Invasibility and stochastic boundedness in monotonic competition models

We give necessary and sufficient conditions for stochastically bounded coexistence in a class of models for two species competing in a randomly varying environment. Coexistence is implied by mutual invasibility, as conjectured by Turelli. In the absence of invasibility, a species converges to extinction with large probability if its initial population is small, and extinction of one species must occur with probability one regardless of the initial population sizes. These results are applied to a general symmetric competition model to find conditions under which environmental fluctuations imply coexistence or competitive exclusion.     

Bacterial competition in serial transfer culture

A mathematical model of bacterial competition for a single growth-limiting substrate in serial transfer culture is formulated. Each bacterial strain is characterized by a growth response function, e.g. Monod function determined by a maximum growth rate and half-saturation nutrient concentration, and the length of its lag phase following the dilution event. The goal of our study is to understand what factors determine an organisms fitness or competitive ability in serial transfer culture. A motivating question is: how many strains can coexist in serial transfer culture? Unlike competition in the chemostat, coexistence of two strains can occur in serial transfer culture. Numerical simulations suggest that more than two may coexist.     

Global dynamics of microbial competition for two resources with internal storage

We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model. B. Li’s research was partially supported by NSF grants DMS 0211614 and DMS 0616445. H. L. Smith’s research was supported in part by NSF grant DMS 0414270.     

Coexistence of two types on a single resource in discrete time

Armstrong and McGehee (1980) have shown that two species modeled in continuous time can coexist on a single resource provided that one species oscillates autonomously. This paper demonstrates the parallel result in discrete time. I consider a deterministic model of two asexual types in a single patch competing for a single resource, and show that such systems generically produce oscillatory coexistence or bistability if one of the types displays periodic or chaotic behavior in isolation. The conditions for coexistence or bistability are derived in terms of the convexity of the functions describing fitness as a function of resource availability. I also analyze whether or not a stable type, a type with a stable equilibrium population size when considered in isolation, can invade a periodic orbit of an unstable type, and show that the same convexity condition distinguishes these two cases. The widely considered exponential or Ricker model for population dynamics lies on the boundary between the two cases and is highly degenerate in this context.     

Analysis of a lottery competition model with limited nutrient availability

How a plant species utilizes a limited nutrient is important for its survival. The purpose of this work is to examine how nutrient utilization mechanisms (for seed production) affect the coexistence of competing plant species. We construct a revised lottery model that uses one of three possible kinds of nutrient utilization functions. In all cases the models suggest that two species can coexist under certain circumstances, but that three species cannot coexist, at least when the nutrient utilization functions are continuous functions of nutrient uptake. However, in the discontinuous case three species can coexist in a state of sustained oscillations. The results suggest that one need pay close attention to the differences in the nutrient utilization mechanisms among competing plant species in order to ascertain the competitive outcome.     

Brain-derived neurotrophic factor levels in the nervous system of wild-type and neurotrophin gene mutant mice

Although brain-derived neurotrophic factor is the most abundant and widely distributed neurotrophin in the nervous system, reproducible determinations of its levels have been hampered by difficulties in raising suitable monoclonal antibodies. Following immunization of mice with recombinant fish and mammalian brain-derived neurotrophic factor, monoclonal antibodies were generated and used in an immunoassay based on the recognition of two different epitopes. Neither antibody crossreacts with neurotrophin homodimers other than brain-derived neurotrophic factor, although reactivity was detected with brain-derived neurotrophic factor/neurotrophin-3 heterodimers. As both nerve growth factor and neurotrophin-3 are known to affect the development of a variety of neurons expressing the brain-derived neurotrophic factor (bdnf) gene, this assay was used to determine levels in tissues isolated from newborn mice carrying a null mutation in the nerve growth factor (ngf) or the neurotrophin-3 (nt3) gene. Marked differences were observed between mutants and wild-type littermates in the PNS, but not in the CNS, suggesting that neither nerve growth factor nor neurotrophin-3 is a unique regulator of brain-derived neurotrophic factor levels in the newborn mouse CNS.     

Cranial sensory neuron development in the absence of brain-derived neurotrophic factor in BDNF/Bax double null mice

To investigate the role of brain-derived neurotrophic factor (BDNF) in differentiation of cranial sensory neurons in vivo, we analyzed development of nodose (NG), petrosal (PG), and vestibular (VG) ganglion cells in genetically engineered mice carrying null mutations in the genes encoding BDNF and the proapoptotic Bcl-2 homolog Bax. In bax(-/-) mutants, ganglion cell numbers were increased significantly compared to wild-type animals, indicating that naturally occurring cell death in these ganglia is regulated by Bax signaling. Analysis of bdnf(-/-)bax(-/-) mutants revealed that, although the Bax null mutation completely rescued cell loss in the absence of BDNF, it did not rescue the lethality of the BDNF null phenotype. Moreover, despite rescue of BDNF-dependent neurons by the bax null mutation, sensory target innervation was abnormal in double null mutants. Vagal sensory innervation to baroreceptor regions of the cardiac outflow tract was completely absent, and the density of vestibular sensory innervation to the cristae organs was markedly decreased, compared to wild-type controls. Moreover, vestibular afferents failed to selectively innervate their hair cell targets within the cristae organs in the double mutants. These innervation failures occurred despite successful navigation of sensory fibers to the peripheral field, demonstrating that BDNF is required locally for afferent ingrowth into target tissues. In addition, the bax null mutation failed to rescue expression of the dopaminergic phenotype in a subset of NG and PG neurons. These data demonstrate that BDNF signaling is required not only to support survival of cranial sensory neurons, but also to regulate local growth of afferent fibers into target tissues and, in some cells, transmitter phenotypic expression is required.     

The expression and putative role of brain-derived neurotrophic factor and its receptor in bovine sperm

The neurotrophin family of proteins promote the survival and differentiation of nerve cells and are thought to play an important role in development of reproductive tissues. The objective of the present study was to detect the presence of Brain-derived neurotrophic factor (BDNF) and its receptor TrkB in bovine sperm, and explore the potential role of BDNF in sperm function. We demonstrated that both the neorotrophin BDNF and the tyrosine kinase receptor protein TrkB were expressed in ejaculated bovine sperm. Furthermore, BDNF per se was secreted by sperm. Insulin and leptin secretion by bovine sperm were increased (P < 0.01) when cells were exposed to exogenous BDNF, whereas insulin was decreased by K252a. Therefore, we inferred that BDNF could be a regulator of sperm secretion of insulin and leptin through the TrkB receptor. Sperm viability and mitochondrial activity were both decreased (P < 0.05) when the BDNF/TrkB signaling pathway was blocked with K252a. Furthermore, BDNF promoted apoptosis of bovine sperm through TrkB binding (P < 0.05). In conclusion, these observations provided evidence that BDNF secreted by bovine sperm was important in regulation of insulin and leptin secretion in ejaculated bovine sperm. Furthermore, BDNF may affect sperm mitochondrial activity and apoptosis, as well as their viability.     

Small-scale species richness in forest canopy gaps: the role of niche limitation versus the size of the species pool

Abstract. The form of the relationship between local species richness and the number of species in the surrounding region can be used as a test between competing theories of community structure. For 32 canopy gaps in New Zealand Nothofagus forest, we examined the relationship between the number of vascular plant species in 0.2-m² quadrats within the gap and the species richness of the whole gap. We found no evidence that competition for a limited number of niches placed an upper limit on the number of locally co-occurring species. Rather, the mean number of species in quadrats within canopy gaps increased in direct proportion to gap species richness. This relationship held after we controlled for potentially confounding factors, including variation in forest floor substrate, and gap size, age, shape and orientation. Our results suggest that even over relatively small spatial scales, local species richness can be constrained by the size of the species pool in the immediately surrounding region.     

Founder control and coexistence in a simple model of asymmetric competition for light

Size asymmetry in plant light acquisition complicates predictions of competitive outcomes in light-limited communities. We present a mathematically tractable model of asymmetric competition for light and discuss its implications for predicting outcomes of competition during establishment in two-, three-, and many-species communities. In contrast to the resource-reduction model of symmetric competition for a single resource, the model we present predicts that outcomes of asymmetric competition for light will sometimes depend on the timing of establishment and the consequent hierarchy among species in canopy position. Competitive outcomes in the model depend on the minimum light requirements (L(c)) and self-shading of species lower in the canopy compared to the light available (L(out)(*)) beneath species higher in the canopy. Succession progresses towards species with decreasing values for L(c), but arrested successions occur when initial dominants have relatively high values for L(c) but low values for L(out)(*), leading to founder control. A theoretically limitless number of species may coexist in competition for light when dominance is founder controlled. These model predictions have implications for an array of applied ecological questions, including methods to control invasive species in light-limited restored ecosystems.     

The analysis and regulation for the dynamics of a temperate bacteriophage model

The purpose of this paper is to study the asymptotical behavior of a temperate bacteriophage model in chemostat, which was first proposed by Levin et al. [B.R. Levin, F.M. Stewart, L. Chao, Resource-limited growth, competition and predation: A model and experiment studies with bacteria and bacteriophage, Am. Nat. 125 (1977) 3]. Firstly, a classification for the equilibria of the model and their stability are obtained; secondly, sufficient conditions for uniform persistence are obtained; thirdly, sufficient conditions for the global asymptotic behavior are given, and simulations for the model are presented. The theoretical results show that there are more than eight cases for the classification of the model, and that the decrease (increase) of the nutrient concentration or average lytic time (flow rate) is beneficial to the survival of the sensitive cells. Both the simulated and theoretical results show that there is a possibility of switch phenomena or a periodical outburst of the phages and the lysogens, which is caused by the internal factors rather than by some external environment. Finally, the simulation and regulation of the dynamics of the model with experimental data are presented.     

Association between histamine-containing mast cells and sensory nerves in the skin and airways of control and capsaicin-treated pigs

Summary The association between mast cells (visualized by routine staining and immunohistochemistry for histamine) and capsaicin-sensitive nerves (containing calcitonin gene-related peptide (CGRP) and substance P (SP)) was studied in the pig. In the 1-ethyl-3(3-diethylaminopropyl)carbodiimide (EDCDI)-fixed skin tissue, histamine-containing mast cells and CGRP/SP-positive nerves were found in close association around blood vessels. In the EDCDI-fixed airway mucosa, only single histamine-containing mast cells were detected. However, many alcian blue-positive mast cells were found, sometimes close to the airway epithelium where CGRP/SP-containing nerve fibres were absent 2 days after systemic capsaicin pretreatment, but no changes in the number and distribution of tissue mast cells, granulocytes or lymphocytes, or the number of blood leukocytes were detected. Local injection of allergen, histamine and capsaicin into the skin of pigs actively sensitized with ascaris antigen caused a rapid light red-flare (vasodilation) reaction. Allergen and histamine, but not capsaicin, also produced plasma protein extravasation. In contrast to the absent flare, the protein extravasation response still occurred in capsaicin-treated pigs. The sensitivity to ascaris antigen was mediated by an IgE-like antibody. We conclude that a functional and morphological relationship exists between histamine-containing mast cells and capsaicin-sensitive sensory nerves in the pig skin. Mast cells and sensory nerves are also found in the airway mucosa and appear to be closely associated with the epithelium.     

Mathematical models of microbial growth and competition in the chemostat regulated by cell-bound extracellular enzymes

A mathematical model of growth and competitive interaction of microorganisms in the chemostat is analyzed. The growth-limiting nutrient is not in a form that can be directly assimilated by the microorganisms, and must first be transformed into an intermediate product by cell-bound extracellular enzymes. General monotone functions, including Michaelis-Menten and sigmoidal response functions, are used to describe nutrient conversion and growth due to consumption of the intermediate product. It is shown that the initial concentration of the species is an important determining factor for survival or washout. When there are two species whose growth is limited by the same nutrient, three different modes of competition are described. Competitive coexistence steady states are shown to be possible in two of them, but they are always unstable. In all of our numerical simulations, the system approaches a steady state corresponding to the washout of one or both of the species from the chemostat.Research supported by NSF grant DMS-90-96279Research supported by NSERC grant A-9358     

Intraspecific competition as a regulating factor limiting the number of transconjugants in soil

A laboratory study was carried out to determine survival of transconjugant cells ofPseudomonas fluorescens intro duced into sterile soil. The transconjugant survived significantly better when it was the only strain inoculated into the soil; when introduced into soil pre-colonized by the recipient strain, the transconjugant was undetectable. These results indicate that intraspecific competition is a regulating factor limiting the number of transconjugants in soil.     

Primary sensory neurons of the rat showing calcitonin gene-related peptide immunoreactivity and their relation to substance P-, somatostatin-, galanin-, vasoactive intestinal polypeptide- and cholecystokinin-immunoreactive ganglion cells

Summary By use of the indirect immunofluorescence technique the distribution of calcitonin gene-related peptide (CGRP)-like immunoreactivity (LI) has been analyzed in cervical and lumbar dorsal root ganglia of untreated and colchicine-treated rats. In addition, lumbar ganglia were examined 2 weeks after transection of the sciatic nerve. The occurrence of CGRP-positive cells in relation to ganglion cells containing substance P-, somatostatin-, galanin-, cholecystokinin (CCK)-, and vasoactive intestinal polypeptide (VIP)/peptide histidine isoleucin (PHI)-LI has been evaluated on consecutive sections as well as using elution-restaining and double-staining techniques.CGRP-LI was observed in many ganglion cells of all sizes ranging in diameter from 15 m to 65 m. Thus, this peptide occurs also in the large primary sensory neurons. In contrast to the sensory peptides described to date, CGRP-positive cells constituted up to 50% of all and 70% of the medium-sized neurons, thus being the most frequently occurring peptide in sensory neurons so far encountered. Subpulations of CGRP-positive neurons were shown to contain substance P-, somatostatin-, or galanin-LI and some CGRP-positive neurons contained both substance P- and galanin-LI. In fact, most substance P-, somatostatin- and galanin-positive cell bodies were CGRP-immunoreactive. The coexistence analysis further revealed that galanin and substance P often coexisted and that some cells contained both substance P- and somatostatin-LI, whereas no coexistence between galanin and somatostatin has as yet been seen. VIP/PHI-LI was only shown in a few cells in untreated or colchicine-treated rats. However, after transcetion of the sciatic nerve numerous VIP/PHI-positive cells were observed, some of which also contained CGRP-LI.The present results indicate that a CGRP-like peptide is present in a wide range of primary sensory neurons probably not related to specific sensory modalities. Often this peptide coexists with other biologically active peptides. Taken together these findings suggest that CGRP may have a generalized function.     

RT97: a marker for capsaicin-insensitive sensory endings in the rat skin

The mouse monoclonal antibody RT97, which recognises the 200-kDa neurofilament subunit in its phosphorylated form, selectively labels the somata of sensory A-fibres (large light cells) in the dorsal root ganglion of the rat. We have tested the hypothesis that this antibody also visualises large diameter sensory fibres and their end structures in peripheral tissue, in particular in the skin. RT97 immunoreactivity is found in endings that are known to be served by myelinated afferent fibres, including Meissner-like endings, Merkel discs, hair follicle receptors, Pacinian corpuscles and free nerve endings. RT97 immunoreactivity has not, however, been observed in endings of presumably unmyelinated sensory fibres (intraepidermal fibres immunoreactive for substance P and calcitonin gene-related peptide) or in sympathetic fibres innervating sweat glands and blood vessels. In addition, neither systemic (100–150 mg/kg as adults) nor perineural capsaicin pre-treatment affects RT97 immunoreactivity in the skin. The data indicate that RT97 is a useful marker in the study of the capsaicin-insensitive sensory innervation of the skin and possibly other peripheral organs.     

Resource partitioning and competition for shells between intertidal hermit crabs on the outer coast of Washington

Summary Resource partitioning was quantified for 6 species of intertidal hermit crabs in the genus Pagurus, that occur on the outer coast of Washington. This, together with field evidence of shell shortage and with laboratory experiments to quantify the mechanism of interactions for shells, allowed estimation of the relative intensities of inter-and intraspecific competition between these species. The findings were that: (1) the magnitude of intraspecific competition was greater than any single interspecific competitive effect for all of the species; and (2) the relative proportion of intraspecific competition was greater for the middle and upper intertidal species than for the lower intertidal species. Studies at several outer coast sites supported these generalizations. Both of these findings are consistent with the hypothesis that competitive divergence has occurred in the past. The structure of the outer coast hermit crab assemblage is compared with that of the San Juan Archipelago hermit crab assemblage. Differences between the two do not seem to be the result of adaptive responses to the presence of more competing species in the former group.     

Glial cell line-derived neurotrophic factor (GDNF) is a neurotrophic factor for sensory neurons: Comparison with the effects of the neurotrophins

We compared the effects of glial cell line-derived neurotrophic factor (GDNF) on dorsal root ganglion (DRG) sensory neurons to that of nerve growth factor (NGF), brain-derived neurotrophic factor (BDNF), and neurotrophin 3 (NT-3). All of these factors were retrogradely transported to sub-populations of sensory neuron cell bodies in the L4/L5 DRG of neonatal rats. The size distribution of ¹²⁵I-GDNF-labeled neurons was variable and consisted of both small and large DRG neurons (mean of 506.60 μm²). ¹²⁵I-NGF was preferentially taken up by small neurons with a mean cross-sectional area of 383.03 μm². Iodinated BDNF and NT-3 were transported by medium to large neurons with mean sizes of 501.48 and 529.27 μm², respectively. A neonatal, sciatic nerve axotomy-induced cell death model was used to determine whether any of these factors could influence DRG neuron survival in vivo. GDNF and NGF rescued nearly 100% of the sensory neurons. BDNF and NT-3 did not promote any detectable level of neuronal survival despite the fact that they underwent retrograde transport. We examined the in vitro survival-promoting ability of these factors on neonatal DRG neuronal cultures derived from neonatal rats. GDNF, NGF, and NT-3 were effective in vitro, while BDNF was not. The range of effects seen in the models described here underscores the importance of testing neuronal responsiveness in more than one model. The biological responsiveness of DRG neurons to GDNF in multiple models suggests that this factor may play a role in the development and maintenance of sensory neurons. © 1997 John Wiley & Sons, Inc. J Neurobiol 32: 22–32, 1997.