Although biophysical yield responses to local warming have been studied, we know little about how crop yield growth—a function of climate and technology—responds to global temperature and socioeconomic changes. Here, we present the yield growth of major crops under warming conditions from preindustrial levels as simulated by a global gridded crop model. The results revealed that global mean yields of maize and soybean will stagnate with warming even when agronomic adjustments are considered. This trend is consistent across socioeconomic assumptions. Low-income countries located at low latitudes will benefit from intensive mitigation and from associated limited warming trends (1.8 °C), thus preventing maize, soybean and wheat yield stagnation. Rice yields in these countries can improve under more aggressive warming trends. The yield growth of maize and soybean crops in high-income countries located at mid and high latitudes will stagnate, whereas that of rice and wheat will not. Our findings underpin the importance of ambitious climate mitigation targets for sustaining yield growth worldwide.

Aim Recent changes in crop yields have implications for future global food security, which are likely to be affected by climate change. We developed a spatially explicit global dataset of historical yields for maize, soybean, rice and wheat to explore the historical changes in mean, year-to-year variation and annual rate of change in yields for the period 1982-2006. Location This study was conducted at the global scale. MethodsWe modelled historical and spatial patterns of yields at a grid size of 1.125°by combining global agricultural datasets related to the crop calendar and harvested area in 2000, country yield statistics and satellite-derived net primary production. Modelled yields were compared with other global datasets of yields in 2000 (M3-Crops and MapSPAM) and subnational yield statistics for 23 major crop-producing countries. Historical changes in modelled yields were then examined.Results Modelled yields explained 45-81% of the spatial variation of yields in 2000 from M3-Crops and MapSPAM, with root-mean-square errors of 0.5-1.8 t ha −1 . Most correlation coefficients between modelled yield time series and subnational yield statistics for the period 1982-2006 in major crop-producing regions were greater than 0.8. Our analysis corroborated the incidence of reported yield stagnations and collapses and showed that low and mid latitudes in the Southern Hemisphere (0-40°S) experienced significantly increased year-to-year variation in maize, rice and wheat yields in 1994-2006 compared with that in 1982-93. Main conclusions Our analyses revealed increased instability of yields across a broad region of the Southern Hemisphere, where many developing countries are located. Such changes are likely to be related to recent yield stagnation and collapses. Although our understanding of the impacts of recent climate change, particularly the incidence of climate extremes, on crop yields remains limited, our dataset offers opportunities to close parts of this knowledge gap.

We shall investigate several properties of the integralwith a natural number k, a non-negative integer j and a complex variable θ, where ∆ k (x) is the error term in the divisor problem of Dirichlet and Piltz. The main purpose of this paper is to apply the "elementary methods" and the "elementary formulas" to derive convergence properties and explicit representations of this integral with respect to θ for k = 2.

Climatic change through global warming and drought is a major issue for agricultural production. Most researchers who discuss climate changes report the yield changes estimated by using crop process models; however, studies focusing on the impact of climatic change on agricultural product markets are very few. This paper examines the relationship between climatic change and world food markets, i.e., supply and demand of crops, by using a world food model and newly estimated yield functions. These yield functions include rainfall and temperature as climate variables, and the estimated parameters are used in the world food model. The stationarity of these yield data is tested and appropriate functional forms are selected. The results suggest that yields of major crops will decrease because of rising temperatures in many countries and regions, however, market price impacts of changes in production of these crops are not large because of trade. The countries which suffer severe damage because of higher temperature may need to consider changes in cropping patterns and practices.

Climate change will have significant impacts on the rain-fed rice production ecosystem, and particularly on the ecosystem's hydrology and water resources. Under rain-fed lowland conditions, substantial variations among fields in grain yield are commonly observed, but a method that can account for field-scale yield variability to produce regional-scale yield estimates is lacking, thereby limiting our ability to predict future rice production under changing climate and variable water resources. In this study, we developed a model for estimating regional yields of rainfed lowland rice in Northeast Thailand, by combining a simple crop model with a crop calendar model. The crop model incorporates the effects of two important resources (water and nitrogen) on crop growth. The biomass accumulation is driven by water use, whereas the nitrogen supply determines canopy development and thereby constrains crop water use. Accounting for the wide range of planting dates and the strong photoperiod-sensitive characteristics of rice varieties through the calendar model is an essential component in determining regional yield estimates. The present model does not account for the effects of mid-season drought or flooding, but was nonetheless able to explain the spatial and temporal yield variations at the province level for the past 25 years. Thus, it can be used as a prototype for simulating regional yields of rainfed lowland rice.

Let (x) be the error term in the Dirichlet divisor problem. The purpose of this paper is to study the difference between two kinds of mean value formulas of (x), that is, the mean value formulas x 1 (u) k du and n x (n) k with a natural number k. In particular we study the case k = 2 and 3 in detail.

Soybean rust (SBR), caused by Phakopsora pachyrhizi (Sydow & Sydow), has become a serious issue in Brazil. As Brazil is one of the largest soybean-producing and exporting countries in the world, a considerable decrease in soybean production due to SBR would have a significant impact on the global soybean market. SBR-resistant cultivars have been developed to prevent a decrease in soybean production. This study was conducted to evaluate the effect of SBR-resistant cultivars on soybean production and the soybean market in Brazil using a supply and demand model. This model consists of functions of yield, cultivated area, exports, and stock changes of soybean and soybean products, demand for soybean products, and price linkages. Five scenarios were simulated to evaluate the economic impact of adopting SBR-resistant cultivars as follows: One without SBR infection, two with serious production losses due to SBR in the south and southeast regions and all the states of Brazil, and two with the adoption of SBR-resistant cultivars in the south and south-east regions and all the states of Brazil. Our simulations suggest that adopting SBR-resistant cultivars reduces the cost of controlling SBR by approximately half and is essential for sustainable soybean production and a stable global soybean market.

A supply and demand model for rice in Cambodia, which includes among other factors evapotranspiration as a water supply variable impacting regional yields and planted areas, is developed to aid in the design of agricultural policies and planning. Impacts are determined stochastically by drawing on water cycle distributions and evaluating the resulting variation in production and price bands for local rice markets. The results of the baseline analyses indicate that production of wet and dry season rice steadily increases and the consumption per capita slightly decreases due to the negative income elasticity. Results of a partial stochastic analyses show that the production of rice in regions where elevations are high and the land vulnerable to flooding are the most sensitive to increased fluctuations in water supply. The changes also affect the rice market through equilibrium price changes. The upper price band, which is the width between average and 90th percentile, is larger than the lower band, which is the width between average and tenth percentile, suggesting that the situation of low income consumers could grow worse under an unstable environment with relatively larger upward price spikes. The results imply that development of irrigation facilities and water management systems maybe required for Cambodian provinces which rely heavily on agriculture, particularly rice production, under increasing climatic variation.