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Soil seed banks were sampled in undisturbed soil and after soil had been disturbed by tillage (tine, harrow or plough). Seeds were sorted by size and shape, and counted. Size-number distributions were fitted by power law equations that allowed the identification of self-similarity and self-affinity. Self-affinity and thus non-random size-number distribution prevailed in undisturbed soil. Self-similarity and thus randomness of size-number distribution prevailed after tillage regardless of the intensity of disturbance imposed by cultivation. The values of fractal dimensions before and after tillage were low, suggesting that short-term, short-range factors govern size-number distribution of soil seed banks.

Plants and plant communities dynamics, strategies, processes, changes and their relationships with functional and adaptative traits can be envisioned and studied at various scales, either in space, time or both [

Seed size is long known to be a highly heritable trait and with relatively few exceptions seed size shows very low levels of within species variability [

Soil seed banks are also the result of an intricate number of interactions between plants and short and long-term environmental conditions and changes [

Size-number distribution of seeds can be described either by power law or by Weibull equations [

Seed size varies across a wide range of values, which can attain for individual plant communities as much as six orders of magnitude [

Our hypothesis is that size-number distribution of seeds reflects past events including disturbances that can be detected by fitting power law equations and adopting self-similar and self-affine concepts of fractal geometry, including the magnitude of fractal dimension. Therefore, we investigated seed banks in soils not disturbed by Man for several years and evaluated the effect of soil disturbances on the type and magnitude of fractal dimensions in size-number distributions. Soil tillage was chosen as disturbance because it minimizes or completely avoids the risk of seed destruction and because it provides an easy and fast way to impose disturbances of increasing intensity. In this study we used three types of tillage—tine, harrow and plough—known to represent a series of increasing disturbance of soil structure and properties.

Overall, a total of 60,643 seeds were counted: 49% in the nine cores sampled before tillage down to 20 cm depth, 41% and 10% in the six cores sampled after tillage down to 20 cm depth (after plough and tine) and in the three cores sampled after tillage down to 10 cm depth (after harrow), respectively. Either before or after tillage, non-spherical seeds were more abundant than spherical seeds, their percentage ranging between 53% (in nine cores taken before tillage) and 62% (in three cores taken after harrowing). Given the adequacy of mesh side to estimate seed volume [

Twenty species belonging to 10 families were identified (

Species, families, biological type, and importance as weed according to [

Species | Family | Biological type | Importance as weed |
---|---|---|---|

Amaranthaceae | Therophyte | 2 | |

Amaranthaceae | Therophyte | 3 | |

Amaranthaceae | Therophyte | 3 | |

Asteraceae | Therophyte | 3 | |

Brassicaceae | Therophyte | 3 | |

Brassicaceae | Therophyte | 3 | |

Brassicaceae | Therophyte | 2 | |

Brassicaceae | Therophyte | − | |

Caryophyllaceae | Therophyte | 2 | |

Caryophyllaceae | Therophyte | 2 | |

Caryophyllaceae | Therophyte | 2 | |

Caryophyllaceae | Therophyte | 3 | |

Fabaceae | Therophyte | − | |

Juncaceae | Therophyte | 1 | |

Plantaginaceae | Therophyte or Hemicryptophyte | 2 | |

Poaceae | Hemicryptophyte | 3 | |

Poaceae | Hemicryptophyte | − | |

Poaceae | Therophyte or Hemicryptophyte | 3 | |

Polygonaceae | Hemicryptophyte | 1 | |

Resedaceae | Hemicryptophyte | 2 |

Importance as weed: 1, of minor importance; 2, important in a few situations, although it may be widespread as a minor weed; 3, important competitive weed occurring in many crops and situations [

No seed was found in any of the 10 random samples of the mineral fraction of the 0.297 mm or lesser mesh side and of materials not retained by the 0.149 mm mesh side. Therefore, it is highly unlikely that seed losses occurred as a result of reducing the amount of material to be screened under stereomicroscope or of not using sieves with mesh sides smaller than 0.149 mm.

Fitting the reparameterized power function of Equation (4) to the 477 samples (396 samples 2.5-cm depth, 36 pooled samples 10-cm depth, 45 pooled samples 20-cm depth) was always possible. The adjusted coefficient of determination (^{2}_{adj}) ranged between 0.839 and >0.999 with a mean value (±SE) of 0.977 ± 0.001. All equations met the conditions for acceptance at the first or after the second attempt. In 82% of the cases, fitted equations required only one term, 16% two terms, 2% three terms, and no equation needed the four terms of the full candidate model. Size-number distribution of seeds showed self-similarity in 44% of samples, self-affinity in 56% of samples. Whenever

However, more important than the relatively small predominance of samples in which seed-size distribution implies self-affinity is the partition of self-similarity and self-affinity between undisturbed (non-tilled) soil and tilled soil. Because harrowing was done only down to a 10 cm depth while tine and plough could be done down to 20 cm depth (see Experimental Section below) size-number distributions before tillage were modeled for 0–10 cm and 0–20 cm, with the results before and after tillage summarized in

Considering samples of undisturbed soil down to 10 cm depth, single values of

In general, tillage clearly increased the frequency of self-similarity. After tine, self-similarity was found in 33% of total and spherical seeds and in 100% of non-spherical seeds, while before tine, self-similarity was found in 33% or less of samples and was completely absent from the plot where tine was to be done. After harrow, self-similarity was found in 33% of total seeds and in 66% of spherical and non-spherical seeds while before harrow self-similarity was found in 22% of samples and almost completely absent from the plot where harrow was to be done. Finally, after plough self-similarity was found in 66% of spherical and non-spherical seeds while before plough self-similarity was found in 33% or less of samples and again in 33% of samples from the plot where plough was to be done.

Value (points) or range (bars) of size-number distributions of seeds expressed by

In black, samples from the plot assigned to plough; in red, from the plot assigned to tine; in blue, from the plot assigned to harrow. In all panels (and in each depth interval of undisturbed soil) the first block of

As for the value of

Similarly, no significant differences were found among

Analyzing total, spherical and non-spherical seeds again no significant differences were found between

Altogether these results suggest that soil disturbance by tillage considerably alters size-number distributions of seeds in soil shifting the distribution from predominantly self-affine in undisturbed soils to predominantly self-similar in tilled soils. On the contrary, the larger

Probing deeper size-number distributions of seeds in soil before and after tillage involved fitting Equation (4) to all seeds (spherical plus non-spherical), and separately to spherical and non-spherical seeds at 2.5 cm soil depth intervals down to 10 cm (after harrow only) or to 20 cm (undisturbed and after plough and tine).

Starting with all seeds (

Value (points) or range (bars) of size-number distributions of seeds expressed by

In black, samples from the plot assigned to plough; in red, from the plot assigned to tine; in blue, from the plot assigned to harrow. Points indicate self-similarity, bars indicate self-affinity.

As happened when

Considering spherical seeds alone (

Value (points) or range (bars) of size-number distributions of seeds expressed by

In black, samples from the plot assigned to plough; in red, from the plot assigned to tine; in blue, from the plot assigned to harrow. Points indicate self-similarity, bars indicate self-affinity.

As happened when

Considering non-spherical seeds alone (

Contrary to what happened when

Value (points) or range (bars) of size-number distributions of seeds expressed by

In black, samples from the plot assigned to plough; in red, from the plot assigned to tine; in blue, from the plot assigned to harrow. Points indicate self-similarity, bars indicate self-affinity.

Clearly self-affinity prevailed in undisturbed soil and shifted to self-similarity after tillage either when all seeds (spherical plus non-spherical), spherical seeds or non-spherical seeds were examined. In general, before or after tillage, the frequency of self-similarity was higher in spherical seeds. In undisturbed soil, before tillage, self-similarity was always more frequent in the plot that was later ploughed followed by the plot that was later harrowed in all seeds and spherical seeds, but not in non-spherical seeds where the plot that was later tined was second. Given the setup of plots in the field, as plough was located higher, harrow lower and tine intermediate (see

Conversely, soil depth plays a role in the change of the larger ^{−4} for coefficients, lack of fit with ^{2} = 0.947), in spherical seeds (^{2} = 0.957) and in non-spherical seeds (^{−4} for coefficients, lack of fit with ^{2} = 0.857).

Relationship between

Blue and diamonds all seeds (spherical plus non-spherical); purple and circles spherical seeds; green and triangles non-spherical seeds. Equations for undisturbed soil, all seeds ^{2}; spherical seeds ^{2}; non-spherical seeds ^{2}. Equations for tillage by tine, all seeds ^{2}; spherical seeds ^{2} − 0.002^{3}. Equation for tillage by harrow, non-spherical seeds ^{3}.

In all cases the larger

Fitting a polynomial equation to describe the relationship between the larger ^{−4} for coefficients, lack of fit with ^{2} = 0.792), in spherical seeds (^{−4} for coefficients, lack of fit with ^{2} = 0.938) and in non-spherical seeds (^{−4} for coefficients, lack of fit with ^{2} = 0.925). In all seeds and non-spherical seeds the larger

(

Fitting a polynomial equation to describe the relationship between the larger ^{2} = 0.896) with the larger

Fitting a polynomial equation to describe the relationship between the larger

Broadly speaking, in undisturbed soil, self-affinity was largely prevalent meaning that size-number distribution of seeds was not random but depended upon the size of seeds itself. Thus, it would depend on the functional differences among seeds of different sizes, which would respond differently to past environmental conditions and constraints. However, this adaptive response of the soil seed bank to past environmental conditions and constraints is clearly disrupted by tillage, almost irrespective of the intensity of the disturbance it imposed, with soil seed banks showing a generalized pattern of randomness of seed size distribution after either tine, harrow or plough.

Randomness of seed distribution after tillage was previously stated [

However, and not surprisingly, tillage of high intensity of disturbance like plough differs from tillage of low intensity of disturbance like tine because in addition to self-affinity the relationship between

Fractal dimension was found to range between 1.07 and 1.41 in landscape topography [

Considering only samples after tillage,

However,

Altogether these results imply, even in the absence of short-time, short-range disturbances imposed by tillage factors governing size-number distribution of soil seed banks still operate at remarkably short-time, short-range levels. The fast response of size-number distribution of soil seed banks to environmental pressures implied by these results is even more noticeable because it results from sampling soil seed bank after the germination of the most part of constituents of transient seed bank fraction. Thus, only the short and long-term persistent fractions of the seed bank as defined and adopted in [

It remains an open question whether such short-range dependency is a particular adaptation of plants thriving in the notoriously unpredictable Mediterranean environment where this study was conducted or a general feature of soil seed banks dominated by therophytes.

Field work was done in Herdade Experimental da Mitra (Mitra Experimental Farm), Universidade de Évora, located near Évora, Southern Portugal (38° 32' N, 8° 1' W). The site was an area of open

Three plots perpendicular to the slope, 6 × 2 m^{2} each and 3 m apart were defined and each plot randomly assigned to one tillage treatment (

Four days after the first sampling, ropes were removed and tillage was done following the best agronomic practices. Plough was done with a two-furrow moldboard (three passes, reversing direction at each pass) followed by one pass of disk harrow with eleven 24''-blades (

Five days after tillage ropes were again tied to poles left in the field (

Samples were taken from the freezer as needed and kept two days at room conditions before being processed. Each sample (a cylinder 5 cm Ø, 2.5 cm height) was sequentially sieved with hand disaggregation under a gentle stream of hot water through a series of ten sieves 2.38, 0.85, 0.71, 0.56, 0.425, 0.355, 0.297, 0.25, 0.212 and 0.149 mm mesh side. Fractions retained by sieves with mesh side 0.355 mm or higher, composed by coarser materials and clearly visible organic matter were separately transferred to Whatman 540 paper, excess water removed by suction, materials dried in an electric oven at 60 °C and stored before seeds were sorted and counted. Fractions retained by sieves with mesh side 0.297 mm or smaller were sunk in 25 mL of magnesium sulfate distilled water solution (250 g L^{−1}), gently stirred during two minutes in order to separate the mineral component from the organic component seeds included and after two additional minutes of rest, floating materials were transferred to Whatman 540 paper [

Fractions retained by sieves 0.85 mm or lower were examined under a stereomicroscope while those retained by 2.380 mm mesh side were examined with naked eye. Seeds were considered viable according to their resistance to pressure by tweezers [

Ten random samples of the mineral fraction of the 0.297 mm or lesser meshes and of the materials not retained by the 0.149 mm mesh were processed and inspected for lost seeds as described above.

No attempt was done to identify the species of each and every seed but only the identification of all species present in all samples. Identification was done using published seed identification guides [

The approach and procedures of Casco ^{®}2010 (Microsoft Corporation).

The power law is expressed as:
_{S}_{>s} = ^{D}_{S}_{>s} is the proportion of seeds greater than a given size which is equated with the mesh side _{S}_{>s} when _{S}_{>s} = ln

Expressing the mesh side _{min} which is known in any given sample (almost always _{min} = 0.149 mm), then _{min} and Equation (2) reduces to:
_{S}_{>s’} = _{min} the proportion _{Y>s’} of seeds greater than the mesh side _{min} is necessarily unity, implying that ln

Equation (3) describes a self-similar power model of seed-size distribution in which the relationship between seed size expressed by ln _{S}_{>s’} is constant across the whole range of _{S}_{>s’} may not be constant across all values of _{S}_{>s’} that can be expressed by:
_{S}_{>s’} = ^{2} + ^{3} + ^{4}

The reparameterized power function presented in Equation (4) was fitted by stepwise regression without replication forced through the origin using the least squares method with an experiment-wise confidence level for coefficients of ^{2} using the

Equations only accepted after checking that ln _{S}_{>s’} ≤ 0 for any value of ln _{S}_{>s’} decreased monotonically with ln ^{2} using the

After being fitted and accepted, equations were back-transformed as:_{S}_{>s’} = ^{D + A ln s’ + B (ln s’)2 + C (ln s’)3}
^{2} + ^{3}]

Comparisons of means involving only two samples were made by exact two-tailed Student’s ^{2}) are presented as proportion of the maximum ^{2} possible [

Power law and the resulting analogs of fractal and multifractal dimensions can be used to characterize size-number distributions of soil seed banks and the effects of soil disturbances on them.

In the absence of soil disturbance by tillage soil seed bank responses to past events results in the prevalence of self-affinity, meaning that size-number distributions are not independent from seed size itself.

Soil disturbance by tine, harrow or plough breaks this dependency and is immediately reflected in the shift from self-affinity to self-similarity of size-number distribution of soil seed banks, meaning that tillage imposes randomness to size-number distribution regardless of the intensity of soil disturbance induced by tillage.

As could be expected, the magnitude of fractal dimensions after tillage shows that size-number distributions of soil seed banks responded to short-term, short-range factors. However, before and after tillage the values of fractal dimensions were almost the same, which means that in undisturbed soils the size-number distributions of soil seed banks were also being affected and responding to short-term, short-range factors.

This work was funded through European Community under the project EC AIR-CT-920029. Thanks are due to Carla Barreto (then at Department of Biology, University of Évora) for the enormous amount of work she did processing samples and counting seeds; to Mário Carvalho (Department of Fitotecnia, University of Évora) for all discussions about tillage, agriculture and soils, and also for his advice and help in the design and execution of tillage experiment; to an anonymous reviewer for comments and suggestions to the manuscript.

The author declares no conflict of interest.