soil partitioning effect of an earthworm burrow system

Bio lFe~Sof l s (1987) 3:121-124 Biology and Fertility

°f S o i l s © Springer-Verlag 1987

Soil partitioning effect of an earthworm burrow system*

A. Kretzschmar Station de Recherches sur la Faune du Sol, INRA, 17 rue Sully, F - 2 1 034 Dijon, France

Summary. Through the simulation of an earthworm burrow system and the calculation of the shortest pathway from the bottom of the system to the surface, using a succession of burrows, it is shown that the borrow system leads to a partition of soil space. The characteristics of the resulting heterogeneity, the size of this partitioning and the length of the shortest pathways are discussed with regard to the functional relationship between the burrow system and the soil.

Key words: Earthworm - Aporrectodea, sp. - Bur- rows - Simulation - Soil heterogeneity

Progress in soil biology is made as a result of species identification, population density estimation and functional structure quantification. The role of soil- living organisms in soil formation is regarded as the effect of a great variety of behavioural adaptations to the variations of soil conditions. In his introduc- tory paper for the symposium on Darwin, Ghilarov underlined, following the works of Darwin, the com- bined effect of "a continually recurrent cause" and "the influence of organisms on their environment, i.e., the dependence of the milieu, of the environment, on their activity" (Ghilarov 1983).

Earthworm burrow systems are generally regarded as a large-sitze porosity where water and gas flows are fairly rapid, i.e., comparable to those at the soil surface. The functional estimation of the role of these systems has to take into account the pattern of structural relationships between the differ-

*Dedicated to the late Prof. Dr. M.S. Ghilarov

ent burrows and to explain the relationships between burrow functions, earthworm behaviour and the biological needs of earthworms.

In a previous paper (Kretzschmar, unpublished), it was proposed to study the main topological properties of these systems through simulated systems (the methods and main results are summarized below). Here I want to focus on a particular point: the fact that, when diffusion processes are considered through the burrow system, it is possible to esti- mate a particular pathway, from the bottom to the surface,which is shorter and more efficient with regard to gas exchange; the determination of this shortest pathway leads to the observation of a partition of the deep soil space, which is also discussed below.

Material and methods

From the field observation of earthworm burrow systems (mainly due to Aporrectodea sp.) (Kretzschmar 1982), simula- tions were performed through the modelling of four main characteristics: mean length of burrow unit, angular orientation, middle coordinates and diameter (Kretzschmar, unpublished). In the case of the field-observed burrow system, the actual distribution of the above-mentioned characteristics has been calculated; then, the model of these distributions was fitted using the Uwhaus procedure, a program for estimating the non-linear parameter (Bachacou et al. 1981). To obtain the simulated burrow system, each burrow is defined by estimating the middle coordinates using previous methods, then the top and bottom coordinates according to the length and angular orientation, then the diameter; the entire system is considered within a column of soil, and the density of the system is determined by the number of burrow units contained in this column. The shortest pathway from the bottom of the burrow system to the soil surface was computed as follows: from a point P at the bottom of the burrow system, the minimal distance to each burrow is calculated (if the projected point on the line running in the direction of the burrow is outside the

122 A. Kretzschmar: Partitioning effect of earthworm burrows

burrow extremities, the minimal distance is calculated between P and the closest extremity); then the ratio of this distance to the vertical extension of the burrow is calculated. When this ratio is at its minimum, (considering successively every burrow unit) the corresponding distance is regarded as the most efficient; then the same computation is reiterated from the upper extremity of the selected burrow, and so on. Finally, it is assumed that by sum- ming the minimal distance from the bottom to the surface, an estimation of the shortest pathway can be made.

Totmderstand the partitioning role of this structural characteristic, the burrow systems were simulated over a large sample volume: the horizontal dimensions were 300 × 300 mm; the depth was 1000 mm. The density of the system was chosen to simulate the maximal natural density (1350 burrow units in this volume), the minimal natural density (450 burrow units) and an intermediate density (900 burrow units). All the simulation parameters (burrow length, angular orientation, middle coordinates and diameter) were fixed for the three systems at the same values: burrow length distribution, exponential; mean length, 55 ram; angular orientation (from the horizontal plane) distribution, exponential; sine (a) = 0.78; middle burrow vertical coordinate distribution, exponential; mean value, 300 mm; diameter distribution, normal, ~t = 3.5 mm; o = 1.2); these values for the different parameters correspond to those of the burrow system observed in field conditions at the time of its maximal development (i.e. at the end of winter). The calculations performed with the simulated burrow system enable a comparison to be made of the role of the increasing density of the system without interference due to other parameters.

For the estimation of the shortest pathway, the point P (as defined above) was placed at a number of positions, at a fixed depth below the surface (700 mm), following a square horizontal grid 300 × 300 mm (the maximum area of the simulated volume), where the distance between two successive positions of P was 20 mm, in both directions, i.e. 16 x 16 = 256 positions. For each position, the pathway was identified by the group of burrows which were selected through the above-mentioned program. Then, for each initial position of P, one can calculate the coordinates of the upper burrow extremity, which, at the end of the shortest pathway, opens at the surface. The partitioning effect is observed in grouping on a map (horizontal projection; depth, 700 ram) of all the initial positions of P (identified by their zone number) which are "functionally connected" to the same upper burrow open at the surface ("surface open burrow") through the same shortest pathway.

Results and discussion

The general characteristics of soil partitioning by the burrow system are given in Figs. 1-3. Because of the qualitative aims of this study, the results are limited to t h o s e o b t a i n e d w i t h t h e b o t t o m o f t h e s y s t e m at a

d e p t h o f 700 m m . I t is o b v i o u s t h a t t h e p a t t e r n o f

p a r t i t i o n i n g d e p e n d s o n t h e l e v e l a t w h i c h t h e b o t - t o m ( = d e p a r t u r e l e v e l f o r t h e c o m p u t a t i o n o f t h e

s h o r t e s t p a t h w a y ) is f ixed . C o m p a r e d wi th t h e n u m b e r o f b u r r o w s , t h e n u m -

b e r o f " s u r f a c e o p e n b u r r o w s " is r a t h e r l ow. T h i s c a n b e u n d e r s t o o d b y t h e v e r y i m p o r t a n t e f f ec t , o n t h e t y p e o f c a l c u l a t i o n th is s t u d y has c o m p u t e d , o f l o n g b u r r o w s , c o n s i d e r i n g a t t h e s a m e t i m e tha t t h e

1 1 I 3 3 . . . . . 3 3 3 3 3 3 3 3 3 3 3 3

1 1 I~/~ 4 4 4 413 3 3 3 3 3 3 3

1 1 ? 4 4 4 4 4 J 3 3 3 3 3 3 3 3

1 i ~ 4 4 4 4 ~ 3 3 3 3 3 3 3 3

1 i ~ 3 3 3 3, 3 3 3 3

1 1 1 I~3 3 3 3 3 3 3 3 3 3 3 3 141 \

1 1 1 3 3 3 3 3 3

1 1 1 1 114 4 4 4 13 3 3 3 3 3 3

1 1 1 1 1 ~ 4 4 ~ 3 3 3 3 3 3 3

1 1 1 1 1 1~4 4 y 3 3 3 3 3 3 3

1 1 1 1 1 1 1 ~ / ' 3 3 3 3 3

1 1 1 1 1 1 1 1 C 3 i ~ 3 3 3 3 I 2 2 2

1 1 1 ]~ I 1 1 1-- 1 ~ 3, 3 3 3 12 2 2

I I I I I I I i I ~ 2 2 2 2 2 2 2

1 1 1 i -- 1 1 1 1 1 1 ~ 2 2 2 2 2 I--2|2

Fig. 1. Partition of the horizontal level (700 mm depth) for the minimal density of the burrow system (450 units); "surface open burrows" are marked boldface (relative to the corresponding zone number)

1 l l 4 ~ 1 ,,,4 4 4

1 1 1 1 1 1 " ~ 4

1 1 1 1 1 1 1

I i 1 1 1 I 1

1 1 1 I 1 1 1

1 I 1 1 1 1 1 111

1 1 1 1 1 1 I

I 1 i I i 1 I

1 1 1 1 1 1 1

1 1 1 1 1 1 :

! 1 1 1 1 1 1~ 2

/ I I I i l ~ 2 2

i 1 i 1 i 1~ 2 2

/ 1 1 1 1 [/2 2 2

I 1 1 1 1 1 2 2 2

/ 1 1 1 1 I 2 2 2

5 5 S 5 1 _ 5 1 5 / 3 3 3 3 /

5 5 5 5/3 3 3 3 3

3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3

3 3 3 1313 3 3 3 3 3

3 3 3 3 3 3 3 3 3

33j~ 3 3 2. 3 3 3 3

3 3 3 3 3 3

2 2 2 2 ~ 3 3 3 3 3

2 2 2 2 2 2 2 ~ 3 3

2 2 2 2 2 2 2 2 ~ 3

2 2 2 2 2 2 2 2 2 121

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

Fig. 2. Partition of the horizontal level (700 mm depth) for the intermediate density of the burrow system (900 units); "surface open burrows" are marked as for Fig. 1

e x p o n e n t i a l d i s t r i b u t i o n o f b u r r o w l e n g t h l e a d s t o a v e r y l o w p r o b a b i l i t y fo r l o n g b u r r o w s .

E v e n c o n s i d e r i n g a l a r g e s a m p l e v o l u m e of soi l , t h e p a r t i t i o n i n g e f f e c t c a n n o t b e o b s e r v e d e n t i r e l y in

this w a y ; t h e z o n e s w h i c h h a v e t h e s a m e " s u r f a c e

A. Kretzschmar: Partitioning effect of earthworm burrows 123

s 5 5 [ , 7 , , 7 1 8 8 8 8 1 9

° °'15 ~ , , ~ , " ' L___V' ' " , C 2 2 ' o ° v'o ' ( ' ' ' ' ' ' '

5 5 , 6 e , 5 " '

5 5 5 -5 ~ 5 , 2 9 2 ~,, 3 - - - ~ , , / ~ , ,

/ \ lal ~ , 5 / = = 2 2 = = =t_4~ =N~ 3 3 3

', ', [~'!'i == i i =2 ~2 ~ ==~ 32 3= ~g . 3. Partition of the horizontal level (700 mm depth) for the maximal density of the burrow system (1350 units); "surface open burrows" are marked as for Fig. 1

open burrow" are too large to be observed entirely. This leads us to focus on the problem of sample volume in the field measurement of the effect of earthworm burrow system on water or gas flows.

Moreover , it is possible to observe that the "surface open burrows" do not always open into the area above their zone of influence, especially when the burrow density is high. This can result in functional heterogeneity in certain cases such as:

- Deep soil cracks which may affect a zone of vegetation which is not directly above

- Deep root activity that may depend on surface conditions not in the immediate vicinity of the plant itself.

From a general point of view, the size of the horizontal partitioning effect of an earthworm burrow system has to be taken into account when the functional effect of the system is researched, instead of only the observations concerning one or some isolat- ed burrows. This is the case when the relationships between earthworm burrow systems and root systems are studied.

Effect of increasing density

The complexity of the partitioning increases with the density of the burrow system, but not linearly. When the density increases from 450 to 900 units per sample volume, the complexity does not change (4 and 5

Table 1. Minimum value of the shortest pathway relative to each zone (mm), according to the density of the burrow system

Density Zone number (units)

450 1 2 3 4

290.1 257.54 155.72 223.23

900 1 2 3 4

136.62 134.29 132.61 297.0

1 2 3 4

1350 135.56 66.13 136.64 122.29

6 7 8 9

129.25 149.82 150.62 159.65

5

261.5

5

132.45

zones, respectively, with no specific pattern), but when the density reaches 1350 units, the number of zones is 9 and a pattern of interpenetration can be observed (zone 2, over zone 3, into zone 4; zone 6 into zone 5).

The estimation of the average value of the shortest pathway following the density, calculated over all the initial positions of P (256), decreases when the density increases: 270.82 mm (SE + 56.5 mm) when density = 450 units; 193.53 mm (SE _+ 42.2 mm) when density '= 900 units; and 153.36 mm (SE + 31.5 mm) at the maximum density (1350 units). These values are significantly different at the 1% probability level. As was noted by Kretzschmar (unpublished), it can be considered that the average shortest pathway length reachs a minimum value of around 150 ram, which does not change significantly when the density increases. But in the case of a large sample volume, the minimum value of the shortest pathways relative to each zone can observed (the average shortest pathway length for each zone is not calculable because no zone is entirely observed). In Table 1, these minimal values for each zone are given. At each density, the heterogeneity between the different zones is important, and when the density increases, the probability of a long burrow increases; then a very short pathway can occur, as for zone 2 in the case of maximum density. It can be considered that, at one level of density, most of the zones are characterized by the same minimal shortest pathway length; thus, there is no important differ- ence between the intermediate density and the maximum density, where for every zone (expect zones 4 and 5 in the case of the intermediate density, which are not sufficiently represented by the simulation, and except zone 2 in the case of maximum density) the minimal pathway length is around 135 ram. The

124 A. Kretzschmar: Partitioning effect of earthworm burrows

variation of the average length of the shortest pathway, when density increases, is only relevant to the case of a long burrow. In field observations this can lead to surface heterogeneity.

Conclusion

The examination of the part ioning effect due to the pat tern of an ear thworm burrow system leads to observations about the nature and the origin of the heterogenei ty in transfer processes relevant to soil functions. One of the most interesting problems in this field of research is to understand at which de- gree of accuracy the populat ion of ear thworms can be considered as having built the appropr ia te system, or what is the r andom effect of the general activity on the pat tern which we are able to distin- guish.

The other point is to focus on the question of sample volume in field exper imentat ion and in considering the burrows as a functional system or as a collection of independent units.

The simulation of particular patterns of earthworm burrow systems enables some propert ies of these systems which are not observable by field exper iments to be investigated, to try out different sample volumes in this field of research and to give some limits to the interpretation of relationships between the system patterns and their expected functions.

References

Bachacou J, Masson JP, Millier C (1981) Manuel de la programa- thrque statistique Amance. INRA, Paris

Ghilarov MS (1983) Darwin's formation of vegetable mould - its philosophical basis. In: Satchell JE (ed) Earthworm ecology: from Darwin to vermiculture. Proc Internat Meeting 1-5 Sept 1981 Grange-over-Sands. Chapman and Hall, London, pp 1--4

Kretzschmar A (1982) Description des gaieties de vers de terre et variations saisonnirres des rrseaux (observations en conditions naturelles). Rev Ecol Biol Sol 19:576-591

Received May 17, 1986

soil partitioning effect of an earthworm burrow system

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