Page - 137 - in Biodiversity and Health in the Face of Climate Change

137 7.2.3.1 Connection to  Biodiversity with  Fractals Benoit Mandelbrot’s (1983) book the “The Fractal Geometry of Nature” applied fractal geometry to common natural phenomena, such as coastlines, rivers, trees, leaves and snowflakes. The book argues that fractals are an essential tool for under- standing the natural world (Mandelbrot 1983). Mandlebrot (1983, p.  1) reasoned that  “clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line”, but are  rather com- prised of fragmented, self-similar repeated patterns. Figure  7.1 shows examples of fractals that occur in nature. Ecologists have used fractal geometry to determine the biodiversity of an envi- ronment (Tokeshi and Arakaki 2012). The fractal dimension, D, has been used to determine habitat quality (Imre and Bogaert 2004), landscape structure and compo- sition (Pe’er et  al. 2013), habitat complexity (Dibble and Thomaz 2009) and species richness (Stevens 2018). The relative lack of fractals has been used to identify man- made landscapes (Pe’er et  al. 2013). Irme and Bogaert (2004) used fractals to deter- mine the habitat quality of 49 pine tree (Pinus sylvestris L.) woodlots in Belgium. The authors hypothesised that if the woodlots were created due to habitat fragmen- tation − the process through which large habitats are broken up into small parcels − then the fractal dimensions of the boundaries of these habitats should all be simi- lar (Imre and Bogaert 2004). Fractal similarity for the boundary shape of the wood- lots was found, highlighting that the 49 patches of woodland were once one large pine forest and were created as a result of habitat fragmentation. Dibble and Thomaz (2009) examined whether fractal dimension D scores could quantitatively describe the complexity of 11 species of aquatic plants, and if the D score could be used to predict density of invertebrates found within these aquatic plants. D scores were a good predictor of plants’ complexity; plant species with high numbers of finely dis- sected leaves or roots had higher D scores compared to plants with single leaves. Furthermore, a significant relationship was found between D score and density of invertebrates; more complex plants, as measured by D score, were associated with a greater number of invertebrates. Stevens (2018) investigated whether fractal dimensions of the tree silhouette of a habitat would differ based on the species rich- ness of plants, animals and fungi in that habitat. There was a significant difference in D scores between high or low species rich habitats; D scores were higher in tree silhouettes of high species-rich habitats compared to tree silhouettes of low species- rich habitats. 7.2.3.2 Fractal Dimension and  Preference Could the fractal dimension D predict environmental preference? Initially, inconsis- tent results were found, with studies showing preference for fractal patterns with both high and low D scores (Taylor 2001). Thinking that perhaps this inconsistency was related to the source of the D scores, Spehar et  al. (2003) investigated prefer- ence for fractals generated by nature (e.g. trees, mountains, clouds), human beings 7 Theoretical Foundations of  Biodiversity and  Mental Well-being Relationships