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Population dynamics in variable environments. IV. Weak ergodicity in the Lotka equation.

The Hilbert projective metric is applied to the continuous-time Lotka equation in demography to establish weak ergodicity: populations with the same time-varying fecundity and mortality schedules ultimately have the same age composition. The analysis displays clearly the dynamic content of Lotka's equation and identifies a contraction operator which forces convergence of birth sequences over time. The relationship between primitivity in the discrete (Leslie) and continuous (Lotka) demographic models is made clear.

Birth Rate↗

What limits the Serengeti zebra population?

The populations of the ecologically dominant ungulates in the Serengeti ecosystem (zebra, wildebeest and buffalo) have shown markedly different trends since the 1960s: the two ruminants both irrupted after the elimination of rinderpest in 1960, while the zebras have remained stable. The ruminants are resource limited (though parts of the buffalo population have been limited by poaching since the 1980s). The zebras' resource acquisition tactics should allow them to outcompete the ruminants, but their greater spatial dispersion makes them more available to predators, and it has been suggested that this population is limited by predation. To investigate the mechanisms involved in the population dynamics of Serengeti zebra, we compared population dynamics among the three species using demographic models based on age-class-specific survival and fecundity. The only major difference between zebra and the two ruminants occurred in the first-year survival. We show that wildebeest have a higher reproductive potential than zebra (younger age at first breeding and shorter generation time). Nevertheless, these differences in reproduction cannot account for the observed differences in the population trends between the zebra and the ruminants. On the other hand, among-species differences in first-year survival are great enough to account for the constancy of zebra population size. We conclude that the very low first-year survival of zebra limits this population. We provide new data on predation in the Serengeti and show that, as in other ecosystems, predation rates on zebras are high, so predation could hold the population in a "predator pit". However, lion and hyena feed principally on adult zebras, and further work is required to discover the process involved in the high mortality of foals.

Animals↗

The biology behind lichenometric dating curves.

Lichenometry is used to date late-Holocene terminal moraines that record glacier fluctuations. Traditionally, it relies upon dating curves that relate diameters of the largest lichens in a population to surface ages. Although widely used, the technique remains controversial, in part because lichen biology is poorly understood. We use size-frequency distributions of lichens growing on well-dated surfaces to fit demographic models for Rhizocarpon geographicum and Pseudophebe pubescens, two species commonly used for lichenometry. We show that both species suffer from substantial mortality of 2-3% per year, and grow slowest when young-trends that explain a long-standing contradiction between the literatures of lichenometry and lichen biology. Lichenometrists interpret the shape of typical dating curves to indicate a period of rapid juvenile "great growth," contrary to the growth patterns expected by biologists. With a simulation, we show how the "great growth" pattern can be explained by mortality alone, which ensures that early colonists are rarely found on the oldest surfaces. The consistency of our model predictions with biological theory and observations, and with dozens of lichenometric calibration curves from around the world, suggests opportunities to assess quantitatively the accuracy and utility of this common dating technique.

Alaska↗

Sex, sex-ratios, and the dynamics of pelagic copepod populations.

I examine how the population biology of pelagic copepods depends on their mating biology using field data and a simple demographic model. Among calanoid copepods, two distinct patterns emerge. First, copepods that lack seminal receptacle and require repeated mating to stay fertilized have near equal adult sex ratios in field populations. Winter population densities are orders of magnitude less than the critical population density required for population persistence, but populations survive winter seasons as resting eggs in the sediment. Population growth in these species is potentially high because they have on average a factor of 2 higher egg production rates than other pelagic copepods. Second, other copepods require only one mating to stay fertile, and populations of these species have strongly female-skewed adult sex-ratios in field populations. Resting eggs have not been described within this group. Winter population sizes are well predicted by the critical density required for population persistence which, in turn, is closely related to the body-size-dependent mate-search capacity. Thus, the different requirements for mating lead in the first case to a more opportunistic reproductive strategy that implies rapid colonization of the pelagic during productive seasons, and in the second case to a strategy that allows maintenance of a pelagic populations during unproductive seasons. Positive density dependent population growth during periods of low population density ('Allee effect') amplifies population density variation during winter into the subsequent summer, thus explaining why summer densities appear to depend more on winter densities than on current growth opportunities in pelagic copepods.

Animals↗

Pseudoepidemics of heroin addiction.

Smooth unimodal skewed distributions, sometimes referred to as "epidemic-like" curves, are often used as evidence of time to time changes in incidence. Data on year of onset from groups of treated heroin addicts are generally alleged to reflect incidence, and this distribution is used to evaluate effectiveness and predict future needs. This paper describes the development of simple demographic models which demonstrate the production of epidemic-like curves without changes in incidence, ascertainment or duration of disorder. These graphic models are relevant to other non-infectious disorders where there is continuing exposure to the etiologic agents and where intervals between onset and ascertainment are not uniformly distributed.

Disease Outbreaks↗

The Gompertz equation as a predictive tool in demography.

The Gompertz demographic model describes rates of aging and age-independent mortality with the parameters alpha and A, respectively. Estimates of these parameters have traditionally been based on the assumption that mortality rates are constant over short to moderate time periods. This assumption is questionable even for very large samples assayed over short time intervals. In this article, we compare several methods for estimating the Gompertz parameters, including some that do not assume constant mortality rates. A maximum likelihood method that does not assume constant mortality rates is shown to be best, based on the bias and variance of the Gompertz parameter estimates. Moreover, we show how the Gompertz equation can then be used to predict mean longevity and the time of the nth percentile of mortality. Methods are also developed that assign confidence intervals to such estimates. In some cases, these statistics may be estimated accurately from only the early deaths of a large cohort, thus providing an opportunity to estimate longevity on long-lived organisms quickly.

Computer Simulation↗

The monitoring of British breeding birds: a success story for conservation science?

For almost four decades the British Trust for Ornithology has monitored populations of the commoner 35-50% of species of British breeding birds. The monitoring involves surveillance of numbers, breeding output and survival rates across the whole of the United Kingdom. A formal alert system allows serious declines to be identified and brought to the attention not only of conservationists and those responsible for countryside policy but also the general public. Demographic modelling, the gathering of ancillary information and linked research programmes allow the causes of declines to be identified. The paper details the operation of the programme, illustrated by examples. The system has resulted in the widespread declines in farmland birds that occurred in the last quarter of the 20th century being brought to the attention of conservation scientists, campaigners, policy-makers, politicians and the public. From this (and from the associated understanding of the causes of the declines) have stemmed policies aimed at reducing the problems and a commitment by government to halt the declines. The success of the programme rests on scientifically rigorous design and analysis, on a partnership between volunteer birdwatchers (who do most of the fieldwork) and professional ecologists (responsible for design and analysis) and on effective interaction between scientists and policy makers.

Animals↗

A biologically motivated partitioning of mortality.

For over a century, actuaries and biologists working independently of each other have presented arguments for why total mortality needs to be partitioned into biologically meaningful subcomponents. These mortality partitions tended to overlook genetic diseases that are inherited because the partitions were motivated by a paradigm focused on aging. In this article, we combine and extend the concepts from these disciplines to develop a conceptual partitioning of total mortality into extrinsic and intrinsic causes of death. An extrinsic death is either caused or initiated by something that orginates outside the body of an individual, while an intrinsic death is either caused or initiated by processes that originate within the body. It is argued that extrinsic mortality has been a driving force in determining why we die when we do from intrinsic causes of death. This biologically motivated partitioning of mortality provides a useful perspective for researchers interested in comparative mortality analyses, the consequences of population aging, limits to human life expectancy, the progress made by the biomedical sciences against lethal diseases, and demographic models that predict the life expectancy of future populations.

Aging↗

Period and cohort dynamics in fertility norms at the onset of the demographic transition in Kenya 1978-1998.

A characteristic of African pre-transitional fertility regimes is large ideal family size. This has been used to support claims of cultural entrenchment of high fertility. Yet in Kenya fertility rates have fallen. In this paper this fall is explored in relation to trends in fertility norms and attitudes using four sequential cross-sectional surveys spanning the fertility transition in Kenya (1978, 1984, 1989 and 1998). The most rapid fall in the reported ideal family size occurred between 1984 and 1989, whilst the most rapid fall in the total fertility rate occurred 5 to 10 years later, between 1989 and 1998. Thus these data, spanning the fertility transition in Kenya, support the traditional demographic model that demand for fertility limitation drives fertility decline. These data also suggest that the decline in fertility norms over time was partly a period effect, as the reported ideal family size was seen to fall simultaneously in all age cohorts, and partly a cohort effect, as older age cohorts reporting higher ideal family sizes were replaced by younger cohorts reporting lower ideal family sizes. These data also suggest that a new fertility norm of four children may have developed by 1989 and continued until 1998. This is consistent with, and perhaps could have been used to predict, the stall in the Kenyan fertility decline after 1998.

Adolescent↗

Patterns of grief reaction after pregnancy loss.

Analysis of three waves of Perinatal Grief Scale scores for 194 bereaved subjects over the course of two years revealed patterns of change different from those commonly noted in the literature. Less than half the sample matched the "normal" model; the rest exhibited non-normal patterns that did not fit the alternative psychological models. Demographic variables and pregnancy history, both before and after the loss, help explain some of the differences in direction of the grief response.

Abortion, Spontaneous↗

Impact of clonal growth on effective population size in Hymenoxys herbacea (Asteraceae).

By influencing the proliferation of different genotypes, clonal growth can affect the maintenance of genetic variability and magnitude of genetic drift within plant populations. However, estimates of effective population size rarely incorporate the contribution of both asexual and sexual reproduction. We estimated effective size (Ne) for two populations of the clonal, self-incompatible plant, Hymenoxys herbacea, using a stage-structured demographic model for organisms with asexual and sexual recruitment and then examined the impact of reproductive strategy using an elasticity analysis. Plant rosettes monitored in two successive years had high survival rates in both populations (mean 0.94). The mean number of sexually derived recruits per initial ramet was 0.041 (SE 0.039), whereas the mean number of clonal recruits was 0.61 (SE 0.90). Effective size was 1642 and 5769 in the two populations and the Ne/N ratio averaged 0.34, comparable to values for other clonal species. Elasticity analysis indicated that increases in both clonal and sexual recruitment cause an increase in Ne while increasing the variance reduced Ne. However, Ne was more sensitive to changes in the mean and variance of asexual recruitment than sexual recruitment. These results highlight the importance of considering asexual modes of reproduction when examining the role of genetic stochasticity in populations.

Asteraceae↗

[Strategic controlling in the consideration of social demographic changes in social medical services].

Annually the Medizinische Dienst der Krankenversicherung Westfalen-Lippe (MDK-WL) performs approximately 120,000 nursing care assessments according to the 11th social statute book (SGB XI). A prospective reflection on the amount of expert assessments and the spectrum of services for the Nursing Care Insurance until 2020, was performed in order to establish a long term strategic controlling. The insured party makes the request for nursing care according to their personal estimation when the need for assistance is increasing. To predict the future amount of expert assessments you have to take into consideration the social background of the families in addition to age and gender (there is a clear correlation between age and the need of assistance). The database from nursing care assessments in 2001 was projected on a demographic model for the region of Westfalen-Lippe. The amount of requests correlates as expected with the patients age and increases exponentially. The incidence in the need of care shows relevant gender differences, but taken into consideration the very different age structure, the overall incidence is very similar. Against the background of the current nursing care law, the MDK-WL has to deal with an annual increase in assessments of 2 %. The requests for single persons are extremely often without foundation (55 % not substantially in need of care vs. 35 %). Looking at the requests of couples, it shows that the ones for women are more often unfounded then the ones for men (39 % vs. 32 %). It is necessary to take the development of the amount of single living persons into consideration to achieve more accurate predictions for the amount of assessments.

Age Factors↗

Long-term impacts of the Exxon Valdez oil spill on sea otters, assessed through age-dependent mortality patterns.

We use age distributions of sea otters (Enhydra lutris) found dead on beaches of western Prince William Sound, Alaska, between 1976 and 1998 in conjunction with time-varying demographic models to test for lingering effects from the 1989 Exxon Valdez oil spill. Our results show that sea otters in this area had decreased survival rates in the years following the spill and that the effects of the spill on annual survival increased rather than dissipated for older animals. Otters born after the 1989 spill were affected less than those alive in March 1989, but do show continuing negative effects through 1998. Population-wide effects of the spill appear to have slowly dissipated through time, due largely to the loss of cohorts alive during the spill. Our results demonstrate that the difficult-to-detect long-term impacts of environmental disasters may still be highly significant and can be rigorously analyzed by using a combination of population data, modeling techniques, and statistical analyses.

Accidents↗

The emergence of humans: the coevolution of intelligence and longevity with intergenerational transfers.

Two striking differences between humans and our closest living relatives, chimpanzees and gorillas, are the size of our brains (larger by a factor of three or four) and our life span (longer by a factor of about two). Our thesis is that these two distinctive features of humans are products of coevolutionary selection. The large human brain is an investment with initial costs and later rewards, which coevolved with increased energy allocations to survival. Not only does this theory help explain life history variation among primates and its extreme evolution in humans; it also provides new insight into the evolution of longevity in other biological systems. We introduce and apply a general formal demographic model for constrained growth and evolutionary tradeoffs in the presence of life-cycle transfers between age groups in a population.

Animals↗

Generalizing Fisher's "reproductive value": Nonlinear, homogeneous, biparental systems.

Biparental demographic models violate linearity. However, in their early "dilute" stages before limited environment resources bring need for competitive selection, first-degree-homogeneous relations obtain. For them, a reproductive-value function of the initial coordinates is defined to recapitulate their contribution to the asymptotically dominating mode of exponential growth: now the generalized Fisher reproductive value of one sex is altered by relative numbers of the other sex. The new reproductive-value function is also derived for general systems of homogeneous-first-degree differential and difference equations, and is shown to grow from the start at the asymptotic growth rate.

Journal Article↗

A populationwide coalescent analysis of Icelandic matrilineal and patrilineal genealogies: evidence for a faster evolutionary rate of mtDNA lineages than Y chromosomes.

Historical inferences from genetic data increasingly depend on assumptions about the genealogical process that shapes the frequencies of alleles over time. Yet little is known about the structure of human genealogies over long periods of time and how they depart from expectations of standard demographic models, such as that attributed to Wright and Fisher. To obtain such information and to examine the recent evolutionary history of mtDNA and Y-chromosome haplotypes in the Icelandic gene pool, we traced the matrilineal and patrilineal ancestry of all 131,060 Icelanders born after 1972 back to two cohorts of ancestors, one born between 1848 and 1892 and the other between 1798 and 1742. This populationwide coalescent analysis of Icelandic genealogies revealed highly positively skewed distributions of descendants to ancestors, with the vast majority of potential ancestors contributing one or no descendants and a minority of ancestors contributing large numbers of descendants. The expansion and loss of matrilines and patrilines has caused considerable fluctuation in the frequencies of mtDNA and Y-chromosome haplotypes, despite a rapid population expansion in Iceland during the past 300 years. Contrary to a widespread assumption, the rate of evolution caused by this lineage-sorting process was markedly faster in matrilines (mtDNA) than in patrilines (Y chromosomes). The primary cause is a 10% shorter matrilineal generation interval. Variance in the number of offspring produced within each generation was not an important differentiating factor. We observed an intergenerational correlation in offspring number and in the length of generation intervals in the matrilineal and patrilineal genealogies, which was stronger in matrilines and thus contributes to their faster evolutionary rate. These findings may have implications for coalescent date estimates based on mtDNA and Y chromosomes.

Alleles↗

Physiological effects on demography: a long-term experimental study of testosterone's effects on fitness.

Understanding physiological and behavioral mechanisms underlying the diversity of observed life-history strategies is challenging because of difficulties in obtaining long-term measures of fitness and in relating fitness to these mechanisms. We evaluated effects of experimentally elevated testosterone on male fitness in a population of dark-eyed juncos studied over nine breeding seasons using a demographic modeling approach. Elevated levels of testosterone decreased survival rates but increased success of producing extra-pair offspring. Higher overall fitness for testosterone-treated males was unexpected and led us to consider indirect effects of testosterone on offspring and females. Nest success was similar for testosterone-treated and control males, but testosterone-treated males produced smaller offspring, and smaller offspring had lower postfledging survival. Older, more experienced females preferred to mate with older males and realized higher reproductive success when they did so. Treatment of young males increased their ability to attract older females yet resulted in poor reproductive performance. The higher fitness of testosterone-treated males in the absence of a comparable natural phenotype suggests that the natural phenotype may be constrained. If this phenotype were to arise, the negative social effects on offspring and mates suggest that these effects might prevent high-testosterone phenotypes from spreading in the population.

Age Factors↗

Plant reproductive allocation predicts herbivore dynamics across spatial and temporal scales.

Life-history theory suggests that iteroparous plants should be flexible in their allocation of resources toward growth and reproduction. Such plasticity could have consequences for herbivores that prefer or specialize on vegetative versus reproductive structures. To test this prediction, we studied the response of the cactus bug (Narnia pallidicornis) to meristem allocation by tree cholla cactus (Opuntia imbricata). We evaluated the explanatory power of demographic models that incorporated variation in cactus relative reproductive effort (RRE; the proportion of meristems allocated toward reproduction). Field data provided strong support for a single model that defined herbivore fecundity as a time-varying, increasing function of host RRE. High-RRE plants were predicted to support larger insect populations, and this effect was strongest late in the season. Independent field data provided strong support for these qualitative predictions and suggested that plant allocation effects extend across temporal and spatial scales. Specifically, late-season insect abundance was positively associated with interannual changes in cactus RRE over 3 years. Spatial variation in insect abundance was correlated with variation in RRE among five cactus populations across New Mexico. We conclude that plant allocation can be a critical component of resource quality for insect herbivores and, thus, an important mechanism underlying variation in herbivore abundance across time and space.

Animals↗