 # Research Methods

What is natural log, and why would I use it?

The natural log, ln = e = 2.718282, but that doesn’t tell you much does it?

It is often the case in nature, that as one dimension of an organism increases (like length) it’s biomass or volume increase more rapidly because with each increase in length, there is an even greater increase in volume or biomass. This relationship is referred to as a natural log relationship (see Figure 1 below) where there is a gradual curving increase in the volume or biomass with increasing length. Figure 1. The curve of a natural log relationship between earthworm length and ash-free-dry biomass is illustrated here with actual earthworm data (over 1000 individuals), each earthworm is represented by a single triangle, or data point.

While the figure above shows a nice looking curve, and clearly there is a strong relationship between length and biomass, it is difficult to generate an equation that describes this relationship that doesn’t involve very complex terms. However, if we transform the data by taking the natural log of the length and biomass measures, something very interesting happens. The relationship between ln(earthworm length) and ln(AFDearthworm biomass) is linear (see Figure 2 below). Using a basic statistical method called linear regression; it is now quite straightforward to find an equation that describes the relationship between our two variables. Once we find this equation, we can used it to predict one variable if you know the other. In the case of earthworms, we used this method to find an equation that allows us to predict ash-free-dry biomass, which is difficult to measure directly, from length, which is easy to measure. Figure 2. Once the same data shown in Figure 1 is transformed by taking the natural log of each, the relationship between ln(earthworm length) and ln(ash-free-dry biomass) is a straight line.  Using linear regression we can generate a simple equation describing this relationship which we can later use to estimate ash-free-dry biomass of earthworms simply by measuring their length.

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