Adiabatic solution for the Ohmic cable equation. An homogeneous cell, prospects for electronic measurements]

Exact and adiabatic electrotonic solutions [1] were calculated for reconstructed motoneurone and hippocampal interneurone in case of linear and exponential ramp stimulation by the fixed current, potential or homogenous electric field. For the rising exponential ramp the solutions are identical. In case of the decaying exponent the adiabatic solution becomes an asymptote for the exact one if the stimulus decays slower than relaxation of the initial conditions in the cell. If the stimulus decays faster, the asymptote is the current or potential axis, depending on the stimulation mode. For electrotonically short cell, the exact solution approaches the asymptote faster. The solution for the exponentially rising field does not depend on the dendritic tree configuration and depends only on the effective electrotonic length of the neurone. It could be useful to apply ramp stimulation, especially exponential ramp of the electric field, to estimate electrotonic parameters of cells.     

Mark—Recapture Accurately Estimates Census for Tuatara,a Burrowing Reptile

Abstract: Estimates of population size are necessary for effective management of threatened and endangered species, but accurate estimation is often difficult when species are cryptic. We evaluated effectiveness of mark–recapture techniques using the Lincoln–Peterson estimator for predicting true census size of a population of tuatara (Sphenodon punctatus), a burrowing reptile that is a conservation priority in New Zealand. We found that Lincoln–Peterson estimates (NŇ = 85) were accurate for predicting the census size (N = 87) after only a 3-day mark–recapture survey. We recommend this method as a cost-effective way to accurately estimate population size for isolated, inaccessible tuatara populations, because it requires limited personnel, expertise, and time, and has low environmental impact on fragile sites.     

Ultrastructural differentiation during drosophila neurogenesis in vitro

Drosophila melanogaster neuroblasts differentiate in vitro, and each gives rise to a cluster of about 18 daughter neurons. Electron microscopic observations of single clusters show that axons from daughter neurons form a neuropile within the cluster of cell bodies. The neuropile increases in size and complexity for several hours, during which time chemical, and probably electrotonic, synapses form between neurites. Clear vesicles with diameters of about 35 nm and dense core vesicles with diameters of about 60 and 160 nm were detected. The development of the neuropile indicates that the prerequisite cell recognition phenomena were manifested during differentiation in vitro, and the complexity of the neuropile suggests it may have attained the capacity to process information.     

Formation of novel central and peripheral connections between molluscan central neurons in organ cultured ganglia

An in vitro organ culture system for buccal ganglia of the adult snail, Helisoma, is described. The system supports: (1) maintenance of characterstic electrophysiological parameters of identified neurons over seven days of culture; (2) choline metabolism including uptake and synthesis over the same duration; (3) sprouting and growth of neurons in response to axotomy; (4) the formation of novel central electrotonic connections between identified neurons as a result of sprouting and growth. These observations on neuronal growth and the formation of connections are similar to those made with in vivo culture. The use of in vitro culture allows precise manipulations not previously possible. When buccal ganglia are cultured in vitro with the cut distal ends of peripheral nerve trunks held closely apposed, axons of neurons 5R and 5L in the nerve trunks are capable of forming electrotonic connections similar to central connections. The capability of these neurons to form electrotonic connections via their peripheral axons implies that special structures (i. e., central neurites) are not required for the formation of connections; and neither are special environments (i. e., the central neurites) required for these connections.     

SEXUAL SIZE DIMORPHISM AS A CORRELATED RESPONSE TO SELECTION ON BODY SIZE: AN EMPIRICAL TEST OF THE QUANTITATIVE GENETIC MODEL

We artificially selected for body size in Drosophila melanogaster to test Lande's quantitative genetic model for the evolution of sexual size dimorphism. Thorax width was used as an estimator of body size. Selection was maintained for 21 generations in both directions on males only, females only, or both sexes simultaneously. The correlated response of sexual size dimorphism in each selection regime was compared to the response predicted by four variants of the model, each of which differed only in assumptions about input parameters. Body size responded well to selection, but the correlated response of sexual size dimorphism was weaker than that predicted by any of the variants. Dimorphism decreased in most selection lines, contrary to the model predictions. We suggest that selection on body size acts primarily on growth trajectories. Changes in dimorphism are caused by the fact that male and female growth trajectories are not parallel and termination of growth at different points along the curves results in dimorphism levels that are difficult to predict without detailed knowledge of growth parameters. This may also explain many of the inconsistent results in dimorphism changes seen in earlier selection experiments.     

On estimating the growth function of tumors

The growth rate of a cancerous tumor as a function of its age is a subject of intellectual and practical importance, as it influences both the effectiveness of proposed screening programs and the strategy of treatment. Obtaining direct evidence on the growth rate is quite difficult, owing to the ethical necessity to intervene when cancer is confirmed. The reasonable assumption that there is a common growth function of age and that probability of detection of a tumor in a short time period is proportional to its size allow the growth function to be inferred from data on sizes at detection. These results can be generalized to allow for individual variation in the rate of traversal of the common growth function. An estimator for the growth function from data on size at detection is obtained. Simulations indicate that it performs reasonably. Application of this estimator to data on a large series of cases of breast cancer at U.T. M. D. Anderson Hospital indicates that the growth function in the range of sizes seen at detection, can be adequately described by exponential growth, with rather large individual-to-individual variations in growth rate.     

A Comparative Statistical Analysis of Genetic Distances. I - Estimation of Distances and of their Variances: Distribution of the Estimators

We present a Monte-Carlo simulation analysis of the statistical properties of absolute genetic distance and of Nei's minimum and standard genetic distances. The estimation of distances (bias) and of their variances is analysed as well as the distributions of distance and variance estimators, taking into account both gamete and locus samplings. Both of Nei's statistics are non-linear when distances are small and consequently the distributions of their estimators are extremely asymmetrical. It is difficult to find theoretical laws that fit such asymmetrical distributions. Absolute genetic distance is linear and its distributions are better fit by a normal distribution. When distances are medium or large, minimum distance and absolute distance distributions are close to a normal distribution, but those of the standard distance can never be considered as normal. For large distances the jack-knife estimator of the standard distance variance is bad; another standard distance estimator is suggested. Absolute distance, which has the best mathematical properties, is particularly interesting for small distances if the gamete sample size is large, even when the number of loci is small. When both distance and gamete sample size are small, this statistic is biased.     

Dendritic analysis of lobster stretch receptor neurons: Electrotonic properties with single and distributed inputs

Using steady-state cable analysis as derived by Rall, electrotonic properties of the dendritic trees of the tonic stretch receptor neuron of the spiny lobster, Panulirus interruptus,have been examined. By directly measuring the somatic input resistance and by visualizing the dendritic trees of this neuron by backfilling the axon with cobalt, the electrotonic properties of the dendritic trees have been derived. The calculated membrane resistivity is 800-3600 -cm ². Voltage and current transfer functions were calculated for (a) single dendritic tips the size observed in the cobalt preparations and (b) for processes 2 µm or smaller, as observed in electron microscopy. Current transfer to the soma was high in both cases (greater than 80%). Voltage transfer was 22% for large and 4% for small dendrites. When a more natural simultaneous conductance change at the tips of all major dendrites was modeled, voltage transfer was 84% and current transfer 56%. But the dynamic range of the cell (rheobase to saturation) is well-predicted by varying the simultaneous inputs, not by scaling up a single input, thus illustrating that convenient indices of electrotonic properties may not prove useful in appreciating the integrative properties of a neuron.     

Adiabatic solution of the Ohmic cable equation. General theory, homogeneous cylindrical fiber]

An adiabatic solution of the Ohmic cable equation is suggested, which reduces the non-stationary equation to a stationary form. The adiabatic length constant of the stationary equation is time-dependent. The adiabatic solutions for the boundary conditions that change in time linearly and exponentially were studied. In the latter case, the adiabatic length constant does not depend on time though it differs from the usual length constant. The cable input characteristics of exact and adiabatic solutions were compared in the cases of the voltage- and current-clamp, and electric field stimulation. The adiabatic and exact solutions are identical for the rising exponential stimuli. For the falling exponential stimuli, the adiabatic solution determines the exact asymptotic solution if the stimulus decays slower than the relaxation of initial conditions. It is propose to use linear and exponential ramp stimulation in electrotonic measurements.     

Effects of electrical coupling on the cone-horizontal cell circuit in the catfish retina

Based on experimental data, a model of the cone-horizontal cell (L-HC) circuit has been developed for the luminosity channel of the catfish retina and impulse responses of cones and L-HC's were replicated for various experimental conditions. Negative feedback from L-HC to the cone pedicle and increases in the dc levels of L-HC (H ⁰), that produce increases in the feedback gain, convert monophasic impulse responses to those that are biphasic, smaller and faster. Electrical coupling of cones and L-HC's lead to decremental spread of 2 radially outgoing waves with time courses of the coupled cones and L-HC's dependent on the spatial organization of the negative feedback circuit: however, the L-HC's impulse response on spreading outward shows an initial increase before decreasing. Interactions of the cone and L-HC waves were studied using Laplace transforms and the convolution theorem. The presence of a negative feedback circuit leads to deviations of the electrotonic decay from an exponential function. As a result of the dependency of the feedback gain on H ⁰, electrical coupling introduces non-linearities in the cone-L-HC circuit that are dependent on the mean illuminance level.     

Bias of maximum likelihood estimator of intraclass correlation

Summary A bias correction was derived for the maximum likelihood estimator (MLE) of the intraclass correlation. The bias consisted of two parts: a correction from MLE to the analysis of variance estimator (ANOVA) and the bias of ANOVA. The total possible bias was always negative and depended upon both the degree of correlation and the design size and balance. The first part of the bias was an exact algebraic expression from MLE to ANOVA, and the corrected estimator by this part was ANOVA. It was also shown that the first correction term was equivalent to Fisher's reciprocal bias correction on hisZ scores. The total possible bias of MLE was large for small and moderate samples. Relative biases were larger for small parametric values and vice versa. To ensure a relative bias less than 10% assuming an intraclass correlation of 0.025, which is not unusual in most of the animal genetic studies, the total number of observations (N) should be not less than 500. From a design point of view, minimum bias occurred atn = 2, the minimum family size possible, underN fixed.     

Estimating the strength of selective sweeps from deep population diversity data

Selective sweeps are typically associated with a local reduction of genetic diversity around the adaptive site. However, selective sweeps can also quickly carry neutral mutations to observable population frequencies if they arise early in a sweep and hitchhike with the adaptive allele. We show that the interplay between mutation and exponential amplification through hitchhiking results in a characteristic frequency spectrum of the resulting novel haplotype variation that depends only on the ratio of the mutation rate and the selection coefficient of the sweep. On the basis of this result, we develop an estimator for the selection coefficient driving a sweep. Since this estimator utilizes the novel variation arising from mutations during a sweep, it does not rely on preexisting variation and can also be applied to loci that lack recombination. Compared with standard approaches that infer selection coefficients from the size of dips in genetic diversity around the adaptive site, our estimator requires much shorter sequences but sampled at high population depth to capture low-frequency variants; given such data, it consistently outperforms standard approaches. We investigate analytically and numerically how the accuracy of our estimator is affected by the decay of the sweep pattern over time as a consequence of random genetic drift and discuss potential effects of recombination, soft sweeps, and demography. As an example for its use, we apply our estimator to deep sequencing data from human immunodeficiency virus populations.     

Using pedigree reconstruction to estimate population size: genotypes are more than individually unique marks

Estimates of population size are critical for conservation and management, but accurate estimates are difficult to obtain for many species. Noninvasive genetic methods are increasingly used to estimate population size, particularly in elusive species such as large carnivores, which are difficult to count by most other methods. In most such studies, genotypes are treated simply as unique individual identifiers. Here, we develop a new estimator of population size based on pedigree reconstruction. The estimator accounts for individuals that were directly sampled, individuals that were not sampled but whose genotype could be inferred by pedigree reconstruction, and individuals that were not detected by either of these methods. Monte Carlo simulations show that the population estimate is unbiased and precise if sampling is of sufficient intensity and duration. Simulations also identified sampling conditions that can cause the method to overestimate or underestimate true population size; we present and discuss methods to correct these potential biases. The method detected 2–21% more individuals than were directly sampled across a broad range of simulated sampling schemes. Genotypes are more than unique identifiers, and the information about relationships in a set of genotypes can improve estimates of population size.     

Using maximum likelihood to estimate population size from temporal changes in allele frequencies.

We develop a maximum-likelihood framework for using temporal changes in allele frequencies to estimate the number of breeding individuals in a population. We use simulations to compare the performance of this estimator to an F-statistic estimator of variance effective population size. The maximum-likelihood estimator had a lower variance and smaller bias. Taking advantage of the likelihood framework, we extend the model to include exponential growth and show that temporal allele frequency data from three or more sampling events can be used to test for population growth.     

Fission yeast cells grow approximately exponentially

How the rate of cell growth is influenced by cell size is a fundamental question of cell biology. The simple model that cell growth is proportional to cell size, based on the proposition that larger cells have proportionally greater synthetic capacity than smaller cells, leads to the prediction that the rate of cell growth increases exponentially with cell size. However, other modes of cell growth, including bilinear growth, have been reported. The distinction between exponential and bilinear growth has been explored in particular detail in the fission yeast Schizosaccharomyces pombe. We have revisited the mode of fission yeast cell growth using high-resolution time-lapse microscopy and find, as previously reported, that these two growth models are difficult to distinguish both because of the similarity in shapes between exponential and bilinear curves over the two-fold change in length of a normal cell cycle and because of the substantial biological and experimental noise inherent to these experiments. Therefore, we contrived to have cells grow more than twofold, by holding them in G2 for up to 8 h. Over this extended growth period, in which cells grow up to 5.5-fold, the two growth models diverge to the point that we can confidently exclude bilinear growth as a general model for fission yeast growth. Although the growth we observe is clearly more complicated than predicted by simple exponential growth, we find that exponential growth is a robust approximation of fission yeast growth, both during an unperturbed cell cycle and during extended periods of growth.     

ESTIMATION OF PARAMETERS OF INBREEDING AND GENETIC DRIFT IN POPULATIONS WITH OVERLAPPING GENERATIONS

Many long‐lived plant and animal species have nondiscrete overlapping generations. Although numerous models have been developed to predict the effective sizes (N_e) of populations with overlapping generations, they are extremely difficult to apply to natural populations because of the large array of unknown and elusive life‐table parameters involved. Unfortunately, little work has been done to estimate the N_e of populations with overlapping generations from marker data, in sharp contrast to the situation of populations with discrete generations for which quite a few estimators are available. In this study, we propose an estimator (EPA, estimator by parentage assignments) of the current N_e of populations with overlapping generations, using the sex, age, and multilocus genotype information of a single sample of individuals taken at random from the population. Simulations show that EPA provides unbiased and accurate estimates of N_e under realistic sampling and genotyping effort. Additionally, it yields estimates of other interesting parameters such as generation interval, the variances and covariances of lifetime family size, effective number of breeders of each age class, and life‐table variables. Data from wild populations of baboons and hihi (stitchbird) were analyzed by EPA to demonstrate the use of the estimator in practical sampling and genotyping situations.     

Seed size and emergence time within a stand of wild radish (Raphanus raphanistrum L.): the establishment of a fitness hierarchy

Summary To determine the role of seed size in creating adult plants of different reproductive success, individual seedlings were marked and periodically censused in a natural stand of wild radish (Raphanus raphanistrum L.) in Hamden, Connecticut. Maximum cotyledon witdth is a useful field estimator of seed weight in this species, although dramatic variation in the availability of water can modify this relationship. Using maximum cotyledon width as a linear estimate of seed weight showed that an increase in seed weight gives rise to a disproportionately large increase in an individual's total reproductive output. Analysis of covariance demonstrated that reproductive output is influenced more heavily by seed weight (maximum cotyledon width) than by emergence time. Genetic variation for seed size has been maintained in this population, suggesting that selection favoring large seeds during the seedling stage may be counteracted by selection for large numbers of seeds.     

Estimation of specific growth rate from cell density measurements

For modelling purposes it is of great importance to derive the specific growth rate as a function of time from biomass measurements. Traditional methods such as exponential or polynomial fitting do not give satisfactory results nor do these methods take the noise characteristics of the biomass measurements into account. Standard recursive techniques, such as Kalman filtering, use only the data up to the time under consideration and are dependent of a good initial estimation. This paper describes a technique based on combining subsequent backward and forward extended Kalman filtering to give a smoothing estimator for the specific growth rate. The estimator does not need an initial value and is shown to have a single tuning parameter. The applicability of the estimator is demonstrated on batch and fed-batch cultivations of two organisms: Bordetella pertussis and Neisseria meningitidis.     

Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects

We examine the utility of the action potential (AP) duration (APD) restitution curve slope in predicting the onset of electrical alternans when electrotonic and memory effects are considered. We develop and use two ionic cell models without memory that have the same restitution curve with slope >1 but different AP shapes and, therefore, different electrotonic effects. We also study a third cell model that incorporates short-term memory of previous cycle lengths, so that it has a family of S1-S2 restitution curves as well as a dynamic restitution curve with slope >1. Our results indicate that both electrotonic and memory effects can suppress alternans, even when the APD restitution curve is steep. In the absence of memory, electrotonic currents related to the shape of the AP, as well as conduction velocity restitution, can affect how alternans develops in tissue and, in some cases, can prevent its induction entirely, even when isolated cells exhibit alternans. When short-term memory is included, alternans may not occur in isolated cells, despite a steep APD restitution curve, and may or may not occur in tissue, depending on conduction velocity restitution. We show for the first time that electrotonic and memory effects can prevent conduction blocks and stabilize reentrant waves in two and three dimensions. Thus we find that the slope of the APD restitution curve alone does not always well predict the onset of alternans and that incorporating electrotonic and memory effects may provide a more useful alternans criterion.     

Population size estimates based on the frequency of genetically assigned parent–offspring pairs within a subsample

Estimating population density as precise as possible is a key premise for managing wild animal species. This can be a challenging task if the species in question is elusive or, due to high quantities, hard to count. We present a new, mathematically derived estimator for population size, where the estimation is based solely on the frequency of genetically assigned parent–offspring pairs within a subsample of an ungulate population. By use of molecular markers like microsatellites, the number of these parent–offspring pairs can be determined. The study's aim was to clarify whether a classical capture–mark–recapture (CMR) method can be adapted or extended by this genetic element to a genetic‐based capture–mark–recapture (g‐CMR). We numerically validate the presented estimator (and corresponding variance estimates) and provide the R‐code for the computation of estimates of population size including confidence intervals. The presented method provides a new framework to precisely estimate population size based on the genetic analysis of a one‐time subsample. This is especially of value where traditional CMR methods or other DNA‐based (fecal or hair) capture–recapture methods fail or are too difficult to apply. The DNA source used is basically irrelevant, but in the present case the sampling of an annual hunting bag is to serve as data basis. In addition to the high quality of muscle tissue samples, hunting bags provide additional and essential information for wildlife management practices, such as age, weight, or sex. In cases where a g‐CMR method is ecologically and hunting‐wise appropriate, it enables a wide applicability, also through its species‐independent use.