A relatively low potato tuber number provides less competition per unit area and allows the crop's energy and resources to be used to produce larger potatoes for the fresh or processing markets.
Correct balanced nutrition is critical to increase potato tuber number. Phosphate, potassium, and calcium have all been shown to have effects on tuber number.
Phosphate availability at tuber initiation is important to ensure maximum tuber set, especially if potato tuber numbers need to be increased for certain varieties, or where the market demands a large number of smaller tubers (e.g. seed production).
This study from Wales shows the effect of phosphorus on increasing total tuber number and overall yield.
While potatoes are very responsive to fresh phosphate, the economic optimum rate is often difficult to define. Rates will depend on soil type and soil test results. Where sufficient soil phosphate is not available for growth, foliar phosphate ensures rapid availability.
This study from Scotland shows the effect of foliar phosphorus on increasing total potato tuber number. Applied just before tuber initiation foliar phosphate increases total tuber number.
Because phosphorus is relatively immobile in the soil it is important that fertilizer P is placed close to the tuber, banding the fertilizer usually works better than broadcasting, especially on soils with the potential for very high phosphorus lock-up.
This chart below shows the influence of soil pH on the availability of phosphorus due to precipitation by calcium at high pH and fixation by iron and aluminium at low pH.
Potassium can influence the numbers of tubers which are set. Its form also needs to be considered. This study from England shows the effect of potassium form on increasing total potato tuber number.
These trials from India demonstrate the yield increase due to potassium and also the benefit from potassium sulfate (SOP) rather than potassium chloride (MOP).