# What is the yield gap? How to calculate the yield gap?

Food is necessary for our life and directly or indirectly from crops. To keep food security, we need to know how many crop productions have achieved and how much crop potential need to excavate. Here I introduced the relavent variables involved in estimating yield gap and visualized the links among those variables and yield gap in Figure 1. Figure 2 and 3 are then exploited to illustrate the key logic of two extensively used methods on estimating yield gap.

1. Concepts of different yield

Potential yield (PY) is the yield of a crop cultivar when grown with optimal environmental conditions (Fischer, 2015). The limitation of water and nutrition is counteracted by management practices (irrigation and fertilization). And, the crop is protected from any pests and diseases by applying pesticides. PY is location-specific and determined only by climatic conditions (radiation and temperature), atmospheric CO2 concentration, and genetic traits, which is the maximum yield of a crop cultivar in a certain climate.

Water-limited potential yield (PYw) is the yield of a crop cultivar when grown in rainfed situations where water supply depending on precipitation (Fischer, 2015). This yield is obtained with no other limitation except water supply. PYw is the most relevant benchmark for rainfed regions because the magnitude of PYw depends on the amount of water supply used for crop growth. The water supply depends directly on the amount of precipitation in the rainfed region which no water for irrigation.

Farm yield (FY) is defined as the actual yield achieved in a field. It is the final result of multiple factors, such as environmental factors, management practices, pests, and diseases (Fischer, 2015). It reflects the current state of the environment and management level.

Yield gap (Yg) is the difference between PY (for the region without water limitation, such as irrigated or wet region) or PYw (for the rainfed region) and FY (Van Ittersum et al., 2013). It represents the desirable increases in yield by improving management practices.

2. Methods for calculating Yg at a global scale

Statistic based on climate spatial pattern

Here I use 5*5 grids as a case. If we have a grid map of actual yield like ①, the number in each grid represents the yield level of this grid. Also, we have a grid climate date corresponding to grids.

We can classify each grid based on climatic conditions, such as temperature and moisture index, and group grids with similar climatic conditions into the same climate zone. We get a map with different colors for different climate zone like ②.

We rank the yield in the same climate zone from lowest to highest, then assume the highest yield or 99% quantile of yield distribution as the potential yield. We get the potential yield corresponding to climate zone like ③.

We link each grid with climate zone then potential yield. We get a map of potential yield like ④.

At last, we calculate the difference between the corresponding grids in map ① and map ④. We get the map of the yield gap like ⑤.

Simulation by process-based crop models

The crop model is an effective tool to study the interaction between crop and environment and is used to simulate the yield gap. Potential yield is simulated by the crop model, which is driven by climate data and optimal management practices. Farm yield is from observation or simulated using actual management practices. At last, the yield gap is calculated as the difference between potential yield and farm yield.

Noticeably, statistics-based results, which are obtained from existing observation, are true for history. But these results do not take into account the effects of changing environmental factors, such as warming and increasing CO2 concentration. Therefore these results can not reflect the future variation of yield gap under ongoing climate change. Crop models that integrate empirical relationships with theoretical understandings to simulate the crop growth, might be the possible tools to study the effects of climate change on the yield gap. However, the predictability of the crop model depends on the structure of the crop model. The more theoretical understandings are included, the more relialbe the model havs. Therefore, we need a crop model that accounts for ecosystem theories more in the description of crop growth.

References

• Fischer, & R., A. . (2015). Definitions and determination of crop yield, yield gaps, and of rates of change. Field Crops Research, 9-18.
• Van Ittersum, M. K. , Cassman, K. G. , Grassini, P. , Wolf, J. , Tittonell, P. , & Hochman, Z. . (2013). Yield gap analysis with local to global relevance—a review. Field Crops Research, 143(1), 4-17.
• Johnston, M. , Licker, R. , Foley, J. , Holloway, T. , Mueller, N. D. , & Barford, C. , Kucharik C. , (2011). Closing the gap: global potential for increasing biofuel production through agricultural intensification. Environmental Research Letters, 6(3), 034028.
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