scholarly journals The Moran process on 2-chromatic graphs

2020 ◽  
Vol 16 (11) ◽  
pp. e1008402
Author(s):  
Kamran Kaveh ◽  
Alex McAvoy ◽  
Krishnendu Chatterjee ◽  
Martin A. Nowak
Keyword(s):  
Graph Coloring ◽  
Evolutionary Dynamics ◽  
Population Heterogeneity ◽  
Graph Connectivity ◽  
Regular Graphs ◽  
Breeding Sites ◽  
Moran Model ◽  
Colored Graphs ◽  
Moran Process

Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.

scholarly journals Evolutionary graph theory revisited: when is an evolutionary process equivalent to the Moran process?

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150334 ◽  
Author(s):  
Karan Pattni ◽  
Mark Broom ◽  
Jan Rychtář ◽  
Lara J. Silvers
Keyword(s):  
Graph Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Process ◽  
Structured Populations ◽  
Fixation Probability ◽  
Finite Populations ◽  
Moran Model ◽  
Moran Process ◽  
Evolutionary Graph Theory ◽  
Associated Matrix

Evolution in finite populations is often modelled using the classical Moran process. Over the last 10 years, this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such population is whether a rare mutant has a higher or lower chance of fixating (the fixation probability) than the Moran probability, i.e. that from the original Moran model, which represents an unstructured population. As evolutionary graph theory has developed, different ways of considering the interactions between individuals through a graph and an associated matrix of weights have been considered, as have a number of important dynamics. In this paper, we revisit the original paper on evolutionary graph theory in light of these extensions to consider these developments in an integrated way. In particular, we find general criteria for when an evolutionary graph with general weights satisfies the Moran probability for the set of six common evolutionary dynamics.

THE MATING PATTERNS OF FEMALES WHEN TERRITORIAL DIFFERENCES AMONG MALES ARE REDUCED: A TEST IN THE POLYGYNOUS BEAUGREGORY DAMSELFISH

Behaviour ◽  
2001 ◽  
Vol 138 (6) ◽  
pp. 691-708 ◽  
Author(s):  
◽  
◽  
◽  
Keyword(s):  
Random Mating ◽  
Breeding Site ◽  
Male Reproduction ◽  
Male Reproductive Success ◽  
Mating Pattern ◽  
Breeding Sites ◽  
Site Structure ◽  
Artificial Breeding ◽  
Stegastes Leucostictus

AbstractUsing the Caribbean beaugregory damselfish (Stegastes leucostictus) we tested whether patterns of male reproduction could be modified by reducing differences among males, in this case by giving males identical artificial breeding sites. Previous studies have shown that very few males using the natural small rubble habitat reproduced and variations in male reproductive success were based mainly on the differences in the quality of their natural breeding sites. By providing males with identical artificial breeding sites, we tested whether females would be less likely to confine their reproduction to only a few of the available males. We examined male reproductive patterns by first simulating females choosing males (1) 'randomly,' (i.e. the number of males that receive eggs is based on each female randomly choosing a mate from a group of males), or (2) 'exclusively' (i.e. only one female mates with one male on a given day), or (3) 'highly selectively' (i.e. this is the typical polygynous pattern in which many females select the same few males). We tested these simulations against the actual daily amounts of eggs deposited and the number of different males that received eggs in each of 4 summers. Although the regression trend line from the daily patterns did resemble the Random Mating Pattern, egg clutches were more widely dispersed than random but less dispersed than the Exclusive Mating Pattern. That is, with more females mating on a particular day, more males received eggs. We speculated that this might have resulted from females aggressively excluding other females from mating with the same male on a given day. In contrast, males using the variable quality natural sites rarely mated and those that did receive eggs, received them in larger amounts than males using the artificial sites. Thus, for natural sites, more females seemed to be mating with the same few males. Perhaps for these natural sites any intra-female aggression may have been ineffective when so few superior spawning sites were available. For males using the artificial sites, the total amount of eggs received over a two-month period was nonrandom and resembled the 'highly selected pattern.' This resulted from some males receiving egg clutches on more days. Other traits, besides breeding site structure, may have been important in causing different females to select the same males on subsequent days.

scholarly journals Fitness dependence of the fixation-time distribution for evolutionary dynamics on graphs

2018 ◽  
Author(s):  
David Hathcock ◽  
Steven H. Strogatz
Keyword(s):  
Complete Graph ◽  
Time Distribution ◽  
Evolutionary Dynamics ◽  
Structured Populations ◽  
Relative Fitness ◽  
Death Process ◽  
Fixation Time ◽  
Large Network ◽  
Moran Process ◽  
Fitness Dependence

Evolutionary graph theory models the effects of natural selection and random drift on structured populations of mutant and non-mutant individuals. Recent studies have shown that fixation times, which determine the rate of evolution, often have right-skewed distributions. Little is known, however, about how these distributions and their skew depend on mutant fitness. Here we calculate the fitness dependence of the fixation-time distribution for the Moran Birth-death process in populations modeled by two extreme networks: the complete graph and the one-dimensional ring lattice, each of which admits an exact solution in the limit of large network size. We find that with non-neutral fitness, the Moran process on the ring has normally distributed fixation times, independent of the relative fitness of mutants and non-mutants. In contrast, on the complete graph, the fixation-time distribution is a weighted convolution of two Gumbel distributions, with a weight depending on the relative fitness. When fitness is neutral, however, the Moran process has a highly skewed fixation-time distribution on both the complete graph and the ring. In this sense, the case of neutral fitness is singular. Even on these simple network structures, the fixation-time distribution exhibits rich fitness dependence, with discontinuities and regions of universality. Applications of our methods to a multi-fitness Moran model, times to partial fixation, and evolution on random networks are discussed.

scholarly journals Multi-Omic Analysis of Symbiotic Bacteria Associated With Aedes aegypti Breeding Sites

2021 ◽  
Vol 12 ◽  
Author(s):  
Katherine D. Mosquera ◽  
Luis E. Martinez Villegas ◽  
Sacha J. Pidot ◽  
Chinhda Sharif ◽  
Sven Klimpel ◽  
...  
Keyword(s):  
Aedes Aegypti ◽  
Water Samples ◽  
Gravid Female ◽  
Breeding Site ◽  
Gene Clusters ◽  
Symbiotic Bacteria ◽  
Potential Contribution ◽  
Breeding Sites ◽  
Mosquito Breeding

Mosquito breeding sites are complex aquatic environments with wide microbial diversity and physicochemical parameters that can change over time during the development of immature insect stages. Changes in biotic and abiotic conditions in water can alter life-history traits of adult mosquitos but this area remains understudied. Here, using microbial genomic and metabolomics analyses, we explored the metabolites associated with Aedes aegypti breeding sites as well as the potential contribution of Klebsiella sp., symbiotic bacteria highly associated with mosquitoes. We sought to address whether breeding sites have a signature metabolic profile and understand the metabolite contribution of the bacteria in the aquatic niches where Ae. aegypti larvae develop. An analysis of 32 mosquito-associated bacterial genomes, including Klebsiella, allowed us to identify gene clusters involved in primary metabolic pathways. From them, we inferred metabolites that could impact larval development (e.g., spermidine), as well as influence the quality assessment of a breeding site by a gravid female (e.g., putrescine), if produced by bacteria in the water. We also detected significant variance in metabolite presence profiles between water samples representing a decoupled oviposition event (oviposition by single females and manually deposited eggs) versus a control where no mosquito interactions occurred (PERMANOVA: p < 0.05; R2 = 24.64% and R2 = 30.07%). Five Klebsiella metabolites were exclusively linked to water samples where oviposition and development occurred. These data suggest metabolomics can be applied to identify compounds potentially used by female Ae. aegypti to evaluate the quality of a breeding site. Elucidating the physiological mechanisms by which the females could integrate these sensory cues while ovipositing constitutes a growing field of interest, which could benefit from a more depurated list of candidate molecules.

scholarly journals Measuring the distribution of fitness effects in somatic evolution by combining clonal dynamics with dN/dS ratios

2019 ◽  
Author(s):  
Marc J Williams ◽  
Luiz Zapata ◽  
Benjamin Werner ◽  
Chris Barnes ◽  
Andrea Sottoriva ◽  
...  
Keyword(s):  
Evolutionary Dynamics ◽  
Quantitative Model ◽  
Driver Mutations ◽  
Cancer Evolution ◽  
Sequencing Data ◽  
Synonymous Mutations ◽  
Fitness Effects ◽  
Somatic Evolution ◽  
Normal Oesophagus

AbstractThe distribution of fitness effects (DFE) defines how new mutations spread through an evolving population. The ratio of non-synonymous to synonymous mutations (dN/dS) has become a popular method to detect selection in somatic cells, however the link, in somatic evolution, between dN/dS values and fitness coefficients is missing. Here we present a quantitative model of somatic evolutionary dynamics that yields the selective coefficients from individual driver mutations from dN/dS estimates, and then measure the DFE for somatic mutant clones in ostensibly normal oesophagus and skin. We reveal a broad distribution of fitness effects, with the largest fitness increases found for TP53 and NOTCH1 mutants (proliferative bias 1-5%). Accurate measurement of the per-gene DFE in cancer evolution is precluded by the quality of currently available sequencing data. This study provides the theoretical link between dN/dS values and selective coefficients in somatic evolution, and reveals the DFE for mutations in human tissues.

scholarly journals Seasonally specific responses to wind patterns and ocean productivity facilitate the longest animal migration on Earth

2020 ◽  
Vol 638 ◽  
pp. 1-12
Author(s):  
T Hromádková ◽  
V Pavel ◽  
J Flousek ◽  
M Briedis
Keyword(s):  
Evolutionary Dynamics ◽  
Travel Speed ◽  
The Arctic ◽  
Behavioural Plasticity ◽  
Limiting Factor ◽  
Migration Routes ◽  
Breeding Sites ◽  
Ocean Productivity ◽  
Migration Strategies ◽  
Animal Migration

Migratory strategies of animals are broadly defined by species’ eco-evolutionary dynamics, while behavioural plasticity according to the immediate environmental conditions en route is crucial for energy efficiency and survival. The Arctic tern Sterna paradisaea is known for its remarkable migration capacity, as it performs the longest migration known by any animal. Yet, little is known about the ecology of this record-breaking journey. Here, we tested how individual migration strategies of Arctic terns are adapted to wind conditions and fuelling opportunities along the way. To this end, we deployed geolocators on adult birds at their breeding sites in Svalbard, Norway. Our results confirm fundamental predictions of optimal migration theory: Arctic terns tailor their migration routes to profit from (1) tailwind support during the movement phase and (2) food-rich ocean areas during the stopover phase. We also found evidence for seasonally distinct migration strategies: terns prioritize fuelling in areas of high ocean productivity during the southbound autumn migration and rapid movement relying on strong tailwind support during the northbound spring migration. Travel speed in spring was 1.5 times higher compared to autumn, corresponding to an increase in experienced wind support. Furthermore, with their pole-to-pole migration, Arctic terns experience approximately 80% of all annual daylight on Earth (the most by any animal), easing their strictly diurnal foraging behaviour. However, our results indicate that during migration daylight duration is not a limiting factor. These findings provide strong evidence for the importance of interaction between migrants and the environment in facilitating the longest animal migration on Earth.

scholarly journals On the fixation probability of superstars

2013 ◽  
Vol 469 (2156) ◽  
pp. 20130193 ◽  
Author(s):  
Josep Díaz ◽  
Leslie Ann Goldberg ◽  
George B. Mertzios ◽  
David Richerby ◽  
Maria Serna ◽  
...  
Keyword(s):  
Computer Algebra ◽  
Evolutionary Dynamics ◽  
Process Models ◽  
Relative Fitness ◽  
Genetic Mutations ◽  
Fixation Probability ◽  
Mutant Population ◽  
Moran Process ◽  
Limiting Behaviour ◽  
Symbolic Matrix

The Moran process models the spread of genetic mutations through populations. A mutant with relative fitness r is introduced and the system evolves, either reaching fixation (an all-mutant population) or extinction (no mutants). In a widely cited paper, Lieberman et al. (2005 Evolutionary dynamics on graphs. Nature 433 , 312–316) generalize the model to populations on the vertices of graphs. They describe a class of graphs (‘superstars’), with a parameter k and state that the fixation probability tends to 1− r − k as the graphs get larger: we show that this is untrue as stated. Specifically, for k =5, we show that the fixation probability (in the limit, as graphs get larger) cannot exceed 1−1/ j ( r ), where j ( r )= Θ ( r 4 ), contrary to the claimed result. Our proof is fully rigorous, though we use a computer algebra package to invert a 31×31 symbolic matrix. We do believe the qualitative claim of Lieberman et al. —that superstar fixation probability tends to 1 as k increases—and that it can probably be proved similarly to their sketch. We were able to run larger simulations than the ones they presented. Simulations on graphs of around 40 000 vertices do not support their claim but these graphs might be too small to exhibit the limiting behaviour.

scholarly journals Host genotype and genetic diversity shape the evolution of a novel bacterial infection

2021 ◽  
Author(s):  
Alice K. E. Ekroth ◽  
Michael Gerth ◽  
Emily J. Stevens ◽  
Suzanne A. Ford ◽  
Kayla C. King
Keyword(s):  
Genetic Diversity ◽  
Metal Ion ◽  
Evolutionary Dynamics ◽  
Population Heterogeneity ◽  
Broad Host Range ◽  
Host Genotype ◽  
Pathogen Virulence ◽  
Novel Host ◽  
Host Metal ◽  
Spread Of Infection

AbstractPathogens continue to emerge from increased contact with novel host species. Whilst these hosts can represent distinct environments for pathogens, the impacts of host genetic background on how a pathogen evolves post-emergence are unclear. In a novel interaction, we experimentally evolved a pathogen (Staphylococcus aureus) in populations of wild nematodes (Caenorhabditis elegans) to test whether host genotype and genetic diversity affect pathogen evolution. After ten rounds of selection, we found that pathogen virulence evolved to vary across host genotypes, with differences in host metal ion acquisition detected as a possible driver of increased host exploitation. Diverse host populations selected for the highest levels of pathogen virulence, but infectivity was constrained, unlike in host monocultures. We hypothesise that population heterogeneity might pool together individuals that contribute disproportionately to the spread of infection or to enhanced virulence. The genomes of evolved populations were sequenced, and it was revealed that pathogens selected in distantly-related host genotypes diverged more than those in closely-related host genotypes. S. aureus nevertheless maintained a broad host range. Our study provides unique empirical insight into the evolutionary dynamics that could occur in other novel infections of wildlife and humans.

scholarly journals SuDS and amphibians - are constructed wetlands really benefitting nature and people?

2018 ◽  
Vol 27 (Supplement) ◽  
pp. 21-24
Author(s):  
D. O’Brien ◽  
J. Hall ◽  
A. Miró ◽  
M. Rae ◽  
R. Jehle
Keyword(s):  
Constructed Wetlands ◽  
Social Groups ◽  
High Quality ◽  
Breeding Sites ◽  
Major Threat ◽  
Global Biodiversity ◽  
Urban People ◽  
Sustainable Drainage Systems ◽  
New Habitats

While urbanisation is a major threat to global biodiversity, it also brings opportunities for some species. Sustainable Drainage Systems (SuDS) have been installed in all Scottish cities to reduce flood and pollution risk and they can also offer new habitats for wildlife. We studied SuDS in Inverness and the Scottish Central Belt to assess their value as amphibian breeding sites, habitats, and as places where urban people can experience nature. The nine-year study revealed that many SuDS were of similar ecological quality to wider countryside ponds but that the quality of ponds is not equitably distributed between neighbourhoods inhabited by different socio-economic classes. However, the findings suggest ways to improve the design and management of SuDS for people and nature, making access to high quality ponds available to all social groups.

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