## The Keyfitz Centennial Symposium on Mathematical Demography

### Organizers

John Bongaarts
PGY, Population Council
John Casterline
Lazarus Professor of Population Studies
Hal Caswell
Biology, Woods Hole Oceanographic Institution
Noreen Goldman
Woodrow Wilson School, Princeton University
Josh Goldstein
Ron Lee
Demography and Economics, University of California, Berkeley
Biology, Stanford University

Nathan Keyfitz (1913--2010) made fundamental and highly influential contributions to demography over a long and productive career. His work was characterized by an elegance of approach and a depth of insight that came from a deep recognition of the interplay among models, data, and interpretation. This symposium, marking the 100th anniversary of his birth, will bring together a diverse set of scientists studying, to use Keyfitz's term, the mathematics of population. The main goal of the Symposium is to serve as a forum for presentation of ongoing research on the mathematics of population. The program will encompass research on human and non-human populations, and both theoretical and applied research. In bringing together both mathematical demographers and population biologists, the symposium will adhere to Keyfitz's view, from his first book to his last, that population itself as an object worthy of study, not limited to particular species: [This book] tries to gather together, and as far as possible to systematize, the most relevant parts of that large body of mathematical theory concerned with the growth processes of human and animal populations. '' Introduction to the Mathematics of Population (1968) ... the general drift of their replies was that ... there was nothing that could be usefully added. We were monumentally wrong. We hadn't noticed the world of whales and birds and land animals, i.e., the world of biology.'' Applied Mathematical Demography, 3rd Edition (2005) The symposium program will be a mix of theoretical and applied work -- mathematical exercises as well as empirical work that make use of models and techniques that draw on mathematical demography. The symposium program will be structured so as to encourage maximum exchange among scholars in attendance. Sharing of work in progress will be encouraged (and therefore there will be no requirement to prepare manuscripts of presentations). The goal is to stimulate discussion, cooperation, and collaboration.

### Accepted Speakers

Juha Alho
Department of Social Research, University of Helsinki
Annette Baudisch
Max Planck Research Group on Modeling the Evolution of Aging, Max Planck Institute for Demographic Research Rostock, Germany
James Carey
Entomology, University of California, Davis
Joel Cohen
Laboratory of Populations, Rockefeller University
Jean-Michel Gaillard
Life Science, CNRS University of Lyon
Carol Horvitz
Department of Biology, University of Miami
James Holland Jones
Department of Anthropology, Stanford University
Jean-Dominique Lebreton
Evolutionary Ecology, CEFE CNRS
Nan Li
Population Division/DESA, United Nations
Rob Mare
Sociology, University of California, Los Angeles
Jessica Metcalf
Zoology, Oxford University
Steve Orzack
NA, Fresh Pond Research Institute
Bob Schoen
Population Research Institute, Pennsylvania State University
David Steinsaltz
Anatoli Yashin
Sociology, Duke University
Emilio Zhageni
Monday, June 24, 2013
Time Session
08:30 AM

Shuttle to MBI

08:45 AM
09:00 AM

Breakfast

09:00 AM
09:15 AM

Welcome and Introduction: Marty Golubitsky

09:15 AM
09:35 AM

Nathan Keyfitz and his work

09:35 AM
10:05 AM
Bob Schoen - Intrinsic Linkages in Dynamic Multistate Populations

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.

10:10 AM
10:50 AM

Break

10:50 AM
11:20 AM
Hal Caswell - Sensitivity Analysis in Mathematical Demography

Sensitivity Analysis in Mathematical Demography

11:20 AM
11:40 AM

Discussion

11:40 AM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Jean-Dominique Lebreton - An overview of Vertebrate 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:

1. Most vertebrates have a discrete life cycle, with a seasonal or nearly seasonal sexual reproduction, and primarily age-dependent variation in demographic traits.

2. 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.

3. 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).

4. 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.

5. 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.

6. 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.

02:30 PM
03:00 PM
James Carey - Estimating age structure in insect populations using the captive cohort method

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.

03:00 PM
03:20 PM

Discussion

03:20 PM
03:40 PM

Break

03:40 PM
04:40 PM

Panel Discussion: Human and Non Human

04:55 PM
06:55 PM

Reception and Poster Session

07:10 PM

Shuttle pick-up from MBI

Tuesday, June 25, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM

TBD

09:35 AM
10:05 AM
Jean-Michel Gaillard - Demographic patterns in populations of long-lived and iteroparous mammals

Demographic patterns in populations of long-lived and iteroparous mammals

10:05 AM
10:25 AM

Discussion

10:25 AM
10:55 AM

Break

10:55 AM
11:25 AM
Annette Baudisch - New theory needed to explain the evolution of senescence

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.

11:30 AM
12:00 PM
James Holland Jones - Evolvability of the Human Life History

Evolvability of the Human Life History

12:05 PM
02:30 PM

Lunch Break

02:30 PM
03:00 PM
Ron Lee - On the evolution of intergenerational division of labor, menopause and transfers among adults and offspring

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.

03:00 PM
03:25 PM

Discussion

03:25 PM
03:45 PM

Break

03:45 PM
04:45 PM

Panel Discussion: Future Applications of Keyfitz Work

05:00 PM

Shuttle pick-up from MBI

Wednesday, June 26, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
David Steinsaltz - Modelling the accumulation of small-effect deleterious alleles in the evolution of senescence

Modelling the accumulation of small-effect deleterious alleles in the evolution of senescence

09:35 AM
10:05 AM
Anatoli Yashin - Mathematical Demography of Aging

Mathematical Demography of Aging

10:05 AM
10:25 AM

Discussion

10:25 AM
10:50 AM

Break

10:50 AM
11:20 AM
Andrei Rogers - Multiregional demography: migration and population redistribution

Multiregional demography: migration and population redistribution

11:25 AM
11:55 AM
Joel Cohen - Taylor's law of fluctuation scaling: from bacteria to humans and beyond

L. R. Taylor (1961) and colleagues observed that, in many species, the logarithm of the variance of the density (individuals per area or volume) of a set of comparable populations was an approximately linear function of the logarithm of the mean density: for some a > 0, log(variance of population density) = log(a) + b × log(mean population density). This relationship came to be known as Taylor's law (TL) of fluctuation scaling. TL has been verified in hundreds of species from bacteria to humans and beyond: in populations of stem cells, stock market trading, precipitation, packet switching on the Internet, measles cases, and the occurrence of single nucleotide polymorphisms. We will give some empirical examples of TL and some recent theoretical developments regarding the origins, interpretations, and consequences of TL.

11:55 AM
12:15 PM

Discussion

12:15 PM
02:30 PM

Lunch Break

02:30 PM
03:00 PM
Nan Li - Are low-fertility populations sustainable?

Fertility levels decline to below replacement is a common trend; and it will lead to declining populations that press less on environment and resources but suffer increase in the pension burdens of pay-you-go systems. Funded pension systems transfer cohorts saving to consumption, and hence their pension burdens are invariant to fertility change. Comparing the difference between the pension burdens of the two systems in certain periods could provide relevant information to the decision on whether or not to establish funded pension systems to cope with low fertility. A time-referred cohort old-dependence ratio is proposed in this paper, which is comparable to the period old-dependence ratio at a certain time, purely demographic, and could be computed for all the countries and areas of the world. Examples are given for China, Japan and Republic of Korea, which indicate that low-fertility populations are sustainable, but require more sophisticated means to sustain.

03:05 PM
03:35 PM
Emilio Zhageni - Formal demography of kinship

Formal demography of kinship

03:35 PM
03:55 PM

Discussion

04:10 PM

Shuttle pick-up from MBI

Thursday, June 27, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Juha Alho - Measuring Trends in Nuptiality

Stochastic formation of marriages is considered in continuous time. The models are parametrized in terms of the overall level of nuptiality, the relative propensity to marry by age, and the mutual attraction of potential spouses in different ages. Such measures can be used to describe time trends in the nuptiality of human populations. It is shown that if the overall intensity of nuptiality is taken to be a possibly weighted average of the intensities of the two sexes, but in a transformed scale, then different choices of scale lead to alternative concepts of population of risk, and as such to different two-sex models. Statistical estimation of the model parameters is considered, and its use in stochastic microsimulation is demonstrated.

09:35 AM
10:05 AM
Jessica Metcalf - Applied Demographic Modeling for Rubella

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.

10:05 AM
10:25 AM

Discussion

10:25 AM
10:50 AM

Break

10:50 AM
11:20 AM
Hui Zheng - Modeling Temporal Changes in Inequality

Modeling Temporal Changes in Inequality

11:25 AM
11:55 AM
Rob Mare - Demography of Social Mobility

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.

11:55 AM
12:15 PM

Discussion

12:15 PM
02:30 PM

Lunch Break

02:30 PM
03:00 PM
Shripad Tuljapurkar - When does the Human Dependency Ratio Become Binding?

The dependency ratio is the number of young and non-working old supported by an average worker. That ratio is a principal determinant of realized per-capita consumption, which in turn depends on productivity, and desired per-capita consumption. Human wellbeing in turn depends in large part on realized consumption. Before the rise of the modern industrial state, population growth rate determined the dependency ratio and hence affected wellbeing. In the reverse direction, fertility and mortality varied with wellbeing, and hence so did growth rate. The result was a feedback system that produced population equilibrium at which dependency was binding, an essentially Malthusian equilibrium. In industrial states, the link between fertility and wellbeing has weakened. However, the growth of wellbeing depends on growth in productivity, consumption, and dependency. Now the growth rate of dependency can and does become binding.

03:00 PM
03:10 PM

Discussion

03:10 PM
03:30 PM

Break

03:30 PM
04:30 PM

Panel Discussion: Policy

04:45 PM

Shuttle pick-up from MBI

Friday, June 28, 2013
Time Session
07:45 AM

Shuttle to MBI

08:00 AM
08:30 AM

Breakfast

08:30 AM
09:00 AM
Carol Horvitz - Stochastic Demography of Tropical and Subtropical Plan

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.

09:05 AM
09:35 AM
Steve Orzack - Nathan Keyfitz, the beginning and the end: investigations into human development at the beginning and end of human life

Nathan Keyfitz's contributions to formal and to applied demography began and ended with an outstanding ability to distill and focus analyses so to generate fundamental insights from even the most unpromising models and data. I will attempt to channel a small amount of his ability. I will present analyses of the demographic and genetic trajectory of the human sex ratio from conception to birth and analyses of the dynamics and statics of morbidity and mortality across the course of human life and across cohorts. Both analyses generate fundamental new insights into human development.

09:35 AM
10:00 AM

Discussion

10:00 AM
10:20 AM

Break

10:20 AM
10:50 AM
John Bongaarts - Projecting mortality at the end of the epidemiological transition

Projecting mortality at the end of the epidemiological transition

10:55 AM
11:25 AM
Noreen Goldman - Insights into human survival: from the South Pacific to East Asia

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.

11:25 AM
11:50 AM

Discussion

11:50 AM
12:15 PM

Closing Session

12:30 PM

Shuttle Airport/ Shuttle to Hotel

Name Email Affiliation
Alho, Juha juha.alho@helsinki.fi Department of Social Research, University of Helsinki
Ameyaw, Edmund Essah edmund.ameyaw@bison.howard.edu Mathematics Department, Mathematics Department, Howard University
Baudisch, Annette baudisch@demogr.mpg.de Max Planck Research Group on Modeling the Evolution of Aging, Max Planck Institute for Demographic Research Rostock, Germany
Bongaarts, John jbongaarts@popcouncil.org PGY, Population Council
Carey, James jrcarey@ucdavis.edu Entomology, University of California, Davis
Casterline, John casterline.10@sociology.osu.edu Lazarus Professor of Population Studies
Caswell, Hal hcaswell@whoi.edu Biology, Woods Hole Oceanographic Institution
Clark, Samuel samclark@uw.edu Department of Sociology, University of Washington
Cohen, Joel Joel.Cohen@rockefeller.edu Laboratory of Populations, Rockefeller University
Davison, Raziel razieldavison@gmail.com Modeling the Evolution of Aging Working Group, Max Planck Institute for Demographic Research
Engelman, Michal mengelman@uchicago.edu Sociology, University of Chicago
Fujiwara, Masami Fujiwara@tamu.edu Department of Wildlife and Fisheries Sciences, Texas A & M University
Gaillard, Jean-Michel Jean-Michel.Gaillard@univ-lyon1.fr Life Science, CNRS University of Lyon
Garcia-Guerrero, Victor vmgarcia@colmex.mx Centre of Demographic, Urban and Enviromental Studies, El Colegio de MÃƒÂ©xico
Goldman, Noreen ngoldman@princeton.edu Woodrow Wilson School, Princeton University
Gurski, Katharine kgurski@howard.edu Mathematics, Howard University
Hicks, Ashley hicks.266@osu.edu Human Sciences, The Ohio State University
Horvitz, Carol carolhorvitz@miami.edu Department of Biology, University of Miami
Jones, James jhj1@stanford.edu Department of Anthropology, Stanford University
Kamp Dush, Claire kamp-dush.1@osu.edu Human Sciences, The Ohio State University
Keyfitz, Barbara bkeyfitz@math.ohio-state.edu Department of Mathematics, The Ohio State University
Keyfitz, Robert rkeyfitz@hotmail.com
Lebreton, Jean-Dominique jean-dominique.lebreton@cefe.cnrs.fr Evolutionary Ecology, CEFE CNRS
Lee, Ron rlee@demog.berkeley.edu Demography and Economics, University of California, Berkeley
Li, Nan li32@un.org Population Division/DESA, United Nations
Mare, Robert mare@ucla.edu Sociology, University of California, Los Angeles
Marschall, Libby marschall.2@osu.edu Evolution, Ecology and Organismal Biology, The Ohio State University
Menken, Jane menken@colorado.edu Department of Sociology, Institute for Behavioral Sciences (IBS)
Metcalf, Jessica charlotte.metcalf@zoo.ox.ac.uk Zoology, Oxford University
Odden, Colin odden.2@sociology.osu.edu Sociology, Ohio State University
Oli, Madan olim@ufl.edu Wildlife Ecology and Conservation, University of Florida
Orzack, Steven orzack@freshpond.org NA, Fresh Pond Research Institute
Paredes Orozco, Guillermo paredesorozco.1@osu.edu Sociology, Ohio State University
Parker, Daniel dmp336@psu.edu Anthropology and Demography, Pennsylvania State University
Rau, Roland roland.rau@uni-rostock.de Sociology and Demography, University of Rostock
S.R. Srinivasa Rao, Arni arrao@gru.edu Biostatistics and Epidemiology, Georgia Regents University
SÃ¡nchez Gassen, Nora nora.sanchez@sociology.su.se Demography Unit, Department of Sociology, Stockholm University
Schmeer, Kammi schmeer.1@osu.edu Sociology, Institute for Population Research, The Ohio State University
Schmertmann, Carl schmertmann@fsu.edu Economics, Florida State University
Schoen, Robert rschoen309@att.net Population Research Institute, Pennsylvania State University
Siewe, Nourridine nourridine@aims.ac.za Mathematics, Howard University
Steinsaltz, David steinsal@stats.ox.ac.uk
Thomas, Jason jrt17@psu.edu Sociology, The Pennsylvania State University
Tuljapurkar, Shripad tulja@stanford.edu Biology, Stanford University
Vindenes, Yngvild yngvild.vindenes@bio.uio.no Centre for Ecological and Evolutionary Synthesis, Department of Biosciences, University of Oslo
Wrigley-Field, Elizabeth wrigleyfield@wisc.edu Department of Sociology; Center for Demography and Ecology, University of Wisconsin
Yakubu, Abdul-Aziz ayakubu@Howard.edu Dept. of Mathematics, Howard University
Yashin, Anatoliy aiy@duke.edu Sociology, Duke University
Zagheni, Emilio emilio.zagheni@qc.cuny.edu
Zheng, Hui zheng.64@sociology.osu.edu Sociology, The Ohio State University
Measuring Trends in Nuptiality

Stochastic formation of marriages is considered in continuous time. The models are parametrized in terms of the overall level of nuptiality, the relative propensity to marry by age, and the mutual attraction of potential spouses in different ages. Such measures can be used to describe time trends in the nuptiality of human populations. It is shown that if the overall intensity of nuptiality is taken to be a possibly weighted average of the intensities of the two sexes, but in a transformed scale, then different choices of scale lead to alternative concepts of population of risk, and as such to different two-sex models. Statistical estimation of the model parameters is considered, and its use in stochastic microsimulation is demonstrated.

New theory needed to explain the evolution of senescence

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.

Projecting mortality at the end of the epidemiological transition

Projecting mortality at the end of the epidemiological transition

Estimating age structure in insect populations using the captive cohort method

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.

Sensitivity Analysis in Mathematical Demography

Sensitivity Analysis in Mathematical Demography

Taylor's law of fluctuation scaling: from bacteria to humans and beyond

L. R. Taylor (1961) and colleagues observed that, in many species, the logarithm of the variance of the density (individuals per area or volume) of a set of comparable populations was an approximately linear function of the logarithm of the mean density: for some a > 0, log(variance of population density) = log(a) + b Ã— log(mean population density). This relationship came to be known as Taylor's law (TL) of fluctuation scaling. TL has been verified in hundreds of species from bacteria to humans and beyond: in populations of stem cells, stock market trading, precipitation, packet switching on the Internet, measles cases, and the occurrence of single nucleotide polymorphisms. We will give some empirical examples of TL and some recent theoretical developments regarding the origins, interpretations, and consequences of TL.

Demographic patterns in populations of long-lived and iteroparous mammals

Demographic patterns in populations of long-lived and iteroparous mammals

Insights into human survival: from the South Pacific to East Asia

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.

Stochastic Demography of Tropical and Subtropical Plan

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.

Evolvability of the Human Life History

Evolvability of the Human Life History

An overview of Vertebrate 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:

1. Most vertebrates have a discrete life cycle, with a seasonal or nearly seasonal sexual reproduction, and primarily age-dependent variation in demographic traits.

2. 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.

3. 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).

4. 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.

5. 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.

6. 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.

On the evolution of intergenerational division of labor, menopause and transfers among adults and offspring

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.

Are low-fertility populations sustainable?

Fertility levels decline to below replacement is a common trend; and it will lead to declining populations that press less on environment and resources but suffer increase in the pension burdens of pay-you-go systems. Funded pension systems transfer cohorts saving to consumption, and hence their pension burdens are invariant to fertility change. Comparing the difference between the pension burdens of the two systems in certain periods could provide relevant information to the decision on whether or not to establish funded pension systems to cope with low fertility. A time-referred cohort old-dependence ratio is proposed in this paper, which is comparable to the period old-dependence ratio at a certain time, purely demographic, and could be computed for all the countries and areas of the world. Examples are given for China, Japan and Republic of Korea, which indicate that low-fertility populations are sustainable, but require more sophisticated means to sustain.

Demography of Social Mobility

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.

Applied Demographic Modeling for Rubella

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.

Nathan Keyfitz, the beginning and the end: investigations into human development at the beginning and end of human life

Nathan Keyfitz's contributions to formal and to applied demography began and ended with an outstanding ability to distill and focus analyses so to generate fundamental insights from even the most unpromising models and data. I will attempt to channel a small amount of his ability. I will present analyses of the demographic and genetic trajectory of the human sex ratio from conception to birth and analyses of the dynamics and statics of morbidity and mortality across the course of human life and across cohorts. Both analyses generate fundamental new insights into human development.

Multiregional demography: migration and population redistribution

Multiregional demography: migration and population redistribution

Intrinsic Linkages in Dynamic Multistate Populations

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.

Modelling the accumulation of small-effect deleterious alleles in the evolution of senescence

Modelling the accumulation of small-effect deleterious alleles in the evolution of senescence

When does the Human Dependency Ratio Become Binding?

The dependency ratio is the number of young and non-working old supported by an average worker. That ratio is a principal determinant of realized per-capita consumption, which in turn depends on productivity, and desired per-capita consumption. Human wellbeing in turn depends in large part on realized consumption. Before the rise of the modern industrial state, population growth rate determined the dependency ratio and hence affected wellbeing. In the reverse direction, fertility and mortality varied with wellbeing, and hence so did growth rate. The result was a feedback system that produced population equilibrium at which dependency was binding, an essentially Malthusian equilibrium. In industrial states, the link between fertility and wellbeing has weakened. However, the growth of wellbeing depends on growth in productivity, consumption, and dependency. Now the growth rate of dependency can and does become binding.

Mathematical Demography of Aging

Mathematical Demography of Aging

Formal demography of kinship

Formal demography of kinship

Modeling Temporal Changes in Inequality

Modeling Temporal Changes in Inequality

Applied Demographic Modeling for Rubella
Jessica Metcalf

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

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 mor

Projecting mortality at the end of the epidemiological transition

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 dem

Demography of Social Mobility
Robert Mare

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 -

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

New theory needed to explain the evolution of senescence
Annette Baudisch

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

Demographic patterns in populations of long-lived and iteroparous mammals
Jean-Michel Gaillard

Demographic patterns in populations of long-lived and iteroparous mammals

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

An overview of Vertebrate Demography
Jean-Dominique Lebreton

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

Sensitivity Analysis in Mathematical Demography

Intrinsic Linkages in Dynamic Multistate Populations
Robert Schoen

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 com

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