Oblique Transmission, Conformity, and Preference in the Evolution of Altruism

The evolution of altruism is frequently studied using models of non-random assortment, including kin selection. In genetic kin selection models, under certain assumptions including additive costs and benefits, the criterion for altruism to invade a population is Hamilton's rule. Deviations from Hamilton's rule occur when vertical transmission has cultural and genetic components, or when costs and benefits are combined multiplicatively. Here, we include oblique and vertical cultural transmission and genetic transmission in four models--two forms of parent-to-offspring altruism, sibling-to-sibling altruism, and altruism between offspring that meet assortatively--under additive or multiplicative assumptions. Oblique transmission may be conformist (anti-conformist), where the probability that an individual acquires a more common cultural variant is greater (less) than its frequency. Inclusion of conformist or anti-conformist oblique transmission may reduce or increase the threshold for invasion by altruism relative to Hamilton's rule. Thresholds for invasion by altruism are lower with anti-conformity than with conformity, and lower or the same with additive rather than multiplicative fitness components. Invasion by an allele that increases the preference for altruism does not depend on oblique phenotypic transmission, and with sibling-to-sibling altruism, this allele's invasion threshold can be higher with additive rather than multiplicative fitnesses.

INVESTIGATING THE ROLE OF WITHIN- AND BETWEEN-PATCH MOVEMENT IN A DYNAMIC MODEL OF DISEASE SPREAD

The impact of human mobility on the spreading of disease in a metapopulation is emphasized on interconnecting between patches, whereas the current volume of movement within the local population is usually neglected. Here, the role of internal commuters is taken into account by two means, a local transmission rate and the volume of internal commuters. Dynamic model of human mobility in the metapopulation with gravity coupling is presented. In conjunction with the disease spreading, the impact on invasion threshold and epidemic final size are analyzed. For two-patch model, we show that under fixing parameters in gravity model, the existence of invasion threshold depends on the difference of local transmission rates and the proportion of internal commuters between two patches. For a fully connected network with an identical transmission rate, the difference in patch final sizes is driven by patch distribution of internal commuters. By neglecting the effect of spatial variation in a simple core–satellite model, we show that the heterogeneity of internal commuters and gravity coupling induce a complex pattern of threshold, which depend mostly on the exponent in gravity model, and are responsible for the differences among local epidemic sizes.

Modelling Vector Transmission and Epidemiology of Co-Infecting Plant Viruses

Co-infection of plant hosts by two or more viruses is common in agricultural crops and natural plant communities. A variety of models have been used to investigate the dynamics of co-infection which track only the disease status of infected and co-infected plants, and which do not explicitly track the density of inoculative vectors. Much less attention has been paid to the role of vector transmission in co-infection, that is, acquisition and inoculation and their synergistic and antagonistic interactions. In this investigation, a general epidemiological model is formulated for one vector species and one plant species with potential co-infection in the host plant by two viruses. The basic reproduction number provides conditions for successful invasion of a single virus. We derive a new invasion threshold which provides conditions for successful invasion of a second virus. These two thresholds highlight some key epidemiological parameters important in vector transmission. To illustrate the flexibility of our model, we examine numerically two special cases of viral invasion. In the first case, one virus species depends on an autonomous virus for its successful transmission and in the second case, both viruses are unable to invade alone but can co-infect the host plant when prevalence is high.

Design and analysis of CRISPR-based underdominance toxin-antidote gene drives

ABSTRACTCRISPR gene drive systems offer a mechanism for transmitting a desirable transgene throughout a population for purposes ranging from vector-borne disease control to invasive species suppression. In this simulation study, we assess the performance of several CRISPR-based underdominance gene drive constructs employing toxin-antidote principles. These drives disrupt the wild-type version of an essential gene using a CRISPR nuclease (the toxin) while simultaneously carrying a recoded version of the gene (the antidote). Drives of this nature allow for releases that could be potentially confined to a desired geographic location. This is because such drives have a nonzero invasion threshold frequency, referring to the critical frequency required for the drive to spread through the population. We model drives which target essential genes that are either haplosufficient or haplolethal, using nuclease promoters with expression restricted to the germline, promoters that additionally result in cleavage activity in the early embryo from maternal deposition, and promoters that have ubiquitous somatic expression. We also study several possible drive architectures, considering both “same-site” and “distant-site” systems, as well as several reciprocally targeting drives. Together, these drive variants provide a wide range of invasion threshold frequencies and options for both population modification and suppression. Our results suggest that CRISPR toxin-antidote underdominance drive systems could allow for the design of highly flexible and potentially confinable gene drive strategies.

Modeling the Effects of Resource-Driven Immune Defense on Parasite Transmission in Heterogeneous Host Populations

Individuals experience heterogeneous environmental conditions that can affect within-host processes such as immune defense against parasite infection. Variation among individuals in parasite shedding can cause some hosts to contribute disproportionately to population-level transmission, but we currently lack mechanistic theory that predicts when environmental conditions can result in large disease outbreaks through the formation of immunocompromised superspreading individuals. Here, I present a within-host model of a microparasite’s interaction with the immune system that links an individual host’s resource intake to its infectious period. For environmental scenarios driving population-level heterogeneity in resource intake (resource scarcity and resource subsidy relative to baseline availability), I generate a distribution of infectious periods and simulate epidemics on these heterogeneous populations. I find that resource scarcity can result in large epidemics through creation of superspreading individuals, while resource subsidies can reduce or prevent transmission of parasites close to their invasion threshold by homogenizing resource allocation to immune defense. Importantly, failure to account for heterogeneity in competence can result in under-prediction of outbreak size, especially when parasites are close to their invasion threshold. More generally, this framework suggests that differences in conditions experienced by individual hosts can lead to superspreading via differences in resource allocation to immune defense alone, even in the absence of other heterogeneites such as host contacts.

Experimental evidence of a pathogen invasion threshold

Host density thresholds to pathogen invasion separate regions of parameter space corresponding to endemic and disease-free states. The host density threshold is a central concept in theoretical epidemiology and a common target of human and wildlife disease control programmes, but there is mixed evidence supporting the existence of thresholds, especially in wildlife populations or for pathogens with complex transmission modes (e.g. environmental transmission). Here, we demonstrate the existence of a host density threshold for an environmentally transmitted pathogen by combining an epidemiological model with a microcosm experiment. Experimental epidemics consisted of replicate populations of naive crustacean zooplankton ( Daphnia dentifera ) hosts across a range of host densities (20–640 hosts l −1 ) that were exposed to an environmentally transmitted fungal pathogen ( Metschnikowia bicuspidata ). Epidemiological model simulations, parametrized independently of the experiment, qualitatively predicted experimental pathogen invasion thresholds. Variability in parameter estimates did not strongly influence outcomes, though systematic changes to key parameters have the potential to shift pathogen invasion thresholds. In summary, we provide one of the first clear experimental demonstrations of pathogen invasion thresholds in a replicated experimental system, and provide evidence that such thresholds may be predictable using independently constructed epidemiological models.

Bifurcation Analysis of a Chemostat Model of Plasmid-Bearing and Plasmid-Free Competition with Pulsed Input

A chemostat model of plasmid-bearing and plasmid-free competition with pulsed input is proposed. The invasion threshold of the plasmid-bearing and plasmid-free organisms is obtained according to the stability of the boundary periodic solution. By use of standard techniques of bifurcation theory, the periodic oscillations in substrate, plasmid-bearing, and plasmid-free organisms are shown when some conditions are satisfied. Our results can be applied to control bioreactor aimed at producing commercial producers through genetically altered organisms.

Heterogeneity in susceptible–infected–removed (SIR) epidemics on lattices

The percolation paradigm is widely used in spatially explicit epidemic models where disease spreads between neighbouring hosts. It has been successful in identifying epidemic thresholds for invasion, separating non-invasive regimes, where the disease never invades the system, from invasive regimes where the probability of invasion is positive. However, its power is mainly limited to homogeneous systems. When heterogeneity (environmental stochasticity) is introduced, the value of the epidemic threshold is, in general, not predictable without numerical simulations. Here, we analyse the role of heterogeneity in a stochastic susceptible–infected–removed epidemic model on a two-dimensional lattice. In the homogeneous case, equivalent to bond percolation, the probability of invasion is controlled by a single parameter, the transmissibility of the pathogen between neighbouring hosts. In the heterogeneous model, the transmissibility becomes a random variable drawn from a probability distribution. We investigate how heterogeneity in transmissibility influences the value of the invasion threshold, and find that the resilience of the system to invasion can be suitably described by two control parameters, the mean and variance of the transmissibility. We analyse a two-dimensional phase diagram, where the threshold is represented by a phase boundary separating an invasive regime in the high-mean, low-variance region from a non-invasive regime in the low-mean, high-variance region of the parameter space. We thus show that the percolation paradigm can be extended to the heterogeneous case. Our results have practical implications for the analysis of disease control strategies in realistic heterogeneous epidemic systems.