Kinetic theory of age-structured stochastic birth-death processes

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution

Using Meta-Ethnography to Synthesize Relevant Studies: Capturing the Bigger Picture in Dementia with Challenging Behavior within Families

In understanding the range and depth of people’s experiences, it is important to include the wide range of approaches which capture the richness within a given knowledge base. However, systematic reviews using quantitative data alone risk missing findings that can contribute to a better understanding of a research question. In response, meta-ethnography has emerged as a potentially useful method to synthesize and integrate both qualitative and quantitative data from different perspectives using qualitative methodology. In this case study, we describe how we have used meta-ethnography to better understand how families experience dementia. We address a particular issue of selecting the highest quality evidence across a range of epistemologies

Recombination dramatically speeds up evolution of finite populations

We study the role of recombination, as practiced by genetically-competent bacteria, in speeding up Darwinian evolution. This is done by adding a new process to a previously-studied Markov model of evolution on a smooth fitness landscape; this new process allows alleles to be exchanged with those in the surrounding medium. Our results, both numerical and analytic, indicate that for a wide range of intermediate population sizes, recombination dramatically speeds up the evolutionary advance

Relational experiences of people seeking help and assessment for subjective cognitive concern and memory loss

Objective: To understand the experience of people who seek help for subjective cognitive concern and memory loss, including people not referred for further assessment. To understand the patients’ perspective of the medical process of receiving a cognitive assessment. This work is situated within the context of policy priorities for dementia diagnosis. Methods: Participants with and without dementia were recruited through NHS trusts and community organisations in four regional areas in England. Data were collected using longitudinal qualitative interviews. Transcript data were thematically analysed. Results: Sample of 41 people (mean 75 years, 25 dementia diagnoses). Interpretative thematic analyses focused on the presence or absence of trust in relational experiences. There were three transition points where trust could be specifically developed or undermined: 1) deciding to seek help; 2) healthcare practitioners’ response to help-seeking; 3) process and outcome of assessment. Triggers for help-seeking for subjective cognitive concern were being prompted by family and knowing a relative with dementia. When participants perceived healthcare practitioners’ behaviour as dismissive, they had less trust in the outcome of the healthcare encounter. Misunderstandings and absence of trust in assessment processes led to participants stating they did not fully agree with the outcomes of the assessment. Conclusions: Healthcare practitioners have an important role in supporting people with subjective cognitive concern ensuring patients have trust in assessment outcomes. Where the validity of the assessment process is seen as ambiguous, people can be left dealing with uncertainty, rather than being clear about ways they can manage their condition, situation or status

The experience of family carers attending a joint reminiscence group with people with dementia: A thematic analysis

Reminiscence therapy has the potential to improve quality of life for people with dementia. In recent years reminiscence groups have extended to include family members, but carers' experience of attending joint sessions is undocumented. This qualitative study explored the experience of 18 family carers attending 'Remembering Yesterday Caring Today' groups. Semi-structured interviews were transcribed and subjected to thematic analysis. Five themes were identified: experiencing carer support; shared experience; expectations (met and unmet), carer perspectives of the person with dementia's experience; and learning and comparing. Family carers' experiences varied, with some experiencing the intervention as entirely positive whereas others had more mixed feelings. Negative aspects included the lack of respite from their relative, the lack of emphasis on their own needs, and experiencing additional stress and guilt through not being able to implement newly acquired skills. These findings may explain the failure of a recent trial of joint reminiscence groups to replicate previous findings of positive benefit. More targeted research within subgroups of carers is required to justify the continued use of joint reminiscence groups in dementia care

‘They Called Them Communists Then … What D'You Call ‘Em Now? … Insurgents?’. Narratives of British Military Expatriates in the Context of the New Imperialism

This paper addresses the question of the extent to which the colonial past provides material for contemporary actors' understanding of difference. The research from which the paper is drawn involved interview and ethnographic work in three largely white working-class estates in an English provincial city. For this paper we focus on ten life-history interviews with older participants who had spent some time abroad in the British military. Our analysis adopts a postcolonial framework because research participants' current constructions of an amorphous 'Other' (labelled variously as black people, immigrants, foreigners, asylum-seekers or Muslims) reveal strong continuities with discourses deployed by the same individuals to narrate their past experiences of living and working as either military expatriates or spouses during British colonial rule. Theoretically, the paper engages with the work of Frantz Fanon and Edward Said. In keeping with a postcolonial approach, we work against essentialised notions of identity based on 'race' or class. Although we establish continuity between white working-class military emigration in the past and contemporary racialised discourses, we argue that the latter are not class-specific, being as much the creations of the middle-class media and political elite

Fluctuating selection models and Mcdonald-Kreitman type analyses

It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate the consequences of fluctuating selection pressures on the quantification of adaptive evolution using McDonald-Kreitman (MK) style approaches. In agreement with previous work, we show that fluctuating selection can generate evidence of adaptive evolution even when the expected strength of selection on a mutation is zero. However, we also find that the mutations, which contribute to both polymorphism and divergence tend, on average, to be positively selected during their lifetime, under fluctuating selection models. This is because mutations that fluctuate, by chance, to positive selected values, tend to reach higher frequencies in the population than those that fluctuate towards negative values. Hence the evidence of positive adaptive evolution detected under a fluctuating selection model by MK type approaches is genuine since fixed mutations tend to be advantageous on average during their lifetime. Never-the-less we show that methods tend to underestimate the rate of adaptive evolution when selection fluctuates

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded introductory and discussion sections, added corollaries, new results on modifier polymorphisms, minor corrections. 49 pages, 64 reference

Support at Home: Interventions to Enhance Life in Dementia (SHIELD) – evidence, development and evaluation of complex interventions

Background: Dementia is a national priority and this research addresses the Prime Minister’s commitment to dementia research as demonstrated by his 2020 challenge and the new UK Dementia Research Institute. In the UK > 800,000 older people have dementia. It has a major impact on the lives of people with dementia themselves, on the lives of their family carers and on services, and costs the nation £26B per year. Pharmacological cures for dementias such as Alzheimer’s disease are not expected before 2025. If no cure can be found, the ageing demographic will result in 2 million people living with dementia by 2050. People with dementia lose much more than just their memory and their daily living skills; they can also lose their independence, their dignity and status, their confidence and morale, and their roles both within the family and beyond. They can be seen as a burden by society, by their families and even by themselves, and may feel unable to contribute to society. This programme of research aims to find useful interventions to improve the quality of life of people with dementia and their carers, and to better understand how people with dementia can be supported at home and avoid being admitted to hospital. Objectives: (1) To develop and evaluate the maintenance cognitive stimulation therapy (MCST) for people with dementia; (2) to develop the Carer Supporter Programme (CSP), and to evaluate the CSP and Remembering Yesterday, Caring Today (RYCT) for people with dementia both separately and together in comparison with usual care; and (3) to develop a home treatment package (HTP) for dementia, to field test the HTP in practice and to conduct an exploratory trial. Methods: (1) The MCST programme was developed for people with dementia based on evidence and qualitative work. A randomised controlled trial (RCT) [with a pilot study of MCST plus acetylcholinesterase inhibitors (AChEIs)] compared MCST with cognitive stimulation therapy (CST) only. The MCST implementation study conducted a trial of outreach compared with usual care, and assessed implementation in practice. (2) The CSP was developed based on existing evidence and the engagement of carers of people with dementia. The RCT (with internal pilot) compared the CSP and reminiscence (RYCT), both separately and in combination, with usual care. (3) A HTP for dementia, including the most promising interventions and components, was developed by systematically reviewing the literature and qualitative studies including consensus approaches. The HTP for dementia was evaluated in practice by conducting in-depth field testing. Results: (1) Continuing MCST improved quality of life and improved cognition for those taking AChEIs. It was also cost-effective. The CST implementation studies indicated that many staff will run CST groups following a 1-day training course, but that outreach support helps staff go on to run maintenance groups and may also improve staff sense of competence in dementia care. The study of CST in practice found no change in cognition or quality of life at 8-month follow-up. (2) The CSP/RYCT study found no benefits for family carers but improved quality of life for people with dementia. RYCT appeared beneficial for the quality of life of people with dementia but at an excessively high cost. (3) Case management for people with dementia reduces admissions to long-term care and reduces behavioural problems. In terms of managing crises, staff suggested more costly interventions, carers liked education and support, and people with dementia wanted family support, home adaptations and technology. The easy-to-use home treatment manual was feasible in practice to help staff working in crisis teams to prevent hospital admissions for people with dementia. Limitations: Given constraints on time and funding, we were unable to compete the exploratory trial of the HTP package or to conduct an economic evaluation. Future research: To improve the care of people with dementia experiencing crises, a large-scale clinical trial of the home treatment manual is needed. Conclusion: There is an urgent need for effective psychosocial interventions for dementia. MCST improved quality of life and was cost-effective, with benefits to cognition for those on AChEIs. MCST was feasible in practice. Both CSP and RYCT improved the quality of life of people with dementia, but the overall costs may be too high. The HTP was useful in practice but requires evaluation in a full trial. Dementia care research may improve the lives of millions of people across the world. Trial registrations: Current Controlled Trials ISRCTN26286067 (MCST), ISRCTN28793457 (MCST implementation) and ISRCTN37956201 (CSP/RYCT). Funding: This project was funded by the National Institute for Health Research (NIHR) Programme Grants for Applied Research programme and will be published in full in Programme Grants for Applied Research; Vol. 5, No. 5. See the NIHR Journals Library website for further project information

Exact Solution of an Evolutionary Model without Ageing

We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural selection. An exact solution without ageing is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated indicating that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups as many protozoa and coelenterates is discussed.Comment: LaTeX file, 15 pages, 2 ps figures, to appear in Phys. Rev.