Amplification on Undirected Population Structures: Comets Beat Stars

Abstract

The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure. Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade. In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.

Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time

“…Of course, stronger amplifiers of selection are already known 1 , but they are all directed or weighted graphs. Pavlogiannis et al found a class of undirected graphs that they call comets which can have a higher fixation probability than stars for certain graph sizes of more than 100 nodes 33 . Comet-graphs consist of a complete graph with a star attached to one of the nodes.…”

“…With the fast computational method we use for computing fixation probability and time, we are limited to sizes roughly up to N = 23 31 . There are many interesting findings for larger graphs, e.g., that the star is not the strongest amplifier for all sizes, but that comets can have an even higher fixation probability 33 . Our genetic algorithm can be easily combined with other methods of computation or simulation to tackle larger graph sizes.…”

Vaccinomic approach for novel multi epitopes vaccine against severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2)

“…To design a vaccine construct, the elected B and T cells epitopes were fused using appropriate specialized spacer (linkers) sequences in order to generate multi-epitopes peptides [ 44 ]. The linkers KK and GPGPG were introduced between the selected B and T cells epitopes to generate a sequence with minimal junctional immunogenicity [ 45 – 49 ]. The EAAAK linker was also added between the adjuvants sequences and the fused epitopes in order to reach a high level of expression and improved bioactivity of the fused epitopes [ 44 , 46 ].…”

Fixation probability on clique-based graphs

“…The star graph is known to have the strongest amplification among undirected graphs up to now. (Recently, in a limited interval for r, a family of graphs (comets) with higher fixation probability than the star graphs is discovered [7]. )…”