- Email: [email protected]
A new formulation of the geometric series with applications to oribatid (Acari, Oribatida) species assemblages from human-disturbed Mediterranean areas
e c o l o g i c a l m o d e l l i n g 1 9 5 ( 2 0 0 6 ) 402–406
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecolmodel
Short communication
A new formulation of the geometric series with applications to oribatid (Acari, Oribatida) species assemblages from human-disturbed Mediterranean areas Tancredi Caruso a,∗ , Massimo Migliorini b a b
Department of Environmental Sciences “G. Sarfatti”, University of Siena, via Mattioli no 4, 53100-Siena, Italy Department of Evolutionary Biology, University of Siena, via A. Moro no. 2, 53100-Siena, Italy
a r t i c l e
i n f o
a b s t r a c t
Article history:
The mathematical properties of the geometric series are revisited and the model is applied
Received 7 April 2005
to oribatid mite (Acari, Oribatida) assemblages from Mediterranean areas that have been
Received in revised form
disturbed by human activity. In the past, the geometric series has been considered an ideal
9 November 2005
form of Fisher’s log model. However, in some cases data fit both models or the geomet-
Accepted 28 November 2005
ric series offers a better fit. Data presented in this paper and collected from areas heavily
Published on line 19 January 2006
disturbed by human activity show that the species abundance distribution of oribatids is in almost all cases well fitted by the geometric series, indicating a common trend in the
Keywords:
response to disturbance of this assemblage. The proposed new version of the model allows
Geometric series
interesting applications in environmental monitoring because it is easy to outline the quan-
Soil
titative relationship between the abundance of the most abundant species, the total number
Mites
of individuals and the total number of species in the sample. © 2005 Elsevier B.V. All rights reserved.
Disturbance Distribution Species
1.
Introduction
When the ecology of a biological community is structured by some dominant environmental factor there is usually an uneven distribution of species abundances, with a large proportion of rare to very rare species and a small number of species with high sample densities (May, 1975; Magurran, 1988). In its ideal form this distribution may be modelled as a geometric series in which the abundance of the most successful species accounts for a fraction K of the total number of individuals NT , the abundance of the second species accounts for the same fraction K of the remainder and so on, to give
∗
Corresponding author. Tel.: +39 0577232877; fax: +39 0577232806. E-mail address: [email protected] (T. Caruso).
0304-3800/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2005.11.042
Motomura’s equation in the form reported by May (1975): i−1
Ni = NT Ck K(1 − K)
(1)
where Ni is the abundance of the ith species and Ck is a param eter which ensures that Ni = N T . The uneven distribution modelled by the geometric series is usually observed in communities at an early successional stage and in those from harsh or isolated environments (Whittaker, 1960, 1972; Magurran, 1988; Hubbel, 2001). In such environmental conditions one expects the dominance of fewer species (May, 1975).
e c o l o g i c a l m o d e l l i n g 1 9 5 ( 2 0 0 6 ) 402–406
As for soil communities as a whole, although little data are available, some studies on specific assemblages such as collembolans or beetles indicate that species abundance distributions tend towards geometric or log series models at ˚ increasing levels of disturbance (Usher, 1985; Hagvar, 1994; Chung et al., 2000). In the present paper, the geometric series is reformulated to better outline relationships between the sample density of the most abundant species, the total number of species (S) and the rank–abundance structure underlying the distribution. To show how the reshaped model works, it was fitted to a number of soil oribatid community samples from six areas affected by different kinds of anthropogenic disturbance.
If NT > 100 then 1/NT < 0.01. Because these values are usually observed, this term can be approximated to zero. Hence, r−1 K∼ = r
Ni = ri−1
NS = rS−1
2.1.
Reformulation of the geometric series
hence,
(2)
In basic algebra the ith general term of a geometric progression is Bi = ari−1
(3)
where the constant a is the value of the first term (i = 1) and the non-zero constant r is the common ratio. Indeed, it is the ratio between one term and the preceding one. In basic algebra, the sum of the first n terms is known to be: n
B n = B 1 + B2 + · · · + B n =
i=1
B1 − Bn 1−r
(4)
log NS = log rS−1 ⇒ log NS = (S − 1) log r and, S=
log NS +1 log r
(9)
Therefore, when species abundance distributions may be modelled by geometric series, the number of species in the sample may be estimated from the abundance of the most dense species and the total number of individuals.
2.2.
Fit of the model
The geometric series appears as a straight line in a standard rank–abundance plot, in which species are rank ordered from the most to the least abundant, and the abundance of species is plotted on the y-axis on a logarithmic scale. (May, 1975; Magurran, 1988). Let there be an inverse rank order, with the least abundant species having rank 1 and the most abundant species having rank S. From Eq. (8), the log-transformation of abundances is log Ni = log ri−1 ⇒ log Ni = (i − 1) log r and,
Hence, in a species abundance distribution governed by the K parameter of Eq. (2), Eq. (4) takes the form: S
(8)
The subscript index i acts as a ranking index of species from the least abundant (i = 1) to the most abundant (i = S). From Eq. (8) it follows that
The model
NS K= NT
(7)
The final step is the relationship between S and the common ratio r. If, as is usually the case, for i = 1, Ni = 1, then a = 1 and Eq. (3) takes the simplified form:
2.
Let Ni be the abundance of the ith species and NT the total number of individuals in a community sample. Now, let S be the total number of species and NS denote the abundance of the most abundant species. The K parameter of a species abundance geometric series is
403
N i = N 1 + N2 + · · · + N S =
i=1
N 1 − NS 1−r
(5)
From this equation, the relationship between the common ratio r and the constant K is easily calculated considering that:
log Ni = i log r − log r
(10)
From Eq. (10) the expected log-abundances can be calculated, thereby allowing a 2 goodness of fit test. Before running the 2 -test, observed and expected log-abundance values must be standardised to relative percentage frequencies. This method differs from that of Magurran (1988), in which the expected values are calculated from Motomura’s classical equation.
S
• (i) N = NT ; i=1 i • (ii) from Eq. (2), NS = KNT ; • (iii) in a community sample for i = 1, Ni is usually 1.
3.
Under these conditions: K =
r − 1 + 1/NT r
(6)
Application of the model
The following study areas were considered: Orio al Serio airport (Bergamo, northern Italy), a shooting range (Siena, central Italy), the “Leonina” agricultural area (Siena, central Italy), the Castel Volturno Nature Reserve (Castel Volturno, southern Italy), and the “Forni dell’Accesa” mine dump area (Colline
404
e c o l o g i c a l m o d e l l i n g 1 9 5 ( 2 0 0 6 ) 402–406
Metallifere, central Italy). These areas were independently investigated in the framework of different research projects aiming to describe the effects of human disturbance on oribatid species assemblages. From the first (Orio al Serio) to the last area (Forni dell’Accesa) disturbances were, respectively, grassland management in the airport, metal pollution in the surface soil of the shooting range (Pb of the order of 1000 g/g d.w.), agriculture management of fields for corn production, experimental field fires (soil surface temperatures of 100–400 ◦ C), and metal pollution in surface soil due to smelting (Zn 7000 g/g d.w.; Cu 2500 g/g d.w.; Pb 2000 g/g d.w.). The sampling unit was an 8 × 8 × 8 cm box corer in all areas except the Forni dell’Accesa, where a 20 × 20 × 5 cm corer was used. This difference in sample size did not bias results, because the aim was to test whether the species distribution of a single sample is significantly fitted by one model or another. For statistical analysis, only adults were classified (to the species level) and counted. For further details on sampling and laboratory procedures (see Migliorini et al., 2003, 2004, 2005). In each investigated area, six samples were randomly collected from sites where disturbance was suspected or demonstrated to be intense. A total of 30 samples were analysed. The aim was to establish the percentage of cases in which disturbed areas were significantly fitted by the geometric model. Data were also fitted (2 goodness of fit test) with the log series, the log normal model and the broken stick model (Magurran, 1988). Results show that almost 76% of investigated samples were not significantly different from either the geometric or the log series, and only in one case these two models were significantly different from the actual species distribution (Table 1). The log normal and broken stick models did not significantly fit any data. In 59% of cases, the geometric series provided a better fit than the log series (Table 1: compare the p-value for the two distributions). In five cases the log series provided a good to very good fit, while the geometric series was significantly different. A detailed a posteriori data inspection of these samples revealed that the geometric model failed to estimate the abundance and the number of rare species. When the geometric series offered the best fit (n = 18), the mean (±S.D.) difference (absolute value) between the expected and observed species number was 2 ± 3. When the log series had the best fit (n = 7) and the geometric series had a good fit, this difference was 2 ± 2. Pooling these two data subsets (n = 25), the difference was 2 ± 2 and the 95% confidence range was 2 ± 1. Lastly, when the log series fitted data but the geometric series did not (n = 5), the difference was 6 ± 3.
4.
Discussion
The abundance distribution of species from disturbed areas is usually well modelled by the log series or the geometric series ˚ (Usher, 1985; Hagvar, 1994; Chung et al., 2000). Our results confirm this pattern for oribatid mites, and in most cases the geometric model fit data better than the log series. In the proposed formulation, quantitative relationships between the abundance of the most abundant species, the total species number S and the rank–abundance structure underlying distributions are easily calculated. In the geometric model, the total species number of a sample can be reasonably estimated
from the abundance of the most abundant species and the total number of individuals. This result is interesting in the context of environmental monitoring, because soil biodiversity technicians with no expertise in the use of models can easily manage this formulation of the geometric series. As a preliminary study, they could test the model on samples randomly collected from the disturbed areas to be monitored. If the species distribution may be modelled by geometric series, they can successively use the model to rapidly estimate sample species richness. Preston (1948) argued that the geometric or log series may be a consequence of a small sample size. However, in an 8 × 8 × 8 cm sample it is not unusual to find up to 100 adult individuals of oribatid mites or collembolans (Migliorini et al., 2003, 2005). A sample size of 20 × 20 × 5 cm can contain more than 600 adult individuals of oribatid mites. Although as a rule the species number in the sample increases as sample size increases, the species abundance distribution may continue to follow the geometric series. On the contrary, species from undisturbed areas have even abundance distri˚ butions (Usher, 1985; Hagvar, 1994). This pattern is commonly observed within the range of sample sizes usually adopted to study microarthropod assemblages. It therefore seems probable that in microarthropod communities uneven patterns arise from real ecological processes. For instance, in the framework of the neutral theory of Hubbel (2001), the geometric series, Fisher’s log series and Preston’s log normal distribution are different patterns of the same basic S-shaped function; this function is based on a zero-sum multinomial distribution, under the neutral assumption of ecological drift and different rates of species immigration. High immigration rates should shift distributions towards even patterns, lower rates should lead to uneven patterns (Hubbel, 2001). However, it is premature to draw conclusions on the validity of the Hubbell theory when applied to soil communities, and many descriptive (i.e. geometric model) as well as more sophisticated and explanatory (i.e. Harte et al., 1999; Plotkin et al., 2000) models can also efficiently describe the distribution of microarthropod species. Moreover, the neutral processes assumed by Hubbel (2001) could actually interact with niche assembly dynamic, which is usually viewed as process contrasting neutrality. For instance, it is well known that disturbed oribatid assemblages are usually dominated by widely distributed, opportunistic species such as Tectocepheus sarekensis, T. velatus, Scheloribates pallidulus, Punctoribates punctum and Zygoribatula exarata (Franchini and Rockett, 1996; Behan-Pelletier, 1999; Kova´ cˇ et al., 2001). A possible explanation is that disturbance causes a decrease or extinction of sensitive species, thereby allowing colonisation of the space made available by opportunistic species. Opportunistic species may continue to colonise until they dominate the assemblage, thus leading to uneven patterns of species abundance distribution. The process of colonisation could also be driven by the random processes assumed by Hubbel (2001), but the successful colonisation by opportunistic species would nevertheless depend on the negative impact of disturbance on sensitive species. In this hypothetical framework further experimental work is needed, and the geometric series remains a descriptive tool. In this paper the model is reformulated for ecological applications in environmental monitoring, but the ecological significance
ecological modelling
195
405
( 2 0 0 6 ) 402–406
Table 1 – 2 goodness of fit test for the geometric series (GS) and log series (LS) models Sample codes A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 C5 C6 D1 D2 D3 D4 D5 D6 E1 E2 E3 E4 E5 E6
S o − Se 2 2 5 2 2 3 2 4 0 1 2 0 1 5 2 0 1 2 11 11 6 6 3 5 2 3 2 2 1 2
X2 -value for GS 3.49 13 15.06 1.96 0.89 15.53 12.55 4.43 3.91 2.57 5.25 2.71 6.44 15.2 5.35 1.03 7.34 5.57 7.58 87.26 77 33 41 42 2.67 4.64 5.10 11.65 2.47 2.18
p-Level for GS 0.83 <0.05 0.35 0.99 0.99 0.29 0.30 0.99 0.87 0.99 0.92 0.84 0.95 0.55 0.98 0.79 0.12 0.35 0.98 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.99 0.99 0.95 0.23 0.96 0.99
p-Level for LS 0.4 <0.05 0.75 0.6 0.6 0.85 0.6 0.8 0.35 0.25 0.25 0.07 0.001 0.02 0.25 0.85 0.85 0.85 0.85 0.6 0.85 0.12 0.4 0.97 0.45 0.07 0.85 0.65 0.85 0.85
A: managed grassland in an airport; B: Pb polluted soils from a shooting range; C: managed field crops; D: soils from burned Mediterranean maquis woodland; E: Zn, Pb and Cu metal polluted soils from a mining and smelting area. So − Se : absolute value of difference between the observed total number of species and the expected geometric one.
of patterns described by the model must still be understood. One of the reasons for this rather poor state of knowledge is that data on the autoecology of species are still lacking. For instance, the trophic ecology of oribatids is still poorly understood because contrasting results have emerged from recent studies (Schneider et al., 2004; Schneider and Maraun, 2005). Choice experiments on the selection of fungi indicate a limited trophic differentiation (Schneider and Maraun, 2005). In contrast, analyses based on stable isotope ratios (15 N/14 N) indicate that oribatid mites may occupy very different trophic niches (Schneider et al., 2004). If feeding differentiation plays a role in species abundance distribution, the absence of general feeding patterns makes it difficult to build a model for the distribution of soil animal abundance. In conclusion, further research on the basic ecology of soil species will improve the ecological understanding of soil species abundance distribution, thereby increasing the explanatory power of species abundance models.
Acknowledgements We are grateful to Dr. Guido Sanguinetti for the revision of the mathematics. We also thank two anonymous referees for their critical revision which greatly improved the quality of the manuscript.
references
Behan-Pelletier, V.M., 1999. Oribatid mite biodiversity in agroecosystems: role for bioindication. Agric. Ecosyst. Environ. 74, 411–423. Chung, A.Y.C., Eggleton, P., Speight, M.R., Hammond, P.M., Chey, V.K., 2000. The diversity of beetle assemblages in different habitat types Sabah, Malaysia. Bull. Entomol. Res. 90 (6), 475–496. Franchini, P., Rockett, C.L., 1996. Oribatid mites as “indicator” species for estimating the environmental impact of conventional tillage practices. Pedobiologia 40, 27– 225. ˚ Hagvar, S., 1994. Log-normal distribution of dominance as an indicator of stressed soil micro-arthropods communities. Acta Zool. Fenn. 195, 71–80. Harte, J., Kinzig, A., Green, J., 1999. Self-similarity in the distribution and abundance of species. Science 284 (5412), 334–336. Hubbel, S.P., 2001. The unified neutral theory of biodiversity and biogeography. In: Monographs in Population Biology. Princeton University Press, Princeton, p. 375. ˇ L., L’Upta´ cik, ˇ Kova´ c, P., Miklisova, D., Mati, R., 2001. Soil Oribatida and Collembola communities across a land depression in an arable field. Eur. J. Soil Biol. 37, 285–289. Magurran, A.E., 1988. Ecological Diversity and Its Measurement. Croom Helm, London, p. 178.
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May, R.M., 1975. Patterns of species abundances and diversity. In: Cody, M.L., Diamond, J.M. (Eds.), Ecology and Evolution of Communities. Belknap Press of Harvard University Press, Cambridge, MA, pp. 81–120. Migliorini, M., Fanciulli, P.P., Bernini, F., 2003. Comparative analysis of two edaphic zoocoenoses (Acari Oribatida; Hexapoda Collembola) in the area of Orio al Serio Airport (Bergamo, northern Italy). Pedobiologia 47, 9–18. Migliorini, M., Pigino, G., Avanzati, A. M., Salomone, N., Bernini F., 2004. Experimental fires in Mediterranean environment: effects on oribatid mite communities. In: Weigmann, G., Alberti, G., Wohltmann, A. (Eds.), Proceedings of the V Symposium of the European Associations of Acarologists on Phytophaga, Acarine Biodiversity in the Natural and Human Sphere. Luxograph, Palermo, pp. 271–278. Migliorini, M., Pigino, G., Caruso, T., Fanciulli, P.P., Leonzio, C., Bernini, F., 2005. Soil communities (Acari Oribatida; Hexapoda Collembola) in a clay pigeon shooting range. Pedobiologia 49, 1–13. Plotkin, J.B., Potts, M.D., Leslie, N., Manokaran, N., LaFrankie, J., Ashton, P.S., 2000. Species-area curves, spatial aggregation,
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and habitat specialization in tropical forests. J. Theor. Biol. 207, 81–99. Preston, F.W., 1948. The commonness and rarity of species. Ecology 29, 254–283. Schneider, K., Migge, S., Norton, R.A., Scheu, S., Langel, R., Reineking, A., Maraun, M., 2004. Trophic niche differentiation in soil microarthropods (Oribatida, Acari): evidence from stable isotope ratios (15 N/14 N). Soil Biol. Biochem. 36, 1769–1774. Schneider, K., Maraun, M., 2005. Feeding preferences among dark pigmented fungal taxa (“Demantiacaea”) indicate limited trophic niche differentiation of oribatid mites (Oribatida, Acari). Pedobiologia 49, 61–67. Usher, M.B., 1985. Population and community dynamics in the soil ecosystem. In: Atkinson, D., Read, D.J., Usher, M.B. (Eds.), Ecological Interactions in Soil. Blackwell Scientific Publications, Oxford, pp. 243–265. Whittaker, R.H., 1960. Vegetation of the Siskiyou Mountains, Oregon and California. Ecol. Monogr. 30, 279–338. Whittaker, R.H., 1972. Evolution and measurement of species diversity. Taxon 21, 213–251.
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecolmodel
Short communication
A new formulation of the geometric series with applications to oribatid (Acari, Oribatida) species assemblages from human-disturbed Mediterranean areas Tancredi Caruso a,∗ , Massimo Migliorini b a b
Department of Environmental Sciences “G. Sarfatti”, University of Siena, via Mattioli no 4, 53100-Siena, Italy Department of Evolutionary Biology, University of Siena, via A. Moro no. 2, 53100-Siena, Italy
a r t i c l e
i n f o
a b s t r a c t
Article history:
The mathematical properties of the geometric series are revisited and the model is applied
Received 7 April 2005
to oribatid mite (Acari, Oribatida) assemblages from Mediterranean areas that have been
Received in revised form
disturbed by human activity. In the past, the geometric series has been considered an ideal
9 November 2005
form of Fisher’s log model. However, in some cases data fit both models or the geomet-
Accepted 28 November 2005
ric series offers a better fit. Data presented in this paper and collected from areas heavily
Published on line 19 January 2006
disturbed by human activity show that the species abundance distribution of oribatids is in almost all cases well fitted by the geometric series, indicating a common trend in the
Keywords:
response to disturbance of this assemblage. The proposed new version of the model allows
Geometric series
interesting applications in environmental monitoring because it is easy to outline the quan-
Soil
titative relationship between the abundance of the most abundant species, the total number
Mites
of individuals and the total number of species in the sample. © 2005 Elsevier B.V. All rights reserved.
Disturbance Distribution Species
1.
Introduction
When the ecology of a biological community is structured by some dominant environmental factor there is usually an uneven distribution of species abundances, with a large proportion of rare to very rare species and a small number of species with high sample densities (May, 1975; Magurran, 1988). In its ideal form this distribution may be modelled as a geometric series in which the abundance of the most successful species accounts for a fraction K of the total number of individuals NT , the abundance of the second species accounts for the same fraction K of the remainder and so on, to give
∗
Corresponding author. Tel.: +39 0577232877; fax: +39 0577232806. E-mail address: [email protected] (T. Caruso).
0304-3800/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2005.11.042
Motomura’s equation in the form reported by May (1975): i−1
Ni = NT Ck K(1 − K)
(1)
where Ni is the abundance of the ith species and Ck is a param eter which ensures that Ni = N T . The uneven distribution modelled by the geometric series is usually observed in communities at an early successional stage and in those from harsh or isolated environments (Whittaker, 1960, 1972; Magurran, 1988; Hubbel, 2001). In such environmental conditions one expects the dominance of fewer species (May, 1975).
e c o l o g i c a l m o d e l l i n g 1 9 5 ( 2 0 0 6 ) 402–406
As for soil communities as a whole, although little data are available, some studies on specific assemblages such as collembolans or beetles indicate that species abundance distributions tend towards geometric or log series models at ˚ increasing levels of disturbance (Usher, 1985; Hagvar, 1994; Chung et al., 2000). In the present paper, the geometric series is reformulated to better outline relationships between the sample density of the most abundant species, the total number of species (S) and the rank–abundance structure underlying the distribution. To show how the reshaped model works, it was fitted to a number of soil oribatid community samples from six areas affected by different kinds of anthropogenic disturbance.
If NT > 100 then 1/NT < 0.01. Because these values are usually observed, this term can be approximated to zero. Hence, r−1 K∼ = r
Ni = ri−1
NS = rS−1
2.1.
Reformulation of the geometric series
hence,
(2)
In basic algebra the ith general term of a geometric progression is Bi = ari−1
(3)
where the constant a is the value of the first term (i = 1) and the non-zero constant r is the common ratio. Indeed, it is the ratio between one term and the preceding one. In basic algebra, the sum of the first n terms is known to be: n
B n = B 1 + B2 + · · · + B n =
i=1
B1 − Bn 1−r
(4)
log NS = log rS−1 ⇒ log NS = (S − 1) log r and, S=
log NS +1 log r
(9)
Therefore, when species abundance distributions may be modelled by geometric series, the number of species in the sample may be estimated from the abundance of the most dense species and the total number of individuals.
2.2.
Fit of the model
The geometric series appears as a straight line in a standard rank–abundance plot, in which species are rank ordered from the most to the least abundant, and the abundance of species is plotted on the y-axis on a logarithmic scale. (May, 1975; Magurran, 1988). Let there be an inverse rank order, with the least abundant species having rank 1 and the most abundant species having rank S. From Eq. (8), the log-transformation of abundances is log Ni = log ri−1 ⇒ log Ni = (i − 1) log r and,
Hence, in a species abundance distribution governed by the K parameter of Eq. (2), Eq. (4) takes the form: S
(8)
The subscript index i acts as a ranking index of species from the least abundant (i = 1) to the most abundant (i = S). From Eq. (8) it follows that
The model
NS K= NT
(7)
The final step is the relationship between S and the common ratio r. If, as is usually the case, for i = 1, Ni = 1, then a = 1 and Eq. (3) takes the simplified form:
2.
Let Ni be the abundance of the ith species and NT the total number of individuals in a community sample. Now, let S be the total number of species and NS denote the abundance of the most abundant species. The K parameter of a species abundance geometric series is
403
N i = N 1 + N2 + · · · + N S =
i=1
N 1 − NS 1−r
(5)
From this equation, the relationship between the common ratio r and the constant K is easily calculated considering that:
log Ni = i log r − log r
(10)
From Eq. (10) the expected log-abundances can be calculated, thereby allowing a 2 goodness of fit test. Before running the 2 -test, observed and expected log-abundance values must be standardised to relative percentage frequencies. This method differs from that of Magurran (1988), in which the expected values are calculated from Motomura’s classical equation.
S
• (i) N = NT ; i=1 i • (ii) from Eq. (2), NS = KNT ; • (iii) in a community sample for i = 1, Ni is usually 1.
3.
Under these conditions: K =
r − 1 + 1/NT r
(6)
Application of the model
The following study areas were considered: Orio al Serio airport (Bergamo, northern Italy), a shooting range (Siena, central Italy), the “Leonina” agricultural area (Siena, central Italy), the Castel Volturno Nature Reserve (Castel Volturno, southern Italy), and the “Forni dell’Accesa” mine dump area (Colline
404
e c o l o g i c a l m o d e l l i n g 1 9 5 ( 2 0 0 6 ) 402–406
Metallifere, central Italy). These areas were independently investigated in the framework of different research projects aiming to describe the effects of human disturbance on oribatid species assemblages. From the first (Orio al Serio) to the last area (Forni dell’Accesa) disturbances were, respectively, grassland management in the airport, metal pollution in the surface soil of the shooting range (Pb of the order of 1000 g/g d.w.), agriculture management of fields for corn production, experimental field fires (soil surface temperatures of 100–400 ◦ C), and metal pollution in surface soil due to smelting (Zn 7000 g/g d.w.; Cu 2500 g/g d.w.; Pb 2000 g/g d.w.). The sampling unit was an 8 × 8 × 8 cm box corer in all areas except the Forni dell’Accesa, where a 20 × 20 × 5 cm corer was used. This difference in sample size did not bias results, because the aim was to test whether the species distribution of a single sample is significantly fitted by one model or another. For statistical analysis, only adults were classified (to the species level) and counted. For further details on sampling and laboratory procedures (see Migliorini et al., 2003, 2004, 2005). In each investigated area, six samples were randomly collected from sites where disturbance was suspected or demonstrated to be intense. A total of 30 samples were analysed. The aim was to establish the percentage of cases in which disturbed areas were significantly fitted by the geometric model. Data were also fitted (2 goodness of fit test) with the log series, the log normal model and the broken stick model (Magurran, 1988). Results show that almost 76% of investigated samples were not significantly different from either the geometric or the log series, and only in one case these two models were significantly different from the actual species distribution (Table 1). The log normal and broken stick models did not significantly fit any data. In 59% of cases, the geometric series provided a better fit than the log series (Table 1: compare the p-value for the two distributions). In five cases the log series provided a good to very good fit, while the geometric series was significantly different. A detailed a posteriori data inspection of these samples revealed that the geometric model failed to estimate the abundance and the number of rare species. When the geometric series offered the best fit (n = 18), the mean (±S.D.) difference (absolute value) between the expected and observed species number was 2 ± 3. When the log series had the best fit (n = 7) and the geometric series had a good fit, this difference was 2 ± 2. Pooling these two data subsets (n = 25), the difference was 2 ± 2 and the 95% confidence range was 2 ± 1. Lastly, when the log series fitted data but the geometric series did not (n = 5), the difference was 6 ± 3.
4.
Discussion
The abundance distribution of species from disturbed areas is usually well modelled by the log series or the geometric series ˚ (Usher, 1985; Hagvar, 1994; Chung et al., 2000). Our results confirm this pattern for oribatid mites, and in most cases the geometric model fit data better than the log series. In the proposed formulation, quantitative relationships between the abundance of the most abundant species, the total species number S and the rank–abundance structure underlying distributions are easily calculated. In the geometric model, the total species number of a sample can be reasonably estimated
from the abundance of the most abundant species and the total number of individuals. This result is interesting in the context of environmental monitoring, because soil biodiversity technicians with no expertise in the use of models can easily manage this formulation of the geometric series. As a preliminary study, they could test the model on samples randomly collected from the disturbed areas to be monitored. If the species distribution may be modelled by geometric series, they can successively use the model to rapidly estimate sample species richness. Preston (1948) argued that the geometric or log series may be a consequence of a small sample size. However, in an 8 × 8 × 8 cm sample it is not unusual to find up to 100 adult individuals of oribatid mites or collembolans (Migliorini et al., 2003, 2005). A sample size of 20 × 20 × 5 cm can contain more than 600 adult individuals of oribatid mites. Although as a rule the species number in the sample increases as sample size increases, the species abundance distribution may continue to follow the geometric series. On the contrary, species from undisturbed areas have even abundance distri˚ butions (Usher, 1985; Hagvar, 1994). This pattern is commonly observed within the range of sample sizes usually adopted to study microarthropod assemblages. It therefore seems probable that in microarthropod communities uneven patterns arise from real ecological processes. For instance, in the framework of the neutral theory of Hubbel (2001), the geometric series, Fisher’s log series and Preston’s log normal distribution are different patterns of the same basic S-shaped function; this function is based on a zero-sum multinomial distribution, under the neutral assumption of ecological drift and different rates of species immigration. High immigration rates should shift distributions towards even patterns, lower rates should lead to uneven patterns (Hubbel, 2001). However, it is premature to draw conclusions on the validity of the Hubbell theory when applied to soil communities, and many descriptive (i.e. geometric model) as well as more sophisticated and explanatory (i.e. Harte et al., 1999; Plotkin et al., 2000) models can also efficiently describe the distribution of microarthropod species. Moreover, the neutral processes assumed by Hubbel (2001) could actually interact with niche assembly dynamic, which is usually viewed as process contrasting neutrality. For instance, it is well known that disturbed oribatid assemblages are usually dominated by widely distributed, opportunistic species such as Tectocepheus sarekensis, T. velatus, Scheloribates pallidulus, Punctoribates punctum and Zygoribatula exarata (Franchini and Rockett, 1996; Behan-Pelletier, 1999; Kova´ cˇ et al., 2001). A possible explanation is that disturbance causes a decrease or extinction of sensitive species, thereby allowing colonisation of the space made available by opportunistic species. Opportunistic species may continue to colonise until they dominate the assemblage, thus leading to uneven patterns of species abundance distribution. The process of colonisation could also be driven by the random processes assumed by Hubbel (2001), but the successful colonisation by opportunistic species would nevertheless depend on the negative impact of disturbance on sensitive species. In this hypothetical framework further experimental work is needed, and the geometric series remains a descriptive tool. In this paper the model is reformulated for ecological applications in environmental monitoring, but the ecological significance
ecological modelling
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Table 1 – 2 goodness of fit test for the geometric series (GS) and log series (LS) models Sample codes A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 C5 C6 D1 D2 D3 D4 D5 D6 E1 E2 E3 E4 E5 E6
S o − Se 2 2 5 2 2 3 2 4 0 1 2 0 1 5 2 0 1 2 11 11 6 6 3 5 2 3 2 2 1 2
X2 -value for GS 3.49 13 15.06 1.96 0.89 15.53 12.55 4.43 3.91 2.57 5.25 2.71 6.44 15.2 5.35 1.03 7.34 5.57 7.58 87.26 77 33 41 42 2.67 4.64 5.10 11.65 2.47 2.18
p-Level for GS 0.83 <0.05 0.35 0.99 0.99 0.29 0.30 0.99 0.87 0.99 0.92 0.84 0.95 0.55 0.98 0.79 0.12 0.35 0.98 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.99 0.99 0.95 0.23 0.96 0.99
p-Level for LS 0.4 <0.05 0.75 0.6 0.6 0.85 0.6 0.8 0.35 0.25 0.25 0.07 0.001 0.02 0.25 0.85 0.85 0.85 0.85 0.6 0.85 0.12 0.4 0.97 0.45 0.07 0.85 0.65 0.85 0.85
A: managed grassland in an airport; B: Pb polluted soils from a shooting range; C: managed field crops; D: soils from burned Mediterranean maquis woodland; E: Zn, Pb and Cu metal polluted soils from a mining and smelting area. So − Se : absolute value of difference between the observed total number of species and the expected geometric one.
of patterns described by the model must still be understood. One of the reasons for this rather poor state of knowledge is that data on the autoecology of species are still lacking. For instance, the trophic ecology of oribatids is still poorly understood because contrasting results have emerged from recent studies (Schneider et al., 2004; Schneider and Maraun, 2005). Choice experiments on the selection of fungi indicate a limited trophic differentiation (Schneider and Maraun, 2005). In contrast, analyses based on stable isotope ratios (15 N/14 N) indicate that oribatid mites may occupy very different trophic niches (Schneider et al., 2004). If feeding differentiation plays a role in species abundance distribution, the absence of general feeding patterns makes it difficult to build a model for the distribution of soil animal abundance. In conclusion, further research on the basic ecology of soil species will improve the ecological understanding of soil species abundance distribution, thereby increasing the explanatory power of species abundance models.
Acknowledgements We are grateful to Dr. Guido Sanguinetti for the revision of the mathematics. We also thank two anonymous referees for their critical revision which greatly improved the quality of the manuscript.
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