How can we model selectively neutral density dependence in evolutionary games

The problem of density dependence appears in all approaches to the modelling of population dynamics. It is pertinent to classic models (i.e., Lotka-Volterra's), and also population genetics and game theoretical models related to the replicator dynamics. There is no density dependence in the classic formulation of replicator dynamics, which means that population size may grow to infinity. Therefore the question arises: How is unlimited population growth suppressed in frequency-dependent models? Two categories of solutions can be found in the literature. In the first, replicator dynamics is independent of background fitness. In the second type of solution, a multiplicative suppression coefficient is used, as in a logistic equation. Both approaches have disadvantages. The first one is incompatible with the methods of life history theory and basic probabilistic intuitions. The logistic type of suppression of per capita growth rate stops trajectories of selection when population size reaches the maximal value (carrying capacity); hence this method does not satisfy selective neutrality. To overcome these difficulties, we must explicitly consider turn-over of individuals dependent on mortality rate. This new approach leads to two interesting predictions. First, the equilibrium value of population size is lower than carrying capacity and depends on the mortality rate. Second, although the phase portrait of selection trajectories is the same as in density-independent replicator dynamics, pace of selection slows down when population size approaches equilibrium, and then remains constant and dependent on the rate of turn-over of individuals.     

Alamethicin channel kinetics: Studies using fluctuation analysis and multifractal fluctuation analysis

The kinetics of the alamethicine channel incorporated into BLM was studied using detrended fluctuation analysis and multifractal detrended fluctuation analysis. Detrended fluctuation analysis has shown that both the event series formed with dwell times on fixed channel conductivity levels and the event series formed with opened states on all channel conductivity levels are random processes. However, multifractal detrended fluctuation analysis indicated that only dwell times series on fixed channel conductivity levels are random, but the event series formed with opened states on all channel conductivity levels are the correlated multifractal processes.     

Patterns of morphology and behaviour in a cicada guild: A neutral model analysis

Morphological and behavioural patterns were examined in a guild of nine species of eastern Australian cicadas. Co-occurrence in, and structure of, 44 study plots were determined to relate morphological and behavioural patterns to habitat overlap and habitat structure. Multi-variate analyses were employed to generate relationships between the species. Guild substructure shown by the habitat analyses cannot be predicted from the group substructure indicated by the morphology/behaviour analyses. Therefore, extant combinations appear to be random collections from the nine-species pool insofar as morphology and behaviour are concerned. In particular, the most generalized species (in terms of habitat) are relatively extreme in morphology and behaviour, and vice versa. Despite these results, there are weak indications that at least two suites of characters exist, and that one of them is associated with each of the most extreme types of habitat. The reasons for these apparently contradictory results are discussed. There is no evidence to suggest that systematic morphological divergence has occurred in this guild.     

Phospholipid dependence of the neutral sphingomyelinase in rat liver plasma membranes

Investigations have been carried out on the influence of the phospholipid composition of rat liver plasma membranes and of their physico-chemical properties on the activity of membrane-bound neutral sphingomyelinase. The membrane phospholipid composition was modified by the incorporation of different phospholipids into the membrane bilayer by means of lipid transfer proteins, n-butanol delipidation or exogenous sphingomyelinase (Staphylococcus aureus) treatment. The results indicate that the activity of neutral sphingomyelinase in liver plasma membranes depends upon phosphatidyl choline presence in the membrane bilayer and not upon membrane fluidity.     

Cumulant analysis in fluorescence fluctuation spectroscopy

A novel technique for the analysis of fluorescence fluctuation experiments is introduced. Fluorescence cumulant analysis (FCA) exploits the factorial cumulants of the photon counts and resolves heterogeneous samples based on differences in brightness. A simple analytical model connects the cumulants of the photon counts with the brightness epsilon and the number of molecules N in the optical observation volume for each fluorescent species. To provide the tools for a rigorous error analysis of FCA, expressions for the variance of factorial cumulants are developed and tested. We compare theory with experiment by analyzing dye mixtures and simple fluorophore solutions with FCA. A comparison of FCA with photon-counting histogram (PCH) analysis, a related technique, shows that both methods give identical results within experimental uncertainty. Both FCA and PCH are restricted to data sampling times that are short compared to the diffusion time of molecules through the observation volume of the instrument. But FCA theory, in contrast to PCH, can be extended to treat arbitrary sampling times. Here, we derive analytical expressions for the second factorial cumulant as a function of the sampling time and demonstrate that the theory successfully models fluorescence fluctuation data.     

Fixation in haploid populations exhibiting density dependence II: the quasi-neutral case

We determine fixation probabilities in a model of two competing types with density dependence. The model is defined as a two-dimensional birth-and-death process with density-independent death rates, and birth rates that are a linearly decreasing function of total population density. We treat the 'quasi-neutral case' where both types have the same equilibrium population densities. This condition results in birth rates that are proportional to death rates. This can be viewed as a life history trade-off. The deterministic dynamics possesses a stable manifold of mixtures of the two types. We show that the fixation probability is asymptotically equal to the fixation probability at the point where the deterministic flow intersects this manifold. The deterministic dynamics predicts an increase in the proportion of the type with higher birth rate in growing populations (and a decrease in shrinking populations). Growing (shrinking) populations therefore intersect the manifold at a higher (lower) than initial proportion of this type. On the center manifold, the fixation probability is a quadratic function of initial proportion, with a disadvantage to the type with higher birth rate. This disadvantage arises from the larger fluctuations in population density for this type. These results are asymptotically exact and have relevance for allele fixation, models of species abundance, and epidemiological models.     

Ecological exchangeability versus neutral molecular markers: the case of the great tit

Neutral genetic markers, such as mitochondrial DNA (mtDNA) sequences, are commonly used to discover independently evolving groups of populations in nature. These groups are often considered to be units of conservation because they preserve distinct organismal histories. However, because of the time lag between the isolation of populations and the evolution of diagnostic neutral markers, adaptive traits could be unrepresented by units defined by neutral markers. The concept of ecological exchangeability potentially provides a way to preserve populations possessing local adaptations that lack diagnostic neutral markers. Populations are surveyed for differences in fitness traits, either directly, or by examining morphological or genetic traits that could indirectly serve as proxies for them. The purpose of this paper is to compare the nature of units of conservation defined by neutral gene surveys and ecological exchangeability, using data recently available for the great tit Parus major , a wide-ranging Palearctic species. mtDNA surveys reveal a lack of differentiation across thousands of kilometer. In contrast, studies of body size and clutch size show locally adapted differences between populations separated by a few kilometer, meaning that these populations could be classified as ecologically in exchangeable. These two types of markers have dramatically different consequences for the geographic and evolutionary scale of conservation units. The concept of ecological exchangeability might be an inappropriate way to diagnose units of conservation in birds owing to the time required to document local adaptations and their potential ubiquity. Neutral genetic markers continue to provide a theoretically sound way of identifying units of conservation, and these units ought to be integrated into conservation plans without delay.     

Redox state dependence of rotamer distributions in tyrosine and neutral tyrosyl radical

Redox state-dependent changes in the relative orientation of the phenol side chain and the peptide group in model tyrosine have been characterized using specific 2H isotopic labelling and X-band electron paramagnetic resonance (EPR) spectroscopy. Tyrosyl radicals were generated by UV photolysis of tyrosine trapped in rigid polycrystalline basic-aqueous medium at T < or = 170 K. Ring-2H(4) and beta-2H(2) substitutions on tyrosine were used to enhance the lineshape contributions from beta-hydrogen or ring-hydrogen hyperfine interactions, respectively. The EPR lineshape at 120 K of the trapped ring-2H(4)-tyrosyl radical is altered dramatically after annealing at 235 K. In contrast, the lineshape of the beta-2H(2)-tyrosyl radical is impervious to annealing. The effect of annealing on the lineshape therefore arises from a change in the isotropic hyperfine coupling between unpaired pi-electron spin density at the ring carbon atom C(1) and the beta-hydrogen nuclei, which is caused by rotational relaxation of the ring and peptide group about the C(1)-C(beta) bond. EPR simulations indicate angular distributions of the peptide group (R-) of 0 degrees < or = theta(R) < or = 30 degrees and 0 degrees < or = theta(R)< or = 18 degrees in the rigid and relaxed radical states, respectively. Redox-induced changes in the C(1)-C(beta) rotamer distribution must be accounted for in assessments of stable amino acid side chain equilibrium structures, and may influence catalytic tyrosyl radical/tyrosine function in enzymes.     

Time-integrated fluorescence cumulant analysis in fluorescence fluctuation spectroscopy

We introduce a new analysis technique for fluorescence fluctuation data. Time-integrated fluorescence cumulant analysis (TIFCA) extracts information from the cumulants of the integrated fluorescence intensity. TIFCA builds on our earlier FCA theory, but in contrast to FCA or photon counting histogram (PCH) analysis is valid for arbitrary sampling times. The motivation for long sampling times lies in the improvement of the signal/noise ratio of the data. Because FCA and PCH theory are not valid in this regime, we first derive a theoretical model of cumulant functions for arbitrary sampling times. TIFCA is the first exact theory that describes the effects of sampling time on fluorescence fluctuation experiments. We calculate factorial cumulants of the photon counts for various sampling times by rebinning of the original data. Fits of the data to models determine the brightness, the occupation number, and the diffusion time of each species. To provide the tools for a rigorous error analysis of TIFCA, expressions for the variance of cumulants are developed and tested. We demonstrate that over a limited range rebinning reduces the relative error of higher order cumulants, and therefore improves the signal/noise ratio. The first four cumulant functions are explicitly calculated and are applied to simple dye systems to test the validity of TIFCA and demonstrate its ability to resolve species.     

Testing the standard neutral model of biodiversity in lake communities

Hubbell's (2001) neutral model describes how local communities are structured if population dynamics are statistically identical among species in a constant, possibly patchy, environment with random speciation. Tests of this model have been restricted largely to terrestrial communities. Here we tested the fit of this neutral model to fish, zooplankton and phytoplankton species–abundance distributions from 30 well-studied lake communities varying widely in lake size and productivity. We measured the fit of the communities to the neutral model in three ways. All but two zooplankton (7 of 9) and all but three fish (9 of 12) communities were consistent with all three measures of fit. However, all nine phytoplankton communities did not fit the neutral model by at least one measure. This result for phytoplankton communities represents to date the most consistent failure of the standard neutral model to predict the shape of species-abundance distributions.     

Parametric dependence in model epidemics. I: Contact-related parameters

One of the interesting properties of nonlinear dynamical systems is that arbitrarily small changes in parameter values can induce qualitative changes in behavior. The changes are called bifurcations, and they are typically visualized by plotting asymptotic dynamics against a parameter. In some cases, the resulting bifurcation diagram is unique: irrespective of initial conditions, the same dynamical sequence obtains. In other cases, initial conditions do matter, and there are coexisting sequences. Here we study an epidemiological model in which multiple bifurcation sequences yield to a single sequence in response to varying a second parameter. We call this simplification the emergence of unique parametric dependence (UPD) and discuss how it relates to the model’s overall response to parameters. In so doing, we tie together a number of threads that have been developing since the mid-1980s. These include period-doubling; subharmonic resonance, attractor merging and subduction and the evolution of strange invariant sets. The present paper focuses on contact related parameters. A follow-up paper, to be published in this journal, will consider the effects of non-contact related parameters.     

Parametric dependence in model epidemics. I: contact-related parameters

One of the interesting properties of nonlinear dynamical systems is that arbitrarily small changes in parameter values can induce qualitative changes in behavior. The changes are called bifurcations, and they are typically visualized by plotting asymptotic dynamics against a parameter. In some cases, the resulting bifurcation diagram is unique: irrespective of initial conditions, the same dynamical sequence obtains. In other cases, initial conditions do matter, and there are coexisting sequences. Here we study an epidemiological model in which multiple bifurcation sequences yield to a single sequence in response to varying a second parameter. We call this simplification the emergence of unique parametric dependence (UPD) and discuss how it relates to the model's overall response to parameters. In so doing, we tie together a number of threads that have been developing since the mid-1980s. These include period-doubling; subharmonic resonance, attractor merging and subduction and the evolution of strange invariant sets. The present paper focuses on contact related parameters. A follow-up paper, to be published in this journal, will consider the effects of non-contact related parameters.     

Topological structure of the space of phenotypes: the case of RNA neutral networks

The evolution and adaptation of molecular populations is constrained by the diversity accessible through mutational processes. RNA is a paradigmatic example of biopolymer where genotype (sequence) and phenotype (approximated by the secondary structure fold) are identified in a single molecule. The extreme redundancy of the genotype-phenotype map leads to large ensembles of RNA sequences that fold into the same secondary structure and can be connected through single-point mutations. These ensembles define neutral networks of phenotypes in sequence space. Here we analyze the topological properties of neutral networks formed by 12-nucleotides RNA sequences, obtained through the exhaustive folding of sequence space. A total of 4(12) sequences fragments into 645 subnetworks that correspond to 57 different secondary structures. The topological analysis reveals that each subnetwork is far from being random: it has a degree distribution with a well-defined average and a small dispersion, a high clustering coefficient, and an average shortest path between nodes close to its minimum possible value, i.e. the Hamming distance between sequences. RNA neutral networks are assortative due to the correlation in the composition of neighboring sequences, a feature that together with the symmetries inherent to the folding process explains the existence of communities. Several topological relationships can be analytically derived attending to structural restrictions and generic properties of the folding process. The average degree of these phenotypic networks grows logarithmically with their size, such that abundant phenotypes have the additional advantage of being more robust to mutations. This property prevents fragmentation of neutral networks and thus enhances the navigability of sequence space. In summary, RNA neutral networks show unique topological properties, unknown to other networks previously described.     

Receptor current fluctuation analysis in the labellar sugar receptor of the fleshfly

Fluctuations in the receptor current of the labellar sugar receptor of the fleshfly were analyzed. The receptor current was recorded extracellularly as a drop in potential between the tip and the base of the taste sensillum. After treatment with tetrodotoxin, the taste cells completely lost their impulses but retained their receptor currents, thus facilitating analysis of the receptor current without disturbance by impulses. The current fluctuation increased markedly when the sensillum was stimulated with effective sugars: maltose, sucrose, and fructose. The fluctuation increased in parallel with development of the receptor current, which indicates that it occurs as soon as the sugar reaches the apex of the sensory process. Analysis of fluctuations by computation of autocorrelation functions (ACFs) or power spectra (PS) revealed that: (a) the variance (mean square) of fluctuation vs. sugar concentration curve reached a maximum, in contrast to the monotonic increase shown by the receptor current; (b) the ACF was approximated by an exponential term, and its time constant differed according to the sugars used and their concentrations. The time constants for fructose and maltose decreased with increases in sugar concentration. At the concentrations of sugars evoking the same magnitude of receptor current, the time constant for fructose was the largest and that for maltose was the smallest. It was strongly suggested that transduction ion channels are present at the tip region of the sensory process of the sugar receptor cell and are operated directly by sugars.     

Growth and neutral lipid synthesis in green microalgae: A mathematical model

Many green microalgae significantly increased their cellular neutral lipid content when cultured in nitrogen limited or high light conditions. Due to their lipid production potential, these algae have been suggested as promising feedstocks for biofuel production. However, no models for algal lipid synthesis with respect to nutrient and light have been developed to predict lipid production and to help improve the production process. A mathematical model is derived describing the growth dynamics and neutral lipid production of green microalgae grown in batch cultures. The model assumed that as the nitrogen was depleted, photosynthesis became uncoupled from growth, resulting in the synthesis and accumulation of neutral lipids. Simulation results were compared with experimental data for the green microalgae Pseudochlorococcum sp. For growth media with low nitrogen concentration, the model agreed closely with the data; however, with high nitrogen concentration the model overestimated the biomass. It is likely that additional limiting factors besides nitrogen could be responsible for this discrepancy.     

The HKA test revisited: a maximum-likelihood-ratio test of the standard neutral model

We present a maximum-likelihood-ratio test of the standard neutral model, using multilocus data on polymorphism within species and divergence between species. The model is based on the Hudson-Kreitman-Aguade (HKA) test, but allows for an explicit test of selection at individual loci in a multilocus framework. We use coalescent simulations to show that the likelihood-ratio test statistic is conservative, particularly when the assumption of no recombination is violated. Application of the method to polymorphism data from 18 loci from a population of Arabidopsis lyrata provides significant evidence for a balanced polymorphism at a candidate locus thought to be linked to the centromere. The method is also applied to polymorphism data in maize, providing support for the hypothesis of directional selection on genes in the starch pathway.     

Counting channels: a tutorial guide on ion channel fluctuation analysis

Ion channels open and close in a stochastic fashion, following the laws of probability. However, distinct from tossing a coin or a die, the probability of finding the channel closed or open is not a fixed number but can be modified (i.e., we can cheat) by some external stimulus, such as the voltage. Single-channel records can be obtained using the appropriate electrophysiological technique (e.g., patch clamp), and from these records the open probability and the channel conductance can be calculated. Gathering these parameters from a membrane containing many channels is not straightforward, as the macroscopic current I = iNP(o), where i is the single-channel current, N the number of channels, and P(o) the probability of finding the channel open, cannot be split into its individual components. In this tutorial, using the probabilistic nature of ion channels, we discuss in detail how i, N, and P(o max) (the maximum open probability) can be obtained using fluctuation (nonstationary noise) analysis (Sigworth FJ. G Gen Physiol 307: 97-129, 1980). We also analyze the sources of possible artifacts in the determination of i and N, such as channel rundown, inadequate filtering, and limited resolution of digital data acquisition by use of a simulation computer program (available at www.cecs.cl).