Hawks and Doves on Small-World Networks

We explore the Hawk-Dove game on networks with topologies ranging from regular lattices to random graphs with small-world networks in between. This is done by means of computer simulations using several update rules for the population evolutionary dynamics. We find the overall result that cooperation is sometimes inhibited and sometimes enhanced in those network structures, with respect to the mixing population case. The differences are due to different update rules and depend on the gain-to-cost ratio. We analyse and qualitatively explain this behavior by using local topological arguments.Comment: 12 pages, 8 figure

Stochastic population growth in spatially heterogeneous environments

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study the following model for population abundances in $n$ patches: the conditional law of $X_{t+dt}$ given $X_t=x$ is such that when $dt$ is small the conditional mean of $X_{t+dt}^i-X_t^i$ is approximately $[x^i\mu_i+\sum_j(x^j D_{ji}-x^i D_{ij})]dt$, where $X_t^i$ and $\mu_i$ are the abundance and per capita growth rate in the $i$-th patch respectivly, and $D_{ij}$ is the dispersal rate from the $i$-th to the $j$-th patch, and the conditional covariance of $X_{t+dt}^i-X_t^i$ and $X_{t+dt}^j-X_t^j$ is approximately $x^i x^j \sigma_{ij}dt$. We show for such a spatially extended population that if $S_t=(X_t^1+...+X_t^n)$ is the total population abundance, then $Y_t=X_t/S_t$, the vector of patch proportions, converges in law to a random vector $Y_\infty$ as $t\to\infty$, and the stochastic growth rate $\lim_{t\to\infty}t^{-1}\log S_t$ equals the space-time average per-capita growth rate \sum_i\mu_i\E[Y_\infty^i] experienced by the population minus half of the space-time average temporal variation \E[\sum_{i,j}\sigma_{ij}Y_\infty^i Y_\infty^j] experienced by the population. We derive analytic results for the law of $Y_\infty$, find which choice of the dispersal mechanism $D$ produces an optimal stochastic growth rate for a freely dispersing population, and investigate the effect on the stochastic growth rate of constraints on dispersal rates. Our results provide fundamental insights into "ideal free" movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology.Comment: 47 pages, 4 figure

The stability of ecosystems: a brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system, thereby collapsing the trophic interaction, a phenomenon referred to as "the paradox of enrichment". After it was first proposed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator-prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form, inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that, although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms, which may differ among systems, need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models

The Evolutionary Dynamics of a Rapidly Mutating Virus within and between Hosts: The Case of Hepatitis C Virus

Many pathogens associated with chronic infections evolve so rapidly that strains found late in an infection have little in common with the initial strain. This raises questions at different levels of analysis because rapid within-host evolution affects the course of an infection, but it can also affect the possibility for natural selection to act at the between-host level. We present a nested approach that incorporates within-host evolutionary dynamics of a rapidly mutating virus (hepatitis C virus) targeted by a cellular cross-reactive immune response, into an epidemiological perspective. The viral trait we follow is the replication rate of the strain initiating the infection. We find that, even for rapidly evolving viruses, the replication rate of the initial strain has a strong effect on the fitness of an infection. Moreover, infections caused by slowly replicating viruses have the highest infection fitness (i.e., lead to more secondary infections), but strains with higher replication rates tend to dominate within a host in the long-term. We also study the effect of cross-reactive immunity and viral mutation rate on infection life history traits. For instance, because of the stochastic nature of our approach, we can identify factors affecting the outcome of the infection (acute or chronic infections). Finally, we show that anti-viral treatments modify the value of the optimal initial replication rate and that the timing of the treatment administration can have public health consequences due to within-host evolution. Our results support the idea that natural selection can act on the replication rate of rapidly evolving viruses at the between-host level. It also provides a mechanistic description of within-host constraints, such as cross-reactive immunity, and shows how these constraints affect the infection fitness. This model raises questions that can be tested experimentally and underlines the necessity to consider the evolution of quantitative traits to understand the outcome and the fitness of an infection

Implications of CTL-Mediated Killing of HIV-Infected Cells during the Non-Productive Stage of Infection

Patients infected with HIV exhibit orders of magnitude differences in their set-point levels of the plasma viral load. As to what extent this variation is due to differences in the efficacy of the cytotoxic T lymphocyte (CTL) response in these patients is unclear. Several studies have shown that HIV-infected CD4+ T cells also present viral epitopes that are recognized by CTLs before the productive stage of infection, i.e., during the intracellular eclipse phase before the infected cell starts to produce new viral particles. Here, we use mathematical modeling to investigate the potential impact of early killing of HIV-infected cells on viral replication. We suggest that the majority of CTL-mediated killing could occur during the viral eclipse phase, and that the killing of virus-producing cells could be substantially lower at later stages due to MHC-I-down-regulation. Such a mechanism is in agreement with several experimental observations that include CD8+ T cell depletion and antiretroviral drug treatment. This indicates a potentially important role of CTL-mediated killing during the non-productive stage of HIV-infected cells

Polygenic burden in focal and generalized epilepsies

Rare genetic variants can cause epilepsy, and genetic testing has been widely adopted for severe, paediatric-onset epilepsies. The phenotypic consequences of common genetic risk burden for epilepsies and their potential future clinical applications have not yet been determined. Using polygenic risk scores (PRS) from a European-ancestry genome-wide association study in generalized and focal epilepsy, we quantified common genetic burden in patients with generalized epilepsy (GE-PRS) or focal epilepsy (FE-PRS) from two independent non-Finnish European cohorts (Epi25 Consortium, n = 5705; Cleveland Clinic Epilepsy Center, n = 620; both compared to 20 435 controls). One Finnish-ancestry population isolate (Finnish-ancestry Epi25, n = 449; compared to 1559 controls), two European-ancestry biobanks (UK Biobank, n = 383 656; Vanderbilt biorepository, n = 49 494), and one Japaneseancestry biobank (BioBank Japan, n = 168 680) were used for additional replications. Across 8386 patients with epilepsy and 622 212 population controls, we found and replicated significantly higher GE-PRS in patients with generalized epilepsy of European-ancestry compared to patients with focal epilepsy (Epi25: P = 1.64 710-15; Cleveland: P = 2.85 710-4; Finnish-ancestry Epi25: P = 1.80 710-4) or population controls (Epi25: P = 2.35 710-70; Cleveland: P = 1.43 710-7; Finnish-ancestry Epi25: P = 3.11 710-4; UK Biobank and Vanderbilt biorepository meta-analysis: P = 7.99 710-4). FE-PRS were significantly higher in patients with focal epilepsy compared to controls in the non-Finnish, non-biobank cohorts (Epi25: P = 5.74 710-19; Cleveland: P = 1.69 710-6). European ancestry-derived PRS did not predict generalized epilepsy or focal epilepsy in Japanese-ancestry individuals. Finally, we observed a significant 4.6-fold and a 4.5-fold enrichment of patients with generalized epilepsy compared to controls in the top 0.5% highest GE-PRS of the two non-Finnish European cohorts (Epi25: P = 2.60 710-15; Cleveland: P = 1.39 710-2). We conclude that common variant risk associated with epilepsy is significantly enriched in multiple cohorts of patients with epilepsy compared to controls-in particular for generalized epilepsy. As sample sizes and PRS accuracy continue to increase with further common variant discovery, PRS could complement established clinical biomarkers and augment genetic testing for patient classification, comorbidity research, and potentially targeted treatment

Evidence of HIV-1 adaptation to host HLA alleles following chimp-to-human transmission

<p>Abstract</p> <p>Background</p> <p>The cytotoxic T-lymphocyte immune response is important in controlling HIV-1 replication in infected humans. In this immune pathway, viral peptides within infected cells are presented to T-lymphocytes by the polymorphic human leukocyte antigens (HLA). HLA alleles exert selective pressure on the peptide regions and immune escape mutations that occur at some of the targeted sites can enable the virus to adapt to the infected host. The pattern of ongoing immune escape and reversion associated with several human HLA alleles has been studied extensively. Such mutations revert upon transmission to a host without the HLA allele because the escape mutation incurs a fitness cost. However, to-date there has been little attempt to study permanent loss of CTL epitopes due to escape mutations without an effect on fitness.</p> <p>Results</p> <p>Here, we set out to determine the extent of adaptation of HIV-1 to three well-characterized HLA alleles during the initial exposure of the virus to the human cytotoxic immune responses following transmission from chimpanzee. We generated a chimpanzee consensus sequence to approximate the virus sequence that was initially transmitted to the human host and used a method based on peptide binding affinity to HLA crystal structures to predict peptides that were potentially targeted by the HLA alleles on this sequence. Next, we used codon-based phylogenetic models to quantify the average selective pressure that acted on these regions during the period immediately following the zoonosis event, corresponding to the branch of the phylogenetic tree leading to the common ancestor of all of the HIV-1 sequences. Evidence for adaptive evolution during this period was observed at regions recognised by HLA A*6801 and A*0201, both of which are common in African populations. No evidence of adaptive evolution was observed at sites targeted by HLA-B*2705, which is a rare allele in African populations.</p> <p>Conclusion</p> <p>Our results suggest that the ancestral HIV-1 virus experienced a period of positive selective pressure due to immune responses associated with HLA alleles that were common in the infected human population. We propose that this resulted in permanent escape from immune responses targeting unconstrained regions of the virus.</p

Variable Fitness Impact of HIV-1 Escape Mutations to Cytotoxic T Lymphocyte (CTL) Response

Human lymphocyte antigen (HLA)-restricted CD8+ cytotoxic T lymphocytes (CTL) target and kill HIV-infected cells expressing cognate viral epitopes. This response selects for escape mutations within CTL epitopes that can diminish viral replication fitness. Here, we assess the fitness impact of escape mutations emerging in seven CTL epitopes in the gp120 Env and p24 Gag coding regions of an individual followed longitudinally from the time of acute HIV-1 infection, as well as some of these same epitopes recognized in other HIV-1-infected individuals. Nine dominant mutations appeared in five gp120 epitopes within the first year of infection, whereas all four mutations found in two p24 epitopes emerged after nearly two years of infection. These mutations were introduced individually into the autologous gene found in acute infection and then placed into a full-length, infectious viral genome. When competed against virus expressing the parental protein, fitness loss was observed with only one of the nine gp120 mutations, whereas four had no effect and three conferred a slight increase in fitness. In contrast, mutations conferring CTL escape in the p24 epitopes significantly decreased viral fitness. One particular escape mutation within a p24 epitope was associated with reduced peptide recognition and high viral fitness costs but was replaced by a fitness-neutral mutation. This mutation appeared to alter epitope processing concomitant with a reduced CTL response. In conclusion, CTL escape mutations in HIV-1 Gag p24 were associated with significant fitness costs, whereas most escape mutations in the Env gene were fitness neutral, suggesting a balance between immunologic escape and replicative fitness costs

Sub-genic intolerance, ClinVar, and the epilepsies: A whole-exome sequencing study of 29,165 individuals

Both mild and severe epilepsies are influenced by variants in the same genes, yet an explanation for the resulting phenotypic variation is unknown. As part of the ongoing Epi25 Collaboration, we performed a whole-exome sequencing analysis of 13,487 epilepsy-affected individuals and 15,678 control individuals. While prior Epi25 studies focused on gene-based collapsing analyses, we asked how the pattern of variation within genes differs by epilepsy type. Specifically, we compared the genetic architectures of severe developmental and epileptic encephalopathies (DEEs) and two generally less severe epilepsies, genetic generalized epilepsy and non-acquired focal epilepsy (NAFE). Our gene-based rare variant collapsing analysis used geographic ancestry-based clustering that included broader ancestries than previously possible and revealed novel associations. Using the missense intolerance ratio (MTR), we found that variants in DEE-affected individuals are in significantly more intolerant genic sub-regions than those in NAFE-affected individuals. Only previously reported pathogenic variants absent in available genomic datasets showed a significant burden in epilepsy-affected individuals compared with control individuals, and the ultra-rare pathogenic variants associated with DEE were located in more intolerant genic sub-regions than variants associated with non-DEE epilepsies. MTR filtering improved the yield of ultra-rare pathogenic variants in affected individuals compared with control individuals. Finally, analysis of variants in genes without a disease association revealed a significant burden of loss-of-function variants in the genes most intolerant to such variation, indicating additional epilepsy-risk genes yet to be discovered. Taken together, our study suggests that genic and sub-genic intolerance are critical characteristics for interpreting the effects of variation in genes that influence epilepsy