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Peak phosphorus (Rev #7, changes)

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Peak phosphorus


Phosphorus, as part of phosphate compounds, is a key element for plant growth and as such is a key component of fertilizers. Phosphorus compounds used in fertilizers to replace “lost” phosphorus are mostly obtained by mining phosphate rock and collecting guano deposits. Peak phosphorus refers to the point at which the rate of extraction of phosphorus compounds reaches its highest peak and begins to decline. Some models suggest peak phosphorus has already occurred.


Phosphorus is a key element for plant growth. Because it is highly reactive, it generally occurs either in mineral compounds or in guano (excrement from creatures such as birds or bats). The US Geological survey (USGS) (listed below) states

There are no substitutes for phosphorus in agriculture.

Phosphorus is recyclable, and some natural processes such as falling leaves or spreading manure of locally fed animals partially do this. However, both run off from farm lands into water systems and the export of food crops (containing phosphorus) leads to phosphorus depletion over time. Applying phosphorus containing fertilizer can redress this depletion.

For any commodity that is obtained by some form of extraction process, one can attempt to statistically model past extraction levels in an attempt to predict possible future extraction curves. This inevitably involves both simplifying the system under consideration and making modelling assumptions, both of which can lead to criticism of model predictions. Nonetheless the predictions from a model are generally worth considering, if only to systematically invalidate them. One particular model, Hubbert Linearisation, is considered below.

It’s worth emphasising the human issues due to phosphorus availability are likely to start arising at the production peak, not begin when phosphorus is exhausted.

Details of phosphorus deposits and depletion

Plot of production and Hubber prediction for Phosphorus

The peak in the historical record so far for the rate of world phosphate extraction occurred in 1989 and have, although the data is oscillatory and the current trend is upward again. Other scientists claim that production will rise again but that peak will occur in about 30 years.

We consider one statistical model’s predictions here.

Hubbert linearisation

Hubbert linearisation is a simple model, originally developed in the context of modelling oil extraction, for predicting resource extraction rates. It is controversial the extent to which it has been successfully used in the past, with some claiming no accuracy with others claiming that considering exactly what quantity predictions were made about, the method has been reasonably successful. It is presented here for illustrative purposes.

Hubbert linearisation fits a logistic curve to past data in order to form a prediction of both ultimately recoverable reserves (URR) but also an extraction curve. The following modelling results have been obtained (by Dery, listed below):

  1. Peak phosphate extraction rate in the US happened in 1988, in accordance with actual data (to date).

  2. Peak phosphate extraction rate for the entire world happened in 1989, again in accordance with actual data (to date).


Phosphorus is an important element for crops, which it appears cannot be replaced by any other compound. Assuming peak phosphorus extraction is indeed a problem, there are various possible responses:

  1. Due to its behind-the-scenes role phosphates has a relatively low price of around 30 dollars per ton, which limits which deposits are economic to collect/mine. A rise in price may alter the recoverable reserves and peak date.

  2. Farmers applying more tightly specified fertilizer application, and returning animal manure to the soil, may be able to reduce demand for “external” phosphorus.

  3. Composting toilets, urine diversion and composting waste to return phosphorus to the soil may again reduce the need for external phosphorus. However, dealing with human waste requires consideration of safety issues.


  1. Are there alternative models which give different predictions about peak phosphorus? Do these models have better empirical or theoretical support?

  2. How much has surveying for phosphate deposits been constrained by the low price? Assuming a greater monetary budget, is there in fact enough phosphate available that the peak is in the far future?

This reference (Cisse and Mrabet, 2004) suggests a positive answer.

“With phosphate consumption growth estimated at 1-2% per year, global phosphate reserves extend, for all intents and purposes well into the future, for centuries. Meanwhile, depletion of the most economically exploitable reserves can be estimated to occur within a period of 100-130 years.”

  1. Are there further opportunities for phosphorus recycling?


This article was initially derived from the following article (which contains many more details):

  • Dery, P and Anderson, B, Peak Phosphorus, The Oil Drum,, August 17, 2007.

More academic sources include