José Miguel Ponciano

ESTIMATING DENSITY DEPENDENCE, PROCESS NOISE, AND OBSERVATION ERROR

We describe a discrete-time, stochastic population model with density depend ence, environmental-type process noise, and lognormal observation or sampling error. The model, a stochastic version of the Gompertz model, can be transformed into a linear Gaussian state-space model (Kaiman filter) for convenient fitting to time series data. The model has a multivariate normal likelihood function and is simple enough for a variety of uses ranging from theoretical study of parameter estimation issues to routine data analyses in population monitoring. A special case of the model is the discrete-time, stochastic exponential growth model (density independence) with environmental-type process error and lognormal observation error. We describe two methods for estimating parameters in the Gompertz state-space model, and we compare the statistical qualities of the methods with computer simulations. The methods are maximum likelihood based on observations and restricted maximum likelihood based on first differences. Both offer adequate statistical properties. Because the likelihood function is identical to a repeated-measures analysis of variance model with a random time effect, parameter estimates can be calculated using PROC MIXED of SAS. We use the model to analyze a data set from the Breeding Bird Survey. The fitted model suggests that over 70% of the noise in the populations growth rate is due to observation error. The model describes the autocovariance properties of the data especially well. While observation error and process noise variance parameters can both be estimated from one time series, multimodal likelihood functions can and do occur. For data arising from the model, the statistically consistent parameter estimates do not necessarily correspond to the global maximum in the likelihood function. Maximization, simulation, and bootstrapping programs must accommodate the phenomenon of multimodal likelihood functions to produce statistically valid results.

Adaptive Plasmid Evolution Results in Host-Range Expansion of a Broad-Host-Range Plasmid

Little is known about the range of hosts in which broad-host-range (BHR) plasmids can persist in the absence of selection for plasmid-encoded traits, and whether this “long-term host range” can evolve over time. Previously, the BHR multidrug resistance plasmid pB10 was shown to be highly unstable in Stenotrophomonas maltophilia P21 and Pseudomonas putida H2. To investigate whether this plasmid can adapt to such unfavorable hosts, we performed evolution experiments wherein pB10 was maintained in strain P21, strain H2, and alternatingly in P21 and H2. Plasmids that evolved in P21 and in both hosts showed increased stability and decreased cost in ancestral host P21. However, the latter group showed higher variability in stability patterns, suggesting that regular switching between distinct hosts hampered adaptive plasmid evolution. The plasmids evolved in P21 were also equally or more stable in other hosts compared to pB10, which suggested true host-range expansion. The complete genome sequences of four evolved plasmids with improved stability showed only one or two genetic changes. The stability of plasmids evolved in H2 improved only in their coevolved hosts, not in the ancestral host. Thus a BHR plasmid can adapt to an unfavorable host and thereby expand its long-term host range.

Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning.

Hierarchical statistical models are increasingly being used to describe complex ecological processes. The data cloning (DC) method is a new general technique that uses Markov chain Monte Carlo (MCMC) algorithms to compute maximum likelihood (ML) estimates along with their asymptotic variance estimates for hierarchical models. Despite its generality, the method has two inferential limitations. First, it only provides Wald-type confidence intervals, known to be inaccurate in small samples. Second, it only yields ML parameter estimates, but not the maximized likelihood values used for profile likelihood intervals, likelihood ratio hypothesis tests, and information-theoretic model selection. Here we describe how to overcome these inferential limitations with a computationally efficient method for calculating likelihood ratios via data cloning. The ability to calculate likelihood ratios allows one to do hypothesis tests, construct accurate confidence intervals and undertake information-based model selection with hierarchical models in a frequentist context. To demonstrate the use of these tools with complex ecological models, we reanalyze part of Gauses classic Paramecium data with state-space population models containing both environmental noise and sampling error. The analysis results include improved confidence intervals for parameters, a hypothesis test of laboratory replication, and a comparison of the Beverton-Holt and the Ricker growth forms based on a model selection index.

The population biology of bacterial plasmids : A hidden markov model approach

Horizontal plasmid transfer plays a key role in bacterial adaptation. In harsh environments, bacterial populations adapt by sampling genetic material from a horizontal gene pool through self-transmissible plasmids, and that allows persistence of these mobile genetic elements. In the absence of selection for plasmid-encoded traits it is not well understood if and how plasmids persist in bacterial communities. Here we present three models of the dynamics of plasmid persistence in the absence of selection. The models consider plasmid loss (segregation), plasmid cost, conjugative plasmid transfer, and observation error. Also, we present a stochastic model in which the relative fitness of the plasmid-free cells was modeled as a random variable affected by an environmental process using a hidden Markov model (HMM). Extensive simulations showed that the estimates from the proposed model are nearly unbiased. Likelihood-ratio tests showed that the dynamics of plasmid persistence are strongly dependent on the host type. Accounting for stochasticity was necessary to explain four of seven time-series data sets, thus confirming that plasmid persistence needs to be understood as a stochastic process. This work can be viewed as a conceptual starting point under which new plasmid persistence hypotheses can be tested.

Replicated sampling increases efficiency in monitoring biological populations

Observation or sampling error in population monitoring can cause serious degradation of the inferences, such as estimates of trend or risk, that ecologists and managers frequently seek to make with time-series observations of population abundances. We show that replicating the sampling process can considerably improve the information obtained from population monitoring. At each sampling time the sampling method would be repeated, either simultaneously or within a short time. In this study we examine the potential value of replicated sampling to population monitoring using a density-dependent population model. We modify an existing population time-series model, the Gompertz state-space model, to incorporate replicated sampling, and we develop maximum-likelihood and restricted maximum-likelihood estimates of model parameters. Depending on sampling protocols, replication may or may not entail substantial extra cost. Some sampling programs already have replicated samples, but the samples are aggregated or pooled into one estimate of population abundance; such practice of aggregating samples, according to our model, loses considerable information about model parameters. The gains from replicated sampling are realized in substantially improved statistical inferences about model parameters, especially inferences for sorting out the contributions of process noise and observation error to observed population variability.

Evolutionary Paths That Expand Plasmid Host-Range: Implications for Spread of Antibiotic Resistance

The World Health Organization has declared the emergence of antibiotic resistance to be a global threat to human health. Broad-host-range plasmids have a key role in causing this health crisis because they transfer multiple resistance genes to a wide range of bacteria. To limit the spread of antibiotic resistance, we need to gain insight into the mechanisms by which the host range of plasmids evolves. Although initially unstable plasmids have been shown to improve their persistence through evolution of the plasmid, the host, or both, the means by which this occurs are poorly understood. Here, we sought to identify the underlying genetic basis of expanded plasmid host-range and increased persistence of an antibiotic resistance plasmid using a combined experimental-modeling approach that included whole-genome resequencing, molecular genetics and a plasmid population dynamics model. In nine of the ten previously evolved clones, changes in host and plasmid each slightly improved plasmid persistence, but their combination resulted in a much larger improvement, which indicated positive epistasis. The only genetic change in the plasmid was the acquisition of a transposable element from a plasmid native to the Pseudomonas host used in these studies. The analysis of genetic deletions showed that the critical genes on this transposon encode a putative toxin-antitoxin (TA) and a cointegrate resolution system. As evolved plasmids were able to persist longer in multiple naïve hosts, acquisition of this transposon also expanded the plasmids host range, which has important implications for the spread of antibiotic resistance.

Inherent variation in stable isotope values and discrimination factors in two life stages of green turtles.

We examine inherent variation in carbon and nitrogen stable isotope values of multiple soft tissues from a population of captive green turtles Chelonia mydas to determine the extent of isotopic variation due to individual differences in physiology. We compare the measured inherent variation in the captive population with the isotopic variation observed in a wild population of juvenile green turtles. Additionally, we measure diet-tissue discrimination factors to determine the offset that occurs between isotope values of the food source and four green turtle tissues. Tissue samples (epidermis, dermis, serum, and red blood cells) were collected from captive green turtles in two life stages (40 large juveniles and 30 adults) at the Cayman Turtle Farm, Grand Cayman, and analyzed for carbon and nitrogen stable isotopes. Multivariate normal models were fit to the isotope data, and the Bayesian Information Criterion was used for model selection. Inherent variation and discrimination factors differed among tissues and life stages. Inherent variation was found to make up a small portion of the isotopic variation measured in a wild population. Discrimination factors not only are tissue and life stage dependent but also appear to vary with diet and sea turtle species, thus highlighting the need for appropriate discrimination factors in dietary reconstructions and trophic-level estimations. Our measures of inherent variation will also be informative in field studies employing stable isotope analysis so that differences in diet or habitat are more accurately identified.

Evolution of Diversity in Spatially Structured Escherichia coli Populations

ABSTRACT The stochastic Ricker population model was used to investigate the generation and maintenance of genetic diversity in a bacterial population grown in a spatially structured environment. In particular, we showed that Escherichia coli undergoes dramatic genetic diversification when grown as a biofilm. Using a novel biofilm entrapment method, we retrieved 64 clones from each of six different depths of a mature biofilm, and after subculturing for ∼30 generations, we measured their growth kinetics in three different media. We fit a stochastic Ricker population growth model to the recorded growth curves. The growth kinetics of clonal lineages descendant from cells sampled at different biofilm depths varied as a function of both the depth in the biofilm and the growth medium used. We concluded that differences in the growth dynamics of clones were heritable and arose during adaptive evolution under local conditions in a spatially heterogeneous environment. We postulate that under nutrient-limited conditions, selective sweeps would be protracted and would be insufficient to purge less-fit variants, a phenomenon that would allow the coexistence of genetically distinct clones. These findings contribute to the current understanding of biofilm ecology and complement current hypotheses for the maintenance and generation of microbial diversity in spatially structured environments.

Use of Stochastic Models To Assess the Effect of Environmental Factors on Microbial Growth

ABSTRACT We present a novel application of a stochastic ecological model to the study and analysis of microbial growth dynamics as influenced by environmental conditions in an extensive experimental data set. The model proved to be useful in bridging the gap between theoretical ideas in ecology and an applied problem in microbiology. The data consisted of recorded growth curves of Escherichia coli grown in triplicate in a base medium with all 32 possible combinations of five supplements: glucose, NH4Cl, HCl, EDTA, and NaCl. The potential complexity of 25 experimental treatments and their effects was reduced to 22 as just the metal chelator EDTA, the presumed osmotic pressure imposed by NaCl, and the interaction between these two factors were enough to explain the variability seen in the data. The statistical analysis showed that the positive and negative effects of the five chemical supplements and their combinations were directly translated into an increase or decrease in time required to attain stationary phase and the population size at which the stationary phase started. The stochastic ecological model proved to be useful, as it effectively explained and summarized the uncertainty seen in the recorded growth curves. Our findings have broad implications for both basic and applied research and illustrate how stochastic mathematical modeling coupled with rigorous statistical methods can be of great assistance in understanding basic processes in microbial ecology.

The evolution of antibiotic susceptibility and resistance during the formation of Escherichia coli biofilms in the absence of antibiotics

BackgroundExplanations for bacterial biofilm persistence during antibiotic treatment typically depend on non-genetic mechanisms, and rarely consider the contribution of evolutionary processes.ResultsUsing Escherichia coli biofilms, we demonstrate that heritable variation for broad-spectrum antibiotic resistance can arise and accumulate rapidly during biofilm development, even in the absence of antibiotic selection.ConclusionsOur results demonstrate the rapid de novo evolution of heritable variation in antibiotic sensitivity and resistance during E. coli biofilm development. We suggest that evolutionary processes, whether genetic drift or natural selection, should be considered as a factor to explain the elevated tolerance to antibiotics typically observed in bacterial biofilms. This could be an under-appreciated mechanism that accounts why biofilm populations are, in general, highly resistant to antibiotic treatment.