Modelling the lineage of a growing population as an age-dependent branching process

A new model for population growth as a branching process is described. It requires knowledge of the population's age-specific survivorship and fecundity curves. The total population size at any time is calculated by summing across all branches of the tree representing the population's lineage and thus the model also allows the lineage of the developing population to be traced. Use of the model is demonstrated by a hypothetical example. The model could be of particular value in tracing the phylogenetic development of populations and/or species.     

The Galton-Watson branching process as a quantitative tool in parasitology.

Stochastic growth processes abound in the biology of parasitism, and one mathematical tool that is particularly well suited for describing such phenomena is the Galton-Watson branching process. Introduced more than a century ago to settle a debate over the rate of disappearance of surnames in the British peerage, branching processes are applied today in fields as diverse as quantum physics and theoretical computer science. In this article, Dale Taneyhill, Alison Dunn and Melanie Hatcher provide a simple introduction to branching processes, and demonstrate their uses in quantitative parasitology.     

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.     

A condition for the extinction of a branching process with an absorbing lower barrier

Summary A branching process with an absorbing lower barrier is considered. This is a Galton-Watson process with the condition that at any generation the number of individuals is greater than a lower barrier or it is equal to zero (i.e. all individuals in populations which are too small die and have no offspring). A necessary and sufficient condition is given for the process to become extinct with probability one. At the end of the paper there are three illustrating examples.Now at the Division of Mathematics and Statistics, CSIRO, Canberra, A.C.T. 2601, Australia.     

A bisexual multitype branching process with applications in population genetics

A bisexual multiple branching process is studied. Consider a population with respect to three genotypes in both the female and male populations and let $$X(n) = \left\langle {X_1 (n), X_2 (n), X_3 (n)} \right\rangle and Y(n) = \left\langle {Y_1 (n), Y_2 (n), Y_3 (n)} \right\rangle$$ be random vectors giving the number of females and males (respectively) of each genotype in generationn. The mating of females and males is accommodated in the model withZ _ij (n) representing the number of females of theith genotype mated with a male of thejth genotype in generationn. The mating system is such that a female may be mated to only one male but a male may be mated with more than one female. By arranging the nine random variablesZ _ij (n),i, j=1, 2, 3, in a 1×9, vectorZ(n) it is shown that under certain conditions there is a positive constant ? such that when ?>1 the vectorsZ _n /ρⁿ,X _n /ρⁿ andY _n /ρⁿ converge almost surely asn→∞ to random vectors with fixed directions. The paper is divided into four sections. In section 1 the model is described in detail and its potential applications to population genetics are discussed. In section 2, the generating function of the transition probabilities of theZ-process are derived. Section3 is devoted to the study of the limiting behavior of the first and second moments of theZ-process, and in section4 the results of section3 are utilized to study the behavior of the random vectorsZ(n),X(n) andY(n) asn→∞.     

Soil quality and barley growth as influenced by the land application of two compost types

Agricultural use of organic residues offers an attractive method for their safe disposal and a valuable source of organic amendments and nutrients. A field experiment was conducted to investigate the influences of 0, 25, 50 and 100 t/ha spent mushroom compost (SMC), forced aeration compost (FAC) and inorganic fertilizer on soil properties and yield of barley (Hordeum vulgare). The considered soil properties (0-15 cm), after a growing season, included pH, EC, available P, Kjeldahl N, available cations, DTPA extractable elements, soil OC content, and bulk density and grain yield was also determined. Application of organic materials increased organic status of the soil and nutrient content. The effectiveness of the two composts on improving the productivity of the soil varied. SMC produced strongest correlations between soil nutrient levels and plant yield. Neither compost raised soil copper and zinc to levels that were of concern and high application rates decreased iron content.     

Evidence that L-glutamate can act as an exogenous signal to modulate root growth and branching in Arabidopsis thaliana

The roots of many plant species are known to use inorganic nitrogen, in the form of , as a cue to initiate localized root proliferation within nutrient-rich patches of soil. We report here that, at micromolar concentrations and in a genotype-dependent manner, exogenous l-glutamate is also able to elicit complex changes in Arabidopsis root development. l-Glutamate is perceived specifically at the primary root tip and inhibits mitotic activity in the root apical meristem, but does not interfere with lateral root initiation or outgrowth. Only some time after emergence do lateral roots acquire l-glutamate sensitivity, indicating that their ability to respond to l-glutamate is developmentally regulated. Comparisons between different Arabidopsis ecotypes revealed a remarkable degree of natural variation in l-glutamate sensitivity, with C24 being the most sensitive. The aux1-7 auxin transport mutant had reduced l-glutamate sensitivity, suggesting a possible interaction between l-glutamate and auxin signaling. Surprisingly, two loss-of-function mutants at the AXR1 locus (axr1-3 and axr1-12) were hypersensitive to l-glutamate. A pharmacological approach, using agonists and antagonists of mammalian ionotropic glutamate receptors, was unable to provide evidence of a role for their plant homologs in sensing exogenous glutamate. We discuss the mechanism of l-glutamate sensing and the possible ecological significance of the observed l-glutamate-elicited changes in root architecture.     

Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion

In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t+ either the solution of our problem goes to 0 or it stabilizes to a nontrivial stationary solution. We give two typical examples where the stationary solutions can be evaluated upon solving very simple partial differential equations. As a by-product of the extinction case we find a necessary condition for a nontrivial periodic solution to exist. Numerical computations not described below show a rapid stabilization.This work was partially supported by the Centre National de la Recherche Scientifique through ATP 95939900     

Symbiotic nitrogen fixation and nitrate reduction in two peanut cultivars with different growth habit and branching pattern structures

We have investigated the response of two peanut cultivars (TEGUA and UTRE) with different growth habits and branching pattern structures to different nitrogen (N) sources, namely, N-fertilizer or N₂ made available by symbiotic fixation, and analysed the pattern of nitrate reductase (NR) activity in these cultivars. Nitrate and amino acid contents were also examined under these growth conditions. In terms of nitrogen source, cv. TEGUA showed a better response to inoculation with Bradyrhizobium sp. SEMIA 6144 at 40 days after planting, while cv. UTRE responded better to N-fertilizer (5 mM KNO₃). Both cultivars showed different patterns of NR activity in the analyzed plant organs (leaves, roots, and nodules), which were dependent on the N source. When nitrogen became available to the plant through symbiotic N₂ fixation, the patterns of NR activity distribution were different in the two cultivars, with cv. TEGUA showing a higher NR activity in the nodules than in the leaves and roots, and cv. UTRE showing no difference in terms of NR activity among organs. The nitrate and amino acid contents showed a similar trend between the two cultivars, with the highest nitrate content in the leaves of fertilized plants and the highest amino acid content in the nodules. The high nitrate content of the leaves of cv. UTRE indicated the better response of this cultivar to N-fertilizer.     

Participation of two types of actomyosin complexes in the process of superprecipitation

It has been shown that addition of turbidity changes accompanying two different types of actomyosin complexes synchronous function in solution allows observation of biphasic kinetics of superprecipitation.     

Pulsed electromagnetic field: an organic compatible method to promote plant growth and yield in two corn types

Pre-sowing treatment of pulsed electromagnetic fields was used in corn seeds, in both indoor and outdoor conditions, in order to investigate the effect on plant growth and yield. The results of this research showed that pulsed electromagnetic fields can enhance plant characteristics, both under controlled environmental conditions and uncontrolled field conditions. The two varieties responded differently in the duration of magnetic field. Seeds were treated for 0, 15, 30, and 45 min with pulsed electromagnetic field (MF-0, MF-15, MF-30, and MF-45). Common corn variety performed better results in MF-30 treatment, while sweet corn variety performed better in MF-45 treatment. Magnetic field improved germination percentage, vigor, chlorophyll content, leaf area, plant fresh and dry weight, and finally yields. In the very interesting measurement of yield, seeds that have been exposed to magnetic field for 30 and 45 min have been found to perform the best results with no statistical differences among them. Another interesting finding was in root dry weight measurements, where magnetic field has a negative impact in MF-30 treatment in both hybrids, however without affecting other measurements. Enhancements on plant characteristics with economic impact on producer's income could be the future of a modern, organic, and sustainable agriculture.     

Variation of cytosine methylation in response to water availability in two contrasting growth types of an amphibious plant Alternanthera philoxeroides

We used methylation-sensitive amplified polymorphisms (MSAP) to examine the alterations of cytosine methylation in two contrasting growth types of an amphibious plant Alternanthera philoxeroides in response to change of water availability. Using 34 pairs of selective primer combinations, we amplified 1026 and 1128 clear and reproducible bands in root and leaf of A. philoxeroides, respectively. When the aquatic types of plants were transplanted into drought culture, we found a decrease in the overall DNA methylation. When the terrestrial types of plants were transferred into flood culture, we detected a higher frequency of methylation than demethylation events. Alterations of DNA methylation were more evident in root than in leaf in response to change of water availability. When the confounding effects of variable environmental factors were removed, differences of cytosine methylation profiles were observed between two growth types of plants under common growth conditions.     

Residence time distribution of liquid phase in an external-loop airlift bioreactor

The residence time distribution analysis was used to investigated the flow behaviour in an external-loop airlift bioreactor regarded as a single unit and discriminating its different sections. The experimental results were fitted according to plug flow with superimposed axial dispersion and tank-in-series models, which have proved that it is reasonable to assume plug flow with axial dispersion in the overall reactor, in riser and downcomer sections, as well, while the gas separator should be considered as a perfectly mixed zone. Also, the whole reactor could be replaced with 105-30 zones with perfect mixing in series, while its separate zones, that is the riser with 104-27, the downcomer with 115-35 and the gas separator with 25-5 perfectly mixed zones in series, respectively, depending on gas superficial velocity, A_D/A_R ratio and the liquid feed rate.List of Symbols A _D cross sectional area of downcomer (m²) - A _R cross sectional area of riser (m²) - A ₁ A ₂ length of connecting pipes (m) - Bo Bodenstein number (Bo=vL·L/D _ax (-) - C concentration (kg m^–3) - C residence time distribution function - C ₀ coefficientEquation (12) - C _r dimensionless concentration - D _D diameter of downcomer (m) - D _R diameter of riser column (m) - D _ax axial dispersion coefficient (m²s^–1) - H _d height of gas-liquid dispersion (m) - H _L height of clear liquid (m) - i number of complete circulations - L length of path (m) - m order of moments - N _eq number of perfectly mixed zones in series - n _c circulating number - Q _c recirculating liquid flow rate (m³ s^–1) - q _F liquid feed flow rate (m³s^–1) - Q _G gas flow rate (m³s^–1) - Q _T total liquid flow rate (m³s^–1) - r recycle factor - s exponent inEquation (12) regarded as logarithmic decrement of the oscillating part of RTD curve - t time (s) - t _C circulation time (s) - t _s mean residence time (s) - t ₉₉ time necessary to remove 99% of the tracer concentration (s) - V _A volume of connecting pipes (m³) - V _D volume of downcomer (m³) - V _L liquid volume in reactor (m³) - V _R volume of riser (m³) - V _LD linear liquid velocity in downcomer (m s^–1) - V _LR linear liquid velocity in riser (m s^–1) - V _SLD superficial liquid velocity in downcomer (m s^–1) - V _SLR superficial liquid velocity in riser (m s^–1) - x independent variable inEquation (1) - ¯x mean value of x - z axial coordinate - _GR gas holdup in riser - _m(x) central moment of m order - ² variance - dimensionless time     

Survival and growth responses of eight Everglades tree species along an experimental hydrological gradient on two tree island types

Questions: How are the early survival and growth of seedlings of Everglades tree species planted in an experimental setting on artificial tree islands affected by hydrology and substrate type? What are the implications of these responses for broader tree island restoration efforts? Location: Loxahatchee Impoundment Landscape Assessment (LILA), Boynton Beach, Florida, USA. Methods: An experiment was designed to test hydrological and substrate effects on seedling growth and survivorship. Two islands – a peat and a limestone‐core island representing two major types found in the Everglades – were constructed in four macrocosms. A mixture of eight tree species was planted on each island in March of 2006 and 2007. Survival and height growth of seedlings planted in 2006 were assessed periodically during the next two and a half years. Results: Survival and growth improved with increasing elevation on both tree island substrate types. Seedlings' survival and growth responses along a moisture gradient matched species distributions along natural hydrological gradients in the Everglades. The effect of substrate on seedling performance showed higher survival of most species on the limestone tree islands, and faster growth on their peat‐based counterparts. Conclusions: The present results could have profound implications for restoration of forests on existing landforms and artificial creation of tree islands. Knowledge of species tolerance to flooding and responses to different edaphic conditions present in wetlands is important in selecting suitable species to plant on restored tree islands     

Diversity in a complex ecological network with two interaction types

Most studies on ecological networks consider only a single interaction type (e.g. competitive, predatory or mutualistic), and try to developrules for system stability based exclusively on properties of this interaction type. However, the stability of ecological networks may be more dependent on the way different interaction types are combined in real communities. To address this issue, we start by compiling an ecological network in the Doñana Biological Reserve, southern Spain, with 390 species and 798 mu-tualistic and antagonistic interactions. We characterize network structure by looking at how mutualistic and antagonistic interactions are combined across all plant species. Both the ratio of mutualistic to antagonistic interactions per plant, and the number of basic modules with an antagonistic and a mutualistic interaction are very heterogeneous across plant species, with a few plant species showing very high values for these parameters. To assess the implications of these network patterns on species diversity, we study analytically and by simulation a model of this ecological network. We find that the observed correlation between strong interaction strengths and high mutualistic to antagonistic ratios in a few plant species significantly increases community diversity. Thus, to predict the persistence of biodiversity we need to understand how interaction strength and the architecture of ecological networks with different interaction types are combined.     

Efficiency of Calamintha officinalis essential oil as preservative in two topical product types

AIMS: To verify the efficiency of Calamintha officinalis essential oil as natural preservative in two current formulations. METHODS AND RESULTS: The 1.0 and 2.0% (v/v) C. officinalis essential oil was assayed for its preservative activity in two product types (cream and shampoo). The microbial challenge test was performed following the standards proposed by the European Pharmacopoeia Commission (E.P.) concerning topical preparations using standard micro-organisms and in addition wild strains, either in single or mixed cultures were used. The results clearly demonstrated that the C. officinalis essential oil at 2.0% concentration reduced the microbial inoculum satisfying the criterion A of the E.P. in the cream formulation and the criterion B in the shampoo formulation. Standard and wild strains showed a behaviour similar, both in cream and in shampoo formulation, with no significant difference (gerarchic variance, P > 0.05). CONCLUSION: C. officinalis essential oil confirmed its preservative properties but at higher concentration than that shown in previous studies on cetomacrogol cream. SIGNIFICANCE AND IMPACT OF THE STUDY: The nature of the formulation in which an essential oil is incorporated as preservative could have considerable effect on its efficacy.