Fig 1.
Conceptual overview of the networks and resource variability scenarios.
The networks on which our analysis was carried out and a visualisation of the resource variability are shown. The networks are small-world and undirected, compromising 10 and 100 nodes. Resource availability at nodes varies over time in the form of a sine wave. With in phase variability, all nodes experience the same variability. In out of phase the north group (blue) experiences a sine wave 180 degrees out of phase with the south group (red), as illustrated by the colors in the 10 node network.
Table 1.
The four different modes of variability.
They are sine wave functions varying over a base of 1 million kg food resources per year. The amplitude in a mode can either be 5% or 50% and the period of the sine wave can either be 6 years (high frequency) or 70 years (low frequency).
Fig 2.
The cumulative distribution of NEP in the 10 and 100 node networks under the variability scenarios.
(A) Cumulative distribution of NEP in the 10 node and 100 node networks. The cumulative fraction (y-axis) shows the proportion of nodes with a value less than or equal to the associated X value. (B,C,D,E) Effect of resource variability on NEP distributions within the networks. Solid lines indicate in phase resource variability. Dashed lines indicate 180 degrees out of phase resource variability.
Table 2.
The Global Equilibrium Population (GEP, the average population of the nodes in the networks after equilibrium) of the 10 and 100 node networks under the different resource variability scenarios: Low amplitude high frequency (LAHF), low amplitude low frequency (LALF), high amplitude high frequency (HAHF) and high amplitude low frequency (HALF).
GEP is higher under out of phase variability and within the variability scenarios higher under lower amplitude and lower frequency of variability.
Table 3.
The coefficient of variation of the Global Equilibrium Population (GEP, the average population of the nodes in the networks after equilibrium) over time in the different networks and the climate variability scenarios: Low amplitude high frequency (LAHF), low amplitude low frequency (LALF), high amplitude high frequency (HAHF) and high amplitude low frequency (HALF).
GEP is more stable over time in out of phase scenario’s and within the variability scenarios more stable in higher frequency and lower amplitude of variability.
Fig 3.
The effect of closeness centrality on Node Equilibrium Population.
(A) Average resource import and (B) Node Equilibrium Population (NEP) as a function of the closeness centrality of the 100 node network under two out of phase variability scenarios: low amplitude high frequency (LAHF) and high amplitude low frequency (HALF). (C) The coefficient of variation of NEP as a function of closeness centrality for the high amplitude low frequency scenario (HALF).
Fig 4.
The effect of a shock on Node Equilibrium Population.
The decrease in NEP after a shock as a function of (A) the distance to the shock node and (B) the closeness centrality.
Table 4.
The Global Equilibrium Population (GEP, the average population of the nodes in the networks after equilibrium) loss after a shock is applied to a node with low, median or high centrality in the 10 node network.
The increase in population in the shock node is deducted from this. The population loss in the rest of the network is larger when the shock is applied to a node with a higher centrality.