Putting theory to the test: An integrated computational/experimental chemostat model of the tragedy of the commons.

Cooperation via shared public goods is ubiquitous in nature, however, noncontributing social cheaters can exploit the public goods provided by cooperating individuals to gain a fitness advantage. Theory predicts that this dynamic can cause a Tragedy of the Commons, and in particular, a 'Collapsing' Tragedy defined as the extinction of the entire population if the public good is essential. However, there is little empirical evidence of the Collapsing Tragedy in evolutionary biology.

Dispersal Kernels may be Scalable: Implications from a Plant Pathogen.

Aim: Understanding how spatial scale of study affects observed dispersal patterns can provide insights into spatiotemporal population dynamics, particularly in systems with significant long-distance dispersal (LDD). We aimed to investigate the dispersal gradients of two rusts of wheat with spores of similar size, mass, and shape, over multiple spatial scales. We hypothesized that a single dispersal kernel could fit the dispersal from all spatial scales well, and that it would be possible to obtain similar results in spatiotemporal increase of disease when modeling based on differing scales.

Global analysis of a predator-prey model with variable predator search rate.

We consider a modified Holling-type II predator-prey model, based on the premise that the search rate of predators is dependent on the prey density, rather than constant. A complete analysis of the global behavior of the model is presented, and shows that the model exhibits a dichotomy similar to the classical Holling-type II model: either the coexistence steady state is globally stable; or it is unstable, and then a unique, globally stable limit cycle exists. We discuss the similarities, but also important differences between our model and the Holling-type II model.

Division of labor in bacterial populations.

Cooperating behaviors abound across all domains of life, but are vulnerable to invasion by cheaters. An important evolutionary question is to determine mechanisms that stabilize and maintain cooperation levels and prevent population collapse. Policing is one strategy populations may employ to achieve this goal, and it has been observed in many natural populations including microbes.

Strong cooperation or tragedy of the commons in the chemostat.

In [11], a proof of principle was established for the phenomenon of the tragedy of the commons, a center piece for many theories on the evolution of cooperation. A general chemostat model with two species, the cooperator and the cheater, was formulated where the cooperator allocates a portion of the nutrient uptake towards the production of a public good which is needed to digest an externally supplied resource. The cheater does not produce the public good, and instead allocates all nutrient uptake towards its own growth.

Critical thresholds for eventual extinction in randomly disturbed population growth models.

This paper considers several single species growth models featuring a carrying capacity, which are subject to random disturbances that lead to instantaneous population reduction at the disturbance times. This is motivated in part by growing concerns about the impacts of climate change. Our main goal is to understand whether or not the species can persist in the long run.

Tragedy of the commons in the chemostat.

We present a proof of principle for the phenomenon of the tragedy of the commons that is at the center of many theories on the evolution of cooperation. Whereas the tragedy is commonly set in a game theoretical context, and attributed to an underlying Prisoner's Dilemma, we take an alternative approach based on basic mechanistic principles of species growth that does not rely on the specification of payoffs which may be difficult to determine in practice. We establish the tragedy in the context of a general chemostat model with two species, the cooperator and the cheater.

High mortality and enhanced recovery: modelling the countervailing effects of disturbance on population dynamics.

Disturbances cause high mortality in populations while simultaneously enhancing population growth by improving habitats. These countervailing effects make it difficult to predict population dynamics following disturbance events. To address this challenge, we derived a novel form of the logistic growth equation that permits time-varying carrying capacity and growth rate.

The puzzle of partial migration: Adaptive dynamics and evolutionary game theory perspectives.

We consider the phenomenon of partial migration which is exhibited by populations in which some individuals migrate between habitats during their lifetime, but others do not. First, using an adaptive dynamics approach, we show that partial migration can be explained on the basis of negative density dependence in the per capita fertilities alone, provided that this density dependence is attenuated for increasing abundances of the subtypes that make up the population. We present an exact formula for the optimal proportion of migrants which is expressed in terms of the vital rates of migrant and non-migrant subtypes only.

The abundant marine bacterium Pelagibacter simultaneously catabolizes dimethylsulfoniopropionate to the gases dimethyl sulfide and methanethiol.

Marine phytoplankton produce ∼10(9) tonnes of dimethylsulfoniopropionate (DMSP) per year(1,2), an estimated 10% of which is catabolized by bacteria through the DMSP cleavage pathway to the climatically active gas dimethyl sulfide(3,4). SAR11 Alphaproteobacteria (order Pelagibacterales), the most abundant chemo-organotrophic bacteria in the oceans, have been shown to assimilate DMSP into biomass, thereby supplying this cell's unusual requirement for reduced sulfur(5,6). Here, we report that Pelagibacter HTCC1062 produces the gas methanethiol, and that a second DMSP catabolic pathway, mediated by a cupin-like DMSP lyase, DddK, simultaneously shunts as much as 59% of DMSP uptake to dimethyl sulfide production.

Parasite sources and sinks in a patched Ross-Macdonald malaria model with human and mosquito movement: Implications for control.

We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch Ross-Macdonald malaria model with mobile human hosts, mobile vectors, and a heterogeneous environment. We show the existence of a globally stable steady state, and a threshold that determines whether a pathogen is either absent from all patches, or endemic and present at some level in all patches. Each patch is characterized by a local basic reproduction number, whose value predicts whether the disease is cleared or not when the patch is isolated: patches are known as "demographic sinks" if they have a local basic reproduction number less than one, and hence would clear the disease if isolated; patches with a basic reproduction number above one would sustain endemic infection in isolation, and become "demographic sources" of parasites when connected to other patches.

The effectiveness of marine protected areas for predator and prey with varying mobility.

Marine protected areas (MPAs) are regions in the ocean where fishing is restricted or prohibited. Although several measures for MPA performance exist, here we focus on a specific one, namely the ratio of the steady state fish densities inside and outside the MPA. Several 2 patch models are proposed and analyzed mathematically.

Identifying Malaria Transmission Foci for Elimination Using Human Mobility Data.

Humans move frequently and tend to carry parasites among areas with endemic malaria and into areas where local transmission is unsustainable. Human-mediated parasite mobility can thus sustain parasite populations in areas where they would otherwise be absent. Data describing human mobility and malaria epidemiology can help classify landscapes into parasite demographic sources and sinks, ecological concepts that have parallels in malaria control discussions of transmission foci.

Traveling waves in response to a diffusing quorum sensing signal in spatially-extended bacterial colonies.

In the behavior known as quorum sensing (QS), bacteria release diffusible signal molecules known as autoinducers, which by accumulating in the environment induce population-wide changes in gene expression. Although QS has been extensively studied in well-mixed systems, the ability of diffusing QS signals to synchronize gene expression in spatially extended colonies is not well understood. Here we investigate the one-dimensional spatial propagation of QS-circuit activation in a simple, analytically tractable reaction-diffusion model for the LuxR-LuxI circuit, which regulates bioluminescence of the marine bacterium Aliivibrio fischeri.

Dynamical models explaining social balance and evolution of cooperation.

Social networks with positive and negative links often split into two antagonistic factions. Examples of such a split abound: revolutionaries versus an old regime, Republicans versus Democrats, Axis versus Allies during the second world war, or the Western versus the Eastern bloc during the Cold War. Although this structure, known as social balance, is well understood, it is not clear how such factions emerge.

Instability in a generalized Keller-Segel model.

We present a generalized Keller-Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem.

Quorum activation at a distance: spatiotemporal patterns of gene regulation from diffusion of an autoinducer signal.

Quorum sensing (QS) bacteria regulate gene expression collectively by exchanging diffusible signal molecules known as autoinducers. Although QS is often studied in well-stirred laboratory cultures, QS bacteria colonize many physically and chemically heterogeneous environments where signal molecules are transported primarily by diffusion. This raises questions of the effective distance range of QS and the degree to which colony behavior can be synchronized over such distances.

Differential movement and movement bias models for marine protected areas.

Marine protected areas (MPAs) are promoted as a tool to protect overfished stocks and increase fishery yields. Previous models suggested that adult mobility modified effects of MPAs by reducing densities of fish inside reserves, but increasing yields (i.e.

Paradoxical suppression of poly-specific broadly neutralizing antibodies in the presence of strain-specific neutralizing antibodies following HIV infection.

One of the first immunologic responses against HIV infection is the presence of neutralizing antibodies that seem able to inactivate several HIV strains. Moreover, in vitro studies have shown the existence of monoclonal antibodies that exhibit broad crossclade neutralizing potential. Yet their number is low and slow to develop in vivo.

The chemostat with lateral gene transfer.

We investigate the standard chemostat model when lateral gene transfer is taken into account. We will show that when the different genotypes have growth rate functions that are sufficiently close to a common growth rate function, and when the yields of the genotypes are sufficiently close to a common value, then the population evolves to a globally stable steady state, at which all genotypes coexist. These results can explain why the antibiotic-resistant strains persist in the pathogen population.

Conditions for Global Stability of Monotone Tridiagonal Systems with Negative Feedback.

This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincaré-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique steady state is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Two different approaches are discussed to rule out period orbits, one based on direct linearization and another one based on the theory of second additive compound matrices.

Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates.

This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence under the assumption that the rates of the reactions are monotone functions of the concentrations of their reactants. This is satisfied for, yet not restricted to, the most common choices of the reaction kinetics such as mass action, Michaelis-Menten and Hill kinetics.

Senescence and antibiotic resistance in an age-structured population model.

Different theories have been proposed to understand the growing problem of antibiotic resistance of microbial populations. Here we investigate a model that is based on the hypothesis that senescence is a possible explanation for the existence of so-called persister cells which are resistant to antibiotic treatment. We study a chemostat model with a microbial population which is age-structured and show that if the growth rates of cells in different age classes are sufficiently close to a scalar multiple of a common growth rate, then the population will globally stabilize at a coexistence steady state.

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle.