An enzyme kinetic model for describing fermentation processes

An enzyme kinetic model has been proposed to describe fermentation processes. This type of model was chosen because it is biologically sound, can incorporate all of the important engineering control variables, and can draw upon, in its development, the extensive kinetic literature. An intial qualitative test for this model was made on the gluconic acid fermentation. A necessary check of the model was that Monod's empirical cell growth and yield equations were derived as a special case. The model also offered an explanation for the hysteresis behavior of the gluconic acid production rate as a function of gluconolactone.     

The role of stochastic processes in producing nested patterns of species distributions

Nestedness has received considerable attention in community ecology and conservation biology from both theoretical and empirical perspectives. This has lead to the creation of various metrics and null models to analyze nested subsets, all of which rely on the random placement of species to assess significance. However, if immigration and extinction are the processes that underlie species distributions on island systems, then null models might be better determined on the basis of randomly placed individuals. Consequently, we examined the effects of species–abundance distributions (uniform, dominance–decay, random–assortment, and dominance–preemption), island–size distributions (uniform and linear decrease), and total abundances (128, 256, 512, 1024, 2048, 4096 and 8192) on the degree of nestedness and its significance. Generally, matrices of species presence and absence created from the random placement of individuals were nested significantly according to null models based on the random placement of species. Island size and abundance had less of an effect on nestedness in systems dominated by only a few species than in systems in which abundances were distributed more evenly. Stochastic processes, such as the random placement of individuals, predispose systems to evince patterns of nestedness at the species level, which may account, in part, for the ubiquity of nestedness in nature.     

A stochastic flowering model describing an asynchronically flowering set of trees

A general stochastic model is presented that simulates the time course of flowering of individual trees and populations, integrating the synchronization of flowering both between and within trees. Making some hypotheses, a simplified expression of the model, called the 'shoot' model, is proposed, in which the synchronization of flowering both between and within trees is characterized by specific parameters. Two derived models, the 'tree' model and the 'population' model, are presented. They neglect the asynchrony of flowering, respectively, within trees, and between and within trees. Models were fitted and tested using data on flowering of Psidium cattleianum observed at study sites at elevations of 200, 520 and 890 m in Reunion Island. The 'shoot' model fitted the data best and reproduced the strong irregularities in flowering shown by empirical data. The asynchrony of flowering in P. cattleianum was more pronounced within than between trees. Simulations showed that various flowering patterns can be reproduced by the 'shoot' model. The use of different levels of organization of the general model is discussed.     

The role of carrion in maintaining biodiversity and ecological processes in terrestrial ecosystems

Carrion provides a resource for a subset of animal species that deliver a critical ecosystem service by consuming dead animal matter and recycling its nutrients. A growing number of studies have also shown various effects of carrion on different plant and microbial communities. However, there has been no review of these studies to bring this information together and identify priority areas for future research. We review carrion ecology studies from the last two decades and summarise the range of spatial and temporal effects of carrion on soil nutrients, microbes, plants, arthropods, and vertebrates. We identify key knowledge gaps in carrion ecology, and discuss how closing these gaps can be achieved by focusing future research on the (1) different kinds of carrion resources, (2) interactions between different components of the carrion community, (3) the ways that ecosystem context can moderate carrion effects, and (4) considerations for carrion management. To guide this research, we outline a framework that builds on the ‘ephemeral resource patch’ concept, and helps to structure research questions that link localised effects of carrion with their consequences at landscape scales. This will enable improved characterisation of carrion as a unique resource pool, provide answers for land managers in a position to influence carrion availability, and establish the ways that carrion affects the dynamics of species diversity and ecological processes within landscapes.     

Disentangling the importance of ecological niches from stochastic processes across scales

Deterministic theories in community ecology suggest that local, niche-based processes, such as environmental filtering, biotic interactions and interspecific trade-offs largely determine patterns of species diversity and composition. In contrast, more stochastic theories emphasize the importance of chance colonization, random extinction and ecological drift. The schisms between deterministic and stochastic perspectives, which date back to the earliest days of ecology, continue to fuel contemporary debates (e.g. niches versus neutrality). As illustrated by the pioneering studies of Robert H. MacArthur and co-workers, resolution to these debates requires consideration of how the importance of local processes changes across scales. Here, we develop a framework for disentangling the relative importance of deterministic and stochastic processes in generating site-to-site variation in species composition (β-diversity) along ecological gradients (disturbance, productivity and biotic interactions) and among biogeographic regions that differ in the size of the regional species pool. We illustrate how to discern the importance of deterministic processes using null-model approaches that explicitly account for local and regional factors that inherently create stochastic turnover. By embracing processes across scales, we can build a more synthetic framework for understanding how niches structure patterns of biodiversity in the face of stochastic processes that emerge from local and biogeographic factors.     

Synonymy relationship and stochastic processes in determination of flow equations in ecological models

A flow equation obtained through multiple linear regressions is a static concept fixed for a time t. However, experience says that the temporal component makes the information obtained from the flow equation in terms of coefficients of determination. In this paper we show that a 1-degree variation in such coefficients behaves like a Wiener process based on the Gaussian distribution. As an application, we study the destruction of fruits in Cistus albidus L.     

A macroscopic model describing yield and maintenance relationships in aerobic fermentation processes

The present paper presents a generalized treatment of the principles of elemental and enthalpy balances which are applied to aerobic fermentation processes. It is shown that strict relations do exist between the various yield factors of biomass or product on substrate, oxygen, carbon dioxide, and between the various maintenance coefficients. These relations are confirmed from the existing body of literature data on yield and maintenance coefficients. Another consequences of the application of elemental balances is the existence of limits for the maximum biomass yield on substrate and oxygen, which depend on the degree of reduction of the substrates with different degree of reduction. It appears from this model that substrates with a high degree of reduction are C limited and substrates with a low degree of reduction are energy limited. Finally the effects of temperature on yield and maintenance coefficients are analyzed from the existing body of literature data. It can be concluded that the maintenance coefficients follow an Arrhenius type of relationship and that yield is temperature independent. The literature data seem to indicate that a degree of reduction of about 4 is optimal for the carbon and energy needs for biomass formation.     

Stability analysis of a stochastic model for biomolecular selection

The technique of the probability generating function is used to derive the stochastic differential equations for a nonlinear model based on Eigen and Schuster's theory of biomolecular selection and evolution. The stabilities of various steady states are analyzed by using the linear stability approximation. The instability of a small starting population is investigated numerically. The minimum starting populations required for steady-state survival are then estimated for a wide range of parameters.     

The evolution of patch selection in stochastic environments

A null model for habitat patch selection in spatially heterogeneous environments is the ideal free distribution (IFD), which assumes individuals have complete knowledge about the environment and can freely disperse. Under equilibrium conditions, the IFD predicts that local population growth rates are zero in all occupied patches, sink patches are unoccupied, and the fraction of the population selecting a patch is proportional to the patch's carrying capacity. Individuals, however, often experience stochastic fluctuations in environmental conditions and cannot respond to these fluctuations instantaneously. An evolutionary stability analysis for fixed patch-selection strategies reveals that environmental uncertainty disrupts the classical IFD predictions: individuals playing the evolutionarily stable strategy may occupy sink patches, local growth rates are negative and typically unequal in all patches, and individuals prefer higher-quality patches less than predicted by their carrying capacities. Spatial correlations in environmental fluctuations can enhance or marginalize these trends. The analysis predicts that continually increasing environmental variation first selects for range expansion, then selects for persisting coupled sink populations, and ultimately leads to regional extinction. In contrast, continually increasing habitat degradation first selects for range contraction and may select for persisting coupled sink populations before regional extinction. These results highlight the combined roles of spatial and temporal heterogeneity on the evolution of habitat selection.     

A model describing nonlinearities in hearing by active processes with saturation at 40 dB

Data from literature related to nonlinearities of the peripheral part of the hearing system are collected and extended by results from measurements of acoustical responses, masking, cubic difference tones and Zwicker tones. The data indicate 40 dB as a significant value for the dynamic range in neurophysiology as well as for the sensation level in psychoacoustics dividing the total level range into two areas of different characteristics. A preliminary model assuming that the outer hair cells act as an amplifier which contains saturation (corresponding to 40 dB) and feed back to sensitize the inner hair cells is used to describe the measured effects at least qualitatively.     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

The role of habitat selection behavior in population dynamics: source–sink systems and ecological traps

Ecological traps, poor-quality habitat that nonetheless attract individuals, have been observed in both natural and human-altered settings. Until recently, ecological traps were considered a kind of source–sink system, but source–sink theory does not model maladaptive habitat choice, and therefore cannot accurately represent ecological traps or predict their population-level consequences. Although recent models of ecological traps addressed this problem, they used patch-based models containing only two habitats that were very different from one another, but were internally homogeneous. These sorts of patch models may not apply to many real populations, and using them for populations in landscapes with mosaic or gradient habitat structures may be misleading. I developed models that treat source–sink dynamics and ecological traps as special cases of a single process, in which the attractiveness and quality of the habitat are separate variables that can be either positively or negatively related, and in which habitat quality varies continuously throughout the landscape. As expected, sinks are less detrimental to populations than ecological traps, in which preferential use of poor habitat elevates extinction risk. Furthermore, ecological traps may be undetected, and may even appear to be sources, when population sizes are large, but may still prevent recovery in spite of the availability of high-quality habitat when populations drop below threshold levels. Conservation biologists do not routinely consider the possibility that apparent sinks are actually traps, but since traps should be associated with the rapidly changing and novel habitat characteristics primarily produced by human activities, ecological traps should be considered an important and potentially widespread conservation concern.     

The need for stochastic replication of ecological neural networks

Artificial neural networks are becoming increasingly popular as predictive statistical tools in ecosystem ecology and as models of signal processing in behavioural and evolutionary ecology. We demonstrate here that a commonly used network in ecology, the three-layer feed-forward network, trained with the backpropagation algorithm, can be extremely sensitive to the stochastic variation in training data that results from random sampling of the same underlying statistical distribution, with networks converging to several distinct predictive states. Using a random walk procedure to sample error-weight space, and Sammon dimensional reduction of weight arrays, we demonstrate that these different predictive states are not artefactual, due to local minima, but lie at the base of major error troughs in the error-weight surface. We further demonstrate that various gross weight compositions can produce the same predictive state, suggesting the analogy of weight space as a 'patchwork' of multiple predictive states. Our results argue for increased inclusion of stochastic training replication and analysis into ecological and behavioural applications of artificial neural networks.     

Parameter estimation and model selection for Neyman-Scott point processes

This paper proposes an approximative method for maximum likelihood estimation of parameters of Neyman-Scott and similar point processes. It is based on the point pattern resulting from forming all difference points of pairs of points in the window of observation. The intensity function of this constructed point process can be expressed in terms of second-order characteristics of the original process. This opens the way to parameter estimation, if the difference pattern is treated as a non-homogeneous Poisson process. The computational feasibility and accuracy of this approach is examined by means of simulated data. Furthermore, the method is applied to two biological data sets. For these data, various cluster process models are considered and compared with respect to their goodness-of-fit.     

The role of ecological theory in microbial ecology

Microbial ecology is currently undergoing a revolution, with repercussions spreading throughout microbiology, ecology and ecosystem science. The rapid accumulation of molecular data is uncovering vast diversity, abundant uncultivated microbial groups and novel microbial functions. This accumulation of data requires the application of theory to provide organization, structure, mechanistic insight and, ultimately, predictive power that is of practical value, but the application of theory in microbial ecology is currently very limited. Here we argue that the full potential of the ongoing revolution will not be realized if research is not directed and driven by theory, and that the generality of established ecological theory must be tested using microbial systems.     

The ecological role of bacteriocins in bacterial competition

Bacteriocins are an abundant class of antimicrobial molecules that appear to mediate population dynamics within species. The bacteriocins of Escherichia coli have served as a model for exploring the ecological role of these potent toxins. Studies suggest that colicins provide a competitive edge in nutrient-poor environments and that there might be a trade-off between the costs and benefits of colicin production.