On the differential equations of species in competition

Summary It is shown that the ordinary differential equation commonly used to describe competing species are compatible with any dynamical behavior provided the number of species in very large.     

Global bifurcations in the FitzHugh-Nagumo equations for nerve wave propagation

The FitzHugh-Nagumo equations for action potential propagation along nerve axons and the corresponding ordinary differential equations for travelling waves are solved numerically. Above a critical value, a constant bias current can drive a wave-front solution. At the critical value, a global bifurcation occurs. As a result, the wave front switches into a pulse.Based on a thesis by one of the authors (H. F.).     

Ecological advice for the global fisher crisis

Fisheries science was the precursor of population ecology and continues to contribute important theoretical advances. Despite this, fishery scientists have a poor record for applying their insights to real-world fisheries management. Is there a gulf between theory and application or does the high variability inherent in fish populations and complexity of multispecies fisheries demand a different approach to management? Perhaps the solution to the world fisheries crisis is obvious after all?     

On a criterion for survival of species in models governed by difference equations

The difficulty of deciding on the survival of species in models governed by difference equations is pointed out. We show that a recently proposed criterion may overestimate the range of parameter values for which survival is assured.     

On Zeeman's equations for the nerve impulse

A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.     

Requirements for in vitro propagation of seven nitrogen-fixing Alnus species

Studies on the in vitro propagation of Alnus crispa, A. glutinosa, A. incana, A. japonica, A. rubra, A. sinuata and A. viridis indicated interspecific as well as intraspecific variations in their requirements for in vitro culture. The WPM and Blaydes media supported, respectively, growth of A. glutinosa and A. crispa but not that of both species, while the MS medium induced equal or significantly better growth than WPM and Blaydes media for both species. The optimum type and concentration of sugar to be used in the multiplication medium varied with species. Only A. glutinosa showed good growth on sucrose while glucose was optimum for all other species but at different concentrations. All species rooted in 3 weeks on half-strength MS medium including 1 M IBA. All clones of A. glutinosa and A. rubra rooted 100%, whereas easy-to-root and difficult-to-root clones were observed in the other species. In the rooting medium, glucose promoted rooting of the difficult-to-root clones better than sucrose. Survival following transfer to an artificial substrate was 100% for all species. Nodulation tests using pure cultures of two Frankia strains showed 100% nodulation on all Alnus clones.     

On enzymic clotting processes V: Rate equations for the case of arbitrary rate of production of the clotting species

The rate theory for enzyme-triggered coagulation reactions, such as the clotting of fibrin or casein, is extended to the case of an arbitrary rate of production of the clotting species. It is shown that the general expression for the growth of the weight-average molecular weight of the clotting product, -M_w, is given by -M_w = M₁{1 + k_s {∫₀^tP(t)² dt}/P(t)}, where M₁ is the “monomer” molecular weight, k_s the smoluchowskian flocculation rate constant and P(t) the total number of monomers produced by the enzyme in t. In the purely smoluchowskian case P(t) stands for the total number of monomers at the beginning of the clotting process. Numerical examples in which the rate of enzymic production is governed by complete Michaelis-Menten kinetics, are compared to cases in which this rate equals V_max- It is shown that after exhaustion of the substrate the system continues to coagulate in a purely smoluchowskian way. Turbidimetric experiments on the clotting of micelles of whole and κ-casein are presented which suggest inactivation of the enzyme by non-productive binding in the flocs formed.     

Managerial strategies in the captive propagation of endangered species

A captive propagation manager, committed to the welfare of captive populations of exotic animals, must often make decisions that are risky to individual animals. Innovative decisions that place animals at risk are essential to the progress of captive propagation. Such decisions must be grounded thoroughly on peer consultation, the scientific and zoo literature, and where possible on original applied research targeted specifically to the procedure in question. The management of two closely spaced births in a gorilla group is provided as an example.     

Persistence of species obeying difference equations

The question of persistence of interacting species is one of the most important in theoretical ecology; when the system is governed by difference equations this question is particularly difficult to resolve because of the complicated dynamics of the model. The problem has usually been tackled via the concepts of asymptotic stability and global asymptotic stability, however the first is not a strong enough restriction since only orbits starting near a rest point are guaranteed to converge to the rest point, while the second as well as usually being extremely difficult to establish is surely too strong a condition, since it rules out for example a stable limit cycle. It is proposed here that a more biologically realistic criterion, and incidentally one which turns out to be more tractable, is that of cooperativeness, where all orbits are required eventually to enter and remain in a region at a non-zero distance from the boundary (corresponding to a zero value of at least one population). A theorem is proved giving conditions for cooperativeness, and is applied to some examples of predator-prey interactions, simple conditions on the parameters being obtained even for some ranges of the parameters where the dynamics are chaotic.     

Strange attractors in volterra equations for species in competition

It is shown that for more than three competing species, Volterra differential equations with “destructive” nonlinear interactions can display numerically complicated asymptotic dynamics.     

Trans-cellular propagation of Tau aggregation by fibrillar species

Aggregation of the microtubule associated protein Tau is associated with several neurodegenerative disorders, including Alzheimer disease and frontotemporal dementia. In Alzheimer disease, Tau pathology spreads progressively throughout the brain, possibly along existing neural networks. However, it is still unclear how the propagation of Tau misfolding occurs. Intriguingly, in animal models, vaccine-based therapies have reduced Tau and synuclein pathology by uncertain mechanisms, given that these proteins are intracellular. We have previously speculated that trans-cellular propagation of misfolding could be mediated by a process similar to prion pathogenesis, in which fibrillar Tau aggregates spread pathology from cell to cell. However, there has been little evidence to demonstrate true trans-cellular propagation of Tau misfolding, in which Tau aggregates from one cell directly contact Tau protein in the recipient cell to trigger further aggregation. Here we have observed that intracellular Tau fibrils are directly released into the medium and then taken up by co-cultured cells. Internalized Tau aggregates induce fibrillization of intracellular Tau in these naive recipient cells via direct protein-protein contact that we demonstrate using FRET. Tau aggregation can be amplified across several generations of cells. An anti-Tau monoclonal antibody blocks Tau aggregate propagation by trapping fibrils in the extracellular space and preventing their uptake. Thus, propagation of Tau protein misfolding among cells can be mediated by release and subsequent uptake of fibrils that directly contact native protein in recipient cells. These results support the model of aggregate propagation by templated conformational change and suggest a mechanism for vaccine-based therapies in neurodegenerative diseases.     

Conservation and synteny of SSR loci and QTLs for vegetative propagation in four Eucalyptus species

Conservation of microsatellite loci, heterozygous in Eucalyptus grandis, Eucalyptus urophylla, Eucalyptus tereticornis and Eucalyptus globulus, allowed us to propose homeologies among genetic linkage groups in these species, supported by at least three SSR loci in two different linkage groups. Marker-trait associations for sprouting and adventitious rooting ability were also compared in the four species. Putative quantitative trait loci (QTLs) influencing vegetative propagation traits were located on homeologous linkage groups. Our findings indicate high transferability of microsatellite markers between Eucalyptus species of the Symphyomyrtus subgenus and establish foundations for the use of synteny in the genetic analysis of this genus. Microsatellite markers should help integrate eucalypt genetic linkage maps from various sources. The availability of comparative linkage maps provides a basis of more-efficient use of genetic information for molecular breeding and evolutionary studies in Eucalyptus.     

Sampling affects the detection of genetic subdivision and conservation implications for fisher in the Sierra Nevada

The small population of fisher (Pekania pennanti) in the southern Sierra Nevada is completely geographically and genetically isolated putting it at increased risk of extinction. Previous research using a clustered sampling scheme found a high amount of genetic subdivision within the southern Sierra Nevada population hypothesized to be caused by the Kings River Canyon. In this study, we use a larger and more geographically continuous set of genetic samples (n = 127) than was previously available to test this hypothesis and evaluate the genetic structure of the population. Both spatial and non-spatial population assignment models found three primary genetic clusters with moderate divergence between the clusters (F _ST = 0.05–0.13) at 10 microsatellite loci. These clusters appear to be associated with areas around the Kings River and Mountain Home State Demonstration Forest. One model also detected additional fine scale subdivision north of the Kings River that may be evidence of founder effects from a recent population expansion. The amount of population subdivision detected in this study is lower than previously found and indicates that while certain landscape features may reduce gene flow, these landscape features may be less of a barrier than initially thought. In the previous work, samples were collected in clusters which can inflate estimates of population structure by increasing the likelihood of oversampling related individuals. This study demonstrates how clustered sampling from a continuously distributed population can affect the assessment of population subdivision and influence conservation implications.     

On the mechanical properties of the rare endemic cactus Stenocereus eruca and the related species S. gummosus

We examined the hypothesis that the procumbent growth habit of the rare, columnar cactus Stenocereus eruca is in part the result of a diminution of the mechanical properties of stem tissues by comparing the properties of S. eruca plants with those of the putatively closely related semi-erect shrub S. gummosus. Intact stems and surgically removed anatomically comparable regions of the stems of both species were tested in bending and tension to determine their Young's modulus and breaking stress. A computer program was used to evaluate the contribution of each region to the capacity of entire stems to resist bending forces. Our analyses indicate that the principal stiffening agent in the stems of both species is a peripheral tissue complex (= epidermis and collenchyma in the primary plant body) that has a significantly higher tensile breaking stress and greater extensibility for S. gummosus than that of S. eruca. Computer simulations indicate that the wood of either species contributes little to bending stiffness, except in very old portions of S. gummosus stems, because of its small volume and central location in the stem. These and other observations are interpreted to support the hypothesis that S. eruca evolved a procumbent growth habit as the result of manifold developmental alterations some of which reduced the capacity of tissues to support the weight of stems.     

危害广西红树林的四种蓑蛾的发生和传播规律初探

通过对广西北海、山口、钦州、防城港4个红树林集中分布区蓑蛾发生情况进行调查,研究了不同蓑蛾发生规律、行为习性、耐水淹等特性。结果表明:小蓑蛾Acanthopsyche subferalbata Hampson的发生范围最广,褐蓑蛾Mahasena colona Sonan的发生范围最小;桐花树遭受蓑蛾危害最严重,木榄和红海榄的蓑蛾危害较轻,野外未发现蓑蛾危害老鼠勒和海漆;蓑蛾发生程度钦州>防城港>北海>山口,种群呈现以钦州为中心向东西2个海岸带扩散的规律。选择性取食试验、水淹试验和耐饥饿试验表明,蓑蛾属于杂食性昆虫,可取食多种红树植物,易在不同红树植物之间传播;4种蓑蛾耐水淹能力依次为:蜡彩蓑蛾Chalia larminati Heylaerts>小蓑蛾>白囊蓑蛾Chalioides kondonis Mats>褐蓑蛾,耐水淹能力与分布范围基本呈正相关;耐饥饿能力依次为:蜡彩蓑蛾>小蓑蛾>白囊蓑蛾>褐蓑蛾;4种蓑蛾初孵幼虫的爬行速度依次为:白囊蓑蛾>褐蓑蛾>蜡彩蓑蛾>小蓑蛾。     

Variation and morphogenetic characteristics of different Stachys species during microclonal propagation

Morphogeneses of Stachys different species introduced in culturing in vitro have been compared. The frequency of altered forms have been demonstrated to be related to the plant genotype. All regenerants of S. sieboldii, which reproduces in vivo only vegetatively, are phenotypically normal, irrespective of the concentrations of plant growth regulators at which they have been obtained. Only changes in isozyme patterns have been observed in the regenerants grown in media containing at least 10 mg/l benzyl aminopurine (BAP); most of these changes are the absence of a particular component of the pattern. The cross-pollinating species Stachys ocymastrum, which typically reproduces by seeds, has yielded morphologically altered forms even in phytohormone-free media; its isozyme patterns often contained a new component. Analysis of the isoperoxidase patterns of regenerants of both Stachys species obtained with the use of high phytohormone concentrations has demonstrated qualitative and quantitative changes suggesting the appearance of somaclonal variants even in the course of plant regeneration directly from nodal segments, bypassing callus formation. Changes have also been found in Stachys plants regenerating from the callus tissue.     

On the use of genetic divergence for identifying species

Degree of genetic divergence is frequently used to infer that two populations belong to separate species, or that several populations belong to a single species. I explore the logical framework of this approach, including the following assumptions: (i) speciation takes place over very long periods of time; (ii) reproductive isolation is based on the slow accumulation many genetic differences throughout the genome; (iii) genetic divergence automatically leads to reproductive isolation between species; and (iv) pre-mating and post-mating reproductive isolation have a similar genetic basis. I argue that so many exceptions to these assumptions have been demonstrated that they cannot be used with any reliability to distinguish different species. In addition, genetic distance as a species criterion is mostly used within the framework of Mayr's Biological Species Concept and is not free of assumptions about the nature of species or of speciation. The use of genetic distance to infer separate species (or the lack of these) is not parsimonious, its theoretical foundations are not well understood, and it cannot be applied over a wide range of plants and animals. I explore alternative approaches towards solving the species problems normally solved using genetic distance. © 2002 The Linnean Society of London, Biological Journal of the Linnean Society , 2002, 75 , 509–516.