How do classroom-turnover times depend on lecture-hall size?

Academic spaces in colleges and universities span classrooms for 10 students to lecture halls that hold over 600 people. During the break between consecutive classes, students from the first class must leave and the new class must find their desks, regardless of whether the room holds 10 or 600 people. Here we address the question of how the size of large lecture halls affects classroom-turnover times, focusing on non-emergency settings. By adapting the established social-force model, we treat students as individuals who interact and move through classrooms to reach their destinations. We find that social interactions and the separation time between consecutive classes strongly influence how long it takes entering students to reach their desks, and that these effects are more pronounced in larger lecture halls. While the median time that individual students must travel increases with decreased separation time, we find that shorter separation times lead to shorter classroom-turnover times overall. This suggests that the effects of scheduling gaps and lecture-hall size on classroom dynamics depends on the perspective-individual student or whole class-that one chooses to take.

Evolutionary dynamics within and among competing groups.

Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible for profound transitions in evolutionary history, including the origin of cellular life, multicellular life, and even societies. Here, we synthesize a growing literature that extends evolutionary game theory to describe multilevel evolutionary dynamics, using nested birth-death processes and partial differential equations to model natural selection acting on competition within and among groups of individuals. We analyze how mechanisms known to promote cooperation within a single group-including assortment, reciprocity, and population structure-alter evolutionary outcomes in the presence of competition among groups. We find that population structures most conducive to cooperation in multiscale systems can differ from those most conducive within a single group. Likewise, for competitive interactions with a continuous range of strategies we find that among-group selection may fail to produce socially optimal outcomes, but it can nonetheless produce second-best solutions that balance individual incentives to defect with the collective incentives for cooperation. We conclude by describing the broad applicability of multiscale evolutionary models to problems ranging from the production of diffusible metabolites in microbes to the management of common-pool resources in human societies.

Social dilemmas of sociality due to beneficial and costly contagion.

Levels of sociality in nature vary widely. Some species are solitary; others live in family groups; some form complex multi-family societies. Increased levels of social interaction can allow for the spread of useful innovations and beneficial information, but can also facilitate the spread of harmful contagions, such as infectious diseases. It is natural to assume that these contagion processes shape the evolution of complex social systems, but an explicit account of the dynamics of sociality under selection pressure imposed by contagion remains elusive. We consider a model for the evolution of sociality strategies in the presence of both a beneficial and costly contagion. We study the dynamics of this model at three timescales: using a susceptible-infectious-susceptible (SIS) model to describe contagion spread for given sociality strategies, a replicator equation to study the changing fractions of two different levels of sociality, and an adaptive dynamics approach to study the long-time evolution of the population level of sociality. For a wide range of assumptions about the benefits and costs of infection, we identify a social dilemma: the evolutionarily-stable sociality strategy (ESS) is distinct from the collective optimum-the level of sociality that would be best for all individuals. In particular, the ESS level of social interaction is greater (respectively less) than the social optimum when the good contagion spreads more (respectively less) readily than the bad contagion. Our results shed light on how contagion shapes the evolution of social interaction, but reveals that evolution may not necessarily lead populations to social structures that are good for any or all.

Developing a novel device, Eggcell, to improve temperature stability during oocyte collection for IVF.

RESEARCH QUESTION: What temperature fluctuations are oocytes exposed to during oocyte retrieval? Can an alternative method of oocyte retrieval be designed to minimize these fluctuations? DESIGN: Mock oocyte retrieval procedures were performed to investigate the change in temperature when the follicular fluid is drained into collection tubes and when the fluid is subsequently poured into dishes to allow identification of the cumulus-oocyte complex (COC). A new device, the Eggcell, has been designed that addresses the problem of these temperature fluctuations. To confirm its safety and demonstrate the clinical applicability of Eggcell, laboratory validation was performed prior to use with human participants (n = 15). RESULTS: Eggcell meets its design specification to provide temperature stability within the physiological range for aspirated follicular fluid. The COC can be successfully retained within the chamber (n = 180) without evidence of loss or damage to the oocytes or compromise of fertilization rate, blastocyst development or clinical outcome. CONCLUSIONS: This study has demonstrated the successful first stages of development of a new medical device. Further studies are needed for comparative evaluation of clinical outcome with standard technology.

Assortment and Reciprocity Mechanisms for Promotion of Cooperation in a Model of Multilevel Selection.

In the study of the evolution of cooperation, many mechanisms have been proposed to help overcome the self-interested cheating that is individually optimal in the Prisoners' Dilemma game. These mechanisms include assortative or networked social interactions, other-regarding preferences considering the payoffs of others, reciprocity rules to establish cooperation as a social norm, and multilevel selection involving simultaneous competition between individuals favoring cheaters and competition between groups favoring cooperators. In this paper, we build on recent work studying PDE replicator equations for multilevel selection to understand how within-group mechanisms of assortment, other-regarding preferences, and both direct and indirect reciprocity can help to facilitate cooperation in concert with evolutionary competition between groups. We consider a group-structured population in which interactions between individuals consist of Prisoners' Dilemma games and study the dynamics of multilevel competition determined by the payoffs individuals receive when interacting according to these within-group mechanisms. We find that the presence of each of these mechanisms acts synergistically with multilevel selection for the promotion of cooperation, decreasing the strength of between-group competition required to sustain long-time cooperation and increasing the collective payoff achieved by the population. However, we find that only other-regarding preferences allow for the achievement of socially optimal collective payoffs for Prisoners' Dilemma games in which average payoff is maximized by an intermediate mix of cooperators and defectors. For the other three mechanisms, the multilevel dynamics remain susceptible to a shadow of lower-level selection, as the collective outcome fails to exceed the payoff of the all-cooperator group.

A PDE Model for Protocell Evolution and the Origin of Chromosomes via Multilevel Selection.

The evolution of complex cellular life involved two major transitions: the encapsulation of self-replicating genetic entities into cellular units and the aggregation of individual genes into a collectively replicating genome. In this paper, we formulate a minimal model of the evolution of proto-chromosomes within protocells. We model a simple protocell composed of two types of genes: a "fast gene" with an advantage for gene-level self-replication and a "slow gene" that replicates more slowly at the gene level, but which confers an advantage for protocell-level reproduction. Protocell-level replication capacity depends on cellular composition of fast and slow genes. We use a partial differential equation to describe how the composition of genes within protocells evolves over time under within-cell and between-cell competition, considering an infinite population of protocells that each contain infinitely many genes. We find that the gene-level advantage of fast replicators casts a long shadow on the multilevel dynamics of protocell evolution: no level of between-protocell competition can produce coexistence of the fast and slow replicators when the two genes are equally needed for protocell-level reproduction. By introducing a "dimer replicator" consisting of a linked pair of the slow and fast genes, we show analytically that coexistence between the two genes can be promoted in pairwise multilevel competition between fast and dimer replicators, and provide numerical evidence for coexistence in trimorphic competition between fast, slow, and dimer replicators. Our results suggest that dimerization, or the formation of a simple chromosome-like dimer replicator, can help to overcome the shadow of lower-level selection and work in concert with deterministic multilevel selection in protocells featuring high gene copy number to allow for the coexistence of two genes that are complementary at the protocell level but compete at the level of individual gene-level replication. These results for the PDE model complement existing results on the benefits of dimerization in the case of low genetic copy number, for which it has been shown that genetic linkage can help to overcome the stochastic loss of necessary genetic templates.

Long-time behavior of a PDE replicator equation for multilevel selection in group-structured populations.

In many biological systems, natural selection acts simultaneously on multiple levels of organization. This scenario typically presents an evolutionary conflict between the incentive of individuals to cheat and the collective incentive to establish cooperation within a group. Generalizing previous work on multilevel selection in evolutionary game theory, we consider a hyperbolic PDE model of a group-structured population, in which members within a single group compete with each other for individual-level replication; while the group also competes against other groups for group-level replication. We derive a threshold level of the relative strength of between-group competition such that defectors take over the population below the threshold while cooperation persists in the long-time population above the threshold. Under stronger assumptions on the initial distribution of group compositions, we further prove that the population converges to a steady state density supporting cooperation for between-group selection strength above the threshold. We further establish long-time bounds on the time-average of the collective payoff of the population, showing that the long-run population cannot outperform the payoff of a full-cooperator group even in the limit of infinitely-strong between-group competition. When the group replication rate is maximized by an intermediate level of within-group cooperation, individual-level selection casts a long shadow on the dynamics of multilevel selection: no level of between-group competition can erase the effects of the individual incentive to defect. We further extend our model to study the case of multiple types of groups, showing how the games that groups play can coevolve with the level of cooperation.

Analysis of Multilevel Replicator Dynamics for General Two-Strategy Social Dilemma.

Here, we consider a game-theoretic model of multilevel selection in which individuals compete based on their payoff and groups also compete based on the average payoff of group members. Our focus is on multilevel social dilemmas: games in which individuals are best off cheating, while groups of individuals do best when composed of many cooperators. We analyze the dynamics of the two-level replicator dynamics, a nonlocal hyperbolic PDE describing deterministic birth-death dynamics for both individuals and groups. While past work on such multilevel dynamics has restricted attention to scenarios with exactly solvable within-group dynamics, we use comparison principles and an invariant property of the tail of the population distribution to extend our analysis to all possible two-player, two-strategy social dilemmas. In the Stag-Hunt and similar games with coordination thresholds, we show that any amount of between-group competition allows for fixation of cooperation in the population. For the prisoners' dilemma and Hawk-Dove game, we characterize the threshold level of between-group selection dividing a regime in which the population converges to a delta function at the equilibrium of the within-group dynamics from a regime in which between-group competition facilitates the existence of steady-state densities supporting greater levels of cooperation. In particular, we see that the threshold selection strength and average payoff at steady state depend on a tug-of-war between the individual-level incentive to be a defector in a many-cooperator group and the group-level incentive to have many cooperators over many defectors. We also find that lower-level selection casts a long shadow: If groups are best off with a mix of cooperators and defectors, then there will always be fewer cooperators than optimal at steady state, even in the limit of infinitely strong competition between groups.

The replicator dynamics for multilevel selection in evolutionary games.

We consider a stochastic model for evolution of group-structured populations in which interactions between group members correspond to the Prisoner's Dilemma or the Hawk-Dove game. Selection operates at two organization levels: individuals compete with peer group members based on individual payoff, while groups also compete with other groups based on average payoff of group members. In the Prisoner's Dilemma, this creates a tension between the two levels of selection, as defectors are favored at the individual level, whereas groups with at least some cooperators outperform groups of defectors at the between-group level. In the limit of infinite group size and infinite number of groups, we derive a non-local PDE that describes the probability distribution of group compositions in the population. For special families of payoff matrices, we characterize the long-time behavior of solutions of our equation, finding a threshold intensity of between-group selection required to sustain density steady states and the survival of cooperation. When all-cooperator groups are most fit, the average and most abundant group compositions at steady state range from featuring all-defector groups when individual-level selection dominates to featuring all-cooperator groups when group-level selection dominates. When the most fit groups have a mix of cooperators and defectors, then the average and most abundant group compositions always feature a smaller fraction of cooperators than required for the optimal mix, even in the limit where group-level selection is infinitely stronger than individual-level selection. In such cases, the conflict between the two levels of selection cannot be decoupled, and cooperation cannot be sustained at all in the case where between-group competition favors an even mix of cooperators and defectors.

Cellular and humoral immunity in a wild mammal: Variation with age & sex and association with overwinter survival.

Immune defenses are expected to be crucial for survival under the considerable parasite pressures experienced by wild animals. However, our understanding of the association between immunity and fitness in nature remains limited due to both the complexity of the vertebrate immune system and the often-limited availability of immune reagents in nonmodel organisms. Here, we use methods and reagents developed by veterinary researchers for domestic ungulates on blood samples collected from a wild Soay sheep population, to evaluate an unusually broad panel of immune parameters. Our evaluation included different innate and acquired immune cell types as well as nematode parasite-specific antibodies of different isotypes. We test how these markers correlate with one another, how they vary with age-group and sex, and, crucially, whether they predict overwinter survival either within or among demographic groups. We found anticipated patterns of variation in markers with age, associated with immune development, and once these age trends were accounted for, correlations among our 11 immune markers were generally weak. We found that females had higher proportions of naïve T cells and gamma-delta T cells than males, independent of age, while our other markers did not differ between sexes. Only one of our 11 markers predicted overwinter survival: sheep with higher plasma levels of anti-nematode IgG antibodies were significantly more likely to survive the subsequent high mortality winter, independent of age, sex, or weight. This supports a previous finding from this study system using a different set of samples and shows that circulating antibody levels against ecologically relevant parasites in natural systems represent an important parameter of immune function and may be under strong natural selection. Our data provide rare insights into patterns of variation among age- and sex groups in different T-cell subsets and antibody levels in the wild, and suggest that certain types of immune response-notably those likely to be repeatable within individuals and linked to resistance to ecologically relevant parasites-may be most informative for research into the links between immunity and fitness under natural conditions.

Assortment and the evolution of cooperation in a Moran process with exponential fitness.

We study the evolution of cooperation in a finite population interacting according to a simple model of like-with-like assortment. Evolution proceeds as a Moran process, and payoffs from the underlying cooperator-defector game are translated to positive fitnesses by an exponential transformation. These evolutionary dynamics can arise, for example, in a nest-structured population with rare migration. The use of the exponential transformation, rather than the usual linear one, is appropriate when interactions have multiplicative fitness effects, and allows for a tractable characterisation of the effect of assortment on the evolution of cooperation. We define two senses in which a greater degree of assortment can favour the evolution of cooperation, the first stronger than the second: (i) greater assortment increases, at all population states, the probability that the number of cooperators increases, relative to the probability that the number of defectors increases; and (ii) greater assortment increases the fixation probability of cooperation, relative to that of defection. We show that, by the stronger definition, greater assortment favours the evolution of cooperation for a subset of cooperative dilemmas: prisoners' dilemmas, snowdrift games, stag-hunt games, and some prisoners' delight games. For other cooperative dilemmas, greater assortment favours cooperation by the weak definition, but not by the strong definition. We also show that increasing assortment expands the set of games in which cooperation dominates the evolutionary dynamics. Our results hold for any strength of selection.

Beyond Contact Tracing: Community-Based Early Detection for Ebola Response.

INTRODUCTION: The 2014 Ebola outbreak in West Africa raised many questions about the control of infectious disease in an increasingly connected global society. Limited availability of contact information made contact tracing diffcult or impractical in combating the outbreak.  METHODS: We consider the development of multi-scale public health strategies that act on individual and community levels. We simulate policies for community-level response aimed at early screening all members of a community, as well as travel restrictions to prevent inter-community transmission.  RESULTS: Our analysis shows the policies to be effective even at a relatively low level of compliance and for a variety of local and long range contact transmission networks. In our simulations, 40% of individuals conforming to these policies is enough to stop the outbreak. Simulations with a 50% compliance rate are consistent with the case counts in Liberia during the period of rapid decline after mid September, 2014. We also find the travel restriction to be effective at reducing the risks associated with compliance substantially below the 40% level, shortening the outbreak and enabling efforts to be focused on affected areas.  DISCUSSION: Our results suggest that the multi-scale approach can be used to further evolve public health strategy for defeating emerging epidemics.

Meiosis and maternal aging: insights from aneuploid oocytes and trisomy births.

In most organisms, genome haploidization requires reciprocal DNA exchanges (crossovers) between replicated parental homologs to form bivalent chromosomes. These are resolved to their four constituent chromatids during two meiotic divisions. In female mammals, bivalents are formed during fetal life and remain intact until shortly before ovulation. Extending this period beyond ∼35 years greatly increases the risk of aneuploidy in human oocytes, resulting in a dramatic increase in infertility, miscarriage, and birth defects, most notably trisomy 21. Bivalent chromosomes are stabilized by cohesion between sister chromatids, which is mediated by the cohesin complex. In mouse oocytes, cohesin becomes depleted from chromosomes during female aging. Consistent with this, premature loss of centromeric cohesion is a major source of aneuploidy in oocytes from older women. Here, we propose a mechanistic framework to reconcile data from genetic studies on human trisomy and oocytes with recent advances in our understanding of the molecular mechanisms of chromosome segregation during meiosis in model organisms.

Cellular response to the deposition of diesel exhaust particle aerosols onto human lung cells grown at the air-liquid interface by inertial impaction.

The pathogenesis of disease resulting from exposure to diesel exhaust particles (DEP) is often studied using cultured lung cells. Frequently, researchers expose cells to DEP by spiking a suspension of particles in liquid onto the apical surface. This is not representative of in vivo exposure, where aerosols are deposited onto cell surfaces at the air-liquid interface (ALI). Inertial impaction provides an opportunity to deliver high doses of particles with aerodynamic diameters>∼1 µm to the surface of cells in seconds in a reproducible and predictable manner. A custom device was constructed to deposit DEP aerosols onto the surface of Calu-3 and A549 cells grown at the ALI. The pro-inflammatory and toxic cellular response to exposure to the deposited DEP aerosols was measured and compared to the response of cells exposed to DEP as suspensions. Calu-3 cells showed evidence of an oxidative stress response for both exposure types, while there was strong evidence to suggest that the method of aerosol delivery was harmful to the A549 cells.

The generation of diesel exhaust particle aerosols from a bulk source in an aerodynamic size range similar to atmospheric particles.

The influence of diesel exhaust particles (DEP) on the lungs and heart is currently a topic of great interest in inhalation toxicology. Epidemiological data and animal studies have implicated airborne particulate matter and DEP in increased morbidity and mortality due to a number of cardiopulmonary diseases including asthma, chronic obstructive pulmonary disorder, and lung cancer. The pathogeneses of these diseases are being studied using animal models and cell culture techniques. Real-time exposures to freshly combusted diesel fuel are complex and require significant infrastructure including engine operations, dilution air, and monitoring and control of gases. A method of generating DEP aerosols from a bulk source in an aerodynamic size range similar to atmospheric DEP would be a desirable and useful alternative. Metered dose inhaler technology was adopted to generate aerosols from suspensions of DEP in the propellant hydrofluoroalkane 134a. Inertial impaction data indicated that the particle size distributions of the generated aerosols were trimodal, with count median aerodynamic diameters less than 100 nm. Scanning electron microscopy of deposited particles showed tightly aggregated particles, as would be expected from an evaporative process. Chemical analysis indicated that there were no major changes in the mass proportion of 2 specific aromatic hydrocarbons (benzo[a]pyrene and benzo[k]fluoranthene) in the particles resulting from the aerosolization process.

Development of a size-dependent aerosol deposition model utilising human airway epithelial cells for evaluating aerosol drug delivery.

Aerosol delivery to the airways of the human respiratory tract, followed by absorption, constitutes an alternative route of administration for compounds unsuitable for delivery by conventional oral and parenteral routes. The target for aerosol drug delivery is the airways epithelium, i.e. tracheal, bronchial, bronchiolar and alveolar cells, which become the site of drug deposition. These epithelial layers also serve as a barrier to the penetration of inhaled material. An in vitro model for aerosol deposition and transport across epithelia in the human airways may be a good predictor of in vivo disposition. The present preliminary studies begin an investigation that blends the dynamics of aerosol delivery and the basis of an in vitro simulated lung model to evaluate the transport properties of a series of molecular weight marker compounds across human-derived bronchiolar epithelial cell monolayers. An Andersen viable cascade impactor was used as a delivery apparatus for the deposition of size-segregated particles onto monolayers of small airway epithelial cells and Calu-3 cells. It was shown that these cell layers can withstand placement in the impactor, and that permeability can be tested subsequent to removal from the impactor.