Breeding habitat selection behaviors in heterogeneous environments: implications for modeling reintroduction

Animal movement and habitat selection behavior are important considerations in ecology, and remain a major issue for successful animal reintroductions. However, simple rules are often used to model movement or focus only on intrinsic environmental cues, neglecting recent insights in behavioral ecology on habitat selection processes. In particular, social information has been proposed as a widespread source of information for habitat evaluation.
We investigated the role of explicit breeding habitat selection strategies on the establishment pattern of reintroduced populations and their persistence. We considered local movement at the scale of a single population. We constructed a spatially-implicit demographic model that considered five breeding habitat selection rules: 1) random, 2) intrinsic habitat quality, 3) avoidance of conspecifics, 4) presence of conspecifics and 5) reproductive success of conspecifics. The impact of breeding habitat selection was examined for different release methods under various levels of environmental heterogeneity levels, for both long and short-lived monogamous species.
When heterogeneity between intrinsic habitat patch qualities is high, the persistence of reintroduced populations strongly depends on habitat selection strategies. Strategies based on intrinsic quality and conspecific reproductive success lead to a lower reintroduction failure risk than random, conspecific presence or avoidance-based strategies. Conspecific presence or avoidance-based strategies may aggregate individuals in suboptimal habitats. The release of adults seems to be more efficient independent of habitat selection strategy.
We emphasize the crucial role of oriented habitat selection behavior and non ideal habitat selection in movement modeling, particularly for reintroduction.     

A reaction-diffusion system of a predator-prey-mutualist model

Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species—a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations.     

Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population

Let birth rates and death rates be constant, birth rates positive, fertilities additive, and each birth rate not larger than twice any other birth rate. Global convergence to equilibria is proved for the model in the title. There is at most one polymorphic equilibrium or there are a continuum of equilibria. The phase portraits are given. If there is a polymorphic equilibrium, then the largest negatively invariant set in the state space is a continuous curve connecting the two fixation equilibria. This curve coincides with the Hardy-Weinberg manifold exactly when the death rate is additive. Disregarding extinction, the polymorphic equilibria are the same for the continuous model as for the corresponding discrete model exactly when the death rate is additive.     

Selection at a diallelic autosomal locus in a dioecious population

The model used is that of an infinite dioecious population with nonoverlapping discrete generations and random mating. If the fitnesses are constant and heterozygotes are viable, it is proved that the allelic frequencies converge to equilibria as the number of generations tend to infinity. The results complement those of Karlin and Lessard [1] and Selgrade and Ziehe [5] in that hyperbolicity of equilibria is not assumed, use of index theory is avoided and it is determined how the number of equilibria and phase portraits depend on the fitnesses in the most general case. Lessard [2] gives, in the same situation, a condensed proof of convergence of allelic frequencies off the separatrix under the hypothesis that 1 is not an eigenvalue at any equilibrium. Our method of study is elementary.     

Parameter estimation in a special reaction-diffusion system modelling man-environment diseases

An approximation scheme for a reaction-diffusion system with distributed feedback through the boundary is developed. It is used to estimate the strength of the feedback mechanisms from measurements of the states. The results are illustrated by numerical examples.     

Selection-mutation at a diallelic autosomal locus in a dioecious population

The population is assumed to be infinite dioecious with nonoverlapping discrete generations and random mating. It is assumed that the fitnesses and mutation rates are constant, heterozygotes are viable and the mutation rates are less than one-half. It is proved that the allelic frequencies converge to equilibria as the number of generations tends to infinity. The a priori types of phase portraits are determined. The method employed is elementary. The results extend those of [1, 2, 5, 8] to the case of selection-mutation rather than pure selection and those of [7] to the case of an autosomal rather than a sex-linked locus.     

Application of absorbing Markov chains to sib mating populations with selection for a pair of independent diallelic loci

In this paper we consider a sib mating population with a pair of independent diallelic loci. The average, variance, and third order moment about the mean have been calculated for the distribution representing the number of generations needed to reach an absorbing state beginning in any one of the trnsient states. Four cases are analysed: the no selection one and those cases arising from the combination of favorable selective values for the homozygous and heterozygous genotypes for both genes. The different cases are considered separately and compared, but only some typical starting cases have been reported so as to save space. No selective differences were assumed between the two sexes. The formalism of absorbing Markov chains have been used for the calculations.     

Wave-pinning and cell polarity from a bistable reaction-diffusion system

Motile eukaryotic cells polarize in response to external signals. Numerous mechanisms have been suggested to account for this symmetry breaking and for the ensuing robust polarization. Implicated in this process are various proteins that are recruited to the plasma membrane and segregate at an emergent front or back of the polarizing cell. Among these are PI3K, PTEN, and members of the Rho family GTPases such as Cdc42, Rac, and Rho. Many such proteins, including the Rho GTPases, cycle between active membrane-bound forms and inactive cytosolic forms. In previous work, we have shown that this property, together with appropriate crosstalk, endows a biochemical circuit (Cdc42, Rac, and Rho) with the property of inherent polarizability. Here we show that this property is present in an even simpler system comprised of a single active/inactive protein pair with positive feedback to its own activation. The simplicity of this minimal system also allows us to explain the mechanism using insights from mathematical analysis. The basic idea resides in a well-known property of reaction-diffusion systems with bistable kinetics, namely, propagation of fronts. However, it crucially depends on exchange between active and inactive forms of the chemicals with unequal rates of diffusion, and overall conservation to pin the waves into a stable polar distribution. We refer to these dynamics as wave-pinning and we show that this phenomenon is distinct from Turing-instability-generated pattern formation that occurs in reaction-diffusion systems that appear to be very similar. We explain the mathematical basis of the phenomenon, relate it to spatial segregation of Rho GTPases, and show how it can account for spatial amplification and maintenance of polarity, as well as sensitivity to new stimuli typical in polarization of eukaryotic cells.     

Computer modeling of joint selection response of MGE patterns and a polygenic system]

Using computer simulation, selection response of three genome patterns--polygenes, mobile genetic elements (MGEs), and labels of identity by origin (LIOs)--were studied. In each generation of selection, variability of each pattern type was described by on UPGMA tree. Stringent positive truncation selection on an additive polygenic trait and recombination between segments of the genetic map were considered. MGEs were classified into three groups: modifiers (enhancers) of the polygenic expression, markers, and independent copies. It was shown that at generations 30 to 40, 95-96% and 70-80% of respectively enforced and non-enforced active polygenic alleles were fixed (2-3% and 16-17% lost). In all generations, Hkn < or = Dkn of the length of the maximal route along the tree. At the same time, modifier MGEs were fixed for 85-88% (lost for 11-12%); marker MGEs, for 60-70 (lost for 21-25%); and independent copies, for 30-40 (lost for 50-60%). The behavior of independent MGE copies was generally consistent with the predictions of the genetic drift theory, modifier MGEs behaved similarly to the modified polygenes, and marker MGEs exhibited intermediate properties. The LIO patterns showed rapid homozygotization: their variability dropped dramatically between generations 10 and 30. In F50, the final consensus pattern of polygenes included 16 out of 18 enforced and 18 out of 21 non-enforced polygenic alleles. The fixation/loss ratios were 16:3 for modifier MGEs, 15:6 for marker MGEs, and 25:28 (with 7 polymorphic) for independent copies. The LIO consensus pattern contained 13 out of 100 original markers, which formed 26 fragments of one to ten map segments in size; 21 fragments contained active polygenic alleles, and 14 of them had also modifier MGEs. Recombinational shuffling of patterns was not completed. In the course of selection, active polygenic alleles take along adjacent segments, including those containing modifier MGEs and markers. These constitute the conservative part of all consensus patterns while the remaining segments are random.     

Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population with random mating

Global convergence to equilibria is proved for the model in the title under the assumption that death rates (and fertilities) are constant and fertilities are additive and positive. The phase portraits are determined. There is at most one polymorphic equilibrium or there are a continuum of equilibria.     

Spatial patterns produced by a reaction-diffusion system in primary hair follicles

This paper is the third in a series examining the role of a reaction-diffusion (RD) system as the principal mechanism providing spatial information for cell differentiation during hair follicle initiation and development and hair fibre formation. A theoretical mechanism is described by which the RD system supplies positional information during hair follicle development. Solutions of the RD system within the primordial follicle are described as well as the sequence of spatial patterns provides the follicle/epidermis boundary conditions required to account for the density and grouping of follicles during initiation. At the same time the spatial patterns are also shown to be capable of providing the positional information which determines various geometrical aspects of follicle development; in particular the development of follicles at an angle to the skin surface and the initiation and location of sweat glands and sebaceous glands on the follicle.     

The role of a reaction-diffusion system in the formation of hair fibres

Epithelial cells destined to form the hair fibre begin to differentiate while still in the hair follicle bulb. The fibre cells continue to differentiate as they migrate out of the bulb and up the follicle towards the skin surface. The anatomy of the hair follicle and the different cell types observed within the follicle are briefly reviewed. A theoretical scheme for cell differentiation, capable of producing all the observed mature cell types, is presented. A major component of the scheme is a reaction-diffusion system of morphogens similar to that originally proposed by Turing (1952). The mathematical solution of the equations defining the reaction-diffusion system within the follicle bulb is discussed. The sequence of patterns in the spatial distribution of the morphogens expected in the hair follicle bulb is calculated and found to be in good agreement with the sequence of patterns of orthocortical and paracortical cells in the fibre cross section as the diameter of the fibre increases. The spatial patterns of the morphogens are also compared with the shape of the fibre cross section. It is concluded that a reaction-diffusion system may play a major role in the morphogenesis of hair fibres.     

Some analytical results about a simple reaction-diffusion system for morphogenesis

Summary The reaction-diffusion system considered involves only one nonlinear term and is a gradient system. In a bifurcation analysis for the equilibrium states, the global existence of infinitely many solution branches can be shown by the method of Ljusternik-Schnirelmann. Their stability is studied. Using a Ljapunov functional it can be shown that the solutions of the time-dependent system converge to the equilibrium states.     

Zebrafish leopard gene as a component of the putative reaction-diffusion system

It has been suggested, on a theoretical basis, that a reaction-diffusion (RD) mechanism underlies pigment pattern formation in animals, but as yet, there is no molecular evidence for the putative mechanism. Mutations in the zebrafish gene, leopard, change the pattern from stripes to spots. Interestingly each allele gives a characteristic pattern, which varies in spot size, density and connectivity. That mutations in a single gene can generate such a variety of patterns can be understood using a RD model. All the pattern variations of leopard mutants can be generated in a simulation by changing a parameter value that corresponds to the reaction kinetics in a putative RD system. Substituting an intermediate value of the parameter makes the patterns similar to the heterozygous fish. These results suggest that the leopard gene product is a component of the putative RD mechanism.     

The role of a reaction-diffusion system in the initiation of primary hair follicles

A mechanism based on a reaction-diffusion system is proposed for the initiation of hair follicles in the epidermis during fetal development. It is demonstrated that initiation of primary follicles in a series of waves, within the proposed mechanism, is a consequence of the size and shape dependent properties of the reaction-diffusion system without the need for the propagation of signals through the skin. The observed trio grouping of follicles and variation of primary follicle density per unit skin area during development are also correctly predicted. An explanation, based on the reaction-diffusion system and the variation of its characteristic spatial wavelength with time during development, is suggested for the termination of both primary and secondary follicle initiation as well as follicle neogenesis. The proposed initiation mechanism is basically the same as that used to explain various spatial patterns observed in hair fibre formation (Nagorcka & Mooney, 1982).     

Species selection in a reactor-settler system

The competition between flocculating and nonflocculating microorganisms was investigated in a continuous reactor-settler system (e.g. activated sludge). Co existence states were found to be possible, over a certain domain of operating conditions, even with simple monotonic kinetics and simple competition. Multiple solutions exist when coexistence states are unstable. Coexistence solutions are stable when the flocculating bacteria grow faster at feed conditions as in the activated sludge problem. The analysis applies to one or several mixed or plug flow reactors. Other effects, such as enrichment of the recycle stream by the flocculating microorganism or substrate adsorption and storage, may change the structure of solution.     

Fluorescence modeling in a multicomponent system

An extensive fluorescence database for binary tyrosinetryptophan mixtures utilizing 280 nm excitation was collected. The database spanned three orders of magnitude (10(-6)M-10(-3)M) and covered all compositions within this range. A generalized model for describing the multicomponent fluorescence signals as a function of emission wavelength, excitation wavelength, and sample composition was derived. A geometric integral that contained all the geometric factors affecting fluorescence was introduced; thus the model was applicable to various configurations, including the three used in this study: an NADH probe, a backscatter laser-induced fluorescence setup, and a commercial spectroflurometer. A correction factor was proposed that allowed linearization of the fluorescence signals with respect to fluorophore concentrations. The effect of the water Raman on fluorescence spectra was also modeled. The model contains only two wavelength-dependent parameters for each of the components present in a sample, one specifying absorption of the excitation energy and the other specifying the species' fluorescence tendency. These wavelength-dependent parameters were correlated with polynomials. The average prediction error at each wavelength was 10-20%, a major portion of which was attributed to experimental uncertainties.     

Stochastic reaction-diffusion modeling of calcium dynamics in 3D dendritic spines of Purkinje cells

Calcium (Ca²⁺) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression and long-term potentiation at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP₃)-induced Ca²⁺ release. These Ca²⁺ transients happen in response to stimuli from parallel fibers (PFs) from granule cells and climbing fibers (CFs) from the inferior olivary nucleus. These events occur at low numbers of free Ca²⁺, requiring stochastic single-particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca²⁺ transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum, several Ca²⁺ transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca²⁺ transients in different dynamical situations. We test two different models of the IP₃ receptor (IP₃R). The model with nonlinear concentration response of binding of activating Ca²⁺ reproduces experimental results better than the model with linear response because of the filtering of noise. Our results also suggest that Ca²⁺-dependent inhibition of the IP₃R needs to be slow to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli arises from the relative timing of CF influx of Ca²⁺ and IP₃ production sensitizing IP₃R for Ca²⁺-induced Ca²⁺ release. We also model ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca²⁺ transients. Finally, we propose possible ways of recovering Ca²⁺ transients under ataxia.     

昆虫性选择行为研究进展

本文综述了昆虫的各种性选择行为,包括与个体大小有关的性选择行为、与鸣声有关的性选择行为、与“婚礼食物”有关的性选择行为以及精子竞争等。     

Frequency-dependent selection in a wild plant-pathogen system

This study investigated the occurrence of the rust fungus Puccinia chondrillina in clonal populations of its host plant, Chondrilla juncea. In 16 populations spread across eastern Turkey, 48 different multilocus isozyme phenotypes were identified in the host. Of these clones, 88% were restricted to single localities, while the remaining 12% were found in 2–11 populations. For 13 of the 16 plant populations the commonest host clone was always infected. Indeed, at ten sites this clone was the only one found to carry disease. In the remaining three populations the rusted plants were all of the second commonest isozyme type. The possibility of such a tight association of rust incidence with host clone frequency simultaneously across a wide geographic area is very low (P0.023), supporting the contention that the pathogen P. chondrillina may be imposing negative frequency-dependent selection on these C. juncea populations.