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Guest blog by MeVitae

Ecologists have been measuring the biodiversity of ecosystems for millennia. In recent decades, they have taken ideas from physics and information theory to reduce their huge tables of data to simple metrics that are not only easy to understand and compare, but that also accurately measure diversity as a concept.

These same principles can be applied to the workplace, but making an impact in this arena, first requires an understanding of these concepts within our broader ecosystem.

**Measuring biodiversity**

The first and possibly the least insightful measure of biodiversity is called the species richness, which is simply the number of species present in an ecosystem. It doesn’t consider how many members there are of each species and is therefore limited in its usefulness – a more useful measure of diversity would incorporate information about how many members of each species are present.

Ecologists therefore calculate the *entropy* of an ecosystem instead. Entropy can be thought of as the average level of surprise in a system. For example, if I picked a creature from the rainforest at random it would be difficult to predict beforehand what species I would end up with. The result would be a surprise. On the other hand, if I picked a creature at random from a chicken farm, the result is less likely to be a surprise as I would probably end up picking a chicken.

From the entropy, which quantifies the average level of surprise in a system, an effective number of species can be calculated:

- If all species in a system are present in equal numbers, then the effective number of species is equal to the actual number of species.
- If some species are underrepresented compared to others, then the effective number of species will be less than the actual number of species.

The effective number of species can be seen as the diversity of the system – mathematically, it is the number of equally abundant species that would be needed to give the same entropy value. The effective number of species therefore does not have to be a whole number.

**What is entropy and why is it important?**

Entropy is an incredibly powerful concept that is needed to understand and explain not just the modern world and human behavior, but also the universe at large. It was originally developed in the 1800’s to explain how engines work and how gas expands. Physicists now use entropy in all areas of modern physics. For example, it is used to define the direction that time flows in and even determines the surface area of blackholes! Outside of physics, in finance, it is used to quantify the efficiency of markets, and in computing it is used in data compression. As we’ve discussed, entropy is used in ecology to quantify the diversity of ecosystems, but it can also be used to quantify the diversity of a workforce.

**Calculating the entropy and effective number of species in a biological system**

If there are *N* species in an ecosystem, and the *i*th species makes up a fraction *p**i* of the total population of living things, then the entropy, *S*, is defined as:

The effective number of species, *Ñ, *is then given by:

These equations apply to measuring the diversity of a workforce just as much as they apply to measuring biodiversity in a rainforest – and to determining the efficiency of a market or internal combustion engine, the expansion rate of a gas, the direction that time flows, and the surface area of a black hole!

**Calculating diversity in the workforce**

Many organizations take protected characteristics as defined in law, split each characteristic into groups, and find out how many members of their workforce fit into each group.

For example, ethnicity is a protected characteristic and the 2011 UK census defined six aggregated groups: Asian, Black, Chinese, Mixed, White, and Other. These groups make up 7.2, 3.4, 0.9, 1.8, 85.6, and 1.1 per cent of the UK working-age population respectively (these percentages are the *p**i *values in Equation 1, for example, *p**asian **= 0.034 = 3.4%*).

Another example of a protected characteristic is sexual orientation, which the UK Office for National Statistics (ONS) splits into five groups: heterosexual or straight, gay or lesbian, bisexual, other, and don’t know.

If an organization can find out what fraction of its workforce belongs to each group, i.e. find the *p**i* values, then Equation 1 can be used to calculate the entropy, and Equation 2 can be used to calculate the effective number of groups present in the organization. The effective number of groups in an organization can be compared to the effective number of groups in the UK workforce to see which is more diverse.

Using the aggregated ethnic groups from the UK census, the UK working-age population in 2011 had 1.8 effective ethnic groups.

Using the same six aggregated groups:

- the NHS workforce in 2020 had 2.3 effective ethnic groups – and is, therefore, more ethnically diverse than the total UK working-age population
- UK teachers are comprised of 1.5 effective ethnic groups – and are therefore less ethnically diverse than the total UK working-age population (over 90% of UK teachers are white compared to 86% of the UK working-age population).

**Interpreting your diversity numbers**

It is important to realize that quantifying the diversity of your workforce is only the first step. You then need to interpret the measurement and determine what may be impacting your specific level of diversity. There are several factors to consider when interpreting your company’s diversity measurements.

**Small workforces are likely to be less diverse than larger ones.**

For example, a small company with only ten employees is most likely to have one Asian and nine White employees. Such a company would have 1.4 effective ethnic groups. The more employees an organization has, the more you would expect the number of effective groups to match that of the UK as a whole. organizations with over 100 employees should expect their diversity to start to match that of the UK’s total workforce.

**It might not be fair to compare your diversity to the UK workforce.**

If your company is based in a specific geographical area, it might be better to compare your diversity to that of your local area. Conversely, if your organization has international reach, you could compare your diversity to that of a continent or even the whole world. If your organization requires employees to have degree-level qualifications or above, then you could compare your diversity to that of graduates.

**If you find that your organization is lacking in diversity, you should do something about it and measure the impact.**

More diverse workforces have been shown to be more successful across many metrics. One way of improving the diversity of a workforce is via blind recruitment, where potentially biasing information is redacted from CVs before shortlisting.

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