Relative frequency of each triad type as a function of degree of interconnectedness of the participant countries.

<p>Triad types are grouped into four figures based on their general trends and magnitudes. Note that type 8 (panel D) is consistently very infrequent, or almost non-existent: this is expected as type 8 represents three countries simply transporting food products in an endless cycle.</p

Triad significance profiles of agricultural trade networks: by product.

<p>These networks form a distinct superfamily not previously reported for other networks, including an international cargo shipping network.</p

Comparison of the agricultural trade network TSP with known network superfamilies.

<p>The overall agricultural trade network compared to (A) biological regulatory networks and (B) human social networks. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039756#pone-0039756-t001" target="_blank">Table 1</a> for correlation coefficients.</p

Triad distribution for two groups of countries.

<p>Most countries (166) share a similar triad distribution. However, 18 countries (listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039756#pone-0039756-t003" target="_blank">Table 3</a>) differ distinctively from the majority group.</p

How countries allocate their different types of trade connections.

<p>The figure presents the number of trade links that are import only (blue), export only (red), and mutual (black) vs. total links, i.e., the number of trade partners or degree of interconnectedness.</p

Countries (18) whose trade network triad distributions deviate significantly from those of all other countries (166) and their global ranking in terms of isolation in the global agricultural trade network (i.e. Lesotho ranks as the least connected country).

<p>Countries (18) whose trade network triad distributions deviate significantly from those of all other countries (166) and their global ranking in terms of isolation in the global agricultural trade network (i.e. Lesotho ranks as the least connected country).</p

How Does a Divided Population Respond to Change?

<div><p>Most studies on the response of socioeconomic systems to a sudden shift focus on long-term equilibria or end points. Such narrow focus forgoes many valuable insights. Here we examine the transient dynamics of regime shift on a divided population, exemplified by societies divided ideologically, politically, economically, or technologically. Replicator dynamics is used to investigate the complex transient dynamics of the population response. Though simple, our modeling approach exhibits a surprisingly rich and diverse array of dynamics. Our results highlight the critical roles played by diversity in strategies and the magnitude of the shift. Importantly, it allows for a variety of strategies to arise organically as an integral part of the transient dynamics—as opposed to an independent process—of population response to a regime shift, providing a link between the population's past and future diversity patterns. Several combinations of different populations' strategy distributions and shifts were systematically investigated. Such rich dynamics highlight the challenges of anticipating the response of a divided population to a change. The findings in this paper can potentially improve our understanding of a wide range of socio-ecological and technological transitions.</p></div

Shuffling for significance.

Schematic diagram of the rewiring process to create a randomized network.</p

More flows, more edges? Not quite.

The relationship between the sum of all refugee flows and the number of edges in the refugee flow network: (A) the original flow data, and (B) after removing edges with fewer than 100 refugees per year. The relationship is complex and exhibits significant variation, with certain years showing increased flows despite a reduced number of edges.</p

Different snapshots at different times for the case of Δs1*>Δscrit*>Δs2* and with asymmetric variations (where Δs1*=0.6, Δs2*=0.3, Δscrit*=0.5196, with s1*=0.2, s2*=0.5, sR*=0.8, <i>σ</i> = 0.2, with <i>D</i>₁ = 0.05 and <i>D</i>₂ = 0.02, see Video V in S1 File).

<p>Note that the peak initially around </p><p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><p></p><p></p><p></p> disintegrates completely while the other peak dominates temporarily before a new peak emerges suddenly and dominates at the end. The dashed lines show the locations of <p></p><p></p><p></p><p><mi>s</mi><mn>1</mn><mo>*</mo></p><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>s</mi><mn>2</mn><mo>*</mo></p><p></p><p></p><p></p>, and <p></p><p></p><p></p><p><mi>s</mi><mi>R</mi><mo>*</mo></p><p></p><p></p><p></p>, while the solid lines represent the the theoretically calculated threshold(s) for the single peak population distribution case, i.e., <p></p><p></p><p><mo>Δ</mo></p><p><mi>s</mi></p><p><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></p><mo>*</mo><p></p><mo>=</mo><mn>3</mn><p><mn>3</mn></p><mi>σ</mi><mo>/</mo><mn>2</mn><p></p><p></p><p></p>.<p></p