nile Blue), the smaller appendages could sometimes be penetrated21. The dye injection into the beetle elytra upon which the fungi were sitting, actually spread from the elytron into the fungus, thus indicating that in spite of the lack of a haustorium, the fungus is able to extract nutrients from the interior of its host21.Such experiments have not been performed on Rickia species, but the possibility that nutrients may pass from the host into the basis of the fungus cannot be excluded. For this genus, or at least R. gigas, there may, however, be an alternative way to obtain nutrients: the small opening in the circular wall by which the thallus is attached to the host may allow nutrients from the surface of the millipede or from the environment to seep into the foot of the fungus. However, further experiments are needed in order to evaluate this hypothesis. Moreover, we should not exclude a potential role of primary and secondary appendages in Laboulbeniales nutrition, as we still do not understand exactly their functional role on the fungus life cycle11.The predominant position of the Laboulbeniales on the host might be related to the absence or presence of a haustorium. Thus, the haustoriate species of the genus Arthrorhynchus are most frequently encountered in large numbers on the arthrodial membranes of the host’s abdomen, although some thalli are found on legs2,22. At the arthrodial membranes the cuticle is more flexible and therefore might be easier to penetrate by a parasite. Furthermore, most tissues providing/storing nutrition (e.g., fat body) are located within the abdomen. In contrast, non-haustoriate fungi as are often located on more stiff and sclerotized body-parts like the genus Rickia on the legs or body-rings of millipedes7,20,23 or the genus Laboulbenia on the elytra of beetles21,24. A reason for this might be that the non-haustoriate forms, which are only superficially attached to the host need a more or less smooth surface for adherence and can easily become detached from a flexible surface, which is movable in itself, like the arthrodial membrane, while the haustoriate forms are firmly anchored within the hosts’ cuticle.Whereas the vast majority of the more than 2000 described species of Laboulbeniales show no sign of host penetration, haustoria have been reported from some other genera18, including Trenomyces parasitizing bird lice25,26, Hesperomyces growing on coccinellid beetles and Herpomyces on cockroaches (formerly a Laboulbeniales and now in the order Herpomycetales10), with pernicious consequences on the hosts’ fitness18,27. Micro-CT studies on these genera could help to understand the host penetration. In order to fully understand how Laboulbeniales obtain nourishment, although other approaches are, also needed—for the time being it remains a mystery how the non-haustoriate Laboulbeniales sustain themselves. More

Collection and domestication of the wild populationsThe academic permission for collections and research on medicinal plants was obtained from the Head of Biotechnology Department, Research Institute of Modern Biological Techniques, University of Zanjan, Zanjan, Iran. The study complies with all relevant guidelines. Some populations of wild spinaches were harvested during spring season 2013 from the mountain habitat of this wild plant in the Tarom region of Zanjan province from an altitude of 2500–3000 m and were transferred to the greenhouses conditions. The domestication and cultivation experiments were conducted at Research Institute of Modern Biological Techniques, University of Zanjan, 1579° m above sea level, with 48° 28′ longitude and 36° 40′ latitude, from April 2013 to August 2020. The resulted seeds were cultured on pots to produce adequate seeds. The seedlings were transferred to the field with rows spaced 50 cm apart and also 50 cm between plants within the rows. Two seeds per hill were planted in an area of approximately 50 m2. Based on the organic conditions, no fertilization was performed. Thinning was done 25 days after emergence, leaving one plant per hill. The other cultural practices were those normally adopted for cultivation in the region.Mass selection of populationsIn the first year, phenotypic studies were performed during the growing season and weak, diseased and underdeveloped plants were removed from the field before the flowering stage. Then plants with the same phenotype and the desired traits were selected and after harvesting, their seeds were mixed. This election cycle was repeated for 5 years. In the final year, the new mass selected population was compared in a pilot project with cultivated spinach in traits such as yield, resistance to wilt, cold and pests, diseases, and mineral contents. This variety before the certification in the related national organization is a candida cultivar. It is a developed population that will be evaluated in the session of the Iranian variety of introduction committee.The seeds of cultivated spinach (Spinacia oleracea L. |Varamin 88|) were prepared from the Research Institute of Modern Biological Techniques, University of Zanjan, Zanjan, Iran.Performing tests of stability, uniformity and differentiationTo assess morphologically and differentiate advanced uniformity in the studied population (Candida cultivar), the population was managed as a randomized complete block design with three replications over 2 years according to the instructions for spinach differentiation, uniformity, and stability (DUS Testing) of the International Union New Plant Cultivation (UPOV) and some morphological traits on plants or parts of plants. The studied traits included: cotyledon length, presence or absence of anthocyanin in petiole and veins, green color intensity, shrinkage, presence of lobes in the petiole, petiole state, petiole length, foil shape, foil edge shape, tip shape, and part of the length of the petiole, the time of flowering and the color of the seeds.Mineral analysesTo compare the mineral content of mass-selected population-medicinal spinach (MSP) with cultivated spinach (Spinacia oleracea L. var. Varamin 88), both plants were planted in pots and fields on similar conditions. In five leaves stage, plant samples were taken from both leaf and crown sections. The sampling method was such that after removing half a meter from the beginning and end of each plot (to remove the marginal effect) and also removing the two sidelines, five plants were harvested randomly for plant mineral analysis. Atomic absorption spectroscopy was used to determine the mineral content including iron (Fe), zinc (Z), manganese (Mn), and copper (Cu).The dried samples of root-crown and leave were stored, and later grounded and analyzed for iron (Fe), zinc (Z), manganese (Mn), and copper (Cu) in mass-selected variety (MSP) and cultivated spinach (CSP). Studied minerals were measured using atomic absorption spectrometry in the model of GBC AVANTA (GBC scientific equipment Ltd., Melbourne, Vic., Australia).Calibration of AAS was done using the working standard prepared from commercially available metal/mineral standard solutions (1000 μg/mL, Merck, Germany). The most appropriate wavelength, hollow cathode lamp current, gas mixture flow rate, slit width, and other AAS instrument parameters for metals/minerals were selected as given in the instrument user’s manual, and background correction was used during the determination of metals/minerals. Measurements were made within the linear range of working standards used for calibration15,16.The concentrations of all the minerals were expressed as mg/1000 g (ppm) dry weight of the sample. Each value is the mean of three replicate determination ± standard deviation.Scanning electron microscopy (SEM)For SEM studies, the seeds enveloping were removed and were acetolyzed in a 1:9 sulfuric acid-acetic anhydride solution. The seeds were vigorously shaken for 5 min. Then, they were left for 24–48 h in the solution. After this time, seeds were again shaken for 5 min and then washed.in distilled water by shaking for a further 5 min. The seeds were dried overnight and then were mounted on stubs and covered with Au–Pd by sputter coater model SC 7620. After coating, coated seeds were photographed with an LEO 1450 VP Scanning Electron Microscope. All photographs were taken in the Taban laboratory (Tehran, Iran).Statistical analysisThe statistical evaluation including: data transformation, analysis of variance and comparison of means were performed (SPSS software, Version 11.0). The experiment was structured following a randomized complete block design (RCBD) with three replications. Means comparisons were conducted using an ANOVA protected the least significant difference (LSD) test, with the ANOVA confidence levels of 0.95. Data were presented with their standard deviations (SD). More

Dispersal modelsIn this study, the dispersal model consists of two parts, namely, kernel and observation model (Fig. 1). The main purpose of the kernel was employed to estimate the proportion of pollen dispersed from location s′ to location s and calculate the expected number of CP grains. The observation model used the expected number of CP grains as a parameter and described the number of CP grains at location s (Ys) by a specific distribution in the following:$${Y}_{s}sim fleft(left.{y}_{s}right|{{varvec{theta}}}_{s}right),$$
(1)
where f indicates the probability density function (PDF) of the specific distribution. The θs is the parameter vector of the distribution. This study constructed eight different dispersal models combined with two observation models, two kernels, and two conditions of the field border (FB) effect (Table 1). The details of the kernels and observation models were described in the following subsections.Figure 1Graphical summary of the establishment of the dispersal model using ZIP distribution observation model as an example.Full size imageTable 1 List of dispersal models constructed in this study.Full size tableKernelsThe kernel indicates the probability when the pollen emitted at location s′ and would fall down at location s. It can be expressed as γ(s, s′), where s′ is the source location closest to location s. Numerous kernels have been used to describe various dispersal phenomena24. The output of the kernel represents the donor pollen density of location s. In order to calculate the expected number of CP grains, the donor pollen density is multiplied by the average total grain number described as follows:$${lambda }_{s}=Ktimes gamma left(s,{s}^{^{prime}}right),$$
(2)
where λs and K indicate the expected number of CP grains at location s and the average number of grains per cob, respectively. The effect of the FB was introduced into the kernel to suit to the small-scale farming system in Asia. This study assumed that the relation between the pollen density at the first recipient row and the width of the FB displayed an exponential decrease25,26. To evaluate the improvement of the kernel with the FB effect, the kernels without the FB effect were also established in this study.The compound exponential kernel (γExpo) has been used in the previous pollen dispersal study27. Our study introduced the FB effect into this kernel. Therefore, the form of the compound exponential kernel can be expressed as follows:$$gamma_{{{text{Expo}}}} left( {s,s^{prime}} right) = left{ {begin{array}{*{20}l} {K_{e} exp left( { – a_{1} d^{*} left( {s,s^{prime}} right)} right)exp left( { – ksqrt {FB} } right),} \ {K_{e} exp left( { – a_{1} D – a_{2} left( {d^{*} left( {s,s^{prime}} right) – D} right)} right)exp left( { – ksqrt {FB} } right),} \ end{array} } right.begin{array}{*{20}l} {{text{if}},, d^{*} left( {s,s^{prime}} right) le D} \ {{text{if}} ,,d^{*} left( {s,s^{prime}} right) > D,} \ end{array}$$
(3)
where Ke, a1, a2, k, D are the parameters of the kernel. d*(s, s′) indicates the shortest distance between locations s′ and s in which the width of the FB has been subtracted. In the compound exponential kernel without the FB effect, the exponential term of the FB effect was removed and the d*(s, s′) was replaced directly by the shortest distance between s′ and s.The second kernel applied in this study was the modified Cauchy kernel (γCauchy) which was based on the PDF of the Cauchy distribution and the concept of compound distribution. The modified Cauchy kernel is represented as follows:$$gamma_{Cauchy} left( {s,s^{prime}} right) = left{ {begin{array}{*{20}l} {frac{2beta }{{pi left[ {beta^{2} + d^{*} left( {s,s^{prime}} right)^{2} } right]}}{text{exp}}left( { – ksqrt {FB} } right),} \ {frac{2beta }{{pi left[ {beta^{2} + D^{2} + c_{1} left( {d^{*} left( {s,s^{prime}} right) – D} right)^{2} } right]}}{text{exp}}left( { – ksqrt {FB} } right),} \ end{array} } right.begin{array}{*{20}l} {{text{if}} ,,d^{*} left( {s,s^{prime}} right) le D} \ {{text{if}} ,,d^{*} left( {s,s^{prime}} right) > D,} \ end{array}$$
(4)
where the β indicates the decline rate of the curve. Parameters of k and D are same as the compound exponential kernel. c1 indicates the relative slow decrease of pollen density at further distances. Similarly, in the modified Cauchy kernel without the FB effect, the term of the FB effect was removed and the d*(s, s′) was replaced directly by the shortest distance between s′ and s in which the row spacing (0.75 m) had been subtracted.Observation modelsBecause of the high proportions of zero value observations, the present study assumed that the CP grain count followed the zero-inflated Poisson (ZIP) distribution to account for zero-excess condition28. The ZIP distribution was first proposed by Lambert29, and several studies had applied the ZIP distribution to deal with the CP data27,30. The ZIP distribution consists of a Dirac distribution in zero and a Poisson distribution. Therefore, the distribution of CP grain count at location s (Ys) can be expressed as follows:$${Y}_{s}sim mathrm{ZIP}left(1-{q}_{s},{uplambda }_{s}right),$$
(5)
where qs indicates the probability of an observation following a Poisson distribution, and λs is the parameter of Poisson distribution calculated by Eq. (2). Furthermore, the parameter qs can be assumed to depend on the shortest distance between the recipient and donor plants. The border effect is also included in the estimation of qs because it is related to the distance effect. The relationship among distance, border, and the qs can be described using the following logistic function:$${q}_{s}=frac{1}{1+mathrm{exp}({b}_{1}-{b}_{2}{d}^{*}left(s,{s}^{^{prime}}right))},$$
(6)
where b1 and b2 are the parameters of the logistic function. The d*(s, s′) was the shortest distance between s′ and s in the version of dispersal models without the FB effect. The Poisson distribution was also used as an observation model for comparison with the ZIP observation model.Experimental and meteorological data collectionThe pollen dispersal data were collected from experiments performed in 2009 and 2010 at the geographic coordinates 23° 47′ N, 120° 26′ E, and an altitude of 20 m. These experiments were coded as 2009-1, 2009-2, and 2010-1, respectively. The experiment 2009-2 was divided into 2009-2A (without the FB) and 2009-2B (with the FB) based on the presence of the FB. The different layouts of the field experiments were designed to investigate the effect of the FB. Two commercial glutinous maize varieties, black pearl (purple grain) and Tainan No. 23 (white grain), were selected as the pollen donor and pollen recipient, respectively. The distance between the plants in a row was 25 cm, whereas the distance between the rows was 75 cm. The recipient plots consisted of 82 and 91 rows in 2009 and 2010 experiments, respectively.The CP rate was determined based on the differences in grain color on recipient cobs as a result of the xenia effect31. In the sampling framework, the whole field was divided into many grids and corn samples were collected from each grid in the whole field. The CP rate of each grid was calculated using the method presented in a previous study32 and defined as:$$mathrm{CP}left(%right)=left[sum_{i=1}^{n}{Cob}_{i}/left(ntimes Kright)right],$$
(7)

where Cobi and n indicate ith cob and total number of cobs in the grid, respectively. K is the average grain number per cob. Meteorological data were collected from the meteorological station at geographic coordinates 23° 35′ N, 120° 27′ E, and an altitude of 20 m. The detailed experimental setup was described in our previous study33. The study complies with relevant institutional, national, and international guidelines and legislation.Statistical analysesAll statistical analyses were performed using SAS (Statistical Analysis System, version 9.4). The dispersal model parameters were estimated by two methods. First, the nonlinear model estimation was conducted by PROC NLMIXED to evaluate the fitting and predictive abilities of dispersal models. Then the dispersal models with the observation model performed better fitting ability were re-estimated using the Bayesian estimation method to assess the uncertainty by PROC MCMC. In the Bayesian method, the noninformative prior distribution was used to estimate all parameters (Supplementary Table S1). The iteration of Markov Chain was 500,000 times and the burn-in was set to 450,000 iterations. In order to reduce the autocorrelations in the chain, the thinned value was set to 25.The validation method used in this study was the threefold cross-validation for the results of both estimation methods. The data from three experiments were combined and randomly partitioned into three sub-datasets. To avoid the heterogeneity of the different field designs and distances among sub-datasets, the observations from the same field design and same distance were considered as a group, and then partitioned into three parts. Each sub-dataset contained one part of all groups. At each validation run, two sub-datasets were selected as the training set, and the remaining one was used for validation.The fitting ability of the dispersal models was evaluated based on two criteria, namely, Akaike information criterion (AIC), Deviance, and coefficient of determination (R2). The smaller values of AIC or deviance indicate a better fitting. The higher R2 value represents a better fitting performance. The correlation coefficient (r) between the predicted and actual CP rates was used to assess the predictive ability. The deviance information criterion (DIC) was used to evaluate the performance of dispersal model fitting for the Bayesian estimation. The criterion values calculated from three training and validation sets were averaged to assess the overall results. The uncertainty of the model parameter was quantified by the standard deviation (SD) of parameter posterior distribution. The 95% credible intervals of posterior predictive distribution constructed by the 2.5th and 97.5th percentiles of 200,000 samples generated from the posterior predictive distribution were used to assess the predictive uncertainty. Furthermore, to assess the zero-excess condition, the percentage of observed zero CP grain events was compared with the Poisson probability of the zero CP grain event. A zero-excess condition occurred if the observed percentage was higher than the Poisson probability34. More

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