On the intrinsic force of convergence to stability∗

Observed populations differ greatly in the speed with which they approach the stable form, but what determines rates of convergence is not fully understood. The present paper shows that the force of convergence does not approach a fixed value, but oscillates indefinitely around an “intrinsic”; level. That level, h?, is determined by the square of the ratio of the 2 largest eigenvalues of the Leslie matrix. The value of h? can be closely approximated by a simple function that changes directly with the square of the coefficient of variation and inversely with the mean of the stable net maternity function. Population entropy, another measure of dispersion relative to the mean, is also highly correlated with h?.     

Slow‐fast dynamics in a model of population and resource growth

Models of the interaction of population, the economy, and the environment often contain nonlinear functional relationships and variables that move at different speeds. These properties foster apparent unpredictabilities in system behaviour. Using a simple deterministic model of demographic, economic and environmental interactions we illustrate the usefulness of geometric singular perturbation theory in environmental population economics. In contrast to local stability analysis, the theory of slow‐fast dynamics helps to gain new insights into the global behaviour of the system. In particular, the knowledge of the basins of attraction of the stationary states enables one to determine the regions of sustainable future paths of resources and population.     

Dynamics of age- and size-structured populations in fluctuating environments: Applications of stochastic matrix models to natural populations

Recent developments of the theory of stochastic matrix modeling have made it possible to estimate general properties of age- and size-structured populations in fluctuating environments. However, applications of the theory to natural populations are still few. The empirical studies which have used stochastic matrix models are reviewed here to examine whether predictions made by the theory can be generally found in wild populations. The organisms studied include terrestrial grasses and herbs, a seaweed, a fish, a reptile, a deer and some marine invertebrates. In all the studies, the stochastic population growth rate (ln λ _s ) was no greater than the deterministic population growth rate determined using average vital rates, suggesting that the model based only on average vital rates may overestimate growth rates of populations in fluctuating environments. Factors affecting ln λ _s include the magnitude of variation in vital rates, probability distribution of random environments, fluctuation in different types of vital rates, covariances between vital rates, and autocorrelation between successive environments. However, comprehensive rules were hardly found through the comparisons of the empirical studies. Based on shortcomings of previous studies, I address some important subjects which should be examined in future studies.     

Generalized functions in the qualitative study of heterogeneous populations

ABSTRACT

Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.     

Induced population growth and induced technological progress: Their interaction in the accelerating stage

A simple model of Malthusian population growth combined with population‐induced technological progress generates accelerating growth. The model may be relevant for a first stage of growth in which natural resource limitations can be overcome through technological progress; it is not applicable to a later stage in which resource constraints are more resistant. Parameter values are roughly inferred from historical experience. Exogenously more rapid population growth initially depresses income, perhaps for up to several centuries, then raises it without limit. More rapid population growth is desirable only when the social discount rate is less than the ratio of the parameters for induced technical progress and static diminishing returns. Imposed population fluctuations cause inverse movements in incomes, so that induced progress is very difficult to detect empirically even for population fluctuations up to 500 years.     

The experiential knowledge of migrant women about vulnerability during pregnancy: A woman-centred mixed-methods study

ProblemWithin maternity care policies and practice, pregnant migrant women are regarded as a vulnerable population.BackgroundWomen’s experiential knowledge is a key element of woman-centred care but is insufficiently addressed in midwifery practice and research that involves migrant women.AimTo examine if pregnant migrant women’s experiential knowledge of vulnerability corresponds with sets of criteria of vulnerability, and to explore how migrant women make sense of vulnerability during pregnancy.MethodsA sequential two-phased mixed-methods study, conducted in the Netherlands, integrating survey data of 89 pregnant migrant women and focus group data obtained from 25 migrant mothers - living in deprived areas according to the Dutch socio-economic index.ResultsCriteria associated with vulnerability were reported by 65.2% of the participants and 62.9% of the participants reported adverse childhood experiences. On a Visual Analogue Scale, ranging from 0 (not vulnerable) to 10 (very vulnerable), participants self-reported sense of vulnerability showed a mean score of 4.2 (±2.56). Women’s experiential knowledge of vulnerability significantly correlated with the mean sum score of clinical criteria of vulnerability (r .46, p .002) and with the mean sum score of adverse childhood experiences (r .48, p < .001). Five themes emerged from the focus group discussions: “Look beyond who you think I am and see and treat me for who I really am”, “Ownership of truth and knowledge”, “Don’t punish me for being honest”, “Projection of fear” and “Coping with labelling”.ConclusionPregnant migrant women’s experiential knowledge of vulnerability is congruent with the criteria. Calling upon experiential knowledge is an attribute of the humane woman-midwife relationship.     

Populations with constant immigration

We consider a Leslie‐type model of a one‐sex (female) population of natives with constant immigration. The fertility and mortality schedule of the natives may be below or above replacement level. Immigrants retain their fertility and mortality, their children adopt the fertility and mortality of the natives. It is shown how this model may be written in a homogeneous form (without additive term) with a Leslie‐type matrix. Reproductive values of individuals in each age group are discussed in terms of a left eigenvector of this matrix. The homogeneous form of our projection model permits the transformation into a Markov chain with transient and recurrent states. The Markov chain is the basis for the definition of genealogies, which incorporate immigration. It is shown that genealogies describe the life histories of individuals in a population with immigration. We calculate absorption times of the Markov chain and relate them to genealogies. This extends the theory originally designed for closed populations to populations with immigratioa     

Pre‐procreative ages in population stability and cyclicity

Age‐specific models of population renewal (with and without feedback) which imply convergence to a stable state for some levels of fertility or feedback may imply the presence of long‐term cycling around a constant or exponentially changing equilibrium for other levels of fertility or feedback. The switch from one regime to the other is a “bifurcation.”; The conditions for bifurcation involve the roots of an analogue of Lotka's Equation.

Typically bifurcation is induced by raising the strength of feedback or the level of fertility. It has been known since the early 1980s, however, that this is sometimes impossible. It is sometimes impossible even with the linear renewal equation itself and with the most basic of non‐linear models, Lee's cohort feedback model.

Here it is proved that this typical route to bifurcation does not fail for these basic models in the presence of a condition which always holds for realistic applications with higher organisms: the existence of a span of ages before the onset of fertility.

Specifically, a strictly positive lower bound on ages of procreation is proved to be sufficient to guarantee the existence of a rescaling of Lotka's Equation for which the real part of some complex root vanishes. This result holds for absolutely Lebesgue‐integrable (signed) net maternity functions on the positive real line and for absolutely summable (signed) net maternities on the positive integers.

It follows that Coale's rescaling device for the analysis of approach to stability in stable population theory can be implemented for all realistic human net maternity schedules. It also follows that the many special cases of the cohort feedback model throughout population biology will all generate persistent cycling instead of stability if feedback is sufficiently strong.     

Asymptotic properties of the inhomogeneous Lotka‐Von Foerster system

In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution.     

Determining the birth function for an age structured population

This paper deals with an inverse problem in age‐structured population dynamics, namely the recovery of the unknown birth function from the additional or overposed data consisting of the total population over a time interval equal to the maximum life span of the species. Conditions on the data are given to guarantee the existence and uniqueness of a solution, and the question of continuous dependence of the birth function on the data is addressed. Some numerical simulations are presented to indicate that one can in fact use the methods of the paper to reconstruct the birth function.     

The exponential multidimensional demographic projection model

This paper presents the multidimensional demographic projection on the basis of an exponential specification, which avoids the problems associated with the widely used specification on the basis of the linear integration hypothesis. It generalizes earlier work by Gill (1986) on Markov models for closed populations to include the case of open populations. A numerical illustration is also provided.     

Applying a knowledge translation model to the uptake of the Baby Friendly Health Initiative in the Australian health care system

BackgroundThe Baby Friendly Hospital Initiative is a global, evidence-based, public health initiative. The evidence underpinning the Initiative supports practices promoting the initiation and maintenance of breastfeeding and encourages women's informed infant feeding decisions. In Australia, where the Initiative is known as the Baby Friendly Health Initiative (BFHI) the translation of evidence into practice has not been uniform, as demonstrated by a varying number of maternity facilities in each State and Territory currently accredited as ‘baby friendly’. This variance has persisted regardless of BFHI implementation in Australia gaining ‘in principle’ support at a national and governmental level as well as inclusion in health policy in several states. There are many stakeholders that exert an influence on policy development and health care practices.AimIdentify a theory and model to examine where and how barriers occur in the gap between evidence and practice in the uptake of the BFHI in Australia.ResultsKnowledge translation theory and the research to practice pipeline model are used to examine the identified barriers to BFHI implementation and accreditation in Australia.ConclusionAustralian and international studies have identified similar issues that have either enabled implementation of the BFHI or acted as a barrier. Knowledge translation theory and the research to practice pipeline model is of practical value to examine barriers. Recommendations in the form of specific targeted strategies to facilitate knowledge transfer and supportive practices into the Australian health care system and current midwifery practice are included.     

Comparison of microcomputer programs for making population projections: An update

There are many programs for making population projections now available for use with microcomputers. This article reviews six of approximately 15 microcomputer population projection programs. Each program is compared to a standard set of criteria relating to such items as hardware and software requirements, input data requirements and specification of assumptions, methodology and documentation, and summary output indicators. Numerical results from projections of six test data sets reflecting different assumptions about mortality, fertility, and migration are compared. Qualitative comments are included for describing special features and for making an overall assessment of each program.     

The mathematics of sex and marriage,revisited

We analyze the problem of modeling marriages in a two‐sex model of population dynamics. We first deal with the problem of incomplete and inconsistent census data and then use a simulator to compare the performance of a variety of marriage functions in modeling births and couples during the ten‐year period between consecutive U.S. censuses. Unlike most empirical methods for comparing marriage functions based on goodness of fit, the differences in the projections of the various functions in our method are of the same magnitude (or even smaller) than the errors between the projected and real data. We observe that for the population of the United States, the harmonic mean function frequently found and used in the literature is a quite poor performer when compared with many other functions in the family we use.     

Cyclically stable populations∗

The cyclically stable population relaxes the stable population assumption of fixed vital rates and replaces it with the assumption of a recurring sequence of schedules of vital rates. From any point (or stage) in one cycle of the sequence to the same stage in the next cycle, the cyclically stable population grows at a constant rate (λ). While the age composition of the cyclically stable population is different at different stages of the same cycle, it always has the same age composition at the same stage of every cycle. The essential dynamics of the cyclically stable model are captured by its birth projection matrix (BPM). The dominant eigenvalue of the BPM is growth rate A, and the right eigenvector associated with λ gives the within cycle‐birth sequence.

An important special case occurs when λ = 1, and a cyclically stationary population arises. Such populations challenge simplistic ideas about “Zero Population Growth.”; A population projection based on the sets of rates observed in the United States, 1970–90, shows a cyclically stationary population arising in less than 100 years. While it experiences no long term growth, that cyclically stationary population exhibits fluctuations in total size and considerable variability in age structure.     

Supporting women to achieve breastfeeding to six months postpartum – The theoretical foundations of a successful program

BackgroundAlthough the benefits of breastfeeding to six months are well-established, only about half of Australian women succeed. The factors associated with successful breastfeeding are rarely translated into effective interventions. A new educational and support program, called the Milky Way program has been demonstrated to be effective in supporting women to achieve prolonged breastfeeding. In the Milky Way program, breastfeeding is considered an embodied performance which requires an engaged combination of body, mind and spirit. This paper aims to explain how the two theories that informed the program were used to better enable women's long term breastfeeding success.MethodThe theory of self-efficacy is first described as a way to develop women's cognitive processes to organise and execute the course of actions to breastfeed for a longer period of time. Birth territory theory is then presented. This theory discusses women as embodied selves; an essential concept for breastfeeding success. Birth territory theory also describes the effects of the holistic environment on the woman and explores the effects of power that is used in the environment. This power can be used integratively to strengthen the woman's breastfeeding confidence and success or, disintergratively which reduces her confidence and undermines her success.ConclusionStrategies based on self-efficacy theory are helpful, but are not sufficient to promote breastfeeding to six months. Health educators also need to foster the woman's connection to, and trust in, her body and her baby's body to breastfeed spontaneously. Being aware of environmental impacts on how the woman and baby breastfeed; and using one's own power integratively is crucial to women being able to achieve prolonged breastfeeding.     

Macro‐demographic effects of the transition to adulthood: Multistate stable population theory and an application to Italy

We exploit a multistate generalisation of a classical, one‐sex, stable population model to evaluate structural and long‐term effects of changes in the attainment of adulthood. The demographic framework that inspired this paper is provided by Italy, where a strong delay in the transition to adulthood and union formation has been observed over the last several decades. Italy has also experienced very low fertility levels, and the subsequent ageing problems have become of primary concern. We first discuss a theoretical framework based on the model developed by Inaba (1995) and then include the process of transition to adulthood. We consider explicitly some specifications of the general model, and we present two distinct empirical applications, one using macrosimulation and the other one using a linear approximation. Our principal aim is to evaluate the impact of the delay in the attainment of adulthood on reproduction and on the age structure of the population.     

The overuse of intrapartum cardiotocography (CTG) for low-risk women: An actor-network theory analysis of data from focus groups

BackgroundThere is an overuse of cardiotocography for intrapartum fetal monitoring for low-risk women in high-income countries, despite recommendations from evidence-based guidelines.AimTo understand why midwives use cardiotocography for low-risk women despite evidence-based recommendations and to understand the roles of the cardiotocograph machine.MethodThis qualitative study used focus groups for data collection. Thirty-one midwives and three student midwives participated from four different countries: New Zealand, Australia, Denmark, and Norway. Constant comparative analysis, informed by an actor-network theory framework, was the method of data analysis.FindingsCardiotocography was multifaceted and influenced all attendants in the birth environment. The cardiotocograph itself is assigned different roles within the complex networks surrounding childbirth. The cardiotocograph’s roles were as a babysitter, the midwives’ partner, an agent of shared responsibility, a protector that ‘covers your back’, a disturber of normal birth, and a requested guest.DiscussionThe application of the actor-network theory enabled us to understand how midwives perceive cardiotocography. The assigned roles of the cardiotocograph shape its everyday use more than evidence-based guidelines. Discussion of these inconsistencies must inform the use of cardiotocography in the care of women with low-risk pregnancies.ConclusionWe found that the cardiotocograph is a multifaceted actant that influences practice by performing different roles. Drawing on this study, we suggest that actor-network theory could be a helpful theoretical perspective to critically reflect upon the increasing use of technologies within maternity care.     

Implementing midwifery continuity of care models in regional Australia: A constructivist grounded theory study

Problem/backgroundStrong international evidence demonstrates significantly improved outcomes for women and their babies when supported by midwifery continuity of care models. Despite this, widespread implementation has not been achieved, especially in regional settings.AimTo develop a theoretical understanding of the factors that facilitate or inhibit the implementation of midwifery continuity models within regional settings.MethodsA Constructivist Grounded Theory approach was used to collect and analyse data from 34 interviews with regional public hospital key informants.ResultsThree concepts of theory emerged: ‘engaging the gatekeepers’, ‘midwives lacking confidence’ and ‘women rallying together’. The concepts of theory and sub-categories generated a substantive theory: A partnership between midwives and women is required to build confidence and enable the promotion of current evidence; this is essential for engaging key hospital stakeholders to invest in the implementation of midwifery continuity of care models.DiscussionThe findings from this research suggest that midwives and women can significantly influence the implementation of midwifery continuity models within their local maternity services, particularly in regional settings. Midwives’ reluctance to transition is based on a lack of confidence and knowledge of what it is really like to work in midwifery continuity models. Similarly, women require education to increase awareness of continuity of care benefits, and a partnership between women and midwives can be a strong political force to overcome many of the barriers.ConclusionImplementation of midwifery continuity of care needs a coordinated ground up approach in which midwives partner with women and promote widespread dissemination of evidence for this model, directed towards consumers, midwives, and hospital management to increase awareness of the benefits.     

Paving the way for successful twinning:: Using grounded theory to understand the contribution of twin pairs in twinning collaborations

BackgroundTwinning collaborations, where two groups — from educational institutions, hospitals or towns — work together cross-culturally on joint goals, are increasingly common worldwide. Pairing up individuals, so-called twin pairs, is thought to contribute to successful collaboration in twinning projects, but as yet, there is no empirical evidence or theory that offers insight into the value of the pair relationship for twinning.AimTo explore the contribution of one-to-one relationships between twins to twinning projects, as exemplified in projects between Dutch and Moroccan, and Dutch and Sierra Leone midwives.MethodsWe conducted thirteen in-depth interviews with midwives from two twinning collaborations. Interviews were transcribed and analysed using an iterative, grounded theory process, yielding a theoretical understanding of one-to-one twinning relationships for twinning collaborations.FindingsParticipant comments fell into four substantive categories: 1) Being named a twin, 2) moving beyond culture to the personal level, 3) searching for common ground to engage, 4) going above and beyond the twinning collaboration. Their interplay demonstrates the value of twin pairs in paving the way for successful twinning.DiscussionA complex combination of contextual inequities, personality, and cultural differences affect the twin relationship. Trusting relationships promote effective collaboration, however, as ‘trust’ cannot be mandated, it must be built by coaching twins in personal flexibility and (cultural) communication.ConclusionBy offering original insights into the ways twinning relationships are built, our research explores how twin pairs can enhance the success of twinning projects.