Stephen M. Krone

Analyzing animal movements using Brownian bridges.

By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animals mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animals probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.

Influence of humans on evolution and mobilization of environmental antibiotic resistome

The clinical failure of antimicrobial drugs that were previously effective in controlling infectious disease is a tragedy of increasing magnitude that gravely affects human health. This resistance by pathogens is often the endpoint of an evolutionary process that began billions of years ago in non–disease-causing microorganisms. This environmental resistome, its mobilization, and the conditions that facilitate its entry into human pathogens are at the heart of the current public health crisis in antibiotic resistance. Understanding the origins, evolution, and mechanisms of transfer of resistance elements is vital to our ability to adequately address this public health issue.

Increased Transfer of a Multidrug Resistance Plasmid in Escherichia coli Biofilms at the Air-Liquid Interface

ABSTRACT Although biofilms represent a common bacterial lifestyle in clinically and environmentally important habitats, there is scant information on the extent of gene transfer in these spatially structured populations. The objective of this study was to gain insight into factors that affect transfer of the promiscuous multidrug resistance plasmid pB10 in Escherichia coli biofilms. Biofilms were grown in different experimental settings, and plasmid transfer was monitored using laser scanning confocal microscopy and plate counting. In closed flow cells, plasmid transfer in surface-attached submerged biofilms was negligible. In contrast, a high plasmid transfer efficiency was observed in a biofilm floating at the air-liquid interface in an open flow cell with low flow rates. A vertical flow cell and a batch culture biofilm reactor were then used to detect plasmid transfer at different depths away from the air-liquid interface. Extensive plasmid transfer occurred only in a narrow zone near that interface. The much lower transfer frequencies in the lower zones coincided with rapidly decreasing oxygen concentrations. However, when an E. coli csrA mutant was used as the recipient, a thick biofilm was obtained at all depths, and plasmid transfer occurred at similar frequencies throughout. These results and data from separate aerobic and anaerobic matings suggest that oxygen can affect IncP-1 plasmid transfer efficiency, not only directly but also indirectly, through influencing population densities and therefore colocalization of donors and recipients. In conclusion, the air-liquid interface can be a hot spot for plasmid-mediated gene transfer due to high densities of juxtaposed donor and recipient cells.

Spatial structure and nutrients promote invasion of IncP-1 plasmids in bacterial populations

In spite of the importance of plasmids in bacterial adaptation, we have a poor understanding of their dynamics. It is not known if or how plasmids persist in and spread through (invade) a bacterial population when there is no selection for plasmid-encoded traits. Moreover, the differences in dynamics between spatially structured and mixed populations are poorly understood. Through a joint experimental/theoretical approach, we tested the hypothesis that self-transmissible IncP-1 plasmids can invade a bacterial population in the absence of selection when initially very rare, but only in spatially structured habitats and when nutrients are regularly replenished. Using protocols that differed in the degree of spatial structure and nutrient levels, the invasiveness of plasmid pB10 in Escherichia coli was monitored during at least 15 days, with an initial fraction of plasmid-bearing (p+) cells as low as 10−7. To further explore the mechanisms underlying plasmid dynamics, we developed a spatially explicit mathematical model. When cells were grown on filters and transferred to fresh medium daily, the p+ fraction increased to 13%, whereas almost complete invasion occurred when the population structure was disturbed daily. The plasmid was unable to invade in liquid. When carbon source levels were lower or not replenished, plasmid invasion was hampered. Simulations of the mathematical model closely matched the experimental results and produced estimates of the effects of alternative experimental parameters. This allowed us to isolate the likely mechanisms most responsible for the observations. In conclusion, spatial structure and nutrient availability can be key determinants in the invasiveness of plasmids.

Markov Chain Monte Carlo in small worlds

As the number of applications for Markov Chain Monte Carlo (MCMC) grows, the power of these methods as well as their shortcomings become more apparent. While MCMC yields an almost automatic way to sample a space according to some distribution, its implementations often fall short of this task as they may lead to chains which converge too slowly or get trapped within one mode of a multi-modal space. Moreover, it may be difficult to determine if a chain is only sampling a certain area of the space or if it has indeed reached stationarity.In this paper, we show how a simple modification of the proposal mechanism results in faster convergence of the chain and helps to circumvent the problems described above. This mechanism, which is based on an idea from the field of “small-world” networks, amounts to adding occasional “wild” proposals to any local proposal scheme. We demonstrate through both theory and extensive simulations, that these new proposal distributions can greatly outperform the traditional local proposals when it comes to exploring complex heterogenous spaces and multi-modal distributions. Our method can easily be applied to most, if not all, problems involving MCMC and unlike many other remedies which improve the performance of MCMC it preserves the simplicity of the underlying algorithm.

Application of Ecological Network Theory to the Human Microbiome

In healthy humans, many microbial consortia constitute rich ecosystems with dozens to hundreds of species, finely tuned to functions relevant to human health. Medical interventions, lifestyle changes, and the normal rhythms of life sometimes upset the balance in microbial ecosystems, facilitating pathogen invasions or causing other clinically relevant problems. Some diseases, such as bacterial vaginosis, have exactly this sort of community etiology. Mathematical network theory is ideal for studying the ecological networks of interacting species that comprise the human microbiome. Theoretical networks require little consortia specific data to provide insight into both normal and disturbed microbial community functions, but it is easy to incorporate additional empirical data as it becomes available. We argue that understanding some diseases, such as bacterial vaginosis, requires a shift of focus from individual bacteria to (mathematical) networks of interacting populations, and that known emergent properties of these networks will provide insights that would be otherwise elusive.

Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing

We compare convergence rates of Metropolis‐Hastings chains to multi-modal target distributions when the proposal distributions can be of “local” and “small world” type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is “slowly mixing” (in the complexity of the problem) into a chain that is “rapidly mixing.” To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for log-concave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes.

Space, Time, and Host Evolution Facilitate Coexistence of Competing Bacteriophages: Theory and Experiment

We present a joint experimental/theoretical investigation into the roles of spatial structure and time in the competition between two pathogens for a single host. We suggest a natural mechanism by which competing pathogens can coexist when host evolution and competitive dynamics occur on similar timescales. Our experimental system consisted of a single bacterial host species and two competing bacteriophage strains grown on agar plates, with a serial transfer of samples of the bacteriophage population to fresh host populations after each incubation cycle. The experiments included two incubation times and two transfer protocols that either maintained or disrupted the spatial structure of the viruses at each transfer. The same bacteriophage acted as the dominant competitor under both transfer protocols. A striking difference between the treatments is that the weak competitor was able to persist in the long‐incubation experiments but not in the short‐incubation experiments. Mathematical and experimental evidence suggest that coexistence is due to the appearance of resistant mutant host cells that provide a transient “spatiotemporal refuge” for the weaker competitor. Our mathematical model is individual based, captures the stochastic spatial dynamics down to the level of individual cells, and helps to explain the differences in behavior under the various experimental conditions.

Dual Reporter System for In Situ Detection of Plasmid Transfer under Aerobic and Anaerobic Conditions

ABSTRACT We designed a new genetic tool to detect plasmid transfer under anaerobic and aerobic conditions. The system is based on the T7 RNA polymerase gene and a T7 promoter-driven oxygen-independent green fluorescent protein, evoglow, alone or in combination with red fluorescent protein DsRed. Constructs are available as plasmids and mini-mariner transposons.

Fitness benefits of low infectivity in a spatially structured population of bacteriophages

For a parasite evolving in a spatially structured environment, an evolutionarily advantageous strategy may be to reduce its transmission rate or infectivity. We demonstrate this empirically using bacteriophage (phage) from an evolution experiment where spatial structure was maintained over 550 phage generations on agar plates. We found that a single substitution in the major capsid protein led to slower adsorption of phage to host cells with no change in lysis time or burst size. Plaques formed by phage isolates containing this mutation were not only larger but also contained more phage per unit area. Using a spatially explicit, individual-based model, we showed that when there is a trade-off between adsorption and diffusion (i.e. less ‘sticky’ phage diffuse further), slow adsorption can maximize plaque size, plaque density and overall productivity. These findings suggest that less infective pathogens may have an advantage in spatially structured populations, even when well-mixed models predict that they will not.