Journal of Forestry Research (2012) 23(3): 355- 364 DOI 10.1007/s11676-012-0271-3 Application of fractal theory in assessing soil aggregates in Indian trop- ical ecosystems S. K. Tripathi  C. P. Kushwaha  S. K. Basu Received: 2011-05-23 Accepted: 2011-12-19 © Northeast Forestry University and Springer-Verlag Berlin Heidelberg 2012 Abstract : Soil aggregation varies according to climatic and manage- ment factors, and is difficult to measure because of irregular shapes and sizes of soil aggregates. We applied fractal theory to assess soil aggrega- tion as affected by (1) land use change from forest to savanna, (2) nutri- ent additions in forest, ecotone, and savanna ecosystems, and (3) tillage practice and residue treatments in an agro-ecosystem. We used fractal dimensions nonlinear (D non-lin ) and linear (D lin ) based on number of ag- gregates (N) and mass of aggregates (M) (the range of values were 2.6- 2.89 and 2.69- 3.41, respectively) to capture the variations in the sizes of soil aggregates due to land use and treatments/management in these ecosystems. The variation in the values of non-linear fractal dimension based on mass (D Mnon-lin ) was smaller in forest and savanna ecosystems with and without nutrient additions, while the variation was wider in agro-ecosystems with different management practices. Linear fractal dimensions based on number (D Nlin ) and mass (D Mlin ) of aggregates var- ied marginally in these ecosystems and did not capture the variations in soil aggregates well. The variations in non-linear fractal dimension indi- cate that continued nitrogen loading in forest accelerates the formation of macro-aggregates, whereas in savanna the situation was reversed. The values of non-linear fractal dimensions did not show significant change after 6 years of nutrient additions in the ecotone; reflecting a buffering mechanism of this system in soil aggregate formation. On the basis of non-linear fractal dimension values, we conclude that residue retention and minimum tillage are appropriate for proper maintenance of soil ag- gregate stability for sustained crop production in the Indian dry land The online version is available at http:// www.springerlink.com S. K. Tripathi ( )  S. K. Basu Computer Science Department, Banaras Hindu University, Varanasi – 221005, India; Department of Forestry, Mizoram University, Ai- zawl-796009, India. C. P. Kushwaha Centre for Env. Sci. & Tech., Banaras Hindu University, Varanasi-221005, India. Email: sk_tripathi@rediffmail.com ; sktripathi_13@yahoo.com Responsible editor: Zhu Hong agro-ecosystems. Keywords: soil aggregates; fractal; tillage practice; ecosystem; Indian dry tropics Introduction Development of soil structure and aggregation is a dynamic property of soil that depends upon parent material, climate and management factors (Strudley et al. 2008). Soil aggregation has been reported as an important process controlling plant growth and carbon (C) sequestration (Blanco-Canqui and Lal 2004). Microaggregates (<0.3 mm) consist of separate particles, espe- cially clay, that are often coated with fine inorganic and/or or- ganic materials. In contrast, macro-aggregates (>0.3 mm) are the result of binding up of micro-aggregates (Elliott 1986). The abil- ity of these soil aggregates to resist breakdown when soaked in water is important for maintaining permeability for supply of water and air to plant roots. The stability of soil aggregates varies due to agricultural management practices (Pirmoradian et al. 2005), land use, and nutrient inputs (Tripathi et al. 2008). Com- plexity is an intrinsic property of soil because of manifold feed- backs and multi-scale interactions. This creates significant diffi- culties for research, as no experimental sample, site or procedure is sufficient to fully represent the biogeochemical complexity of the natural medium, and thus accurate and efficient characteriza- tion of complex soil systems has become a prerequisite (Pachep- sky et al. 2006). Measurement of total soil aggregate stability with a single pa- rameter is a difficult task because of the irregular shapes and sizes of aggregates. Fractal theory has been successfully used in assessing soil aggregate stability because of its scale-invariant property. Fractal theory has been used to describe soil hydrologic processes (Pachepsky et al. 2003; Martin et al. 2005; Pachepsky et al. 2000, Silvia et al. 2008). Gyldenkaerne and Jorgensen (2000) explained that soil measurements could be simplified in an ecological model by considering a scale (Yue et al. 2003). Many researchers have reported that soil aggregate stability (in ORIGINAL PAPER