The Keyfitz Centennial Symposium on Mathematical Demography
The Intrinsic Linkage approach assumes a linear relationship between a population's age/ state composition, the dominant (intrinsic) component of the projection matrix that moves that population forward, and the resultant population composition. Here, that approach is extended to multistate models, and new relationships are developed to determine population growth and state composition. Under Intrinsic Linkage, a population can be analytically projected to any future point from knowledge of the linkage parameter(s) and the dominant component of the population projection matrices. Illustrative examples show how population values vary with the linkage parameter, how cyclical models can be specified, and how the approach can synthesize cohort analyses.
Sensitivity Analysis in Mathematical Demography
The 7 traditional classes of Vertebrates (3 classes of Fish, Birds, Mammals, Reptiles and Amphibians) encompass around 64 000 species and are by far the best known animal group from a demographic point of view. After having briefly recalled the reasons for the abundance and quality of the demographic information available on Vertebrates, I will review this information, covering the following salient features:
- Most vertebrates have a discrete life cycle, with a seasonal or nearly seasonal sexual reproduction, and primarily age-dependent variation in demographic traits.
- The demographic differences among Vertebrates can naturally be ordered on a "slow- fast gradient" best measured by generation time. From short-lived rodents to cetaceans or sea turtles, the change in generation time is at least 300-fold.
- This variation is strongly linked in an allometric fashion to body weight within groups of species sharing a common general body "ground design", with major differences among groups (e.g., Chiroptera - Bats- vs Rodents; Anseriforms - Ducks, Geese and Swans- vs Procellariiforms (Albatross and related seabirds).
- In relation with the allocation of energetic resources, maximum population growth rate is inversely related to generation time, the longest lived species having thus the smallest maximum growth rate, and as a consequence, the smallest resilience to extra sources of mortality. Together with behavioral and physio-energetic features, this demographic sensitivity induces a genuine "malediction of long-lived species" in face of human activities, with many different illustrations, including the overfishing of stocks of large fish. It is particularly striking that the 5 species of Hominids beside Man are classified as "endangered" by the International Union for Conservation of Nature (IUCN). Over the last 5 centuries, more than one species of Vertebrate got extinct each year.
- Besides the dominant role of age, demographic heterogeneity within age classes has been shown as to be present in a growing number of Vertebrate species and may be quite general.
- Dispersal patterns are less widely known, but clearly show a prominent role of dispersal between birth and first reproduction, with a stronger dispersion of males or females, depending mostly on the class of Vertebrates considered.
I discuss implications of these demographic characteristics of Vertebrate in a changing world, in particular in relation with climate change and the fragmentation of habitats.
My objective is to describe the theoretical foundation, analytical framework and empirical requirements for the use of the death distribution of live-captured insects of unknown age to estimate age structure in their population. I will start with a brief overview of several high tech methods currently used to estimate insect age (and thus population age structure), most of which are costly and all of which are limited. I will then introduce the demographic concept my colleagues and I developed as an alternative to the high-tech approach. Referred to as the captive cohort methods, we show that the death distribution of live-captured individuals of unknown age can be used to: (1) determine the exact age structure of hypothetical stationary populations (i.e. life table identity); ii) estimate the age structure of wild populations using a simple model and reference life tables; and iii) estimate quantitative changes in population mean age and qualitative changes in the age extremes (young and old). I will illustrate the utility of this approach from the results of field studies on the Mediterranean fruit flies populations in Greece, and end with a discussion of the broader implications of this method in both basic and applied ecology.
Demographic patterns in populations of long-lived and iteroparous mammals
Senescence, the physiological decline that results in decreasing survival and/or reproduction with age, remains one of the most perplexing topics in biology. Most theories attempting to explain the evolution of senescence (i.e. antagonistic pleiotropy, mutation accumulation, disposable soma) were developed over half a century ago. Confronted with empirical patterns of survival and reproduction, predictions of the theories do not hold. New theory is needed to shed light on the determinants of patterns of birth and death.
On the evolution of intergenerational division of labor, menopause and transfers among adults and offspringRon Lee
We explain how upward transfers from adult children to their elderly parents might evolve as an interrelated feature of a deepening intergenerational division of labor. Humans have a particularly long period of juvenile dependence requiring both food and care time provided mainly by younger and older adults. We suggest that the division of labor evolves to exploit comparative advantage between young and old adults in fertility, childcare and foraging. Eventually the evolving division of labor reaches a limit when the grandmother's fertility reaches zero (menopause). Continuing, it may hit another limit when the grandmother's foraging time has been reduced to her subsistence needs. Further specialization can occur only with food transfers to the grandmother, enabling her to reduce her foraging time to concentrate on additional childcare. We prove that this outcome can arise only after menopause has evolved. We describe the conditions necessary for both group selection (comparative steady state reproductive fitness) and individual selection (successful invasion by a mutation), and interpret these conditions in terms of comparative advantages.
Demography is often a key driver of the burden of infectious diseases, via both its impact on dynamics and the existence of age-patterns of affliction. Rubella, a directly transmitted, immunising childhood infection is an extreme example of this. Although rubella is generally a mild and even asymptomatic infection of children, infection in the early weeks of pregnancy can lead to birth of a child with Congenital Rubella Syndrome. The syndrome is associated with a range of symptoms, including deafness, blindness, and mental retardation. I will introduce models combining human and epidemiological dynamics for rubella; highlighting their application to the key public health question of when demographic and epidemiological conditions are such that the introduction of the rubella vaccine will not lead to an increase in the burden of Congenital Rubella Sydnrome; and placing this in the current global demographic context.
A socioeconomically differentiated population evolves through differential fertility, mortality, marriage, and migration of socioeconomic groups, as well as through intergenerational social mobility. If mobility processes are non-Markovian -- that is, include net associations of socioeconomic status across more than two generations -- then the demography of mobility is more complex. Many types of multigenerational effects are possible, including those that work through mobility itself and those that work through demographic processes. In some circumstances, multigenerational effects may also arise from remote ancestral conditions, as well as from intergenerational connections between the characteristics of specific more proximate kin. The short and longer run implications of these effects also depend on whether mobility processes depend on the characteristics of one sex or both sexes. This paper describes this array of possible multigenerational effects, shows the conditions under which the socioeconomic characteristics of an individual in one generation may affect future generations, and illustrates these results with data from the Qing Dynasty era of China and the contemporary United States.
Perennial tropical and subtropical plants inhabit inherently variable environments, where both abiotic and biotic features vary from place to place and during the life times of individuals. To address ecological, evolutionary and applied demographic questions, we employ structured models (matrix projection and integral projection) using a framework that includes stage (sometimes age) structure and environmental variability. Projection models are used in two ways, to track population dynamics and to generate sample paths of individuals across the life cycle. The former concerns ecological dynamics and evolutionary demography where fitness is measured as the (stochastic) population growth rate. The latter concerns life histories, life expectancies and the timing of other key events (such as age of first reproduction). In some systems we also address rate of spread across the landscape. Issues we address quantitatively by these methods include: the effect of hurricanes on the impact of native seed predators ; integrating selection on quantitative traits across the life cycle when selection gradients vary over time; trade-offs due to the cost of reproduction; how harvest regime of non-timber forest products affects longevity of trees; life expectancy of pioneer vs shade-tolerant tropical trees; the impact of rarely occurring long distance dispersal vectors to invasion speed; effectiveness of bio-control agents on invasive trees and shrubs; and others. As models are applied to different problems, new issues and new models arise through collaborations.
Projecting mortality at the end of the epidemiological transition
The first part of the talk highlights several of my early papers inspired by Nathan Keyfitz that examine the implications of mortality for a broad range of phenomena: dating a population's time of settlement; examining the impact of mortality change on life expectancy; and identifying the cause of high mortality among never-married individuals. The remainder of the talk examines one aspect of my ongoing work in biosocial surveys: the extent to which clinical and other biological markers enhance mortality prediction in older populations.