Theoretical aspects of extinction by inbreeding depression

Populational extinction due to inbreeding depression is analyzed with simple population genetic and population ecological models. Two alternative genetic mechanisms of inbreeding depression, i.e. recessive deleterious genes and overdominant genes, are assumed in separate analyses in order to examine their relative importance. With both mechanisms the population size and the coefficient of inbreeding are maintained at stable equilibria if there is no non-genetic demographic disturbance or stress. With a certain amount of demographic disturbance the population declines rapidly due to interaction between the decrease of population size and the increase of inbreeding coefficient. Such rapid extinction occurs with both genetic mechanisms. However, in the case of overdominant genes extinction happens only if the equilibrium population size is small and the selection coefficient is large such that segregation load is large. In nature, extinction due to overdominant genes is considered to be much less likely than extinction due to recessive deleterious genes.     

Advocating "one couple with one child" being an optimal choice]

Zero population growth within the next 5 years in China would be reached only if many couples were not allowed to have their own child. On the other hand, if every couple were allowed to have 2 children China's population would reach 1500 million within the next 50 years. It seems advisable to advocate the "1 couple 1 child" idea; couples will have to keep in mind both the national interest and the communist ideology; social welfare to assure good living conditions for the old people will relieve the worries of parents with 1 child only. Most people are willing to follow this decision made by the Communist Party; many people declare their willingness to stick by this rule during their wedding ceremony; many couples send back their permit to have a second child, and many women choose abortion when pregnant with a second permitted pregnancy. By the end of 1979 the proportion of "1 couple 1 child" couples was 90% in many large cities; people realize that the practice of "1 couple 1 child" is the best assurance for the future of the country and of their children. This policy will not result in aging of the population, lack of manpower and shortage of soldiers; even if birth rate were 1% in 1985 the proportion of older people for the next 25 years will still be lower than that in European countries. The problem of aging of the population will not occur in this century, and population policies can always be adjusted when needed. Today's problem is to control population through the "1 couple 1 child" policy, even if it may result in many lonely old people, which is a lesser problem than too many people. Even if China has reduced its population growth by 10 million births each year from 1970 to 1979, the necessity to control population growth is still present, in the interest of the country and economic development.     

Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

A management policy for sika deer based on sex-specific hunting

We consider here a management policy for a sika deer (Cervus nippon) population in the eastern part of Hokkaido. Deer populations are characterized by a large intrinsic rate of population increase, no significant density effects on population growth before population crash, and a relatively simple life history. Our goals of management for the deer population are (1) to avoid irruption with severe damage to agriculture and forestry, (2) to avoid the risk of extinction of the deer population, and (3) to maintain a sustainable yield of deer. To make a robust program on the basis of uncertain information about the deer population, we consider three levels of relative population size and four levels of hunting pressures. We also take into consideration a critical level for extinction, an optimal level, and an irruption level. The hunting pressure for females is set to increase with the population size. We also recommend catching males if the population size is between the critical and optimal levels and catching females and males if the population size is larger than the optimal level. We must avoid cases of irruption or threatened population under various sets of uncertain parameter values. The simulation results suggest that management based on sex-specific hunting is effective to diminish the annual variation in hunting yield. Received: April 8, 1998 / Accepted: December 25, 1998     

Generation carryover of a fraction of population members as an animal adaptation to unstable environmental conditions

Summary A heterogeneous life cycle of individuals in a population was examined on its adaptive significance to an unstable environmental condition. The trend of population growth was simulated by a simple mathematical model in which a part of population in a certain generation was carried over to the next generation without participating in the reproduction. With the increase of the rate of carryover of individuals to the next generation the population fluctuation tended to be stabilized. A minute fraction of population is carried over, the effect is very large to prevent the population decline at a sequence of adverse environmental conditions. The population level increased greatly depending upon the extent of environmental change as far as the rate of carryover took an intermediate value. The optimum proportion of members to be carried over to the next generation was determined by the extent of environmental change and its frequency of occurrence. Contribution from the Entomological Laboratory, College of Agriculture, Kyoto University, No. 451.     

Generation carryover of a fraction of population members as an animal adaptation to unstable environmental conditions

A heterogeneous life cycle of individuals in a population was examined on its adaptive significance to an unstable environmental condition. The trend of population growth was simulated by a simple mathematical model in which a part of population in a certain generation was carried over to the next generation without participating in the reproduction. With the increase of the rate of carryover of individuals to the next generation the population fluctuation tended to be stabilized. A minute fraction of population is carried over, the effect is very large to prevent the population decline at a sequence of adverse environmental conditions. The population level increased greatly depending upon the extent of environmental change as far as the rate of carryover took an intermediate value. The optimum proportion of members to be carried over to the next generation was determined by the extent of environmental change and its frequency of occurrence.     

D. V. Glass on the Problems of a Declining Population

During the past quarter century fertility has dropped below replacement levels in many parts of the world. According to United Nations estimates, in 2005 this was the case in 65 countries, comprising 43 percent of the world's population. In many cases, most notably in Europe and East Asia, the shortfall of fertility from the level that would be necessary in the long run to sustain a stationary population is substantial. In Europe, for example, the average total fertility rate for the period 2000–2005 was 1.4. Indefinite maintenance of such a level implies a shrinkage of the total population by one‐third over a generation–roughly every 30 years. Accompanying that rapid decline of total numbers would be an age structure containing a preponderance of the elderly, posing extreme adjustment difficulties for the economic and social system. Societies that wish to avoid radical depopulation would have to engineer a substantial rise infertility–if not to full replacement level (slightly more than two children per woman), then at least to a level that would moderate the tempo of population decline and make population aging easier to cope with. An additional counter to declining numbers, if not significantly to population aging, could come from net immigration. This is the demographic future assumed in the UN medium‐variant projections for countries and regions currently of very low fertility. Thus, for example, in Europe over the period up to 2050 fertility is assumed to rise to 1.85 and net immigration to amount to some 32 million persons. The UN projections also anticipate further improvement in average life expectancy–from its current level of 74 years to 81 years. This factor slows the decline in population size but accelerates population aging. Under these assumptions, Europe's population would decline from its present 728 million to 653 million by 2050. At that time the proportion of the population over age 65 would be 27.6 percent, nearly double its present share. Demographic change of this nature is not a novel prospect. It was envisioned in a number of European countries and in North America, Australia, and New Zealand in the late 1920s and early 1930s. Concern with the possible economic and social consequences generated much discussion at that time among demographers and social scientists at large and also attracted public attention. Possible policy measures that might reverse the downward trend of fertility were also debated, although resulting in only hesitant and largely inconsequential action. The article by D. V. Glass reproduced below is an especially lucid and concise treatment of demographic changes under conditions of low fertility and their economic and social implications. It appeared in Eugenics Review (vol. 29, no. 1, pp. 39–47) in 1937 when the author was 26 years old. Glass's line of argument is broadly representative of the main focus of demographic analysis in the mid‐1930s on aspects of population dynamics, applying the then still novel analytical tool of the stable population model. It also echoes the work of economists then witnessing the great difficulties capitalist economies faced in adjusting to structural changes in consumer demand and labor supply. While Glass addresses these issues primarily with reference to England and Wales, he sees the issues as affecting all industrialized countries. The Malthusian problem of relentless population growth he persuasively declares to be irrelevant for these countries. The Western world faces the opposite problem: population decline, a trend only temporarily masked by the effects of an age distribution that still has a relatively high proportion of women in the child‐bearing ages, reflecting the higher fertility level of the past. A stationary population, Glass cogently argues, is to be welcomed, and he considers the absolute size at which zero growth would be achieved relatively unimportant. In contrast, a continuous population decline would have “thoroughly disastrous” results in an individualist civilization and in “an unplanned economic system.” And, he concedes, somewhat quaintly, that sustained below‐replacement fertility would pose a great problem “even in a country in which the means of production were owned communally.” Glass's conclusions about the reversibility of low fertility are as pessimistic as those of most informed observers today. Still, he sees hope in a future “rationally planned civilization” that would “produce an environment in which high fertility and a high standard of life will both be possible.” In this context, high fertility means the level necessary to sustain the population in a stationary state. By present‐day standards the level Glass calculates as needed for long‐term zero growth is indeed fairly high: 2.87 children per woman. But that figure reflects the fact that, when he wrote, mortality up to age 50 was still fairly high and fertility occurred almost wholly within marriage; it also assumes zero net immigration. In the last 70 years much has changed in each of these three components of population dynamics, both in England and Wales and in the rest of Europe. Still, Glass's commentary remains highly relevant to the discussion of the problems of low fertility today. David Victor Glass (1911–78) was associated with the London School of Economics throughout much of his scientific career. He followed R. R. Kuczynski as reader in demography in 1945 and became professor of sociology in 1948. His work on demography, population history, and population policy had already made him one of the most influential demographers in pre‐World War II Britain. After the war he rose to international prominence through pioneering work on the Royal Commission of Population; through his research on historical demography, the history of demographic thought, and social mobility; and through founding, in 1947, the journal Population Studies, which he edited until his death.     

Small town growth in the United States: An analysis by size class and by place

Small town population change is an important factor in the urbanization process. We analyzed changes in incorporated places under 10,000 in the United States during the 1940-60 period, making a distinction between changes in population size classes and changes in places grouped by initial size. We made balance sheets for size classes under 1,000, 1,000-2,500, and 2,500-10,000 in order to divide the percent increase by size class into five additive components: (1)growth of places staying in the class, (2) net shifts of growing towns into and out of the class, (8) net shifts of declining towns into and out of the class, (4) addition of new places, and (5) disappearance of places during the time period. Separate tabulations were made by metropolitan location, region, and decade. p ]Places under 10,000 population the initial year grew during both census decades considered. Growth differentials paralleled those generally found for the total population, with the most rapid growth near large cities in the West and (except for non-metropolitan places) over the 1940-60 decade.We found results to be different for population changes of particular size classes. Except in some Urbanized Area locations, the two larger size classes increased in population over both decades. In contrast, the under-1,000 size class declined in almost every case. This decline was not due to decreasing population of places within the class or to the disappearance of places between censuses but rather to the growth of places into larger classes not compensated for by decline of other places into the class or new incorporations.     

The population explosion: Where is it leading?

Over the past few centuries world demography has been characterized by both continuous absolute growth and a steadily increasing rate of growth. From 1650 or earlier to at least 1957 it was always possible to say that never has world population been so large and never has the time necessary for it to double been so short. While there are now some signs to suggest that population doubling times are stabilizing, or even increasing, the population increase in absolute numbers is nevertheless greater each year, and the rate of growth may still be faster than a simple exponential function. There can be little doubt that too large a population, together with the pressures stemming from its demands for an even higher standard of living, sets requirements greater than our planet can safely sustain. This article reviews some aspects of global population data and population dynamics.     

U.S. population in the 21st century: Which scenario is reasonable?

A major Census Bureau study released in January 1989 has evoked renewed warnings in the media and among some population analysts that the U.S. faces population decline in the next century if it does not increase fertility and/or raise immigration. The report's middle scenario rests on an assumed future total fertility rate (TFR) of 1.8, life expectancy of 81.2 years, and net immigration of 500,000 annually. These mid-range assumptions would yield a United States population of 268 million by 2000, peaking at 302 million in 2040 and falling to 292 million by 2080. Questionable assumptions in the report's most likely scenario are discussed. These are:

1. that immigrants bear children at the same rate as their equivalent age and racial group in the United States population.
2. that the high TFR of Hispanics will not raise the overall 1.8 TFR foreseen for whites as the Hispanic proportion of the white population continues to grow.
3. that net yearly immigration will fall to 575,000 in 1990 and 500,000 by 2000. The Census Bureau's "high" assumption of 800,000 net yearly may be more realistic.

The report's low growth scenario projects future population size that is more reassuring than alarming: 264 million in 2000, rising to 288 million in 2030, and falling to 266 million in 2080. Thus, in ninety years the United States would still have 20 million more people than now. While some fear that such slow growth will lower United States influence and bring labor shortages and an aging population, the nation's quality of life would be less at risk with a population of 266 million than with one approaching the one-half billion projected by the Census report's high estimates.     

Population and environment in the twenty-first century

In the past 50 years global population grew by 3.7 billion. There is a large unmet need for family planning and wherever women have been given the means and the information to decide if or when to have the next child, then family size has fallen, often rapidly. However, since the UN 1994 Cairo conference on population and development, support for international family has collapsed and fertility declines in many of the poorest countries have stalled. Amongst some of the most vulnerable groups family size has risen. The investment made in voluntary family planning will largely determine whether, in the next 50 years, the global population grows to something less than 8 billion or to over 10. The trajectory taking us to the higher figure could jeopardize any possibility of transitioning the global economy to a biological sustainability. Much precious time has been lost. Almost all the additional growth in population will take place in the world’s poorest countries, and it is imperative that the international community act to improve access to family planning in those countries, within a human rights frame framework.     

India's population in transition

This demographic profile of India addresses fertility, family planning, and economic issues. India is described as a country shifting from economic policies of self-reliance to active involvement in international trade. Wealth has increased, particularly at higher educational levels, yet 25% still live below the official poverty line and almost 66% of Indian women are illiterate. The government program in family planning, which was instituted during the early 1950s, did not change the rate of natural increase, which remained stable at 2.2% over the past 30 years. 1993 marked the first time the growth rate decline to under 2%. The growth rate in 1995 was 1.9%. The total population is expected double in 36 years. Only Nigeria, Pakistan, and Bangladesh had a higher growth rate and higher fertility in 1995. India is geographically diverse (with the northern Himalayan mountain zone, the central alluvial plains, the western desert region, and the southern peninsula with forest, mountains, and plains). There are regional differences in the fertility rates, which range from replacement level in Kerala and Goa to 5.5 children in Uttar Pradesh. Fertility is expected to decline throughout India due to the slower pace of childbearing among women over the age of 35 years, the increase in contraceptive use, and increases in marriage age. Increased educational levels in India and its state variations are related to lower fertility. Literacy campaigns are considered to be effective means of increasing the educational levels of women. Urbanization is not expected to markedly affect fertility levels. Urban population, which is concentrated in a few large cities, remains a small proportion of total population. Greater shifts are evident in the transition from agriculture to other wage labor. Fertility is expected to decline as women's share of labor force activity increases. The major determinant of fertility decline in India is use of family planning, which has improved in access and use during the 1980s. If India is to keep a stable population under 1.6 billion in the future, Indians may have to accept only one child per family.     

Stalled Fertility Decline in Egypt,Why?

After experiencing rapid decline since the 1980s, fertility in Egypt seemed to be stalling during the second half of the 1990s. In an effort to identify the population segment(s) responsible for the stalling, this study considers fertility trends of women from three standard of living strata (low, middle, and high). Using data collected by the 1988, 1992, 1995, and the 2000 Egypt Demographic and Health Surveys, the study indicates that the reproductive behavior of women from high and middle standards households is largely responsible for stalling of the fertility decline during recent years, and that prospects for a lower fertility in the future is limited, once the gap between the three groups closes. This means that the expectation of achieving replacement fertility Egypt within the next 15 to 20 years is in doubt if the current trends in the both actual and desired fertility of the middle and high strata continued. The key for future decline in fertility is the decline in desired number of children below the current level of 3 children by at least one segment of the population. The fact none of the three population segments expressed a desired fertility below 3 children deprived the society of a vanguard group that leads the rest of the society to replacement level fertility.     

Effects of sterile insect releases on a population under predation or parasitism

Summary A continuous-time differential equation model was constructed which describes the population dynamics of a predator prey system in which sterile prey are released in a program designed to eradicate or reduce the prey population. It was found that the dynamics of the system behave quite differently when predators are present. Two conditions were found which have differing implications for the control program. If the predators still exist when the wild prey population declines to extinction, then the SIRM is assisted by the predators, sometimes to a considereble extent. If the predators decline to extinction before the wild prey population goes extinct, then the predators may or may not assist the SIRM depending on the parameters of the system. If the predators do assist the SIRM, then a potentially dangerous situation exists in which an explosion of the prey population could occur after the predators go extinct. Predator polyphagy would probably minimize this danger of an explosion since it would stabilize the predator population.     

Policy options when population growth slows: The case of Thailand

Thailand reached replacement-level fertility almost a decade ago, although there has been a lag in measuring and recognising the implications of this benchmark event. Fertility could well sink still lower. The momentum of population growth will ensure substantial further increase before the population levels off, but this is not true in all regions. For example, earlier and faster fertility decline in the North, and net outmigration, have led to a situation where some geographical and age segments of the North's population are decreasing. Population policy in Thailand since 1970 has had two major planks: to reduce fertility through an active family planning program, and to distribute population away from the large primate city of Bangkok. The paper discusses whether these policies may need to be modified as a result of the major demographic and socio economic changes that have been taking place. It also discusses the limits to population policy in terms of the likely efficacy of various measures that could be adopted, based on both an assessment of the Thailand situation and the experience of other low-fertility countries.     

The decline and recovery of the Murut tribe of Sabah

Abstract The Murut tribe of Sabah (formerly North Borneo) numbered 30,300 in 1921, decreased to 18,700 in 1951, and increased again to 22,100 in 1960. In 1951, the tribe was a small diminishing section of a slowly growing population; in 1960 it was increasing itself, and the growth rate of the whole population had shot up. Marked variations in the age structures of the Murut and other indigenous tribes accompanied these changes. Between 1920 and 1960 several investigators attempted to explain the decline, but could not show why only one tribe was failing to hold its own among many others which were increasing. Their findings are summarized, and unpublished data from the 1960 census are given which suggest that increasing contacts with the rest of the population, earlier thought to be an important contributor to the decline, were probably the means of saving the Murut from extinction.     

Species diversity preserved in different numbers of nature reserves of the same total area

Conclusion and Summary The expected number of species occurring in different numbers of reserves of the same total area is examined on different assumptions of the spatial distribution and the probability of extinction. The advantage of one large reserve or several smaller ones of equal total area depends on the spatial distributions of species and the stage after the establishement of reserves. In general, several smaller reserves maintain more species immediately after the establishments unless the spatial distribution are uniform or random, whereas one large reserve excels several smaller ones after some rare species have gone extinct unless the spatial distributions are strongly contagious. Since the extinction of rare species must be facilitated as the size of each reserve reduces, the area of a reserve should be larger than the critical area that ensures the persistence of the species. Hence it is concluded that one or a few large reserves are a better strategy in order to maintain the species diversity.     

Simultaneous estimation of mortality and dispersal rates of an artificially released population

Mark-recapture methods cannot estimate both mortality and dispersal rates of a wild population simultaneously. However, when an artificially cultured population is released into an area, the initial population size and the initial population distribution are usually known. If artificially cultured individuals are released with marks or distinguished from wild individuals or if no wild individual exists in the study area, we can estimate both the mortality and dispersal rates of the artificial population. The numbers of dispersed and dead individuals are estimated from the dispersal rate from the diffusion model and the total decreasing rate estimated from a mark-recapture data. We can estimate both the time-dependent and time-independent dispersal rates from the data. We choose the best fit model that has the smallest value of Akaike's Information Criteria. We also consider ‘concentric circles approximation” of spatial distribution, in which the cumulative and frequency distributions are analytically obtained.     

Below-replacement fertility and prospects for labour force growth in Taiwan

Fertility in Taiwan had declined to replacement level in 1983. In 1986–1997, the total fertility rate dropped to 1.7–1.8, with continuing decreases observed in 1997–2001. Fertility will probably be sustained at the 2001 level of 1.48 or even decline further in the future. If the current fertility and labour-force participation rates persist, the size of the labour force will increase only slightly in the next 15 years and begin to shrink soon after 2015. After 2034, the labour force will fall below the current level and Taiwan will face a labour shortage. Though efficient, the policy option of importing more foreign workers is fraught with political sensitivities, especially given the current economic downturn and rising unemployment. Another policy approach, to increase the participation rates for women and mature men, would lead to growth in the labour supply sometime after 2030 and, combined with a modest increase in fertility, would prevent the labour force from falling below its current size in the next 50 years. Notwithstanding that any increase in fertility will have a delayed effect on labour supply, strong incentives are still required to affect fertility behaviour.     

Optimal population and exhaustible resource constraints

A large literature considers the optimal size and growth rate of the human population, trading off the utility value of additional people with the costs of a larger population. In this literature, an important parameter is the social weight placed on population size; a standard result is that a planner with a larger weight on population chooses larger population levels and growth rates. We demonstrate that this result is conditionally overturned when an exhaustible resource constraint is introduced: if the discount rate is small enough, the optimal population today decreases with the welfare weight on population size. That is, a more total-utilitarian social planner could prefer a smaller population today than a more average-utilitarian social planner. We also present a numerical illustration applied to the case of climate change, where we show that under plausible real-world parameter values, our result matters for the direction and magnitude of optimal population policy.