To feed the growing world population, efficient food production is a must. Nitrogen fertilisers play a key role in achieving high crop yields but can also harm the environment. First of all: nitrogen could be leaching into the groundwater, and secondly: the production of fertiliser requires a lot of energy. This blog explains how you can reduce your nitrogen emissions by growing legumes and using a mathematical model to decide what other crops to grow.

Looking at the short-term, growing the crop that generates the most profit is – from a business perspective – the most logical thing to do as a farmer. However, growing that crop multiple seasons in a row will result in soil depletion and lower yields. Furthermore, monocropping also stimulates pest growth. Hence, it is essential to rotate some crops in the long term.

### Crop rotation

In crop rotation, the order in which the crops are grown influences the yield potential and the amount of fertiliser to achieve that yield. For example: legumes have the property that they can fix nitrogen from the air, so they require less fertiliser than other crops. On top of that, they also put some nitrogen in the soil which can be used by the next crop. Therefore, growing legumes also reduces the amount of fertiliser needed for subsequent crops.

The order in which the crops are

grown influences the yield potential

and the amount of fertiliser

Although growing legumes reduces the amount of fertiliser that is needed, it might still be more profitable to grow other crops. The cost of fertiliser influences the decision whether to grow legumes or not. But not all negative environmental aspects are included in the current market price of nitrogen fertiliser. An alternative for the market price is the so-called ‘true price’ of nitrogen fertiliser, in which these negative externalities are assigned as cost. If you use the true price instead of the market price, the optimal crop rotation will more likely contain legumes.

### Find optimal scheme

The number of possible options for the crop rotation scheme is enormous. Even for only ten crops and four seasons, there are already about 10,000 possible crop rotation schemes. Since the order in which crops are grown influences the yield and fertiliser need, it is hard to find the best order by hand, let alone if you would like to try to use different values for the price of fertiliser. The latter is not only useful to incorporate sustainability but also future price changes in your decision-making process.

Fortunately, we have found a way to formulate this decision as a mathematical model which can help you find the optimal order. Using this model, you can try out different crops and prices for fertiliser to define the optimal crop rotation. The higher you set the price for nitrogen fertiliser, the more crops that require the least fertiliser will be used and the more environmental-friendly the rotation is.

We have developed a

mathematical model which can

help you find the optimal

crop rotation scheme

If you are interested in more details of that model and its outcomes you can click here or reach out to us at info@doingthemath.nl for more information. Growing legumes is just one option to make agriculture more sustainable, and other decisions can probably also benefit from using mathematics. So, if you have an application or question, we would be curious to hear from you.