Effect of the population heterogeneity on growth behavior and its estimation

Different types of the Logistic model are constructed based on a simple assumption that the microbial populations are all composed of homogeneous members and consequently, the condition of design for the initial value of these models has to be rather limited in the case of N(t_0)=N_0. Therefore, these models cannot distinguish the dynamic behavior of the populations possessing the same N0 from heteroge-neous phases. In fact, only a certain ratio of the cells in a population is dividing at any moment during growth progress, termed as θ, and thus, ddNt not only depends on N, but also on θ. So θ is a necessary element for the condition design of the initial value. Unfortunately, this idea has long been neglected in widely used growth models. However, combining together the two factors (N0 and θ ) into the initial value often leads to the complexity in the mathematical solution. This difficulty can be overcome by using instantaneous rates (Vinst) to express growth progress. Previous studies in our laboratory sug-gested that the Vinst curve of the bacterial populations all showed a Guassian function shape and thus, the different growth phases can be reasonably distinguished. In the present study, the Gaussian dis-tribution function was transformed approximately into an analytical form (0.5x ibxYi αe=20) that can be conveniently used to evaluate the growth parameters and in this way the intrinsic growth behavior of a bacterial species growing in heterogeneous phases can be estimated. In addition, a new method has been proposed, in this case, the lag period and the double time for a bacterial population can also be reasonably evaluated. This approach proposed could thus be expected to reveal important insight of bacterial population growth. Some aspects in modeling population growth are also discussed.     

Self-thinning lines of organs and aboveground parts based on allometric relationships in overcrowded Pinus densiflora stands

The allometric relationships of mean tree height [`(H)]( μ [`(w)]_x^q ) \bar{H}( \propto \bar{w}_{\rm {x}}^{\theta } ) and of organ mass density [`(d)]<sub>x</sub> ( μ [`(w)]_x^d ) \bar{d}_{\rm {x}} ( \propto \bar{w}_{\rm {x}}^{\delta } ) to mean organ mass [`(w)]_x \bar{w}_{\rm {x}} were studied in self-thinning Pinus densiflora Sieb. et Zucc. stands. Tree height increased significantly with increasing mean mass of organs and aboveground parts on log–log coordinates. The value of the allometric constant θ ranged from 0.2878 to 0.3349. On the other hand, the constant value δ was not significantly different from zero, except for leaves. The value of the allometric constant δ ranged from −0.2926 to 0.0120. According to Weller’s allometric model, the slope of the self-thinning line was calculated from the allometric constants θ and δ. The thinning slope was estimated to be −1.51 in stem, −1.39 in branches, −1.00 in leaf and −1.41 in aboveground parts, respectively. Mass density was high in stem, medium in branches and low in leaves. Mean leaf mass density decreased significantly with decreasing stand density on log–log coordinates, which could be interpreted as indicating the importance of the constant final leaf biomass in overcrowded P. densiflora stands. The self-thinning exponents of branch, stem and aboveground parts were not significantly different from 3/2, which indicated that the 3/2 power law of self-thinning holds for stem mass, branch mass and aboveground mass in overcrowded P. densiflora stands.     

Studying Genetic Code by a Matrix Approach

Following Petoukhov and his collaborators, we use two length n zero-one sequences, α and β, to represent a length n genetic sequence ((a) || (b)){\alpha\choose\beta} so that the columns of ((a) || (b)){\alpha\choose\beta} have the following correspondence with the nucleotides: C ~ (0 || 0)C\sim{0\choose0} , U ~ (1 || 0)U\sim{1\choose0} , G ~ (1 || 1)G\sim{1\choose1} , A ~ (0 || 1)A\sim{0\choose1} . Using the Gray code ordering to arrange α and β, we build a 2 ⁿ ×2 ⁿ matrix C _n including all the 4 ⁿ length n genetic sequences. Furthermore, we use the Hamming distance of α and β to construct a 2 ⁿ ×2 ⁿ matrix D _n . We explore structures of these matrices, refine the results in earlier papers, and propose new directions for further research.     

Comparing body-size growth curves: the Gallucci-Quinn index,and beyond

Gallucci and Quinn suggested that the product L_￥ ·k {L_\infty } \cdot k is a sensible index to compare two growth curves (L _∞, k the usual Bertalanffy parameters). This paper gives four (interrelated) reasons why this index captures some essential features of body-size growth. It also notes that the product k ·L_￥³ k \cdot L_\infty^3 directly compares fish growth at the maximum growth rate.     

Growth parameters and total mortality in Oreochromis niloticus (Linnaeus) from Nyanza Gulf,Lake Victoria

Length-frequency data collected from fish landings in the Kenya waters of Lake Victoria were used to estimate the growth parameters, total mortality rate and growth performance index in Oreochromis niloticus. The asymptotic length, (L _∞) and the ratio of the total mortality rate (Z) to the growth constant (K), were estimated to be 64.6 cm and 3.219 respectively. K was 0.254 y^-1, Z was 0.818 y^-1 and the growth performance index θ′ = Log₁₀ K + 2 log₁₀ L∞ = 3.025, which is rather high as compared to other tilapia populations in natural waters.     

Genetic effects of forest fragmentation in high-density Araucaria angustifolia populations in Southern Brazil

Araucaria angustifolia is an endangered tropical/subtropical coniferous of great interest for conservation due its economical, ecological, and social value. Only 3% of original Araucaria forests remain, which are generally confined to small forest fragments. Forest fragmentation can have serious consequences on genetic process in tree population, affecting long-term fitness and adaptability. To investigate the effects of forest fragmentation on genetic diversity and the structure of A. angustifolia populations, the genetic diversity of eight microsatellite loci was compared in four small fragmented populations (<22 ha), four tree groups (five to 11 trees) occurring in pastures and in three plots in a large continuous population. The clearest effect of fragmentation was the loss of rare alleles (p ≤ 0.05) in fragmented populations (19.4% to 47.2%) and intermediate frequency (0.05 < p ≤ 0.25) and rare alleles (p ≤ 0.05) in tree groups (19% to 86.1%) in comparison to continuous populations. Fragmented populations have significant higher fixation index ( [^(F)]_\textIS = 0.121 \widehat{F}_{\text{IS}} = 0.121 , P < 0.05) than continuous populations ( [^(F)]_\textIS = 0.083 \widehat{F}_{\text{IS}} = 0.083 , P < 0.05). High genetic differentiation was detected among tree groups ( [^(G)]_\textST^￠ = 0.258 \widehat{G}_{{{\text{ST}}}}^{\prime } = 0.258 , P < 0.01) and low among fragments ( [^(G)]_\textST^￠ = 0.031 \widehat{G}_{{{\text{ST}}}}^{\prime } = 0.031 , P < 0.05) and continuous populations ( [^(G)]_\textST^￠ = 0.026 \widehat{G}_{{{\text{ST}}}}^{\prime } = 0.026 , P < 0.05), showing a significant bottleneck effect in tree groups. Evidence that forest fragments have experienced a recent bottleneck was confirmed in at least two studied fragments. The implications of the results for conservation of the fragmented A. angustifolia populations are discussed.     

Influence of {\text{NH - }}{{\text{S}}^\gamma } bonding interactions on the structure and dynamics of metallothioneins

Mammalian metallothioneins ( \textM₇^\textIIMTs {\text{M}}_7^{\text{IIMTs}} ) show a clustered arrangement of the metal ions and a nonregular protein structure. The solution structures of Cd₃-thiolate cluster containing β-domain of mouse β-MT-1 and rat β-MT-2 show high structural similarities, but widely differing structure dynamics. Molecular dynamics simulations revealed a substantially increased number of \textNH - \textS^g {\text{NH - }}{{\text{S}}^\gamma } hydrogen bonds in β-MT-2, features likely responsible for the increased stability of the Cd₃-thiolate cluster and the enfolding protein domain. Alterations in the \textNH - \textS^g {\text{NH - }}{{\text{S}}^\gamma } hydrogen-bonding network may provide a rationale for the differences in dynamic properties encountered in the β-domains of MT-1, -2, and -3 isoforms, believed to be essential for their different biological function.     

Wild genetic diversity preservation in a small-sized first generation breeding population of <Emphasis Type="Italic">Allanblackia floribunda</Emphasis> (Clusiaceae)

Founder group size is of prime importance in tree breeding programs. We determined whether sampling 20-plus trees for breeding in Allanblackia floribunda, a tropical forest tree species that has been recently enrolled in tree improvement program for fruit and seed production, would affect neutral genetic diversity and inbreeding level in both breeding and production populations. Using eight informative microsatellite loci, we: (a) assessed the nuclear genetic diversity of ten natural populations, and of the breeding population in the humid forest zone of Cameroon; (b) investigated temporal effective-size fluctuations in A. floribunda natural populations, with a view to identifying the role of past demographic events in the genetic structure of the studied species; and (c) tested the hypothesis that genetic diversity in a founder group of 20 individuals is not different from that existing in the wild. The eight loci were variable. High levels of genetic diversity (A = 4.96; H _E = 0.59) and moderate differentiation (R _ST = 0.061) were found within and among populations in wild stands. High genetic distances existed between populations ( \textaverage chord distance = 0.\text2769 ±0.00\text554 ) \left( {{\text{average chord distance}} = 0.{\text{2769}} \pm 0.00{\text{554}}} \right) . Eight of the ten surveyed populations showed signs of deviation from mutation-drift equilibrium, suggesting Pleistocene population bottlenecks and fluctuations in effective population size. Mantel tests did not reveal any relationships between genetic and geographic distances. A neighbor-joining dendrogram showed a population structure that could be explained by historical factors. The hypothesis tested has been accepted. However, a slight increase in inbreeding was observed in the breeding population.     

A standard quantitative method to measure acid tolerance of probiotic cells

The aim of this work was to develop a standard quantitative method to measure the acid tolerance of probiotic cells when exposed to a simulated gastric fluid. Three model strains of different cell concentrations were exposed to a standard simulated gastric fluid of fixed volume. The fluid pH ranged from pH 1.5 to 2.5. In general, the death kinetics followed an exponential trend. The overall death constant, k _d, for all strains was found to be in a power relationship with the pH value and the initial cell concentration, and it can be expressed as

Age and growth of Schizopygopsis younghusbandi younghusbandi in the Yarlung Zangbo River in Tibet, China

Schizopygopsis younghusbandi younghusbandi is an endemic species whose distribution is restricted to the middle reaches of the Yarlung Zangbo River, being one of the most important commercial fishes in this area. Age and growth of 606 specimens captured between October 2002 and April 2005 were studied. The range in standard length (L) was 65.7–387.3 mm and total weight (W) was 3.3–772.0 g. The relationship between L and W was W = 0.000909L^2.2493 for males and W = 0.000259L^2.4781 for females. Age, determined from anal scales and lapillus otoliths, ranged from 3 to 18 years. The parameters of von Bertalanffy growth functions, estimated by back-calculated length, were L_￥ = 442.7mm  LL_\infty = 442.7mm\;L, k = 0.0738 year⁻¹ and t ₀  = −1.4 year for males, and L_￥ = 471.4mm  LL_\infty = 471.4mm\;L, k = 0.0789 year⁻¹ and t ₀ = 0.2 year for females. Males and females exhibited statistically significant differences in growth. χ ²-test indicated that von Bertalanffy growth functions could well describe the growth of S. y. younghusbandi. The longevities were 39.2 and 38.2 years for males and females, respectively. Growth inflexion points were 10.2 and 12.0 years for males and females, respectively, but 84.8% of the captures were at the smaller ages. So conservation and management schemes for this population should be considered urgently. In addition, we found that populations from the upstream of the Lhasa River, the downstream of the Lhasa River and the middle reaches of the Yarlung Zangbo River showed statistically significant differences in growth patterns.     

Nitrogen use efficiency of sugarcane in relation to its BNF potential and population of endophytic diazotrophs at different N levels

The nitrogen fixing bacterial endophytes Gluconacetobacter diazotrophicus and Herbaspirillum spp. have been proposed to benefit sugarcane (Saccaharum spp. hybrids) growth. Variable populations of these endophytes exist depending upon ontogenic and climatic variations as well. This study investigates the effect of variable chemical nitrogen application in soil on the population of endophytic diazotrophs, acetylene reduction ability of excised roots, plant N-nutrient use efficiency and probable interactions among different parameters in eight commercial sugarcane varieties of subtropical India. Recovery efficiency (RE), agronomic efficiency (AE), partial factor productivity (PFP) and physiologic efficiency (PE) indicators were used for accounting N-nutrient use efficiency. The population of G. diazotrophicus was more at N₇₅ compared to N₀ and N₁₅₀, whereas Herbaspirillum population increased from N₀ to N₁₅₀. ARA was positively correlated with Gluconacetobacter population in rhizosphere and root, whereas it had poor correlation with Herbaspirillum population. Positive correlation of RE and AE with ARA of roots, Gluconacetobacter and Herbaspirillum populations in roots and stems indicate their positive contribution in total nitrogen uptake by the plant per kg of N applied. Average PFP was 808.9 at N₇₅ compared to 408.7 at N₁₅₀ indicating that N was utilized efficiently at low N input status in sugarcane. Strong positive correlations of AE₇₅ (agronomic efficiency from 75 kg N ha⁻¹ to 150 kg N ha⁻¹) with N-uptake (r ² = 0.615), cane yield (r ² = 0.758) and PFP (r ² = 0.758) and other parameters compared to AE (agronomic efficiency from 0 kg N ha⁻¹ to 75 kg N ha⁻¹ or 150 kg N ha⁻¹) correlations with N-uptake (r ² = 0.111), cane yield (r ² = 0.368) and PFP (r ² = 0.190) indicated that the AE of sugarcane was strongly directed towards producing more cane yield per unit of N fertilizer once the sugarcane plant has established using initial dose of nitrogen and thus AE₇₅ seems to be a more appropriate indicator for accounting N-nutrient use efficiency in sugarcane.     

Effect of physiological heterogeneity of <Emphasis Type="Italic">E. coli</Emphasis> population on antibiotic susceptivity test

According to the instantaneous growth rate (dN/dt) of E. coli CVCC249 growing in batch culture, the entire growth progress was distinguished into four phases: accelerating growth phase, constant growth phase, decelerating growth phase and declining phase, in each of which obvious variation in physiological and biochemical properties was detected, including total DNA, total protein, and MTT-dehydrogenase activity, etc., that led to difference in their antibiotic susceptivity. Antibiotic susceptivity of the population sampled from each phase was tested by Concentration-killing Curve (CKC) approach following the formula N=N ₀/{1+exp[r·(x-BC ₅₀)]}, showing as normal distribution at the individual cell level for an internal population, in which the median bactericidal concentration BC ₅₀ represents the mean level of susceptivity, while the bactericidal span BC ₁₋₉₉=(2lnN ₀)/r indicates the variation degree of the antibiotic susceptivity. Furthermore, tested by CKC approach, the antibiotic susceptivity of E. coli CVCC249 population in each physiological phase to gentamicin or enoxacin was various: susceptivity of the population in the constant growth phase and declining phase all increased compared with that in the accelerating growth phase for gentamicin but declined for enoxacin. The primary investigations revealed that the physiological phase should be taken into account in the context of antibiotic susceptivity and research into antimicrobial mechanism. However there are few reports concerned with this study. Further research using different kinds of antibiotics with synchronized continuous culture of different bacterial strains is required.     

Using scales to clarify the transition from blue-phase to brown-phase fingerling in Notothenia rossii from the South Shetland Islands

Scales and whole otoliths were read for age determination in early stages of Notothenia rossii caught in Potter Cove, South Shetland Islands, in summer seasons 2003–2006 and 2008. The sample comprised blue-phase pelagic fingerlings of 7.0–7.6 cm (TL) of age group 0 year and demersal brown-phase fingerlings/juveniles of 8.5–20.9 cm and predominant age groups 1–2 years. Counting of sclerites facilitated the interpretation of the rings, particularly in the central scale. To clarify two previous issues of controversy, we deduce that the duration of the offshore pelagic blue-phase fingerling stage is less than one year before migration to the nearshore demersal habitat. Furthermore, the first well-defined ring in scales corresponded to the first annulus, while a contiguous ring was a secondary ring sometimes deposited after the first winter during the second year of life, attributable to a shift of habitat from pelagic to demersal. A von Bertalanffy growth curve was computed by combining age/length data of the juvenile phase of N. rossii from this and a previous study at Potter Cove with literature data from the offshore adult population, resulting in the following equation: L_t = 8 6. 9  ( 1- \texte ^{- 0. 0 9 1 (t - 0. 6 6 8 )} ) L_{t} = 8 6. 9 \,\left( { 1- {\text{e}}^{{ - 0. 0 9 1 (t - 0. 6 6 8 )}} } \right) _.     

Did CDM Particles of Mass 2.47 × 10<Superscript>−3</Superscript> eV Interact with Precursor Biopolymers and Nucleic Acids to Initiate and Boost Lifeforms on Earth?

Recent observations and theoretical studies have shown that non-baryonic Cold Dark Matter (CDM), which constitutes about 84% of all matter in the Universe, may feature a complex-scalar-field that carries particles of mass m @ 2.47 ×10 ^{- 3}eV m \cong 2.47 \times {10^{{ - 3}}}eV with the associated Compton range m ^{- 1} @ 8.02 ×10 ^{- 3}cm, {m^{{ - 1}}} \cong 8.02 \times {10^{{ - 3}}}cm, a distance on the scale of extended bionucleic acids and living cells. Such a complex-scalar-field can enter a weak-isospin Lorentz-invariant interaction that generates the flow of right-handed electrons and induces a chirality-imbued quantum chemistry on the m ⁻¹ scale. A phenomenological Volterra-type equation is proposed for the CDM-impacted time development of N, the number of base pairs in the most advanced organism at Earth-age t. The solution to this equation suggests that the boosts in N at t ≅ 1.1 Gyr (advent of the first living prokaryotic cells), at t ≅ 2.9 Gyr (advent of eukaryotic single-celled organisms) and finally at t ≅ 4.0 Gyr (the Cambrian explosion) may be associated with three multi-Myr-duration cosmic showers of the complex-scalar-field CDM particles. If so, the signature of the particles may be detectible in Cambrian rocks.     

Temporal profile of the singlet oxygen emission endogenously produced by photosystem II reaction centre in an aqueous buffer

The temporal profile of the phosphorescence of singlet oxygen endogenously photosensitized by photosystem II (PSII) reaction centre (RC) in an aqueous buffer has been recorded using laser excitation and a near infrared photomultiplier tube. A weak emission signal was discernible, and could be fitted to the functional form a[exp( - t/t₂ ) - exp( - t/t₁ )] a[\exp ( - t/\tau_{2} ) - \exp ( - t/\tau_{1} )] , with $ a > 0 $ a > 0 and $ \tau_{2} > \tau_{1} $ \tau_{2} > \tau_{1} . The value of t₂ \tau_{2} decreased from 11.6 ± 0.5 μs under aerobic conditions to 4.1 ± 0.2 μs in oxygen-saturated samples, due to enhanced bimolecular quenching of the donor triplet by oxygen, whereas that of t₁ \tau_{1} , identifiable with the lifetime of singlet oxygen, was close to 3 μs in both cases. Extrapolations based on the low amplitude of the emission signal of singlet oxygen formed by PSII RC in the aqueous buffer and the expected values of t₁ \tau_{1} and t₂ \tau_{2} in chloroplasts indicate that attempts to analyse the temporal profile of singlet oxygen in chloroplasts are unlikely to be rewarded with success without a significant advance in the sensitivity of the detection equipment.     

Stochastic models of tumor growth and the probability of elimination by cytotoxic cells

The probability of tumor extinction due to the action of cytotoxic cell populations is investigated by several one dimensional stochastic models of the population growth and elimination processes of a tumor. The several models are made necessary by the nonlinearity of the processes and the different parameter ranges explored. The deterministic form of the model is where γ₀, k′₆ and k ₁ are positive constants. The parameter of most import is which determines the stability of the T = 0 equilibrium. With an initial tumor size of one, a (linear) branching process is used to estimate the extinction probability. However, in the case λ = 0 when the linearization of the deterministic model gives no information (T = 0 is actually unstable) the branching model is unsatisfactory. This makes necessary the utilization of a density-dependent branching process to approximate the population. Through scaling a diffusion limit is reached which enables one to again compute the probability of extinction. For populations away from one a sequence of density-dependent jump Markov processes are approximated by a sequence of diffusion processes. In limiting cases, the estimates of extinction correspond to that computed from the original branching process. Table 1 summarizes the results.     

Genetic parameters and predicted selection responses for timber production traits in a Castanea sativa progeny trial: developing a breeding program

Total height, diameter, index volume, stem straightness, apical dominance, and survival were assessed at 8 years from seed in an open-pollinated progeny test of 36 families of European chestnut (Castanea sativa Miller) established at two sites in the Atlantic area of Galicia, Spain. Iterative spatial analysis was applied to eliminate the effect of the spatial dependence in the original data and to estimate accurately genetic parameters for evaluating the potential for selection of the measured trees. Spatial analysis was very beneficial for growth traits and survival, but less so if at all for form traits. Estimated individual heritabilities ranged from moderate to high for growth traits ([^(h)]_i² = 0.29 - 0.42 \widehat{h}_i^2 = 0.29 - 0.42 ) and stem straightness ([^(h)]_i² = 0.24 - 0.42 \widehat{h}_i^2 = 0.{24} - 0.{42} ). High coefficients of additive genetic variance were obtained for volume ( [^(\textC)]\textV_\textA = 36.5 - 41.5% \widehat{\text{C}}{{\text{V}}_{\text{A}}} = {36}.{5} - {41}.{5}\% ) and straightness ( [^(\textC)]\textV_\textA = 44.26 - 53.84% \widehat{\text{C}}{{\text{V}}_{\text{A}}} = {44}.{26} - {53}.{84}\% ). Phenotypic and estimated genetic correlations between growth traits were very high, and correlations between sites indicated that there was no important family × site interaction. No adverse correlations between traits were evident. The results indicate the ample potential for selection in the current progeny trial, where responses to within-family and combined selection for growth traits may be high. Accordingly, three selection scenarios were addressed with the aim to initiate the selection of individuals for implementing the Forest Breeding Plan of Galicia for European chestnut.     

Fine-scale spatial genetic structure and allozymic diversity in natural populations of <Emphasis Type="Italic">Ocotea catharinensis</Emphasis> Mez. (Lauraceae)

In order to establish a strategy for conservation, the distribution of genetic diversity in four natural populations of Ocotea catharinensis in the Brazilian Atlantic rain forest was investigated using 18 allozyme loci. Estimates of the average number of alleles per loci (2.2), percentage of polymorphic loci (83.3%) and expected genetic diversity (0.427) in adult individuals were high; suggesting that all populations have genetic potential for conservation. The inbreeding within populations ([^(f)] = - 0.0 1 1 \hat{f} = - 0.0 1 1 ) and the total inbreeding ([^(F)] = 0. 1 3 3 \hat{F} = 0. 1 3 3 ) suggest population structure, since a high level of divergence among populations ( [^(q)]_\textP = 0. 1 4 3 \hat{\theta }_{\text{P}} = 0. 1 4 3 ) was also detected. Significant values of spatial genetic structure were found inside the four populations. This study demonstrates that the realized gene flow among the remaining populations of O. catharinensis is not sufficient to stop population divergence due to genetic drift and local selection, which threatens the future viability of this species.