Future climate change will impose increased variability on food production and food trading networks. However, the effect of climate variability and sudden shocks on resource availability through trade and its subsequent effect on population growth is largely unknown. Here we study the effect of resource variability and network topology on access to resources and population growth, using a model of population growth limited by resource availability in a trading network. Resources are redistributed in the network based on supply and the distance between nodes (i.e. cities or countries). Resources at nodes vary over time with wave parameters that mimic changes in biomass production arising from known climate variability. Random perturbations to resources are applied to study resilience of individual nodes and the system as a whole. The model demonstrates that redistribution of resources increases the maximum population that can be supported (carrying capacity) by the network. Fluctuations in carrying capacity depend on the amplitude and frequency of resource variability: fluctuations become larger for increasing amplitude and decreasing frequency. Our study shows that topology is the key factor determining the carrying capacity of a node. In larger networks the carrying capacity increases and the distribution of resources in the network becomes more equal. The most central nodes achieve a higher carrying capacity than nodes with a lower centrality. Moreover, central nodes are less susceptible to long-term resource variability and shocks. These insights can be used to understand how worldwide equitable access to resources can be maintained under increasing climate variability.