A representative plot of evolutionary outcomes on the phase plane.

<p>Different colors are used to distinguish qualitatively different solutions in the parameter space (<i>r</i>, <i>pβ</i>). This plot highlights that the inner dynamical feature of renewable resource could be a decisive factor that can derogate the expected consequence of punishment.</p

Individual-based simulation for moderately growing resource.

<p>Three representative phase portraits in <i>x</i> − <i>y</i>/<i>R</i>_<i>M</i> plane using different initial conditions when <i>e</i>_<i>c</i> < <i>r</i> < <i>e</i>_<i>d</i>. Panels show results obtained at powerful (left), moderate (middle), and weak (right) external institutions. Depending on the effectiveness of inspection and punishment a sustainable state can be reached for the first two cases. The specific values are <i>p</i> = 0.5 and <i>β</i> = 0.5 in panel A; <i>p</i> = 0.05 and <i>β</i> = 0.5 in panel B; and <i>p</i> = 0.01 and <i>β</i> = 0.1 in panel C. Other parameters are <i>r</i> = 0.6, <i>N</i> = 1000, <i>R</i>_<i>m</i> = 1000, <i>α</i> = 0.5, and <i>b</i>_<i>m</i> = 0.5 for all cases.</p

Replicator dynamics for rapidly growing resource.

<p>Top panels show the time evolution of the fraction of cooperators and the resource abundance ratio for different parameter values when <i>e</i>_<i>c</i> < <i>e</i>_<i>d</i> < <i>r</i>. Bottom panels show the related phase portraits on <i>x</i> − <i>y</i>/<i>R</i>_<i>m</i> plane. Parameters for Panels A and B: <i>r</i> = 1.0, <i>N</i> = 1000, <i>R</i>_<i>m</i> = 1000, <i>p</i> = 0.5, <i>α</i> = 0.5, <i>β</i> = 0.5, and <i>b</i>_<i>m</i> = 0.5; for Panels C and D: <i>r</i> = 1.0, <i>N</i> = 1000, <i>R</i>_<i>m</i> = 1000, <i>p</i> = 0.2, <i>α</i> = 0.5, <i>β</i> = 0.5, and <i>b</i>_<i>m</i> = 0.5; for Panels E and F: <i>r</i> = 1.0, <i>N</i> = 100, <i>R</i>_<i>m</i> = 100, <i>p</i> = 0.1, <i>α</i> = 0.5, <i>β</i> = 0.5, and <i>b</i>_<i>m</i> = 0.5. Due to the large intrinsic growth rate, the environmental resource will never be depleted. The strength of external institutions determines the relation of competing strategies in the equilibrium state.</p

SD game

<div>Evolution to a full cooperation state from a patch-like initial state in the snow-drift quadrant (T=1.5, S=0.4)</div><div><br></div

Individual-based simulation for rapidly growing resource.

<p>Three representative phase portraits in <i>x</i> − <i>y</i>/<i>R</i>_<i>M</i> plane using different initial conditions when <i>e</i>_<i>c</i> < <i>e</i>_<i>d</i> < <i>r</i>. Panels show results obtained at powerful (left), moderate (middle), and weak (right) external institutions. Due to large growth rate a sustainable state can always be maintained. The strength of inspection and punishment determines only the level of this state. The specific values are <i>p</i> = 0.5, 0.2, and 0.1 for panel A, B, and C, respectively. Other parameters are <i>r</i> = 1.0, <i>N</i> = 1000, <i>R</i>_<i>m</i> = 1000, <i>α</i> = 0.5, <i>β</i> = 0.5, and <i>b</i>_<i>m</i> = 0.5 for all cases.</p

Replicator dynamics for moderately growing resource.

<p>Top panels show the time evolution of the fraction of cooperators and the resource abundance ratio for different parameter values when <i>e</i>_<i>c</i> < <i>r</i> < <i>e</i>_<i>d</i>. Bottom panels show the related phase portraits on <i>x</i> − <i>y</i>/<i>R</i>_<i>m</i> plane. Parameters for Panels A and B: <i>r</i> = 0.6, <i>N</i> = 1000, <i>R</i>_<i>m</i> = 1000, <i>p</i> = 0.5, <i>α</i> = 0.5, <i>β</i> = 0.5, and <i>b</i>_<i>m</i> = 0.5; for Panels C and D: <i>r</i> = 0.6, <i>N</i> = 1000, <i>R</i>_<i>m</i> = 1000, <i>p</i> = 0.05, <i>α</i> = 0.5, <i>β</i> = 0.5, and <i>b</i>_<i>m</i> = 0.5; for Panels E and F: <i>r</i> = 0.6, <i>N</i> = 1000, <i>R</i>_<i>m</i> = 1000, <i>p</i> = 0.01, <i>α</i> = 0.5, <i>β</i> = 0.1, and <i>b</i>_<i>m</i> = 0.5. These plots suggest that a sustainable state can be reached for appropriate inspection and punishment level, but the depleted environment state cannot be avoided if these institutions are ineffective.</p

Supplementary figures from Emergence of leadership in a robotic fish group under diverging individual personality traits

The ESM contains four supplementary figures on the software architecture of the experimental platform, the relationship between the success rate and the number of cooperating fish for different difficulty levels of the foraging tasks, the typical evolutionary processes with fixed tasks of the most difficult level, and the experimental results of the reference model

Genetic Diversity, Population Structure and Linkage Disequilibrium in Elite Chinese Winter Wheat Investigated with SSR Markers

<div><p>To ascertain genetic diversity, population structure and linkage disequilibrium (LD) among a representative collection of Chinese winter wheat cultivars and lines, 90 winter wheat accessions were analyzed with 269 SSR markers distributed throughout the wheat genome. A total of 1,358 alleles were detected, with 2 to 10 alleles per locus and a mean genetic richness of 5.05. The average genetic diversity index was 0.60, with values ranging from 0.05 to 0.86. Of the three genomes of wheat, ANOVA revealed that the B genome had the highest genetic diversity (0.63) and the D genome the lowest (0.56); significant differences were observed between these two genomes (P<0.01). The 90 Chinese winter wheat accessions could be divided into three subgroups based on STRUCTURE, UPGMA cluster and principal coordinate analyses. The population structure derived from STRUCTURE clustering was positively correlated to some extent with geographic eco-type. LD analysis revealed that there was a shorter LD decay distance in Chinese winter wheat compared with other wheat germplasm collections. The maximum LD decay distance, estimated by curvilinear regression, was 17.4 cM (r²>0.1), with a whole genome LD decay distance of approximately 2.2 cM (r²>0.1, P<0.001). Evidence from genetic diversity analyses suggest that wheat germplasm from other countries should be introduced into Chinese winter wheat and distant hybridization should be adopted to create new wheat germplasm with increased genetic diversity. The results of this study should provide valuable information for future association mapping using this Chinese winter wheat collection.</p></div

Genetic diversity at genome level of the Chinese winter wheat revealed by 269 SSR markers.

<p>Genetic diversity at genome level of the Chinese winter wheat revealed by 269 SSR markers.</p

STRUCTURE estimation of the number of populations for K ranging from 1 to 12 by delta K values (

<p>Δ<b>K).</b></p