Genealogy with seasonality,the basic reproduction number,and the influenza pandemic

The basic reproduction number R ₀ has been used in population biology, especially in epidemiology, for several decades. But a suitable definition in the case of models with periodic coefficients was given only in recent years. The definition involves the spectral radius of an integral operator. As in the study of structured epidemic models in a constant environment, there is a need to emphasize the biological meaning of this spectral radius. In this paper we show that R ₀ for periodic models is still an asymptotic per generation growth rate. We also emphasize the difference between this theoretical R ₀ for periodic models and the “reproduction number” obtained by fitting an exponential to the beginning of an epidemic curve. This difference has been overlooked in recent studies of the H1N1 influenza pandemic.     

Condition, growth and reproduction in female red lechwe (Kobus leche leche Gray 1850)

Information on condition, growth and reproduction was collected from a sample of 155 female lechwe in the Linyanti Swamp, northern Botswana. Condition varied significantly with age, reproductive state and season and indications were found of relationships between body mass and the attainment of puberty in young females and body mass and the fertility of adult females. There were also indications that the population was under nutritional stress because of high water levels and that this had caused reductions in the growth rate and fertility of young females. It is suggested that the sensitivity of young females to adverse environmental conditions could be exploited to optimize population monitoring for conservation purposes by using them as an indicator class, rather than monitoring the entire population. Because of relationships between condition, growth and reproduction, it is also suggested that long-term monitoring of condition should form part of any effort to understand population dynamics.     

The relative importance to population increase of fluctuations in mortality,fecundity and the time variables of the reproductive schedule

Summary Previous authors have used simple models to investigate the relative importance to population increase of variations in the total and age-specific reproductive rates. But while acknowledging that the latter were the product of the age specific birth and death rates, they have used their models only to investigate changes in total or age-specific birth rates and have not been concerned with variations in death rates. This paper extends the use of Lewontin's (1965) model, to a wide range of values of r, the exponential rate of population increase. It shows how the relative importance of changes in certain life-history features can change with r and be reversed when r is near to zero. It is also shown that variations in mortality rate are not necessarily best expressed in analogous terms to variations in birth rate. If more suitable terms are used it is seen that changes in mortality rate can be of varying importance depending on the existing mortality rate. They can be overwhelmingly important when the mortality rate is high.     

Generalized stable population theory

In generalizing stable population theory we give sufficient, then necessary conditions under which a population subject to time dependent vital rates reaches an asymptotic stable exponential equilibrium (as if mortality and fertility were constant). If x ₀(t) is the positive solution of the characteristic equation associated with the linear birth process at time t, then rapid convergence of x ₀(t) to x ₀ and convergence of mortality rates produce a stable exponential equilibrium with asymptotic growth rate x ₀–1. Convergence of x ₀(t) to x ₀ and convergence of mortality rates are necessary. Therefore the two sets of conditions are very close. Various implications of these results are discussed and a conjecture is made in the continuous case.     

PHASED DIVISION OF PERIDINIUM CINCTUM F. WESTII (DINOPHYCEAE) AND DEVELOPMENT OF THE LAKE KINNERET (ISRAEL) BLOOM1,2

The yearly bloom of Peridinium cinctum f. westii (Lemm.) Lef. in Lake Kinneret is described and compared with the distribution of dinoflagellates in other freshwater bodies. The physical conditions required by the Wyatt and Horwood model do not fit the actual physical events accompanying the onset of the bloom. In situ measurements of the percentage of cells in division were undertaken to clarify various points about the internal dynamics of the population. The exponential increase of the population occurs when the diurnal percentage of cells in division is not higher than 10–15%. This percentage increases up to 45% in late February–March, but does not cause any increase of population. At this period, the loss rate is nearly equal to the rate of cell increase and is interpreted as massive mortality.     

Neuronal selectivity,population sparseness,and ergodicity in the inferior temporal visual cortex

The sparseness of the encoding of stimuli by single neurons and by populations of neurons is fundamental to understanding the efficiency and capacity of representations in the brain, and was addressed as follows. The selectivity and sparseness of firing to visual stimuli of single neurons in the primate inferior temporal visual cortex were measured to a set of 20 visual stimuli including objects and faces in macaques performing a visual fixation task. Neurons were analysed with significantly different responses to the stimuli. The firing rate distribution of 36% of the neurons was exponential. Twenty-nine percent of the neurons had too few low rates to be fitted by an exponential distribution, and were fitted by a gamma distribution. Interestingly, the raw firing rate distribution taken across all neurons fitted an exponential distribution very closely. The sparseness a ^s or selectivity of the representation of the set of 20 stimuli provided by each of these neurons (which takes a maximal value of 1.0) had an average across all neurons of 0.77, indicating a rather distributed representation. The sparseness of the representation of a given stimulus by the whole population of neurons, the population sparseness a ^p, also had an average value of 0.77. The similarity of the average single neuron selectivity a ^s and population sparseness for any one stimulus taken at any one time a ^p shows that the representation is weakly ergodic. For this to occur, the different neurons must have uncorrelated tuning profiles to the set of stimuli.     

Reproduction rate,feeding process,and leibich limitations in cell populations—Part 1. Feeding stochasticity and reproduction rate

A population of cells suspended in a liquid nutrient medium is considered. The process of growth, division and death of a cell is interpreted mathematically as the Bellman-Harris stochastic process governed by random meetings between the cell and nutrient particles. Growth of a cell is considered to be a result of two processes: mass inflow into and mass outflow from the cell. It is found that, in the absence of food limitations and inhibitors, population growth is not exponential. However, the exponential increase is approached asymptotically over time. Population net growth rate is a variable rather than a constant, but tends over time to a constant value which is the rate of exponential growth. The rate of exponential growth, the probabilities of cell division and death, and the life expectancy of a cell are expressed analytically via average rate of meetings between a cell and nutrient particles. The paper presents an independent phase in calculating mathematical relations between the rate of exponential growth and the concentration of food in a substrate.     

Bayesian inference of species diffusion in the West African Agama agama species group (Reptilia,Agamidae)

The savannah and tropical forest biomes of Africa have a long history of expansion and contraction, and the recent and rapid spread of dry savannah habitats has influenced the spatial and temporal diversification of vertebrate taxa across this region. We used a combination of species tree and phylogeographic methods to describe the spatio-temporal changes through time and across space (= species diffusion) in a clade of seven West African lizard species in the Agama agama species group. A Bayesian species tree diffusion approach was used to compare the relative rates at which species ranges changed across the landscape. We found that some species have high diffusion rates characterized by significant movement in their range location and minor changes to their overall range size, whereas other species show little movement in their range centre with an exponential increase in range size. This discrepancy between the rates that range locations shift versus change in their relative area could be linked to populations tracking their preferred habitats through time. A continuous Bayesian phylogeography approach using a relaxed random walk model was used to estimate the timing and rate of population size change and geographic diffusion in A. picticauda, the single species in the group with an extensive African distribution from Mauritania to Ethiopia. The mean dispersal rate of A. picticauda increased dramatically throughout the Pleistocene, and a Bayesian skyride analysis supports exponential population growth over this same time period. A comparison of genetic diversity across different loci and species suggests that A. lebretoni experienced a mitochondrial selective sweep that has caused a deficit of variation at this locus in relation to nuclear loci.     

REBUILDING SEAL STOCKS IN THE KATTEGAT-SKAGERRAK

The harbor seal ( Phoca vitulina ) population in the Kattegat-Skagerrak area has been dwindling for several centuries due to excessive hunting pressure. Corrected hunting statistics during 1890–1976 are used to estimate changes in population size over the past century. After protection was introduced in the 1960s and 1970s the harbor seal population in the area increased at an exponential rate of 0.12 and exceeded 5,000 animals in 1986. The present rate of population growth is used for modelling the influence of fertility and age-specific mortality. It is found that the observed high rate of increase is only realistic if female fertility rate is very high, the range of juvenile mortality rate is 0.33–0.52 and adult mortality is less than 0.15. Commonly cited higher mortality rates are not realistic in the Kattegat-Skagerrak area.     

Compartment Analysis of Disease Progression in Time. I. Unrestricted Disease Increase

Disease progression in time through presporulating (latent), sporulating (infectious) and postporulating (removal) stages has been modelled as a three-compartment system in the case where no upper bound for total disease increase is considered. Deterministic compartment analysis has been performed based on Jeger's linked differential equations. Some important, well-established epidemilogical principles and concepts have been ‘rediscovered’, clarified or redefined. A new variable, defined as total inoculum reservoir of the host, is suggested as an additional epidemiological concept. Three rate parameters with phytopathological meaning were included in the system: R the constant intrinsic infection rate comparable to the Vanderplankian R_,c, h pathogen's ‘hatching rate’, related to the mean latent period p and g the intrinsic removal rate related to the infectious period i. Another parameter λ₁ is empirical and comparable to the logarithmic, infection rate, sensu Vanderplank if time becomes very large. In the compartment system iR= 0 is a threshold condition for total disease to increase over initial disease level and iR= 1 is a threshold condition for an ‘explosive’ total disease increase that may induce a large epidemic rather than a threshold for total disease to start or to exist. When iR < 1, the total disease level approaches α asymptotically, a finite value, while when iR > 1, the total disease, increase is explosive; only where λ₁=√dh does this increase follows the exponential law at larger t, otherwise the exponential law with the same rate parameter λ₁ underestimates or overstimates the amount of total disease at any time t. Some further implications are discussed and compared with those derived from the Vanderplankian system of epidemiological analysis.     

Estimating reaction norms for predictive population parameters,age specific mortality,and mean longevity in temperature‐dependent cohorts of Culex quinquefasciatus Say (Diptera: Culicidae)

Culex quinquefasciatus plays a major role in the transmission of important parasites and viruses throughout the world. Because temperature is an important limiting factor on growth and longevity of all mosquito species, estimating the reaction norms provides very important basic information for understanding both plasticity and individual variations of the population. In the present study, Cx. quinquefasciatus were maintained at five different constant temperatures (15°, 20°, 23°, 27°, and 30°C) for two subsequent generations. Reproductive population parameters in blood‐fed mated females and longevities of virgin and blood‐fed mated adults reared at different temperatures were compared for the two generations. Longevity increased as temperature decreased within a range of 15° to 30°C for the unmated adults, and 15° to 27°C for the mated and blood‐fed adults. Generation times were as long as 124.07 and 106.76 days for two subsequent generations reared at 15°C, and the highest intrinsic rate of increase (r_m) values were estimated at 0.22 and 0.18, respectively, from the cohorts reared at 27°C. For survival rates, reproductive rates (R₀), and r_m values, 30°C was found to be a critical temperature for this species. These cohorts produced the smallest amount of eggs (R₀= 5.06), r_m values decreasing across generations (from 0.11 to 0.06), and the survival rates from egg to adult were found to be insufficient (16.1 and 10.8%). Additionally, the rate of exponential increase with age and age specific mortalities (b) were calculated for the virgin cohorts. Age specific mortality rates increased as temperature decreased. The increase in mortality rates started to accelerate at 27°C and was more pronounced at 30°C, for both females and males. We estimated the coefficients of variation for the b values in which females have smaller coefficients than those of the males at all temperatures.     

Effect of an exponential feeding regime on the production of Rhodotorula araucariae epoxide hydrolase in Yarrowia lipolytica

Aims: To evaluate the effect of and exponential feeding regime on the production of epoxide hydrolase (EH) enzyme in recombinant Yarrowia lipolytica in comparison to a constant feed strategy. Methods and Results: An exponential feed model was developed and fermentations were fed at six different exponential rates. A twofold increase in EH productivity and a 15% increase in volumetric EH activity was obtained by applying exponential glucose feed rates in fed‐batch cultivation. These responses were modelled to obtain a theoretical optimum feed rate that was validated in duplicate fermentations. The model optimum of 0·06 h^?1 resulted in a volumetric EH activity of c. 5500 U l^?1 h^?1 and a maximum activity of 206 000 U l^?1. This correlated well with model predictions, with a variance of <10%. Conclusions: The use of an exponential feed strategy at a rate of 0·06 h ^{? 1} yielded best results for all key responses which show a clear improvement over a constant feed strategy. Significance and Impact of the Study: The study was the first evaluation of an exponential feed strategy on recombinant Y. lipolytica for the production of EH enzyme. The results suggest a strategy for the commercial production of a valuable pharmaceutical enzyme.     

Historical dynamics of a native cerambycid,Enaphalodes rufulus,in relation to climate in the Ozark and Ouachita Mountains of Arkansas

1. Tree‐ring techniques were used to date larval gallery scars of a native wood borer, Enaphalodes rufulus (Haldeman), in host Quercus rubra L. from eight sites within the Ozark and Ouachita National Forests of Arkansas. 2. Borer densities were quantified throughout the past century as indicated by scars within host tree boles and per capita rate of increase was calculated from one generation to the next. Both of these variables were extrapolated to the regional level. 3. Scar data from 78 Q. rubra revealed that at the regional level borer population growth increased from 1976 to 2000, or 11 generations prior to a recent outbreak. Duration and intensity of eruptive behaviour were variable geographically. 4. Sites with higher outbreak densities also sustained incipient (i.e. growing) populations for a longer time period than sites with lower outbreak densities, which indicates that a greater potential for exponential increase existed at these sites because more borers were present when conditions became favourable for an outbreak. 5. An index of summer soil moisture availability explained almost half of the variation in E. rufulus population growth, which suggests that drought may have been an important causal factor in the recent outbreak.     

The effects of a change in the growth rate of roach, Rutilus rutilus (L.), on the biology of the fish tapeworm Ligula intestinalis (L.)

Investigations into the biology of the roach and the pathogenic tapeworm Ligula intestinalis (L.) populations at Slapton Ley, Devon were carried out between October 1982 and December 1984. Data collected from the lake since 1977 have also been re-analysed to determine how the dramatic improvement in the individual growth rate of the roach over this period may have affected the growth, maturation and life-cycle of Ligula. Only the very young roach at this site become infected, so it was possible to follow cohorts of plerocercoids of similar age through each roach year class. Results for the 1978 and 1983 year classes are presented in detail. The roach grew extremely rapidly from May to August in each year, resulting in a pronounced cyclical pattern of changes in the condition of the roach, with the lowest condition occurring in late winter and spring. The yearly increase in the roach growth rate was accompanied by an increase in plerocercoid growth rate in the 0 + roach, but not in the 1 + roach. The growth rate of the plerocercoids was very high compared to that at other sites. It is usual for the parasite index (PI) of Ligula-infected fish to be high and to increase throughout their first few years of life. At Slapton, however, a lack of multiple infections has prevented high PIs from occurring, and in recent years the growth rate of the roach has been so high that the plerocercoids were unable to maintain a high weight relative to the fish, and the highest PIs occurred in the 0 + roach throughout late winter and spring. In recent year classes, therefore, the maximum PIs and highest pathogenicities coincided with the period of lowest condition in the 0+ roach. Observations of both caged and natural populations of 0+ roach over winter showed that a significant loss of roach containing the larger plerocercoids occurred from the population. In vitro cultivation of Ligula plerocercoids showed that they were capable of maturation at weights of 0.5 g, and only 6 months after having infected the roach. The increase of the growth rate of the plerocercoids in the 0+ roach has therefore resulted in a greater proportion of these plerocercoids being capable of infecting the definitive host. As a result of the increase in individual growth rate of the roach at Slapton, the potential for Ligula transmission, as measured in terms of both their pathogenicity and maturity, has shifted from the 1 + to the 0+ roach.     

Photoautotrophic growth of Marchantia polymorpha L. cells in suspension culture

A cell line of M. polymorpha was grown photoautotrophically in liquid suspension culture using 1% CO₂ in air as sole carbon source. The growth rate in terms of cell dry-weight during the exponential phase was 0.171 and the doubling time was 1.76 d. The rate of increase in chlorophyll was 1.6 times higher than the growth rate. The highest content of chlorophyll was 24 mg g^-1 dry weight, and the photosynthetic activity of the cells in the exponential phase, as calculated from the growth rate, was at least 60 mol mg^-1 chlorophyll h^-1.     

Characteristics of Sasa nipponica grassland as a summer forage resource for sika deer on Mt Ohdaigahara, central Japan

Recently, the sika deer, Cervus nippon Temminck, population has increased on Mt Ohdaigahara, central Japan. The dwarf bamboo, Sasa nipponica Makino et Shibata, is a primary forage plant for sika deer in this area. To demonstrate the characteristics of S. nipponica grassland, especially as summer forage for sika deer, the habitat use intensity of sika deer was estimated by fecal densities, and biomass, growth rate, removal by deer and crude protein content were examined. Sika deer utilized the S.nipponica grassland on Mt Ohdaigahara during summer when the biomass, growth rate and crude protein content of S. nipponica were high. The recent increase in the deer population seems to be partly due to S.nipponica grassland being a favorable summer habitat.     

Relative abundance, rate of increase, and fungal infections of freshwater phytoplankton

Fungal infections of seven species of phytoplankton were examinedin relation to the host species' exponential rate of net increase,and to their proportional contribution to the total phytoplanktonbiovolume. Infections were observed to increase at biovolumeproportions of the host species of as low as 1%. In most algalspecies, infected cells were always found at higher proportions,with the exception of Stephanodiscus rotula and Fragilaria crotonensis.In these two species, high proportions of biovolume were reachedwithout any evidence of infected cells. The increase in infectedcells was usually associated with a growing host population,whereas peak and decreasing densities of infected cells wereusually observed when host populations were declining. The resultsshow that the fungal parasites can exist on their host populationeven if it comprises only a small fraction of the total phytoplanktonbiovolume, and that the parasites become evident while the hostpopulation is still increasing.     

Growth and mortality of larval Myctophum affine (Myctophidae,Teleostei)

The growth and mortality rates of Myctophum affine larvae were analysed based on samples collected during the austral summer and winter of 2002 from south‐eastern Brazilian waters. The larvae ranged in size from 2·75 to 14·00 mm standard length (L_S). Daily increment counts from 82 sagittal otoliths showed that the age of M. affine ranged from 2 to 28 days. Three models were applied to estimate the growth rate: linear regression, exponential model and Laird–Gompertz model. The exponential model best fitted the data, and L₀ values from exponential and Laird–Gompertz models were close to the smallest larva reported in the literature (c. 2·5 mm L_S). The average growth rate (0·33 mm day^?1) was intermediate among lanternfishes. The mortality rate (12%) during the larval period was below average compared with other marine fish species but similar to some epipelagic fishes that occur in the area.     

Population growth potential of Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae) on tomato,potato, and eggplant

The influence of host plant on population dynamics of an invasive pest, Tuta absoluta was studied on three economically important solanaceous crops. Experiments were conducted in laboratory (29 ± 0.5°C, 75 ± 5% RH and a photoperiod of 14:10 hr [L:D]) using tomato (Solanum lycopersicum L.), potato (Solanum tuberosum L.) and eggplant (Solanum melongena L.). Results indicated that intrinsic rate of increase (r), finite rate of increase (λ) and net reproductive rate (R₀) were higher, and mean generation time (T) was the shortest on tomato. Results suggested that T. absoluta developed on all the three plants, and tomato plant was most preferred one. Results suggested that T. absoluta has a potential to become a serious pest on potato and even on eggplant under favourable conditions. We used the life tables of 0.025th and 0.975th percentiles of bootstraps to project the uncertainty of population growth, a new concept.     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve, Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rate r₀. The equilibrium recruitment rate r_s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates of r_s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger than r_s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.