National yield stability
We used the FAOSTAT database (http://www.fao.org/faostat, visited in September 2019) to obtain data on annual crop production (in tons) and area harvested (in hectares) from 1961 to 2010 for 138 crops in 91 populous nations. Following Renard and Tilman16, we accounted for differences among nations in data quality and excluded five nations, namely North Korea, Guinea, Kenya, Mozambique and Zambia, for which at least 20% of the data on area harvested or production were extrapolated by the FAO (see details in16). We calculated for each nation and each year the total annual caloric yield (millions of kcal ha-1). To do so, we first calculated the kcal production of each crop by multiplying the production of each crop by its commodity-specific kilocalorie conversion factor from the USDA Nutrient Database32. In doing so, we were able to compare the production of different crops. Then, we summed these kcal harvests across all crops and divided this value by the sum of harvested area for all crops. We calculated national yield stability (S) as the ratio of mean total annual caloric yield (µT) over its time-detrended standard deviation (σT) for fifty consecutive years (1961–2010). We accounted for a temporal trend of increasing total annual crop yield by implementing a loess regression between annual crop yield and years. σT corresponds to the standard deviation of the residuals of this regression. Finally, we compared this stability index (largely used in the biodiversity-ecological functioning research, e.g.14,16,17,18) with the resilience index used by Zampieri et al.22. Both indices were strongly correlated (r = 0.992), strengthening our findings.
Individual crop yield stability and yield asynchrony
For each country, we quantified the average stability of yields of individual crops as the mean of the inverse of the coefficient of variation of yield of each crop:
$$ {{left( {mathop sum limits_{i = 1}^{N} frac{{mu_{i} }}{{sigma_{i} }}} right)} mathord{left/ {vphantom {{left( {mathop sum limits_{i = 1}^{N} frac{{mu_{i} }}{{sigma_{i} }}} right)} N}} right. kern-nulldelimiterspace} N} $$
(1)
where (mu_{i}) is the temporal mean of crop’s annual kcal yield and (sigma_{i}) its time-detrended standard deviation. Time-detrended crop yield was computed through a loess regression between individual, annual crop yield and years.
We computed the asynchrony between crop yield fluctuations following the index developed by Loreau and De Mazancourt11:
$$ Phi = 1 – frac{{sigma^{2}_{T} }}{{left( {mathop sum nolimits_{i = 1}^{N} sigma_{i} } right)^{2} }} $$
(2)
where Φ is the asynchrony of crop species based on annual caloric yield (millions of kcal ha−1) with (sigma_{T}^{2}) the temporal variance of the time-detrended national yield and (sigma_{i}) the time-detrended standard deviation of each crop’s annual kcal yield. The value of asynchrony varies between zero (perfect synchrony) and one (perfect asynchronous temporal fluctuations).
To test whether yield fluctuations of the most abundant crops have a greater impact on the stability of national food production, we weighted the annual yield of each crop by the proportion of total harvested area occupied by that crop. Average stability of yields of individual crops and yield asynchrony were computed on both the non-weighted and abundance-weighted yields.
Crop diversity
For each country and year, we used both the total number of crop commodities (i.e. crop richness) and the Shannon information index (H′) to quantify crop diversity. H′ weights each crop in a nation by the proportion of total cropland it occupies (pi):
$$ H^{prime } = – mathop sum limits_{i = 1}^{N} left( {p_{i} lnleft[ {p_{i} } right]} right) $$
(3)
with N being the total number of crops grown in a country each year.
The exponential form of the Shannon diversity index gives the effective crop diversity that is the number of crops representing an equal share of harvested area24. In other words, the exponential of the Shannon diversity index weighs all species by their frequency, without favouring either common or rare species24. We averaged the annual effective diversity of crop across the fifty years studied to test the effect of crop diversity on national yield stability.
Agricultural inputs
We extracted the annual national application of nitrogen and the annual cropland area equipped for irrigation from the FAOSTAT database. Because Ireland, New Zealand and Netherlands use much of their fertilizers on pastures rather than croplands, we excluded these nations from our analysis. Similarly, we excluded Egypt because it has 100% of cropland equipped for irrigation. We calculated the annual rates of nitrogen application and irrigation per hectare by dividing their use by the total annual cropland area.
Climate variability
We used global gridded climatic data from the Climate Research Unit of the University of East Anglia33 to compute the year-to-year variability of growing season precipitation and temperature for each country, both strongly affecting the stability of national food production16. From these data, we derived annual precipitation and temperature for each grid cell in a country by taking the sum of monthly precipitation and the mean of monthly temperature values weighted by the proportion of cropland in each grid cell34. We then computed the year-to-year coefficient of variation of cropland-based temperature and precipitation for each country.
Statistical analysis
We used structural equation models (SEMs) to evaluate how irrigation, intensity of use of nitrogen fertilizers and crop diversity affected national yield stability through changes in the average stability of yields of individual crops and asynchrony of yields. SEMs represent a powerful way to disentangle complex mechanisms controlling crop diversity-stability relationships, as previously done in natural ecosystems (e.g.14,15,35,36). We set up two different structural equation models, one based on non-weighted indices of stability of individual crops and asynchrony, the other based on the same indices weighted by the proportion of total harvested area accounted for by each crop. We firstly considered the effects of agricultural inputs and crop diversity on the stability of national food production via the path of average yield stability. The second path quantified the indirect effects of agricultural inputs and crop diversity on national stability via their impacts on crop yield asynchrony. We also accounted for the direct effects of agricultural inputs and crop diversity on national yield stability. Finally, we controlled for the effects of climate variability on total, national yield stability, individual crop yield stability and yield asynchrony. SEMs were run with the lavaan R library37. We used the standardized estimates to compare the relative importance of the different paths. The model fit was evaluated using the Fisher C’score and its associated p values. Because the structural equation model assumes linear relationships between predictors and the dependent variable, we also plotted the relationships between total national yield stability and both asynchrony and average stability of individual crop yield to control for linearity (Fig. 2). Similarly, we investigated the relationships between crop diversity and asynchrony (Fig. 3), as well as between irrigation rate and the average stability of individual crop yield (Fig. 4).
Source: Ecology - nature.com
