Growth specific analysis of Schmid's (1983) data on Down syndrome carriers

After a short introduction to the phenomena of children with Down's syndrome, values describing body status as gained by Schmid at the Aschaffenburg hospital for child disease (F.R.G.) are recalled. In a cross-sectional study values for body height, head circumference and body weight for 393 girls and 436 boys were gathered in 1983 reflecting the status for medically treated patients of the present. After insuring that the scattering of the data keeps within tolerable limits growth specific analysis became a challenge. Body length is approximated with the 2 step model by Sager (1981) comprising a basic function without a growth spurt superimposed by a spurt term. As a result, an usual but somewhat reduced growth spurt can be secured for the girls whilst the boys show no intermediate maximum in growth velocity. Nevertheless velocity keeps well above that for the basic function thus indicating a silent spurt after the definition of Pelez and Sager (1984). Head circumference too is treated with the same model after tests with Czech values for common and gypsy children. As a result, a reduced but acute growth spurt with a growth hump for the increase function has been found for both sexes. In contrast to height, however, a short term formula for values from birth to near pubescence cannot be applied due to the vivid head growth in the postnatal phase. Values for body weight W allow first conclusions after plotting log W against the body length L. In the case of the Down patients, 2 different forms of fundamental relations emerge, one of them related to normal growth, the other to impeded or less differentiated development as found in the rhesus for example. For both cases, mathematical expressions as proposed and used by Sager are applied. Results show near to normal behaviour for the girls and a less intricate course in weight growth for the boys. Results are given in graphs and tables allowing detailed calculations if desired. Quotients of momentary to finally attained values for body height and weight as well as head circumference are added.     

Cell Growth and Division: III. Conditions for Balanced Exponential Growth in a Mathematical Model

In a previous paper, we proposed a model in which the volume growth rate and probability of division of a cell were assumed to be determined by the cell's age and volume. Some further mathematical implications of the model are here explored. In particular we seek properties of the growth and division functions which are required for the balanced exponential growth of a cell population. Integral equations are derived which relate the distribution of birth volumes in successive generations and in which the existence of balanced exponential growth can be treated as an eigenvalue problem. The special case in which all cells divide at the same age is treated in some detail and conditions are derived for the existence of a balanced exponential solution and for its stability or instability. The special case of growth rate proportional to cell volume is seen to have neutral stability. More generally when the division probability depends on age only and growth rate is proportional to cell volume, there is no possibility of balanced exponential growth. Some comparisons are made with experimental results. It is noted that the model permits the appearance of differentiated cells. A generalization of the model is formulated in which cells may be described by many state variables instead of just age and volume.     

A simple method for calculating mosquito mortality rates, correcting for seasonal variations in recruitment

Abstract A simple age‐structured exponential growth model is presented for the analysis of the population dynamics of mosquitoes (Diptera: Culicidae). In this model, the proportion of parous mosquitoes R depends on the birth rate β, and the length of the first gonotrophic cycle g, but not on the mortality rate. If the age structure is fairly constant, R= exp(– βg). Extensions of the model correcting for feeding patterns are given. A simple method is applied to an example of Anopheles gambiae Giles biting density and parity ratio in Côte d'Ivoire (fortnightly sampled longitudinal data set), for calculation of the seasonally fluctuating mortality rate, correcting for effects of recruitment. The seasonal variations in birth rate and mortality rate are discussed in relation to variations in density and rainfall.     

Catch-up growth in short-at-birth NICU graduates

The statural catch-up growth, defined as reaching at least tenth length/height percentile (P10) for normal population standards (-1.28 SD score, SDS), was studied in 73 infants short at birth (length < P10 for gestational age) admitted to NICU. Mean gestational age at birth was 35.2 weeks (range 29-41) and mean birth length standard deviation score -2.31 (-4.52/-1.46). Infants were measured at birth, at 3, 6, 12, 18, and 24 months corrected age and then once a year until 6 years chronological age. Statural catch-up growth was studied, with reference both to normal population standards and to individual genetic target. With reference to normal population standards, 44% of infants had caught-up at 3 months of age, 51% at 3 years, 66% at 4 years and 73% at 6 years. In the case of individual genetic targets, a similar trend was present, but the absolute values were slightly higher from 4 to 6 years (73 vs. 66% and 78 vs. 73%, respectively). Statistically significant changes in mean standard deviations score for chronological age were present from birth to 3 months, 3 to 12 months, 3 to 4 years and 5 to 6 years (p<0.05). No differences were found in this trend of recovery when considering ponderal index (PI) at birth (symmetrical vs. asymmetrical), sex (male vs. female) or gestational age (p>0.05). In the majority of cases infants with short stature at birth admitted to a NICU had a statural catch-up growth within the first years of life. This is more evident when considered in relation to individual genetic target rather than to normal population standards.     

Analyzing growth components in trees

Observed growth, as given, for instance, by the length of successive annual shoots along the main axis of a plant, is mainly the result of two components: an ontogenetic component and an environmental component. An open question is whether the ontogenetic component along an axis at the growth unit or annual shoot scale takes the form of a trend or of a succession of phases. Various methods of analysis ranging from exploratory analysis (symmetric smoothing filters, sample autocorrelation functions) to statistical modeling (multiple change-point models, hidden semi-Markov chains and hidden hybrid model combining Markovian and semi-Markovian states) are applied to extract and characterize both the ontogenetic and environmental components using contrasted examples. This led us in particular to favor the hypothesis of an ontogenetic component structured as a succession of stationary phases and to highlight phase changes of high magnitude in unexpected situations (for instance, when growth globally decreases). These results shed light in a new way on botanical concepts such as "phase change" and "morphogenetic gradient".     

Photoperiod and fur lengths in the arctic fox (Alopex lagopus L.)

Pelage is seasonally dimorphic in the Arctic fox. During the winter, fur lengths for this species are nearly double similar values taken during the summer season. Considerable site-specific differences in fur length are noted. In general, body sites which are exposed to the environment when an Arctic fox lies in a curled position show greater fur lengths in all seasons and greater seasonal variations than body sites that are more protected during rest. Well-furred sites may tend to conserve heat during periods of inactivity, and scantily furred sites may tend to dissipate heat during periods of exercise. The growth of winter fur may compensate for the severe cold of the arctic winter. Changes in fur lengths indicate a definite pattern in spite of individual variations. During the fall months, fur lengths seem to lag behind an increasing body-to-ambient temperature gradient. Both body-to-ambient temperature gradients and fur lengths peak during December through February. From March through June, gradual environmental warming is accompanied by a decrease in average fur lengths. Thus, there appears to be a remarkable parallel between the body-to-ambient temperature gradient and the fur lengths. The growth of fur in the Arctic fox parallels annual changes in ambient temperature and photoperiod.Presented at the Eighth International Congres of Biometerorology, 9–14 September 1979, Shefayim, Israel.     

Mammalian photoperiodic system: formal properties and neuroendocrine mechanisms of photoperiodic time measurement

Photoperiodism is a process whereby organisms are able to use both absolute measures of day length and the direction of day length change as a basis for regulating seasonal changes in physiology and behavior. The use of day length cues allows organisms to essentially track time-of-year and to "anticipate" relatively predictable annual variations in important environmental parameters. Thus, adaptive types of seasonal biological changes can be molded through evolution to fit annual environmental cycles. Studies of the formal properties of photoperiodic mechanisms have revealed that most organisms use circadian oscillators to measure day length. Two types of paradigms, designated as the external and internal coincidence models, have been proposed to account for photoperiodic time measurement by a circadian mechanism. Both models postulate that the timing of light exposure, rather than the total amount of light, is critical to the organism's perception of day length. In mammals, a circadian oscillator(s) in the suprachiasmatic nucleus of the hypothalamus receives photic stimuli via the retinohypothalamic tract. The circadian system regulates the rhythmic secretion of the pineal hormone, melatonin. Melatonin is secreted at night, and the duration of secretion varies in inverse relation to day length; thus, photoperiod information is "encoded" in the melatonin signal. The melatonin signal is presumably "decoded" in melatonin target tissues that are involved in the regulation of a variety of seasonal responses. Variations in photoperiodic response are seen not only between species but also between breeding populations within a species and between individuals within single breeding populations. Sometimes these variations appear to be the result of differences in responsiveness to melatonin; in other cases, variations in photoperiod responsiveness may depend on differences in patterns of melatonin secretion related to circadian variation. Sites of action for melatonin in mammals are not yet well characterized, but potential targets of particular interest include the pars tuberalis of the pituitary gland and the suprachiasmatic nuclei. Both these sites exhibit uptake of radiolabeled melatonin in various species, and there is some evidence for direct action of melatonin at these sites. However, it appears that there are species differences with respect to the importance and specific functions of various melatonin target sites.     

Variation in size and growth of the great scallop Pecten maximus along a latitudinal gradient

Understanding the relationship between growth and temperature will aid in the evaluation of thermal stress and threats to ectotherms in the context of anticipated climate changes. Most Pecten maximus scallops living at high latitudes in the northern hemisphere have a larger maximum body size than individuals further south, a common pattern among many ectotherms. We investigated differences in daily shell growth among scallop populations along the Northeast Atlantic coast from Spain to Norway. This study design allowed us to address precisely whether the asymptotic size observed along a latitudinal gradient, mainly defined by a temperature gradient, results from differences in annual or daily growth rates, or a difference in the length of the growing season. We found that low annual growth rates in northern populations are not due to low daily growth values, but to the smaller number of days available each year to achieve growth compared to the south. We documented a decrease in the annual number of growth days with age regardless of latitude. However, despite initially lower annual growth performances in terms of growing season length and growth rate, differences in asymptotic size as a function of latitude resulted from persistent annual growth performances in the north and sharp declines in the south. Our measurements of daily growth rates throughout life in a long-lived ectothermic species provide new insight into spatio-temporal variations in growth dynamics and growing season length that cannot be accounted for by classical growth models that only address asymptotic size and annual growth rate.     

Differentiation diversity of Argentine cacti and its relationship to environmental factors

Abstract. We studied the differentiation diversity (β-diversity or species turnover) patterns of the three main cactus growth forms (columnar, opuntioid and globose) in 318 (1° × 1°) squares covering Argentina. We analysed the degree of association between species turnover of each growth form with the spatial variation of a set of 15 environmental variables. Species turnover was estimated in two ways: (1) by calculating species turnover along latitudinal and longitudinal gradients and (2) by evaluating the species turnover between each square and its eight surrounding neighbouring grid cells. For the three growth forms, species turnover in latitudinal transects was mostly related to the mean within-transect values of certain environmental variables, while in longitudinal transects it was related to the variation of some environmental variables within the transect rather than to their mean values. For columnar species, transect species turnover was mainly associated with variation in temperature, confirming the temperature-sensivity of this growth form. For opuntioid species, turnover along transects was mainly related to topographic variables. In the case of globose cacti, transect turnover was associated with variation in temperature and rainfall. For the three growth forms, areas of high turnover coincided with marked transitions between different biogeographic provinces, while the areas with lowest species turnover coincide with topographically and climatically uniform plains. Species turnover between individual squares was positively associated with the proportion of summer rainfall in globose cacti, the variation of mean annual temperature in columnar cacti and was negatively related to mean annual temperature in opuntioid cacti. Compared to the other growth forms, globose cacti presented a much larger proportion of squares with a high species turnover. In general, differentiation diversity was lower for the opuntioid and the columnar species, two growth forms with higher dispersal ability and was highest for the globose cacti, which have the lowest dispersal capacity. Environmentally heterogeneous areas, where large-scale transitions between biomes occur, have exceptionally high species turnover, and are important target areas for the conservation of biodiversity.     

Testing the adaptive nature of radiation: growth form and life history divergence in the African grass genus Ehrharta (Poaceae: Ehrhartoideae)

In most documented examples of adaptive radiation, the processes underlying divergence in form and function are poorly explored and remain speculative. Here, data from a comparative seedling growth experiment are used to explore growth form divergence in Ehrharta, a group of grasses that radiated in seasonally arid environments of the Cape region of South Africa. Seedlings of eight Ehrharta species of variable growth form were grown in liquid culture under conditions of high resource availabilty for 56 d, during which time changes in dry mass, allocation, and leaf parameters were measured. The results of this experiment reveal the existence of distinct seedling growth patterns that are associated with differences in adult plant form and seasonal drought survival strategy. Specifically, species that utilize a reseeding strategy have higher seedling growth rates and flower earlier than species that persist by vegetative means. A correlation between species' growth rates and their native substrates suggests that edaphic heterogeneity has been central in directing the evolution of alternative persistence strategies and growth forms. Parsimony reconstruction identifies slow growth and an association with nutrient-deficient sandstone-derived soils as ancestral in Ehrharta, with fast growth evolving after a transition to richer shale- and granite-derived soils. The emergence of annual species in two fast-growth lineages suggests that the latter is a key step in the evolution of an ephemeral strategy. An association between plant function and habitat identifies the radiation of Ehrharta as adaptive.     

Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation.     

Conflicting objectives in chemotherapy with drug resistance

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic treatment. For general cell growth, some results are given, whereas for the special case of Malthusian (exponential) growth of tumor cells and rather general growth rate for normal cells, the optimal strategy is worked out. The latter, from the clinical standpoint, corresponds to maximum drug concentration throughout the treatment.     

Asymptotic worst-case mixing in simple demographic models of HIV/AIDS.

The majority of published modeling work regarding the impact of mixing patterns among subgroups on the spread of HIV infection assumes either that the overall population size remains constant, the aggregate immigration to the population occurs at a constant annual rate, or that no immigration occurs and the population in question declines due to HIV or other causes. In this paper, immigration rates are modeled as simple functions of population size and may be interpreted as aggregate birth rates. This assumption implies asymptotic exponential growth in the disease-free population as long as per capita birth rates exceed per capita mortality rates. The introduction of HIV infection to such a population may change this situation, and the asymptotic population growth rate can be reduced substantially as a result. The specific manner in which this occurs depends in part upon difficult to observe mixing patterns among those with different sexual activity rates. Rather than attempting to explicitly model a variety of mixing patterns, a bound on the impact of worst-case mixing is produced, where "worst case" refers to the mixing pattern that maximizes the asymptotic prevalence of infection, which is equivalent to minimizing the asymptotic population growth rate. These new techniques are illustrated with a numerical example.     

Major Evolutionary Trends in Hydrogen Isotope Fractionation of Vascular Plant Leaf Waxes

Hydrogen isotopic ratios of terrestrial plant leaf waxes (δD) have been widely used for paleoclimate reconstructions. However, underlying controls for the observed large variations in leaf wax δD values in different terrestrial vascular plants are still poorly understood, hampering quantitative paleoclimate interpretation. Here we report plant leaf wax and source water δD values from 102 plant species grown in a common environment (New York Botanic Garden), chosen to represent all the major lineages of terrestrial vascular plants and multiple origins of common plant growth forms. We found that leaf wax hydrogen isotope fractionation relative to plant source water is best explained by membership in particular lineages, rather than by growth forms as previously suggested. Monocots, and in particular one clade of grasses, display consistently greater hydrogen isotopic fractionation than all other vascular plants, whereas lycopods, representing the earlier-diverging vascular plant lineage, display the smallest fractionation. Data from greenhouse experiments and field samples suggest that the changing leaf wax hydrogen isotopic fractionation in different terrestrial vascular plants may be related to different strategies in allocating photosynthetic substrates for metabolic and biosynthetic functions, and potential leaf water isotopic differences.     

Reconstruction of individual life histories of rodents from their teeth and bone

Age changes of bone tissue and molar cementum, and formation of daily layers in dentin of incisors enable us to estimate age and maximum lifespan, season of birth, season of death, sexual maturation, sex in adults, and in combination with tetracycline prebaiting, movements and space distribution of rodents. In hibernating rodents, the hibernation zone formed in incisor dentin can be used to assess inter- and intrapopulation variations in seasonal activity and growth. This approach is illustrated by examples from the study of rodents of the generaApodemus andSicista.     

Potential of Schinopsis lorentzii for dendrochronological studies in subtropical dry Chaco forests of South America

The lack of knowledge about species with well-delimited annual rings has hampered the development of dendrochronological records in the subtropical Chaco region of South America. In this contribution, we present the first tree-ring chronology of Schinopsis lorentzii (Anacardiaceae), a dominant species in the semi-arid Chaco. Cross sections were collected near Las Lajitas, Salta, Argentina, and processed following the methods commonly used in dendrochronology. Annual growth variations between radii from a single individual and between radii from different trees were highly correlated. To determine the climatic parameters that control radial growth, we compared annual tree-ring variations against regional temperature and precipitation records. Correlation functions indicate that tree growth is highly influenced by spring–summer rainfall variations, which represent more than 80% of the total annual precipitation. The chronology, which covers the interval from 1829 to 2004, provides a context for the unprecedented increase in precipitation since the mid-1970s in the region. The climatic-sensitivity of S. lorentzii provides a unique opportunity to reconstruct precipitation variations during past centuries in the extensive semiarid regions of subtropical South America.     

Population dynamics and production of the tropical freshwater shrimp Caridina nilotica (Decapoda: Atyidae) in the littoral of Lake Sibaya

SUMMARY. Seasonal changes in population structure, standing stock levels and production of Caridina nilotica were studied at three sites in the littoral margins of subtropical Lake Sibaya between January 1975 and March 1976. Average population density at these sites declined from a maximum of c. 1400 to a minimum of c. 350 individuals per m² (3.4–0.4 g m^?2 dry wt) during the study, possibly as a result of emigration into peripheral vegetation inundated by rising lake levels. Shrimps bred perennially and, although egg stocks and instantaneous birth rates (b) were highest during summer, no corresponding increases in populaton density were observed, suggesting that the seasonally higher birth rates were offset by higher mortality rates. Population size structure and size-specific sex ratios did not change seasonally to any marked extent. Relative abundance declined with size and females grew larger than males. Clutch size increased linearly as a function of female carapace length. Estimates of overall mean annual somatic production (g m^?2 year^?1 dry wt) for the three sites between January 1975 and January 1976 ranged between c. 132 (egg-ratio method), 37.5 (summation of growth increments) and 24 (Hynes-Hamilton method) at an annual mean standing stock level of 2.7 g m^?2 dry wt (calorific value, 20.34 kJ g^?1 dry wt). Production at sites 1, 2 and 3 decreased in line with declining annual mean standing stocks (5.32, 3.67 and 0.23 g m^?2, respectively). The growth increment method gave an overall mean annual P/B value of 13.9. Egg production amounted to a further 5.6, 3.6 and 0.1 g m^?2 year^?1 dry wt (calorific value, 28.01 kJ g^?1) at sites 1, 2 and 3, or 2.7 g m^?2 year^?1 on average.     

Measured coral luminescence as a freshwater proxy: comparison with visual indices and a potential age artefact

Illuminating slices from massive coral skeletons under ultraviolet light can reveal bright luminescent lines in nearshore corals affected by freshwater river flows. The occurrence and intensity of these lines in long-lived corals can then be used to reconstruct past river flow and rainfall, extending the instrumental records of past tropical climate variability considerably. Earlier studies from the Great Barrier Reef, Australia, have used visual assessments of luminescent line intensity to develop semi-quantitative (though potentially subjective) indices of spatial and temporal variations in freshwater flows. Annual visual assessments and relative coral luminescence intensity (measured by fluorescence spectroscopy) and growth variables are first compared for 89 Porites coral colonies from 30 reefs throughout the length and breadth of the GBR. This demonstrates that simple visual assessments can provide useful information, in the absence of quantitative measurements, of this proxy freshwater tracer. The annual range of measured luminescence between the preceding winter minimum and summer maximum, rather than annual average or annual maximum luminescence is shown to be the most robust measure of freshwater flow. Second, from analyses of the coral colony data and over 40-century-long or longer coral core records, attention is drawn to a potential age artefact in annual average and annual maximum measured coral luminescence. These variables show a significant decline through time, similar to the observed decline in average skeletal density. Although the reasons for this decline are unknown, it could compromise interpretation of long-term variations in freshwater flows and subsequent climatic inferences. This artefact does not appear to affect the annual luminescence range which, it is concluded, is a robust proxy for inter-annual variations in river flow and rainfall.     

Time Inhomogeneous Mutation Models with Birth Date Dependence

The classic Luria–Delbrück model for fluctuation analysis is extended to the case where the split instant distributions of cells are not i.i.d.: the lifetime of each cell is assumed to depend on its birth date. This model takes also into account cell deaths and non-exponentially distributed lifetimes. In particular, it is possible to consider subprobability distributions and to model non-exponential growth. The extended model leads to a family of probability distributions which depend on the expected number of mutations, the death probability of mutant cells, and the split instant distributions of normal and mutant cells. This is deduced from the Bellman–Harris integral equation, written for the birth date inhomogeneous case. A new theorem of convergence for the final mutant counts is proved, using an analytic method. Particular examples like the Haldane model or the case where hazard functions of the split-instant distributions are proportional are studied. The Luria–Delbrück distribution with cell deaths is recovered. A computation algorithm for the probabilities is provided.     

Biochemical and genetic properties of oligomeric structures: a general approach

The oligomers constituted by association of different subunits can exist under multiple forms. In the case of the genetically variable proteins, such a multiplicity leads to numerous questions (i) on the enumerations: what is the number of active forms when a given subunit can make the oligomer inactive, or when the subunits are encoded by s alleles; (ii) on the subunit effects on biochemical properties: how to estimate these effects, are they equal, are there interactions between subunits, etc. Theoretical methods for the study of such oligomeric structures are developed, which mainly rely on linear model techniques. Peculiar properties examined are Vmax and Km, but also the quantities of the various oligomers, which depend on their association law. This approach is extended to the oligomers composed of different sets of subunits, as are for example some enzymes. These aspects are discussed from numerous bibliographic examples, with special reference to molecular interactions (protein complementation or molecular heterosis). Otherwise the genetic application of this theoretical approach is presented: it is possible to consider a genotype as an oligomer of alleles, and thus to study their effects and their interactions, in the one-locus case as well as in the several-loci case. The relevance of this generalization is discussed in connection with two other concepts, the "sequence space" used in molecular evolution and the regression of the genotypic values on the number of alleles used in quantitative genetics.