Asymptotic birth trajectories in the discrete form of stable population theory

This paper seeks to supply a hitherto missing link in the reconciliation of the discrete and continuous formulations of stable population theory—see, for example, Keyfitz (“Introduction to the Mathematics of Population,” Chap. 8, Addison-Wesley, Reading, Mass., 1968). We show that the real exponential component of the birth trajectory has a non-zero (in fact positive) coefficient. Consequently, there is no possibility that oscillatory terms in the series expression for the birth trajectory can be dominant. This is shown by obtaining a formula for the desired coefficient.     

Family structured patterns of mortality in the false Colorado potato beetle

Abstract. 1. The distribution of mortality within and among groups of immature Leptinotursu juncta (Germar) (Coleoptera: Chrysomelidae) was studied in the field at three points in the life-cycle in order to test whether the fates of individuals occupying the same host plant were non-independent.
2. Studies were conducted on eggs subject to cannibalism and predation, on newly hatched larvae subject to predation, and on older larvae subject to parasitism by Myiophurus doryphorue (Riley), a tachinid fly.
3. At all three points in the life-cycle the variance in group-specific survivorship rates was demonstrated to be significantly greater than expected when individual deaths are distributed randomly among groups, with standardized variances ranging from 42% to 52% of the maximum possible.
4. A statistically significant positive correlation was shown between the number of individuals in a group and the group-specific survivorship rate at all three life stages.
5. The distribution of genetic variants within and among groups of larvae showed the groups to be mixtures of full and half siblings, with an average coefficient of genetic relatedness, r , equal to 0.38.     

Selection for intermediate mortality and reproduction rates in a spatially structured population

How local interactions influence both population and evolutionary dynamics is currently a key topic in theoretical ecology. We use a 'well-mixed' analytical model and spatially explicit individual-based models to investigate a system where a population is subject to rare disturbance events. The disturbance can only propagate through regions of the population where the density of individuals is sufficiently high and individuals affected by the disturbance die shortly after. We find that populations where individuals are sessile often exhibit very different dynamic behaviour when compared to populations where individuals are mobile and spatially well mixed. When mutations are allowed which affect either offspring birth rates or mortality rates, the well-mixed populations always evolve to a state where a single disturbance event leads to extinction. Populations often persist substantially longer if individuals are sessile and they disperse their offspring locally. We also find that for sessile populations selection may favour short-lived individuals with limited offspring production. Population dynamics are found to be strongly influenced by the host characters that are evolving and the rate at which host variation is introduced into the system.     

Hormone trajectories leading to human birth

The mechanisms regulating human parturition and labor remain unknown. This ignorance is expensive as preterm birth is responsible for 70% of neonatal mortality and 50% of cerebral palsy. Methods for the prediction of preterm birth and treatments for women in preterm labor have poor efficacy reflecting our limited knowledge of the mechanisms involved. Recent research has supported the view that parturition is a cascade of events that commences early in pregnancy and involves the mother, fetus, placenta, membranes, cervix and myometrium. Although a number of the key hormones and proteins involved have been identified, the relationships between these factors in time and tissues remain unclear. Placental production of Corticotropin-releasing hormone (CRH) is proposed as an early event regulating the cascade of events. Central to the onset of parturition will be a mechanism for progesterone withdrawal and estrogen activation in human. Two forms of progesterone receptor with opposing actions exist in the human myometrium. Progesterone receptor A (PR-A) is a dominant negative repressor of progesterone receptor B (PR-B). Preliminary studies strongly support the hypothesis that the onset of human parturition is initiated by rising concentrations of PR-A in the myometrium.     

Child mortality levels and survival patterns from southern Sudan

Data from a 1985 survey in two major population centres in Southern Sudan, Juba and Wau, were analysed in order to assess childhood mortality levels and the effect of UNICEF's health care programme. There are continuing high levels of childhood mortality. Logistic regression analysis shows significant positive associations between child survival and immunization, oral rehydration therapy and maternal education.     

Effective population size and population subdivision in demographically structured populations

A fast-timescale approximation is applied to the coalescent process in a single population, which is demographically structured by sex and/or age. This provides a general expression for the probability that a pair of alleles sampled from the population coalesce in the previous time interval. The effective population size is defined as the reciprocal of twice the product of generation time and the coalescence probability. Biologically explicit formulas for effective population size with discrete generations and separate sexes are derived for a variety of different modes of inheritance. The method is also applied to a nuclear gene in a population of partially self-fertilizing hermaphrodites. The effects of population subdivision on a demographically structured population are analyzed, using a matrix of net rates of movement of genes between different local populations. This involves weighting the migration probabilities of individuals of a given age/sex class by the contribution of this class to the leading left eigenvector of the matrix describing the movements of genes between age/sex classes. The effects of sex-specific migration and nonrandom distributions of offspring number on levels of genetic variability and among-population differentiation are described for different modes of inheritance in an island model. Data on DNA sequence variability in human and plant populations are discussed in the light of the results.     

Multiple hysteretic patterns from elementary population models

Critical transitions whereby small changes in conditions can cause large and irreversible changes in ecosystem states are a cause of increasing concern in ecology. Here, we focus on the irreversibility of these transitions, formally known as hysteresis. We explore how simple correlations between parameters in Lotka-Volterra predator-prey equations result in a variety of complicated hysteretic patterns. These patterns include “unattainable” stable states that once lost may never be recovered. We suspect these patterns to be common in natural systems, where interactions between diverse assemblages are unavoidable. Thus, understanding underlying hysteretic structures may be necessary for rescuing lost ecosystem states and avoiding future losses.     

Numerical solution of structured population models

Numerical methods are presented for a general mass-structured population model with demographic rates that depend on individual mass, time, and total population mass. Several types of numerical methods are described, Eulerian methods, implicit methods, and the method of characteristics. These methods are compared for a sample problem with an exact solution. The preferred numerical technique combines the method of characteristics with an adaptive grid. Numerical solution of model equations developed for mosquitofish illustrates this method and demonstrates how seasons can play a dominant role in shaping population development.     

Steady-state analysis of structured population models

Our systematic formulation of nonlinear population models is based on the notion of the environmental condition. The defining property of the environmental condition is that individuals are independent of one another (and hence equations are linear) when this condition is prescribed (in principle as an arbitrary function of time, but when focussing on steady states we shall restrict to constant functions). The steady-state problem has two components: (i). the environmental condition should be such that the existing populations do neither grow nor decline; (ii). a feedback consistency condition relating the environmental condition to the community/population size and composition should hold. In this paper we develop, justify and analyse basic formalism under the assumption that individuals can be born in only finitely many possible states and that the environmental condition is fully characterized by finitely many numbers. The theory is illustrated by many examples. In addition to various simple toy models introduced for explanation purposes, these include a detailed elaboration of a cannibalism model and a general treatment of how genetic and physiological structure should be combined in a single model.     

Numerical solution of structured population models

Numerical methods are presented for a general age-structured population model with demographic rates depending on age and the total population size. The accuracy of these methods is established by solving problems for which alternate solution techniques are available and are used for comparison. The methods reliably solve test problems with a variety of dynamic behavior. Simulations of a blowfly population exhibit cyclic fluctuations, whereas a simulated squirrel population reaches a stable age distribution and stable equilibrium population size. Life-history attributes are easily studied from the computed solutions, and are discussed for these examples. Recovery of a stressed population back to equilibrium is examined by computing the transition in age structure, and the transient behavior of other properties of the population such as the per capita growth rate, the average age, and the generation length.     

On harvesting a structured ungulate population

Variation in demographic rates within a spatially structured population could have important consequences for management decisions, harvesting strategies and offtake rates. Although there is a growing body of evidence suggesting that demographic rates vary within populations over a range of spatial scales, there has been little research investigating the consequences of this variation for population management. In this paper, data on the dynamics of two female red deer sub-populations on Rum are analysed, and evidence is presented for differences between the fecundity and mortality rates of the two sub-populations. A simple harvesting model is developed to represent the dynamics of the two sub-populations, including density-independent migration between sub-populations and spatially correlated environmental variability. The highest monetary yield in the model is obtained by harvesting the more resilient sub-population at a higher rate. Surprisingly the losses involved in harvesting both sub-populations at the same rate are insignificant. However, if migration were density-dependent, the size of one sub-population would be more relevant to harvesting policy for the other sub-population. The results of this empirical study are compared to theoretical work on spatially structured populations; it is shown that when a species has complex age- and sex-structured population dynamics, previous theoretical results may not hold.     

Estimating population dynamics trajectories of raptors from a multi-species hierarchical distance sampling model

Community dynamics are essential for ecosystems as they support the functioning of food webs and maintain biodiversity. However, the fluctuations of species abundances are rarely analyzed simultaneously despite their interconnectedness across space and time. We developed a Bayesian multi-species model that estimates community- and taxon-level parameters related to dynamics, abundance, detection probability, and environmental stochasticity. From this model, we analyze the variability of populations of a community of raptors composed of accipiters (sharp-shinned hawk [Accipiter striatus], and Cooper's hawk [A. cooperii]), buteos (red-tailed hawk [Buteo jamaicensis], and red-shouldered hawk [B. lineatus]) and owls (great horned owl [Bubo virginianus], and barred owl [Strix varia]). We show that migration pulses of accipiters, buteos, and dispersal of fledging owls drive variation in raptor abundances, indicating a defined production and dispersal period. Also, large-scale climatic processes such as the North Atlantic Oscillation (NAO) influenced the variation in abundances of raptors. When the NAO was in a positive phase, the abundance of raptors decreased, and inversely. Local weather did not affect raptor population abundances. Our approach facilitated the modelling of species-specific effects of environmental variation and guild-level dynamics that could be used for ecosystem-based conservation measures.     

Density-dependent birth rate, birth pulses and their population dynamic consequences

 In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose a single-species model with stage structure for the dynamics in a wild animal population for which births occur in a single pulse once per time period. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker functions or Beverton-Holt functions, and obtain the threshold conditions for their stability. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos. Received: 13 June 2001 / Revised version: 7 September 2001 / Published online: 8 February 2002     

Estimating population cause-specific mortality fractions from in-hospital mortality: validation of a new method

Background

Cause-of-death data for many developing countries are not available. Information on deaths in hospital by cause is available in many low- and middle-income countries but is not a representative sample of deaths in the population. We propose a method to estimate population cause-specific mortality fractions (CSMFs) using data already collected in many middle-income and some low-income developing nations, yet rarely used: in-hospital death records.

Methods and Findings

For a given cause of death, a community''s hospital deaths are equal to total community deaths multiplied by the proportion of deaths occurring in hospital. If we can estimate the proportion dying in hospital, we can estimate the proportion dying in the population using deaths in hospital. We propose to estimate the proportion of deaths for an age, sex, and cause group that die in hospital from the subset of the population where vital registration systems function or from another population. We evaluated our method using nearly complete vital registration (VR) data from Mexico 1998–2005, which records whether a death occurred in a hospital. In this validation test, we used 45 disease categories. We validated our method in two ways: nationally and between communities. First, we investigated how the method''s accuracy changes as we decrease the amount of Mexican VR used to estimate the proportion of each age, sex, and cause group dying in hospital. Decreasing VR data used for this first step from 100% to 9% produces only a 12% maximum relative error between estimated and true CSMFs. Even if Mexico collected full VR information only in its capital city with 9% of its population, our estimation method would produce an average relative error in CSMFs across the 45 causes of just over 10%. Second, we used VR data for the capital zone (Distrito Federal and Estado de Mexico) and estimated CSMFs for the three lowest-development states. Our estimation method gave an average relative error of 20%, 23%, and 31% for Guerrero, Chiapas, and Oaxaca, respectively.

Conclusions

Where accurate International Classification of Diseases (ICD)-coded cause-of-death data are available for deaths in hospital and for VR covering a subset of the population, we demonstrated that population CSMFs can be estimated with low average error. In addition, we showed in the case of Mexico that this method can substantially reduce error from biased hospital data, even when applied to areas with widely different levels of development. For countries with ICD-coded deaths in hospital, this method potentially allows the use of existing data to inform health policy.     

A survey of structured cell population dynamics

A survey of three types of cell population models is presented in this paper. The main issue in all the surveyed words is whether or not there exists astable type distribution (s.t.d.). In the last few years, many efforts were directed towards describing the most general models which still exhibits.t.d. Progress made in the case ofsize density models are discussed. A slightly extended version of atime continous daughter cell model, studied in Arino et al. (1991), is presented. Recently, some authors have undertaken the task of comparing models of various origins and types. Such works are alluded to in a discussion.     

Mid-arm circumference at birth as predictor of low birth weight and neonatal mortality

In Bangladesh, like other developing countries, most births occur at home or in the community, so logistic problems and taboos prevent the weighing of every newborn child. This study was performed to see whether other simpler measurements could be substituted for weight to identify neonates of low birth weight. A total of 1676 live births at the Chittagong Medical College Hospital constituted the study sample, and this showed a high correlation between mid-arm circumference and birth weight (r=0.792, p<0.000). A mid-arm circumference of <9.0 cm had the best sensitivity and specificity for identifying newborns with a birth weight of less than 2500 g. These neonates were followed up to record neonatal deaths. Neonatal mortality showed an inverse relation with mid-arm circumference. A mid-arm circumference of <9.0 cm and a birth weight of <2500 g were equally useful in predicting neonatal outcome. Mid-arm circumference is a simple, quick and reliable indicator for predicting low birth weight and neonatal outcome, and can be easily measured by medical practitioners and traditional birth attendants (TBAs) in the community of developing countries like Bangladesh.     

Adaptive dynamics for physiologically structured population models

We develop a systematic toolbox for analyzing the adaptive dynamics of multidimensional traits in physiologically structured population models with point equilibria (sensu Dieckmann et al. in Theor. Popul. Biol. 63:309–338, 2003). Firstly, we show how the canonical equation of adaptive dynamics (Dieckmann and Law in J. Math. Biol. 34:579–612, 1996), an approximation for the rate of evolutionary change in characters under directional selection, can be extended so as to apply to general physiologically structured population models with multiple birth states. Secondly, we show that the invasion fitness function (up to and including second order terms, in the distances of the trait vectors to the singularity) for a community of N coexisting types near an evolutionarily singular point has a rational form, which is model-independent in the following sense: the form depends on the strategies of the residents and the invader, and on the second order partial derivatives of the one-resident fitness function at the singular point. This normal form holds for Lotka–Volterra models as well as for physiologically structured population models with multiple birth states, in discrete as well as continuous time and can thus be considered universal for the evolutionary dynamics in the neighbourhood of singular points. Only in the case of one-dimensional trait spaces or when N = 1 can the normal form be reduced to a Taylor polynomial. Lastly we show, in the form of a stylized recipe, how these results can be combined into a systematic approach for the analysis of the (large) class of evolutionary models that satisfy the above restrictions.