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We present a broad class of semi-parametric models for time series of random sums of positive variables. Our methodology allows the number of terms inside the sum to be time-varying and is therefore well suited to many examples encountered in the natural sciences. We study the stability properties of the models and provide a valid statistical inference procedure to estimate the model parameters. It is shown that the proposed quasi-maximum likelihood estimator is consistent and asymptotically normally distributed. This work is complemented by simulation results and applied to annual growth rate time series of white spruce (Picea glauca) trees from a few dozen sites in Quebec spanning 41 years, including one major spruce budworm (Choristoneura fumiferana) outbreak from around 1968 to 1991. We found significant growth reductions due to budworm-induced by defoliation up to two years in the past. Our results also revealed positive effects of maximum temperature, precipitation and the climate moisture index in the summer, as well as negative effects of the climate moisture index in the spring and the maximum temperature in the previous summer. However, considering the interaction of climate and defoliation on growth did not improve the model's performance on this dataset. This study represent a major advances and our result represent an useful tool in the understanding of the combined effects of climate and insect defoliation on tree growth in the face of climate change, where the frequency and the severity of outbreaks, as well as an increase of temperature is expected.

Higher temperatures expected by midcentury increase the risk of shocks to crop production, while the interconnected nature of the current global food system functions to spread the impact of localized production shocks throughout the world. In this study, we analyze the global potential impact of a present-day event of equivalent magnitude to the US Dust Bowl, modeling the ways in which a sudden decline in US wheat production could cascade through the global network of agricultural trade. We use observations of country-level production, reserves, and trade data in a Food Shock Cascade model to explore trade adjustments and country-level inventory changes in response to a major, multiyear production decline. We find that a 4-year decline in wheat production of the same proportional magnitude as occurred during the Dust Bowl greatly reduces both wheat supply and reserves in the United States and propagates through the global trade network. By year 4 of the event, US wheat exports fall from 90.5 trillion kcal before the drought to 48 trillion to 52 trillion kcal, and the United States exhausts 94% of its reserves. As a result of reduced US exports, other countries meet their needs by leveraging their own reserves, leading to a 31% decline in wheat reserves globally. These findings demonstrate that an extreme production decline would lead to substantial supply shortfalls in both the United States and in other countries, where impacts outside the United States strongly depend on a country's reserves and on its relative position in the global trade network.

While a growing proportion of global food consumption is obtained through international trade, there is an ongoing debate on whether this increased reliance on trade benefits or hinders food security, and specifically, the ability of global food systems to absorb shocks due to local or regional losses of production. This paper introduces a model that simulates the short-term response to a food supply shock originating in a single country, which is partly absorbed through decreases in domestic reserves and consumption, and partly transmitted through the adjustment of trade flows. By applying the model to publicly-available data for the cereals commodity group over a 17 year period, we find that differential outcomes of supply shocks simulated through this time period are driven not only by the intensification of trade, but as importantly by changes in the distribution of reserves. Our analysis also identifies countries where trade dependency may accentuate the risk of food shortages from foreign production shocks; such risk could be reduced by increasing domestic reserves or importing food from a diversity of suppliers that possess their own reserves. This simulation-based model provides a framework to study the short-term, nonlinear and out-of-equilibrium response of trade networks to supply shocks, and could be applied to specific scenarios of environmental or economic perturbations.