Effects of Feces on Spatial Distribution Patterns of Grazed Grassland Communities

Agricultural Sciences in China

January 2010

2010, 9(1): 121-129

Effects of Feces on Spatial Distribution Patterns of Grazed Grassland Communities Tamanna Islam1, Eiki Fukuda2, Masae Shiyomi3, Molla Rahman Shaibur4, Shigenao Kawai1 and Mikinori Tsuiki1 The United Graduate School of Agricultural Sciences, Iwate University, Morioka 020-8550, Japan National Agricultural Research Center for Tohoku Region, Morioka 020-0198, Japan 3 Faculty of Science, Ibaraki University, Mito 310-8512, Japan 4 Department of Environmental Science and Health Management, Jessore Science and Technology University, Jessore 7400, Bangladesh 1 2

Abstract Animals excrete feces during grazing. The uneven distribution of feces causes a spatial heterogeneity in grassland communities. In this study, we attempted to clarify the effects of feces on spatial distribution patterns of plant species. A field study was conducted on four grasslands each grazed by a single cow. These four grasslands were defined as Poa pratensis (Kentucky bluegrass) dominated grassland without feces (PoF-), Poa pratensis dominated grassland with feces (PoF+), Zoysia japonica Steud. (Japanese lawngrass) dominated grassland without feces (ZyF-), and Zoysia japonica Steud. dominated grassland with feces (ZyF+). A 50 m line that transects 100 equally spaced quadrats (L-quadrats) was drawn on each of the four grasslands. Each quadrat was 0.50 m × 0.50 m in size and consisted of four equal-area cells of 0.25 m × 0.25 m (S-quadrats). The occurrences of all plant species were recorded in each S-quadrat. The binomial distribution (BD) and beta-binomial distribution (BBD) were used to represent the variation in spatial patterns. The BBD provided a significant description of the frequency distribution of plants per quadrat. A power law was used to calculate the spatial heterogeneity of each species together with the community heterogeneity. The results revealed that the plants on each of the four grasslands were aggregatively distributed. The ZyF+ exhibited greater spatial heterogeneity than the ZyF- due to the uneven deposition of feces by cows grazing on the grasslands. Additionally we also found that the feces had effect on the heterogeneity inZyF+ and did not have effect in PoF+. Key words: beta-binomial distribution, power law, feces, grazing grassland, spatial distribution

INTRODUCTION Animal grazing is one of the main causes for the heterogeneous distribution of grassland communities. Animals excrete feces and urine on grazing grasslands. The excreted feces and urine are unevenly distributed on the grasslands and this affects the physicochemical characteristics of grazing areas, resulting in a high degree of spatial heterogeneity in grasslands. The nutrient cycle could be altered by the nutrient elements and Received 30 March, 2009

thus different nutrient cycling processes could give rise to different ecosystems (Tsuiki et al. 2005). The grazing intensity strongly affects grassland spatial heterogeneity and species diversity of plants (Tsuiki et al. 2005). How does grassland spatial heterogeneity contribute to grassland productivity, sustainability and species diversity? This question has yet to be fully addressed. Several methods, including variance-to-mean ratios, dispersion indices and the fitting of frequency distributions have widely been used to detect patterns from

Accepted 7 July, 2009

Correspondence Molla Rahman Shaibur, Ph D, Assistant Professor, E-mail: [email protected]

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count data in ecology. More complex methods like spatial autocorrelation analysis and geostatistical analysis have been used to examine the relationships of samples or plants within and across rows (Campbell and van der Gaag 1993; Gottwald et al. 1992). Various probability distributions have been used to model spatial patterns including the Poisson distribution, binomial distribution (BD), negative-binomial distribution, and beta-binomial distribution (BBD) (Madden and Hughes 1995; Shiyomi and Yoshimura 2000). Based on the best fit of the observed frequencies, spatial patterns are classified as being random, regular or aggregated (Madden and Hughes 1995; Shiyomi et al. 2000). In random spatial patterns, plants have equal probability of being found at any location. By contrast, in regular distributions, plants are essentially equally spaced relative to each another. In aggregated patterns, plants tend to form clusters. Recent studies have demonstrated that the BBD is the most appropriate distribution to use since the data for plant occurrence is binary (Chen 2007). It has also been demonstrated that the spatial pattern of plant species can be modeled using a power law (Shiyomi et al. 2001; Tsuiki et al. 2005). In the present study, we examined the variation in spatial patterns of grassland plant species in the presence and absence of feces. We used the BBD to assess whether plant species were aggregatively distributed or not both in the presence and absence of feces. A power law was used to investigate the relationship between the observed variance and the binomial variance.

Region of Japan (Morioka, Iwate Prefecture). Data collected between October 1998 and October 2001 were used in this study. A single cow was grazed on each of the four grasslands from May to October each year and fertilizer was not applied. The average bodyweight of the cow was 450 kg which was grazed once in a day. The four grasslands were characterized as (i) Poa pratensis (Kentucky bluegrass) dominated grassland without feces (PoF-), (ii) Poa pratensis dominated grassland with feces (PoF+), (iii) Zoysia japonica Steud. (Japanese lawngrass) dominated grassland without feces (ZyF-) and (iv) Zoysia japonica Steud. dominated grassland with feces (ZyF+). Occurrence of the plan species has been given in Table 1. In the PoF- and ZyF- grasslands feces were removed once a day using a vacuum cleaner, whereas in the PoF+ and ZyF+ grasslands feces were not removed. The area of each of the four grasslands was about 0.25 ha. A 50 m line transect was drawn in each of the four grassland. 100 equally spaced quadrats (0.50 m × 0.50 m; L-quadrats) were located at each transect. Each L-quadrat was subdivided into four 0.25 m × 0.25 m quadrats (S-quadrats). All plant species in each S-quadrat were identified and recorded each October from 1998 to 2001 and each June from 1999 to 2001. Frequencies in all the Lquadrats were calculated for all species. There were 30 to 40 plant species in PoF- and PoF+ and 20 to 30 in ZyF- and ZyF+. Table 1 shows the five most dominant species in each of the four grasslands.

Data analysis

MATERIALS AND METHODS Source of data Data from four grasslands were collected from the National Agricultural Research Center in the Tohoku

Binomial distribution (BD) The BD is generally appropriate for representing the frequency of randomly occurring individuals per L-quadrat (Hughes and Madden 1993; Hughes et al. 1997). If is the estimated occurrence, it can be expressed as:

Table 1 Dominant species of the 4 grasslands with occurrence ( ) Species of PoF-

Occu.

Species of PoF+

Poa pratensis Veronica arvensis Erigeron philadelphicus Digitaria ciliaris Paspalum thunbergii

0.96 0.95 0.78 0.74 0.73

Trifolium repens Poa pratensis Veronica arvensis Dactylis glomerata Duchesnea chrysantha

Occu. 0.83 0.78 0.74 0.63 0.56

Species of ZyF-

Occu.

Species of ZyF+

Occu.

Zoysia japonica Veronica arvensis Trifolium repens Poa pratensis Erigeron philadelphicus

1.00 0.78 0.64 0.46 0.39

Zoysi japonica Trifolium repens Viola verecunda Poa pratensis Veronica arvensis

0.99 0.76 0.61 0.57 0.48

PoF-, Poa pratensis dominated grassland without feces; PoF+, Poa pratensis dominated grassland with feces; ZyF-, Zoysia japonica Steud. dominated grassland without feces; ZyF+, Zoysia japonica Steud. dominated grassland with feces. Occu., occurrence. The same as below.

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Effects of Feces on Spatial Distribution Patterns of Grazed Grassland Communities

(1) Where xj is the frequency of a plant of species i occurring in L-quadrat j, n is the number of S-quadrats in a L-quadrat and N is the number of L-quadrats. Since p is the ratio of the number of occurrences of species i to the total number of S-quadrats, the variance of p is [p(1 - p)/n] and the standard error is [p(1 p)/Nn]1/2 (Madden and Hughes 1999). Beta-binomial distribution (BBD) If the plants are aggregatively distributed (i.e., they are non-randomly distributed) then the probability of a plant occurring (p) will not be constant. This variability of p depends on factors such as environmental conditions, grazing conditions and soil structure. Since p follows a beta distribution in the BBD, it can take values between 0 and 1. The BBD is given by the following equation: Be(α + x, β - x + n)/Be(α + β)

(2)

Where x is the frequency of a plant of species i occurring in a L-quadrat,α and β are positive parameters and Be is the beta function: (3) Be(α + β) = ( α β )/ (α + β)

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For the BBD, θ = 1/(α + β) is the index of heterogeneity or aggregation. When θ = 0, the occurrence distribution is random and aggregation will increase as θ increases. We used the t-distribution [t = θ/s.e.(θ )] to test the null hypothesis θ =0 (Madden and Hughes 1995). The moment estimate of θ is: = [v - np(1 - p)]/[n2p(1 - p) - v]

Where v is the observed variance of species i. The index of heterogeneity for the whole community can be defined as: (5) Where θi is the degree of heterogeneity of species i. Equation (5) is weighted with pi in order to give a large contribution to species having high occurrence frequencies. Binary power law The binary form of Taylor’s power law describes the linear relationship between the observed variance and the binomial variance (Madden and Hughes 1995). It is a measure of heterogeneity. For a whole community with s species this law can be written as:

log(vi/n2) = logA + Blog[pi (1 - pi)/n] for i = 1, 2, …, s Where logA and B are respectively the intercept and the slope of the regression (Tsuiki et al. 2005), pi is the estimated occurrence of species i, and vi is the sample variance of species i. The power law in equation (6) can be expressed by the following linear equation: yi = a + bxi + εi with i = 1, 2, …, s

(7)

Where a and b are constants, xi = log[p i(1 - p i)/n], yi = log(vi/n2) and εi denotes the difference in species i from the regression line (i.e., the residual term). After plotting (xi , yi) for s species (i = 1, 2, ..., s), the spatial heterogeneity of species i was then determined as follows: (1) if the coordinates of species i are on the line y = x, species i forms a random pattern; (2) if the coordinates of species i are above the line y = x, species i forms a more heterogeneous pattern than random; and (3) if the coordinates of species i are below the line y = x, species i forms a less heterogeneous pattern

(4)

(6)

than random. The line estimated using regression analysis weighted by pi expresses a characteristic of the plant community. We assume that εi follows a normal distribution with N(0, σ2) under the conditions of the regression analysis. An estimated regression line located above the line y = x for the whole range of x observed in the survey indicates that the entire community tends to be more heterogeneous than a random distribution. The value of δi indicates the degree of heterogeneity or the discrepancy from a random expectation for species i. δi can be defined as:

δi = α + (β - 1) xi + εi for i = 1, 2, …, s

(8)

Using the following equation, an index of heterogeneity for the whole community can be defined as: (9) A large δc indicates high spatial heterogeneity at the community level, while a small δc indicates that the community has low heterogeneity (Shiyomi et al. 2001).

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RESULTS Distribution pattern Frequency distributions of Poa pratensis in PoF-, PoF+ and of Veronica arvensis in ZyF- and ZyF+ in October 1998 together with expected frequencies for the BBD and BD are shown in Fig.1. For all the considered data, we found that the BBD provided a much better description of the frequency distribution of occurred plants than the BD (Fig.1). Similar results for these four grasslands were found for the data from June 1999 to October 2001 (data not shown). Table 2 shows the estimated θ for the BBD for the five most dominant species from October 1998 to October 2001. The results for the BBD are in good agreement with the t-test for θ (P < 0.05) (Table 2). For the five most dominant species of the four grasslands, θ > 0 indicates that these species were aggregatively distributed (Table 2). Table 3 shows that the values of θc in PoF- were higher than that in PoF+ in October 1998, June 1999,

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October 2000, and June 2001. In October 1999, June 2000 and October 2001, the values of θc in PoF+ were higher than that in PoF- (Table 3). For October 1998 values of θc in ZyF- were higher than those in ZyF+ (Table 3). In ZyF+, the θc values were higher than those in ZyF- during June 1999 to October 2001 (Table 3). Mean plant occurrences ranged from 0 to 1 from October 1998 to October 2001 for Dactylis glomerata L. in PoF- and PoF+ and for Poa pratensis in ZyF- and ZyF+, as determined by estimating the expected probabilities of occurrence of the plants (Table 4). There was a higher probability for plants in the F+ grassland than in the F- grassland, with a larger p across all the data sets from the F+ grassland than from the F- grassland (Table 4). Similar results for all dominant species in these four grasslands were found during October 1998 to October 2001 (data not shown).

Binary power law Fig.2 shows the results of applying the power law to

Fig. 1 Frequency distributions of Poa pratensis in (A) PoF- (Poa pratensis dominated grassland without feces), (B) PoF+ (Poa pratensis dominated grassland with feces), and of Veronica arvensis in (C) ZyF- (Zoysia japonica Steud. dominated grassland without feces) and (D) ZyF+ (Zoysia japonica Steud. dominated grassland with feces) grasslands together with expected frequencies for the BBD and BD in October 1998. Obs. is observed frequency, BBD is expected frequencies for beta-binomial distribution, and BD is the binomial distribution. The BBD shows aggregative pattern for maximum likelihood estimates of p and θ .

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Table 2 Estimated θ of BBD for the top five dominated species of four grasslands during October 1998 to October 2001 Grassland PoF-

PoF+

ZyF-

ZyF+

Year

Species Poa pratensis Veronica arvensis Erigeron philadelphicus Digitaria ciliaris Paspalum thunbergii Trifolium repens Poa pratensis Veronica arvensis Dactylis glomerata L. Duchesnea chrysantha Zoysia japonica Veronica arvensis Trifolium repens Poa pratensis Erigeron philadelphicus Zoysia japonica Trifolium repens Viola verecunda Poa pratensis Veronica arvensis

1998 Oct.

1999 Jun.

1999 Oct.

2000 Jun.

2000 Oct.

2001 Jun.

2001 Oct.

1.13 1.07 0.68 1.13 1.03 0.58 0.87 0.96 0.46 1.20 1.83 0.63 0.79 0.67 0.11 0.68 0.29 0.92 2.12

1.38 0.85 0.37

0.52 0.97 0.61 1.12 0.60 0.32 1.30 0.31 0.32 0.78 2.33 0.41 0.68 0.44 1.88 0.49 0.32 1.00 2.87

0.29 1.40 0.50

0.12 1.35 0.61 0.97 0.82 0.48 0.95 0.58 0.49 1.04 1.66 0.48 0.46 0.56 4.48 0.58 0.08 1.00 0.35

0.05 0.43 0.33

0.58 2.22 0.18 1.08 0.99 0.49 0.87 1.50 0.43 0.74 1.71 0.72 1.27 0.79 1.45 0.28 0.26 0.78 0.92

*

0.57 0.58 0.47 0.60 0.33 0.61 1.23 0.86 0.99 0.50 2.60 0.64 0.51 1.04 1.05

*

0.97 0.70 1.03 0.43 0.26 0.57 0.63 0.48 0.80 0.49 4.97 0.51 0.20 0.66 0.82

*

1.68 0.75 0.89 0.68 0.55 0.77 0.77 0.44 0.82 0.59 9.77 0.57 0.13 0.73 0.49

The t-test was used to test the equality of θ = 0. p-value for H0:θ = 0 is 0.05. - indicates that we could not calculate this value because the dominated plants species Japanese lawngrass were most available plants in the ZyF- paddock. * indicates that June is the seedling period of Digitaria ciliaris, at which it does not show the flower.

Table 3 Analysis of estimated θ of BBD for whole community heterogeneity of the four grasslands during October 1998 to October 2001 Year

PoF-

PoF+

ZyF-

ZyF+

1998 Oct. 1999 Jun. 1999 Oct. 2000 Jun. 2000 Oct. 2001 Jun. 2001 Oct.

0.93 1.00 0.80 0.92 0.91 1.19 0.84

0.88 0.86 0.84 1.45 0.76 0.77 0.85

0.71 0.64 0.77 0.44 0.58 0.45 0.82

0.70 1.07 1.22 1.28 1.54 2.54 1.03

Table 4 Estimated parameters of p of BBD for four grasslands during October 1998 to October 2001 Year 1998 Oct. 1999 Jun. 1999 Oct. 2000 Jun. 2000 Oct. 2001 Jun. 2001 Oct. 1)

PoF-

PoF+

ZyF-

0.40 (32) 1) 0.36 (30) 0.22 (31) 0.27 (35) 0.19 (34) 0.17 (35) 0.13 (34)

0.63 (35) 0.62 (31) 0.26 (35) 0.29 (37) 0.22 (37) 0.31 (36) 0.17 (34)

0.46 (25) 0.51 (25) 0.28 (22) 0.48 (23) 0.26 (23) 0.44 (21) 0.31 (21)

ZyF+ 0.57 0.73 0.30 0.57 0.38 0.51 0.45

(30) (37) (33) (38) (36) (37) (33)

The values in paranthesis indicate the number of species occurred.

the PoF- grassland for October 1998. Most of the points were above the binomial line (Fig.2). R2 = 0.98 indicates that 98% of the variation of the observed variance can be explained by the variation in the estimated variance (Fig.2). The binary power law well described the relationship between the observed and binomial variances in

Fig. 2 Application of power law to the PoF- (Poa pratensis dominated grassland without feces) grassland for October 1998. The x and y axises were estimated variance and observed variance, respectively. Solid line indicated the power law estimated from data and broken line indicated the y = x, respectively.

the proportion of plants occurring per quadrat. The estimated intercept and slope were significantly (P<0.05) greater than 0 and 1, respectively. Table 5 shows the estimated power law for the four grasslands from October 1998 to October 2001. The large value of R2 indicates that the regression line fits the data well. The regression equation and y=x were compared using analysis of variance (ANOVA). The results reveal that most of the points were above the binomial line for all the

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regression (Table 5). Since the slope > 1 for all the grasslands, the larger x-value is the larger the difference between the regression line and y = x (Table 5). These results demonstrate that the plants in each of the four grasslands were aggregatively distributed. Fig.3 illustrates the relationship between the mean occurrence p and the spatial heterogeneity δ for the four grasslands in October 1998. In the PoFgrassland, Poa pratensis (Po), Veronica arvensis (Va), Erigeron philadelphicus (Ep), and Paspalum thunbergii (Pt) have high δ at relatively high p. Zoysia japonica (Zy), Agrostis alba (Aa) and Rumex acetosella (Ra) have high δ at low p (Fig.3-A). In the PoF+ grassland, Poa pratensis (Po) and Trifolium repens (Tr) exhibit high δ at relatively high p. Sonchus asper (So), Anthoxanthum odoratum (Ao), Digitaria ciliaris (Di), and Rumex acetosella (Ra) have high δ at relatively low p (Fig.3-B). In the ZyF- grassland, we found that Veronica arvensis (Va) and Trifolium repens (Tr) have high d at relatively high p, whereas Agrostis clavata (Ac) and Duchesnea chrysantha have high δ at low p (Fig.3-C). In the ZyF+ grassland, Trifolium repens (Tr) and Poa pratensis (Po) have high δ at relatively high p, whereas Zoysia japonica (Zy) have low δ at relatively high p. Festuca arundinacea (Fa) and Setaria viridis (Sv) have high δ at low p (Fig.3-D).

The values in Table 6 show that the values of δc in PoF- were higher than those in PoF+ from October 1998 to October 2000. We also found that the values of δc in PoF+ were higher than those in PoF- in June 2001 and October 2001. The δc values in ZyF+ were higher than those in ZyF- from October 1998 to October 2001 (Table 6).

DISCUSSION AND CONCLUSION In the study period feces were not removed from the PoF+ and ZyF+ grasslands. The feces excreted by grazing cows on the grasslands were unequally distributed. Feces contain considerable amounts of nutrients. The fertility of the soil under feces became nutrient rich because of the nutrients supplied by the feces and consequently the environmental conditions in those grasslands were heterogeneous. Plants in the PoF- and ZyF- grasslands were unable to receive nutrients from the feces because the feces were removed from those grasslands, so the environmental conditions remained similar everywhere in those grasslands. The seeds distributed over the grassland through feces may lead to the regeneration of grassland plants and the generation of new plant species. Therefore, the mean occurrences were larger in the PoF+ and ZyF+ grasslands than in the PoF- and ZyF- grasslands (Table 4).

Table 5 Estimated power law for four grasslands during October 1998 to October 2001 Year

Model

1998 Oct.

Power law R2 p-value for H0:b = 1 Power law R2 p-value for H0:b = 1 Power law R2 p-value for H0:b = 1 Power law R2 p-value for H0:b = 1 Power law R2 p-value for H0:b = 1 Power law R2 p-value for H0:b = 1 Power law R2 p-value for H0:b = 1

1999 Jun.

1999 Oct.

2000 Jun.

2000 Oct.

2001 Jun.

2001 Oct.

PoF-

PoF+

ZyF-

ZyF+

y = 1.21x + 0.66 0.98 0.05 y = 1.17x + 0.59 0.98 0.05 y = 1.18x + 0.60 0.99 0.05 y = 1.21x + 0.67 0.98 0.05 y = 1.18x + 0.61 0.98 0.05 y = 1.19x + 0.65 0.98 0.05 y = 1.18x + 0.62 0.98 0.05

y = 1.16x + 0.57 0.98 0.05 y = 1.15x + 0.55 0.98 0.05 y = 1.14x + 0.51 0.98 0.05 y = 1.15x + 0.58 0.97 0.05 y = 1.17x + 0.58 0.98 0.05 y = 1.19x + 0.65 0.98 0.05 y = 1.16x + 0.56 0.98 0.05

y = 1.19x + 0.62 0.97 0.05 y = 1.19x + 0.59 0.98 0.05 y = 1.18x + 0.58 0.99 0.05 y = 1.16x + 0.50 0.98 0.05 y = 1.17x + 0.54 0.99 0.05 y = 1.17x + 0.54 0.99 0.05 y = 1.21x + 0.66 0.99 0.05

y = 1.19x + 0.62 0.99 0.05 y = 1.16x + 0.62 0.97 0.05 y = 1.16x + 0.62 0.96 0.05 y = 1.17x + 0.55 0.98 0.05 y = 1.17x + 0.65 0.97 0.05 y = 1.17x + 0.60 0.95 0.05 y = 1.19x + 0.67 0.97 0.05

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Fig. 3 Relationship between spatial heterogeneity (δ) and mean occurrence (p) for the four grasslands in October 1998 (A-D). PoF- (Poa pratensis dominated grassland without feces), PoF+ (Poa pratensis dominated grassland with feces), ZyF- (Zoysia japonica Steud. dominated grassland without feces), and ZyF+ (Zoysia japonica Steud. dominated grassland with feces). Aa, Agrostis alba; Ac, Agrostis clavata; Ao, Anthoxanthum odoratum; Cg, Cerastium glomeratum; Dc, Duchesnea chrysantha; Dg, Dactylis glomerata; Di, Digitaria ciliaris; Ep, Erigeron philadelphicus; Fa, Festuca arundinacea; Lj, Lysimachia japonica; Po, Poa pratensis; Pt, Paspalum thunbergii; Ra, Rumex acetosella; Sa, Sonchus asper; So, Sonchus asper; Sv, Setaria viridis; To, Taraxacum officinale; Tr, Trifolium repens; Va, Veronica arvensis; Vv, Viola verecunda; Zy, Zoysia japonica. δc is the community heterogeneity.

Table 6 Community heterogeneity of the four grasslands during October 1998 to October 2001 Year

PoF-

PoF+

ZyF-

ZyF+

1998 Oct. 1999 Jun. 1999 Oct. 2000 Jun. 2000 Oct. 2001 Jun. 2001 Oct.

0.36 0.35 0.34 0.34 0.33 0.31 0.34

0.34 0.32 0.30 0.33 0.31 0.34 0.36

0.26 0.35 0.25 0.24 0.14 0.24 0.28

0.29 0.37 0.37 0.33 0.37 0.35 0.37

In this study, the observed frequency distributions of most plants species in the four grasslands did not agree with the BD because they were distributed in an aggregative pattern that followed the BBD (Figs.1 and 2). Skellam (1948) introduced the BBD in statistical ecology and derived the BBD from binomial and beta distributions (Boswell et al. 1979). Subsequently, the BBD was used in various fields of agriculture including phytopathology (Irwin 1954; Kemp and Kemp 1956a, b), vegetation and plant diseases (Hughes and Madden 1993; Madden and Hughes 1994, 1995). The BBD has two parameters: the expected probability of the occurrence of a plant ( ) and the aggregation index (θ). The values of θ vary from -1/n to . Sometimes the lower limit of θ may be 0. Our results reveal that the plants were distributed in an aggregative pattern and

thus the BD cannot adequately describe the observed data. The BBD captured the observed heterogeneity in the occurrence; therefore, the BBD gave a better fit to the data than the BD (Fig.1) (Kemp 1956b). Similar results were obtained for the data from June 1999 to October 2001 (data not shown). The data used was a count data set for which the BBD is the appropriate discrete model. Taylor’s (1961) power law was adjusted by Madden and Hughes (1995) to observe the spatial distributions of plant disease, and subsequently the power law was extended for many grassland plant species. We used a power law in our study to determine whether the plants in the four grasslands were distributed heterogeneously or not. In the power law, the intercept and slope were estimated by linear regression analysis using the least squares method. The power law provided a good description of the observed variance in the present case (Fig.2), confirming that this law is adequate for analyzing the occurrence patterns of plants. The better results of the power law illustrated that plants in the four grasslands tended to be aggregatively distributed (Table 5). The power law results were very consistent for the different years. We found that some common species had a high δ

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at a high p, whereas other common species had a low δ at a high p (Fig.3). The rare species also showed a similar tendency. This means that there is no relationship between δ and p. The main cause of spatial heterogeneity is the heterogeneity of the environment, such as soil fertility, the physical properties of the soil and stereoscopic plant architecture (Shiyomi and Yoshimura 2000). We found that the values of δc in PoF- were higher than those in PoF+ from October 1998 to October 2000 (Table 6). The difference between the values of in δc PoF- and PoF+ is not so high. Therefore, we can say that feces did not have any effect on PoF+. This may be due to immobilization of nutrients or priming effect might have taken place (Stevenson 1986), as a result, loss of native N (nitrogen) may have ensued or other unknown cause may be involved. It was reported that application of organic matter to soils did not have any positive effect on Amaranthus growth, even the growth decreased (Molla and Huq 2002). Clark et al. (1995) also found that application of municipal solid waste compost caused N deficiencies in plants and decreased plant yield. By contrast, PoF- had δ c lower values than PoF+ from June 2001 to October 2001 (Table 6). Similar results were also found for ZyF+ and ZyF- from October 1998 and October 2001 (Table 6). Various statistics can be used to assess the degree of non-randomness of disease incidence at the level of the sampling unit. In this study, the θ of the BBD and δ from the power law were used to assess the degree of heterogeneity (Table 2 and Fig.3). Both parameters indicate that the plants were aggregatively distributed. Using the θc, we found that in October 1998, June 1999, October 2000, and June 2001, PoF- had higher θc than PoF+. On the contrary, PoF- showed lower θc than PoF+ in October 1999, June 2000 and October 2001 (Table 3). Similar results were found in Zy grassland. Therefore, it is difficult to draw any conclusion about the effect of feces on community heterogeneity. On the other hand, using the power law it was possible to conclude that the feces had effect on the heterogeneity in ZyF+ and did not have effect in PoF+ (Table 6). In ZyF+, the main cause might be the animal dung and urine had the effect on the redistribution of nutrients within the grazed area (Chapman et al. 2007). Although

Tamanna Islam et al.

few studies have applied the power law, it is a powerful time- and labor-saving tool for understanding grassland community heterogeneity. The results can be summarized as showing that the distribution of plants in a quadrat was clearly aggregated, indicating that non-random variability among groups of plants. The observed plants showed that the spatial heterogeneity patterns of the Zy (Zoysia japonica Steud. dominated grassland) community differed due to cow dung excretion. Our results provide some insights into conservation methods for plant populations in grassland ecosystems.

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