Total Branch Length Research Articles

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by Tm the mth coalescent time, when m + 1 lineages coalesce into m lineages, and An(t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, An(t), and the coalescence times, Tm, are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t → 0, the number of coalesced lineages n - An(t) follows a Poisson distribution, and as m → n, $$n\left(n-1\right){T}_{m}/2N\left(0\right)$$ follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference.

On the external branches of coalescents with multiple collisions

A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Lambda-coalescents) is provided. This recursion is used to derive asymptotic results as the sample size n tends to infinity for the joint moments of the external branch lengths and for the moments of the total external branch length of the Bolthausen-Sznitman coalescent. These asymptotic results are based on a differential equation approach, which is as well useful to obtain exact solutions for the joint moments of the external branch lengths for the Bolthausen-Sznitman coalescent. The results for example show that the lengths of two randomly chosen external branches are positively correlated for the Bolthausen-Sznitman coalescent, whereas they are negatively correlated for the Kingman coalescent provided that n >= 4.

A flexible ancestral genome reconstruction method based on gapped adjacencies.

BackgroundThe "small phylogeny" problem consists in inferring ancestral genomes associated with each internal node of a phylogenetic tree of a set of extant species. Existing methods can be grouped into two main categories: the distance-based methods aiming at minimizing a total branch length, and the synteny-based (or mapping) methods that first predict a collection of relations between ancestral markers in term of "synteny", and then assemble this collection into a set of Contiguous Ancestral Regions (CARs). The predicted CARs are likely to be more reliable as they are more directly deduced from observed conservations in extant species. However the challenge is to end up with a completely assembled genome.ResultsWe develop a new synteny-based method that is flexible enough to handle a model of evolution involving whole genome duplication events, in addition to rearrangements, gene insertions, and losses. Ancestral relationships between markers are defined in term of Gapped Adjacencies, i.e. pairs of markers separated by up to a given number of markers. It improves on a previous restricted to direct adjacencies, which revealed a high accuracy for adjacency prediction, but with the drawback of being overly conservative, i.e. of generating a large number of CARs. Applying our algorithm on various simulated data sets reveals good performance as we usually end up with a completely assembled genome, while keeping a low error rate.AvailabilityAll source code is available at http://www.iro.umontreal.ca/~mabrouk.

RETRACTED ARTICLE: Alteration of astrocytes and Wnt/β-catenin signaling in the frontal cortex of autistic subjects

BackgroundAutism is a neurodevelopmental disorder characterized by impairments in social interaction, verbal communication and repetitive behaviors. To date the etiology of this disorder is poorly understood. Studies suggest that astrocytes play critical roles in neural plasticity by detecting neuronal activity and modulating neuronal networks. Recently, a number of studies suggested that an abnormal function of glia/astrocytes may be involved in the development of autism. However, there is yet no direct evidence showing how astrocytes develop in the brain of autistic individuals.MethodsStudy subjects include brain tissue from autistic subjects, BTBR T + tfJ (BTBR) and Neuroligin (NL)-3 knock-down mice. Western blot analysis, Immunohistochemistry and confocal microscopy studies have been used to examine the density and morphology of astrocytes, as well as Wnt and β-catenin protein expression.ResultsIn this study, we demonstrate that the astrocytes in autisitc subjects exhibit significantly reduced branching processes, total branching length and cell body sizes. We also detected an astrocytosis in the frontal cortex of autistic subjects. In addition, we found that the astrocytes in the brain of an NL3 knockdown mouse exhibited similar alterations to what we found in the autistic brain. Furthermore, we detected that both Wnt and β-catenin proteins are decreased in the frontal cortex of autistic subjects. Wnt/β-catenin pathway has been suggested to be involved in the regulation of astrocyte development.ConclusionsOur findings imply that defects in astrocytes could impair neuronal plasticity and partially contribute to the development of autistic-like behaviors in both humans and mice. The alteration of Wnt/β-catenin pathway in the brain of autistic subjects may contribute to the changes of astrocytes.

REPRODUCTIVE ALLOCATION AND NUTRIENT RELATIONSHIPS IN CUPHEA: A SEMI-DOMESTICATED OILSEED CROP

Interrelationships between ontogeny, allometric mass, and carbon (C): nitrogen (N): phosphorus (P) ratios were quantified in Cuphea, a semi-domesticated indeterminate and phenotypically plastic potential oilseed crop. Relative growth rate and net assimilation rate were estimated as functions of growth stages, phenotypic traits and C:N:P ratios. Ontogenically, N:P ratios in reproductive and metabolic tissues were least variable and were mainly affected by allometric leaf mass and relative growth rate. Reproductive mass is best predicted by allometric stem mass and C:N ratio in structural and metabolic tissues; whereas, net assimilation rate is best predicted by allometric total branch length and relative growth rate. The conservative N:P ratios found in reproductive and metabolic tissues are important in determining reproductive allocation in Cuphea. Large antagonistic effects of C:N on N:P ratios found in different plant tissues suggest that maximum reproductive allocation can be attained by manipulating N:P ratio during ontogeny. A greater investment of resources in reproduction may be possible for this semi-domesticated crop if nutrient and mass allocation to supporting stems and roots can be altered for the benefit of reproductive biomass.

Atorvastatin enhances neurite outgrowth in cortical neurons in vitro via up-regulating the Akt/mTOR and Akt/GSK-3β signaling pathways

To investigate whether atorvastatin can promote formation of neurites in cultured cortical neurons and the signaling mechanisms responsible for this effect. Cultured rat cerebral cortical neurons were incubated with atorvastatin (0.05-10 μmol/L) for various lengths of time. For pharmacological experiments, inhibitors were added 30 min prior to addition of atorvastatin. Control cultures received a similar amount of DMSO. Following the treatment period, phase-contrast digital images were taken. Digital images of neurons were analyzed for total neurite branch length (TNBL), neurite number, terminal branch number, and soma area by SPOT Advanced Imaging software. After incubation with atorvastatin for 48 h, the levels of phosphorylated 3-phosphoinoside-dependent protein kinase-1 (PDK1), phospho-Akt, phosphorylated mammalian target of rapamycin (mTOR), phosphorylated 4E-binding protein 1 (4E-BP1), p70S6 kinase (p70S6K), and glycogen synthase kinase-3β (GSK-3β) in the cortical neurons were evaluated using Western blotting analyses. Atorvastatin (0.05-10 μmol/L) resulted in dose-dependent increase in neurite number and length in these neurons. Pretreatment of the cortical neurons with phosphatidylinositol 3-kinase (PI3K) inhibitors LY294002 (30 μmol/L) and wortmannin (5 μmol/L), Akt inhibitor tricribine (1 μmol/L) or mTOR inhibitor rapamycin (100 nmol/L) blocked the atorvastatin-induced increase in neurite outgrowth, suggesting that atorvastatin promoted neurite outgrowth via activating the PI3K/Akt/mTOR signaling pathway. Atorvastatin (10 μmol/L) significantly increased the levels of phosphorylated PDK1, Akt and mTOR in the cortical neurons, which were prevented by LY294002 (30 μmol/L). Moreover, atorvastatin (10 μmol/L) stimulated the phosphorylation of 4E-BP1 and p70S6K, the substrates of mTOR, in the cortical neurons. In addition, atorvastatin (10 μmol/L) significantly increased the phosphorylated GSK-3β level in the cortical neurons, which was prevented by both LY294002 and tricribine. These results suggest that activation of both the PI3K/Akt/mTOR and Akt/GSK-3β signaling pathways is responsible for the atorvastatin-induced neurite outgrowth in cultured cortical neurons.

Soil Nutrient, Woody Understory and Shoot and Root Growth Responses of Pinus brutia Ten. Saplings to Fire

Nine years after a wildfire, above- and below-ground morphology of Pinus brutia Ten. saplings and the microsite factors prevailing in understorey (unburned area) and postfire conditions (burned area) of the Forest Park of Thessaloniki were studied. Major stand characteristics (density, tree canopy cover, tree height, crown height, and diameter) were measured in the unburned area. Light and soil conditions as well as plant cover of woody species were recorded in both areas (burned and unburned). A random sample of pine saplings, of uniform age, was taken from both burned and unburned areas, and their above-ground (height, diameter, number and total length of branches, needle biomass) and below-ground morphological characteristics (taproot length, total length of coarse and fine roots, and number of coarse roots) were measured. Data analysis showed that above- and below-ground morphology of pine saplings was adversely affected in saplings grown in understorey conditions, compared to those grown in postfire conditions. P. brutia is a shade-intolerant tree species and thus the light conditions seem to be the critical factor affecting the growth of pine saplings. Light is not a limiting factor in the burned area compared to the understorey, where density of the tree canopy limits available light.

In Vitro Studies of Interferon-alpha Neurotoxicity (P01.248)

Objective: To determine the mechanism of interferon-alpha (IFNa) toxicity in neurons. Background Elevated IFNa in the CNS is linked to cognitive dysfunction in patients with inflammatory CNS diseases such as HIV-associated dementia. Previous studies showed that IFNa treatment of neuronal cultures caused a dose dependent decrease in dendritic branching and length, mostly prevented after pre-treatment with IFNa neutralizing antibodies. Design/Methods: Primary neurons were extracted from rat fetal cortices and cultured for 14 days. Neurons were treated with 1000 U/ml of IFNα for multiple time points prior to protein extractions or immunofluorescence staining. Protein extracts were analyzed using Western blot. Neurons were analyzed for dendritic length and branching using ImagePro. Results: After 24hrs of IFNα treatment, average total length of branches per neuron was significantly reduced. By 48hrs the number of branches per neuron was significantly decreased. To begin to evaluate the mechanism of decreased dendritic arborization, microtubule associate protein 2 (MAP2), a cytoskeleton protein required for dendritic growth and stability in neurons, was examined. IFNα causes a decrease in total MAP2 protein levels as soon as 2 hrs after treatment that remain decreased compared to controls through 48 hrs. MAP2 association with microtubules, required for neuronal function and dendritic stability, is regulated by phosphorylation, specifically at the Ser126 site on MAP2. Preliminary data shows a decrease in phosphorylation at Ser136 on MAP2 after IFNα treatment. STAT1 phosphorylation was examined in order to begin to determine the signaling cascade after IFNα receptor engagement. Phosphorylated STAT1 peaks 2 hrs after IFNα administration. Conclusions: The neurotoxicity of IFNα is complex since it has direct and indirect effects on neuronal function. Our studies suggest that IFNα is in part acting through its receptor to reduce MAP2 expression in neurons. Determining the mechanism of IFNα neurotoxicity could lead to therapies for cognitive dysfunction during neuroinflammation. Supported by: VA Merit award 0007. Disclosure: Dr. Tyor has nothing to disclose. Dr. Fritz-French has nothing to disclose. Dr. Welshhans has nothing to disclose. Dr. Zhang has nothing to disclose. Dr. Sas has nothing to disclose. Dr. Bassell has nothing to disclose.

Maternal Care Received by Individual Pups Correlates with Adult CA1 Dendritic Morphology and Synaptic Plasticity in a Sex‐Dependent Manner

Maternal care is an important environmental factor for rats early in life. Adult offspring from dams exhibiting extremely high versus low maternal care differ remarkably in dendritic complexity and long-term synaptic potentiation in the CA1 area. However, >70% of the pups do not belong to these extreme categories of maternal care, questioning the general relevance of these observations. Therefore, the present study investigated whether the influence of maternal care is discernable over its entire range and can serve as an index predicting later CA1 structure and function. The amount of licking and grooming (%LG) received was determined for each pup during the first postnatal week. In males, both total apical branch length and dendritic complexity correlated significantly and positively with %LG. In females, we observed a nonsignificant negative correlation, also when controlled for variations in oestradiol and progesterone levels. The correlation in females was significantly different from that in males. No significant correlation was observed between the %LG and the amount of synaptic potentiation, either in male or in female offspring, regardless of whether slices had been treated with corticosterone or vehicle. However, in male rats, the degree of potentiation seen after corticosterone compared to vehicle treatment was almost significantly related to the %LG received early in life; this differed significantly from that observed in females. The data from the present study suggest that %LG received early in life results in mild, yet sex-dependent effects on adult CA1 structure and function.

CRH-R1 and CRH-R2 differentially modulate dendritic outgrowth of hippocampal neurons

Corticotropin-releasing hormone (CRH) has been implicated to be involved in the development of dendrites in brain. In the present study, we examined the effect of CRH on dendrite outgrowth in primary cultured hippocampal neurons and defined the specific CRH receptor subtype involved. Treatment of neurons with increasing concentration of CRH resulted in an increase in the total dendritic branch length (TDBL) of neurons compared with untreated neurons over 2-4days period of treatment. These effects can be reversed by the specific CRH-R1 antagonist antalarmin but not by the CRH-R2 antagonist astressin 2B. Treatment of neurons with urocortin II, the exclusive CRH-R2 agonist, significantly decreased TDBL of the cultured neurons. These effects can be reversed by the CRH-R2 antagonist astressin 2B. Our results suggest that CRH-R1 and CRH-R2 differentially modulate the dendritic growth of hippocampal neurons in culture.

Effect of Spraying Nitrogen and Some Plants Extracts in the Vegetative Growth on (Lavandula officinalis L)

This study was conducted in the special nursery in Mansour - Baghdad at 2011. to study the effect nitrogen 05 and 02 grams per liter in the form of urea as well as spraying four plant extracts which are Glycyrrhiz glabra uritica dioica Allium sativum Trigonella foenum – graecum and concentration of 5 grams per liter of distilled water and every extract plant in addition to the control treatment. Treatments were applied three times and the first was applied at 15-5-2011and the following applications were 15 days after the first application. Experiment were conducts using complete randomized block design with three replicates. Results, were analyzed using least significant differences at 5% probability. The results are summarized as follows:It was to spray the extract of Glycyrrhiza glabra significant effect in plant height it was 26.86 cm / plant compared to the treatment which was 2305 cm / plant, as well as to spray the extract of Uritica dioica significant effect in stem diameter of the main plant which was 0.34 cm with different insignificantly in compare with treatment of spraying extract of Trigonella foenum – graecum compared to the treatment was 0.21 cm also surpassed the treatment spraying 0.5 grams per liter of nitrogen significantly recipe in the number of branches per plant the number of branches 17.30 compared to the treatment comparison which reached 12.93.Either as the number of plant leaves it has surpassed the treatment spray Glycyrrhiza glabra extract significantly compared to other transaction it was 51083 leaf / plant compared to the treatment of non-spray amounting to 38783 leaf / plant and the results showed than spray treatment Glycyrrhiza glabra extract significantly in the description of total length of branches amounting to 395.90 cm / plant It also surpassed the treatment spray extract Uritica dioica significantly in the dry weight of leaves and was 61.13 gram / plant which was not different from the treatment of nitrogen 05 gram / L. As for the percentage content of chlorophyll pigment in the leaves was surpassed by 0.5 gN/L treatment of spraying nitrogen amounting to 33.60% which did

A General Principle of Neural Arbor Branch Density

The tree-like structures of a neuron that are responsible for distributing (axons) or collecting (dendrites) information over a region of the brain are called arbors. The size of the territory occupied by an arbor and the density of the arbor branches within that territory are important for computation because these factors determine what fraction of a neural map is sampled by a single cell and at what resolution [1]. Arbor territory size and branch density can vary by many orders of magnitude; however, we have identified a universal relationship between these two physical properties revealing a general neural architectural design principle. All of the arbors (axons and dendrites) we have studied (including fish retinal ganglion cells, rodent Purkinje cells, and the cortical arbors of various neural classes from rat, cat, monkey, and human) are found to be systematically less dense when they cover larger territories. This relationship can be described as a power law. Of several simple biological explanations explored, we find that this relationship is most consistent with a design principle that conserves the average number of connections between pairs of arbors of different sizes.

Assessing variability in root traits of wild Lupinus angustifolius germplasm: basis for modelling root system structure

Intra-specific variation in root system architecture and consequent efficiency of resource capture by major crops has received recent attention. The aim of this study was to assess variability in a number of root traits among wild genotypes of narrow-leafed lupin (Lupinus angustifolius L.), to provide a basis for modelling of root structure. A subset of 111 genotypes of L. angustifolius was selected from a large germplasm pool based on similarity matrices calculated using Diversity Array Technology markers. Plants were grown for 6 weeks in the established semi-hydroponic phenotyping systems to measure the fine-scale features of the root systems. Root morphology of wild L. angustifolius was primarily dominated by the taproot and first-order branches, with the presence of densely or sparsely distributed second-order branches in the late growth stage. Large variation in most root traits was identified among the tested genotypes. Total root length, branch length and branch number in the entire root system and in the upper roots were the most varied traits (coefficient of variation CV >0.50). Over 94% of the root system architectural variation determined from the principal components analysis was captured by six components (eigenvalue >1). Five relatively homogeneous groups of genotypes with distinguished patterns of root architecture were separated by k-means clustering analysis. Variability in the fine-scale features of root systems such as branching behaviour and taproot growth rates provides a basis for modelling root system structure, which is a promising path for selecting desirable root traits in breeding and domestication of wild and exotic resources of L. angustifolius for stressful or poor soil environments.

Effect of pruning history on growth and dry mass partitioning of jatropha on a plantation site in Madagascar

While technical aspects of oil processing of seeds of jatropha are under intensive investigation, comparably little is known about the performance of jatropha in the field. We investigated the effects of water availability (rainfed versus irrigated) and pruning-induced differences in plant stature on growth, biomass partitioning, and canopy size at a plantation site in Madagascar in 2010. Plants of different pruning types differed in trunk height (43 versus 29 cm) and primary branches total length (171 versus 310 cm). The two pruning types had effects on dry mass formation and leaf area projection (LAP) during the vegetation period. Trees which had a shorter trunk and longer lateral branches produced more biomass and had a higher LAP. Total dry mass formation varied from 489 to 912 g m � 2 and LAP from 3.26 to 7.37. Total aboveground biomass increased from 2.3 � 0.5 to 4.89 � 1.4 kg tree � 1 and from 4.6 � 1.8 to 8.9 � 1.0 kg tree � 1 for the pruning types with shorter and longer lateral branches, respectively. Growth of twigs and leaves was positively correlated with total length of branches. Relative dry mass allocation to branches, twigs and leaves, length of twigs per cm of branches and specific leaf area (13.57 � 0.72 m 2 kg � 1 ) were not affected by pruning and water supply. Trees with shorter branches had higher LAD. Results indicate that pruning type should be considered as a management tool to optimize biomass production. Detailed studies on effects of canopy size and shape on radiation interception and growth are required to improve the productivity of jatropha. a 2011 Published by Elsevier Ltd.

Exuberant growth and synapse formation of olfactory sensory neuron axonal arborizations

Neural connections in the adult nervous system are established with a high degree of precision. Several examples throughout the nervous system indicate that this precision is achieved by first establishing an initial exuberant immature pattern of connectivity that is then sculpted into the adult pattern via pruning. This often emerges as an activity-dependent process. In the olfactory system, sensory axons from neurons expressing the same odorant receptor project with high precision to specific glomerular structures in the olfactory bulb. This process undergoes maturation-dependent refinements that are not fully understood. Due to technical impediments that have made it difficult to focus on single axons, it is unknown whether olfactory sensory projections are established in an exuberant fashion. Here we developed a novel technique of electroporation that allowed us to simultaneously label single olfactory sensory neuron (OSN) axonal arbors and their presynaptic specializations. Using this method we were able to incorporate plasmids into OSNs at an immature stage, thereby allowing a time-course study of axonal arbor development and synapse formation in single olfactory sensory axons. We observed that the number of branch points, the total branch length, and the number and density of presynaptic specializations peaked at postnatal day 8 and decreased afterwards. Our data demonstrate that olfactory sensory axons develop in an exuberant way, both in terms of branch growth and synaptic composition. We hypothesize that exuberant branches and synapses are eliminated to achieve the mature pattern in a process likely to be regulated by neural activity.

Maternal deprivation and dendritic complexity in the basolateral amygdala

RationaleMaternal deprivation at postnatal day 3 was reported to enhance fear learning in a sex specific manner. Since the amygdala is critically involved in fear conditioning we examined here whether maternal deprivation regulates dendritic complexity in this area. ObjectiveTo assess whether maternal deprivation regulates dendritic complexity in the basolateral amygdala of male and female rats. MethodsUsing the Golgi-impregnation method, we studied whether 24 h of maternal deprivation on postnatal day 3 alters dendritic complexity of pyramidal and stellate cells in the basolateral amygdala of adult male and female rats. ResultsMaternal deprivation did not affect the total branch length, number of branch points and primary dendrites or dendritic complexity index in male and female offspring. ConclusionAlthough a brief period of maternal deprivation increases fear conditioned responses, it did not affect dendritic complexity in the basolateral amygdala. This suggests that other cellular substrates for learning and memory, e.g. at synaptic or cellular level, underlie the enhanced expression of fear memories after exposure to early life stress.This article is part of a Special Issue entitled ‘Anxiety and Depression’.

Low-frequency noise in planar Hall effect bridge sensors

The low-frequency characteristics of planar Hall effect bridge sensors are investigated as function of the sensor bias current and the applied magnetic field. The noise spectra reveal a Johnson-like spectrum at high frequencies, and a 1/ f-like excess noise spectrum at lower frequencies, with a knee frequency of around 400 Hz. The 1/ f-like excess noise can be described by the phenomenological Hooge equation with a Hooge parameter of γ H = 0.016. The detectivity is shown to depend on the total length, width and thickness of the bridge branches. The detectivity is improved by the square root of the length increase. Moreover, the detectivity is shown to depend on the amplitude of the applied magnetic field, revealing a magnetic origin to part of the 1/ f noise.

Toward an Efficient Method of Identifying Core Genes for Evolutionary and Functional Microbial Phylogenies

Microbial community metagenomes and individual microbial genomes are becoming increasingly accessible by means of high-throughput sequencing. Assessing organismal membership within a community is typically performed using one or a few taxonomic marker genes such as the 16S rDNA, and these same genes are also employed to reconstruct molecular phylogenies. There is thus a growing need to bioinformatically catalog strongly conserved core genes that can serve as effective taxonomic markers, to assess the agreement among phylogenies generated from different core gene, and to characterize the biological functions enriched within core genes and thus conserved throughout large microbial clades. We present a method to recursively identify core genes (i.e. genes ubiquitous within a microbial clade) in high-throughput from a large number of complete input genomes. We analyzed over 1,100 genomes to produce core gene sets spanning 2,861 bacterial and archaeal clades, ranging in size from one to >2,000 genes in inverse correlation with the α-diversity (total phylogenetic branch length) spanned by each clade. These cores are enriched as expected for housekeeping functions including translation, transcription, and replication, in addition to significant representations of regulatory, chaperone, and conserved uncharacterized proteins. In agreement with previous manually curated core gene sets, phylogenies constructed from one or more of these core genes agree with those built using 16S rDNA sequence similarity, suggesting that systematic core gene selection can be used to optimize both comparative genomics and determination of microbial community structure. Finally, we examine functional phylogenies constructed by clustering genomes by the presence or absence of orthologous gene families and show that they provide an informative complement to standard sequence-based molecular phylogenies.

Relative input strength rapidly regulates dendritic structure of chick auditory brainstem neurons.

Competition between presynaptic inputs has been suggested to shape dendritic form. This hypothesis can be directly tested on bitufted, auditory neurons in chicken nucleus laminaris (NL). Each NL neuron contains two relatively symmetrical dendritic arbors; the dorsal dendrites receive excitatory glutamatergic input from the ipsilateral ear, and the ventral dendrites receive corresponding input from the contralateral ear. To assess the effect of relative synaptic strength on NL dendrites, we used single-cell electroporation; electrophysiology; and live, two-photon laser scanning microscopy to manipulate both the amount and the balance of synaptic input to the two matching sets of dendrites. With simultaneous activation, both sets of dendrites changed together, either growing or retracting over the imaging period. In contrast, stimulation of only one set of dendrites (either dorsal or ventral) resulted in the unstimulated dendrites losing total dendritic branch length, whereas the stimulated dendrites exhibited a tendency to grow. In this system, balanced input leads to balanced changes in the two sets of dendrites, but imbalanced input results in differential changes. Time-lapse imaging revealed that NL dendrites respond to differential stimulation by first decreasing the size of their unstimulated dendrites and then increasing the size of their stimulated dendrites. This result suggests that the relative activity of presynaptic neurons dynamically controls dendritic structure in NL and that dendritic real estate can rapidly be shifted from inactive inputs to active inputs.

Estimation of parameters in large offspring number models and ratios of coalescence times

The ratio of singletons to the total number of segregating sites is used to estimate a reproduction parameter in a population model of large offspring numbers without having to jointly estimate the mutation rate. For neutral genetic variation, the ratio of singletons to the total number of segregating sites is equivalent to the ratio of total length of external branches to the total length of the gene genealogy. A multinomial maximum likelihood method that takes into account more frequency classes than just the singletons is developed to estimate the parameter of another large offspring number model. The performance of these methods with regard to sample size, mutation rate, and bias, is investigated by simulation. The expected value of the ratio of the total length of external branches to the total length of the whole tree is, using simulation, shown to decrease for the Kingman coalescent as sample size increases, but can increase or decrease, depending on parameter values, for Λ coalescents. Considering ratios of tree statistics, as opposed to considering lengths of various subtrees separately, can yield better insight into the dynamics of gene genealogies.