Study on models of single populations: an expansion of the logistic and exponential equations

Using the adsorption theory of chemical kinetics, a new equation concerning the growth of single populations is presented:

$\text{d}\text{X}\text{d}\text{t}\text{=}\text{μ}{}_{\mathrm{c}}\text{X(1 ?)}\text{X}\text{X}{}_{\mathrm{m}}\text{1?}\text{X}\text{X}{}_{\mathrm{m}}{}^{\mathrm{\prime }}$

or in its integral form:

$\text{ln}\text{X}\text{X}{}_{\mathrm{o}}\text{?}\text{ln}\text{X}{}_{\mathrm{m}}\text{?X}\text{X}{}_{\mathrm{m}}\text{?X}{}_{\mathrm{o}}\text{+}\text{X}{}_{\mathrm{m}}\text{X}{}^{\mathrm{\prime }}{}_{\mathrm{m}}\text{X}{}_{\mathrm{m}}\text{?X}\text{X}{}_{\mathrm{m}}\text{?X}{}_{\mathrm{o}}\text{=μ}{}_{\mathrm{c}}\text{(t?t}{}_{\mathrm{o}}\text{)}$

This equation attempts to explain the relationship between population increment and limiting resources. It can be reduced to either the logistic or exponential equation under two extreme conditions. The new equation has three parameters, X_m, X′_m and μ_c, each of which has ecological significance. $\text{X}{}_{\mathrm{m}}\text{X′}{}_{\mathrm{m}}$ concerns the efficiency of nutrient utilization by an organism. Its value is between zero and one. With ratios approaching unity, the efficiency is high; lower ratios indicate that population increment is quickly restricted by limiting resources. μ_c, is a velocity parameter lying between μ_e, (exponential growth) and μ_L (logistic growth), and is dependent on the value of $\text{solX}{}_{\mathrm{m}}\text{X′}{}_{\mathrm{m}}$. From μ_c we can predict the time course of population incremental velocity ($\text{d}\text{X}\text{d}\text{t}$), and can observe that it is not symmetrical, unlike that derived from the logistic equation. At $\text{X}{}_{\mathrm{m}}\text{X′}{}_{\mathrm{m}}\text{= 1}$ the maximum velocity of the population increment predicted from the new equation is twice that of the logistic equation.Population growth in nature seems to support the new equation rather than the logistic equation, and it can be successfully fitted by means of a least square method.     

Arachidonic acid metabolism in rabbit renal cortex. Formation of two novel dihydroxyeicosatrienoic acids

[1-14C]Eicosatetraenoic (arachidonic) acid was incubated with a low speed (17,000 X g) rabbit renal cortical supernatant or with a cortical microsomal suspension fortified with NADPH for 15 min at 37 degrees C. The products which were less polar than prostaglandins on reversed phase high performance liquid chromatography were identified by gas chromatography-mass spectrometry. Both the fortified microsomes and the low speed supernatant formed significant amounts of two novel metabolites, 11,12-dihydroxy-5,8,14-eicosatrienoic acid and 14,15-dihydroxy-5,8,11-eicosatrienoic acid. Other identified products were 19- and 20-hydroxyeicosatetraenoic acid, 19-oxoeicosatetraenoic acid, and in the low speed supernatant, eicosatetraen-1,20-dioic acid. The metabolites were not formed in significant amounts by high speed cortical supernatant or by nonfortified cortical microsomes. Carbon monoxide inhibited formation of these compounds, indicating that they may be formed by the cytochrome P-450-linked renal monooxygenase systems.     

Effects of red light on the growth of intact wheat and barley coleoptiles

The final lengths of intact dark-grown coleoptiles vary with species and cultivar. The growth distribution pattern in the apical 25-mm growing zone and the absolute amount of growth in each zone depend on the age and species of the coleoptile. A comparative study of several cultivars of wheat, Triticum vulgare, and barley, Hordeum vulgare, indicates that the growth distribution pattern in 30- to 38-mm coleoptiles varies with the species and cultivar. In barley, there are two patterns of growth distribution among the several cultivars, whereas in wheat, all cultivars exhibit a common zonal growth pattern. The total growth of coleoptiles, initially 30 to 38 mm in length, during a 24-hour dark incubation period is the same in dark-grown coleoptiles as in those irradiated with 3 minutes of red (660 nm) light prior to the incubation period. The growth distribution pattern in the growing zone of this 30- to 38-mm coleoptile is, however, altered by red light. Growth of the apical 5-mm zone is stimulated by red light and the zonal growth 5 to 10 mm below the apex is only slightly affected, whereas growth in the zones 10 to 15 to 20, and 20 to 25 mm below the apex is inhibited. This growth distribution pattern in irradiated coleoptiles changes as the coleoptile increases in length. The response of a zone following exposure to red light is dependent upon the age of the seedlings irradiated. The over-all effect of red light on growth of the intact coleoptile varies with the length of the coleoptile. In young seedling 20 to 29 mm in length, the cells of the coleoptile can compensate for the effects of red light, with the over-all growth of the dark-grown and irradiated coleoptile about the same. As the seedling grows older, the cells of the coleoptile can no longer make up for the effects of red light, and the over-all effect changes from compensation to pronounced inhibition.     

Phylogeny of snakes (Serpentes): Combining morphological and molecular data in likelihood,Bayesian and parsimony analyses

Abstract

The phylogeny of living and fossil snakes is assessed using likelihood and parsimony approaches and a dataset combining 263 morphological characters with mitochondrial (2693 bp) and nuclear (1092 bp) gene sequences. The ‘no common mechanism’ (NCMr) and ‘Markovian’ (Mkv) models were employed for the morphological partition in likelihood analyses; likelihood scores in the NCMr model were more closely correlated with parsimony tree lengths. Both models accorded relatively less weight to the molecular data than did parsimony, with the effect being milder in the NCMr model. Partitioned branch and likelihood support values indicate that the mtDNA and nuclear gene partitions agree more closely with each other than with morphology. Despite differences between data partitions in phylogenetic signal, analytic models, and relative weighting, the parsimony and likelihood analyses all retrieved the following widely accepted groups: scolecophidians, alethinophidians, cylindrophiines, macrostomatans (sensu lato) and caenophidians. Anilius alone emerged as the most basal alethinophidian; the combined analyses resulted in a novel and stable position of uropeltines and cylindrophiines as the second‐most basal clade of alethinophidians. The limbed marine pachyophiids, along with Dinilysia and Wonambi, were always basal to all living snakes. Other results stable in all combined analyses include: Xenopeltis and Loxocemus were sister taxa (fide morphology) but clustered with pythonines (fide molecules), and Ungaliophis clustered with a boine‐erycine clade (fide molecules). Tropidophis remains enigmatic; it emerges as a basal alethinophidian in the parsimony analyses (fide molecules) but a derived form in the likelihood analyses (fide morphology), largely due to the different relative weighting accorded to data partitions.     

A differential scanning calorimetric study of the bovine lens crystallins

Differential scanning calorimetry was performed on the five major lens crystallin fractions [HM-alpha, alpha, beta H, beta L, and (beta s + gamma)] of the bovine lens as well as on more purified forms of alpha- and gamma-crystallins. All were found to be relatively thermally stable although the alpha-crystallin were found to at least partially unfold at an approximately 10 degrees C lower temperature than the beta and gamma fractions. Increasing protein concentration had little effect on gamma-crystallin thermograms but had marked effects on those of the alpha- and beta-crystallins. Increases in the thermal stability with increasing protein concentration for the beta-crystallins can be explained most simply by the known beta L/beta H equilibrium, but, in the case of the alpha-crystallins, excluded volume effects may be an important factor. In both cases, the increased stability at high concentrations could be of physiological relevance. As well as the expected endothermic unfolding transitions, all of the lens crystallins revealed exothermic peaks that correlate with protein precipitation. Interestingly, this phenomenon occurs only after extensive structural alteration in the case of the alpha-crystallins but is present very early in the initial stages of structural perturbation of the beta- and gamma-crystallins.