On the distribution of the time to extinction in the stochastic logistic population model

1982 ◽  
Vol 14 (4) ◽  
pp. 687-708 ◽  
Author(s):  
R. H. Norden

The aim of this paper is to investigate the distribution of the extinction times, T, of the stochastic logistic process from both the numerical and the theoretical standpoint. The problem is approached first by deriving formulae for the moments of T; it is then shown that in most cases T is, very nearly, a gamma variate. Some simulated results are given and these agree well with the theory. Furthermore, a consideration of the process conditioned on non-extinction is shown to be an effective way of obtaining a large t (time) description of the unconditioned process. Finally, a more general form of the model in which the death-rate as well as the birth-rate is ‘density-dependent' is considered, and by comparison with the usual form of the model the effect on T of this additional factor is assessed.

1982 ◽  
Vol 14 (04) ◽  
pp. 687-708 ◽  
Author(s):  
R. H. Norden

The aim of this paper is to investigate the distribution of the extinction times,T, of the stochastic logistic process from both the numerical and the theoretical standpoint. The problem is approached first by deriving formulae for the moments ofT; it is then shown that in most casesTis, very nearly, a gamma variate. Some simulated results are given and these agree well with the theory. Furthermore, a consideration of the process conditioned on non-extinction is shown to be an effective way of obtaining a larget(time) description of the unconditioned process. Finally, a more general form of the model in which the death-rate as well as the birth-rate is ‘density-dependent' is considered, and by comparison with the usual form of the model the effect onTof this additional factor is assessed.


1986 ◽  
Vol 13 (4) ◽  
pp. 517 ◽  
Author(s):  
KR Every

A decline in the koala population on Phillip I , has been evident for some time. This study, in an area set apart from public access, quantifies some aspects of this decline. A triple-count technique for a closed population model, with the freedom that the probability of sighting can vary between the surveys, was used to obtain an estimate of the population within a 65-ha study area. The initial population, in June 1980, was estimated to be 117; this declined to 62 in 3.5 years, during which period 23 deaths and 24 births were recorded. The decline, which averaged 16 koalas per year, is discussed in terms of the low birth rate, of dispersal, and of the contribution of predation by dogs to the death rate.


1960 ◽  
Vol 3 ◽  
pp. 59-73 ◽  
Author(s):  
Leo A. Orleans

Whereas throughout most of the world the results of the 1953 censusregistration of Communist China, reporting a population of 582·6 million, evoked anxiety and even alarm, the Communists expressed only pride and overwhelming confidence. As a people “liberated from the oppressive chains of capitalism,” Communist leaders felt that their horizons were unlimited and that feeding and caring for a population of this size presented no problems under a system in which people are “the most precious of all categories of capital.” The simultaneous release of vital rates which indicated a birth rate of 37 per thousand population and a death rate of 17 per thousand, further stressed the “great vitality of the people of new China.” The 2 per cent, natural increase (excess of births over deaths), resulting in an annual population growth of some 12 million, was declared, in line with Marxist doctrine, to be an asset in a country with vast new lands and unexploited natural resources, where additional people create additional wealth.


2019 ◽  
Author(s):  
Mark D. Scheuerell ◽  
Casey P. Ruff ◽  
Joseph H. Anderson ◽  
Eric M. Beamer

SummaryAssessing the degree to which at-risk species are regulated by density dependent versus density independent factors is often complicated by incomplete or biased information. If not addressed in an appropriate manner, errors in the data can affect estimates of population demographics, which may obfuscate the anticipated response of the population to a specific action.We developed a Bayesian integrated population model that accounts explicitly for interannual variability in the number of reproducing adults and their age structure, harvest, and environmental conditions. We apply the model to 41 years of data for a population of threatened steelhead troutOncorhynchus mykissusing freshwater flows, ocean indices, and releases of hatchery-born conspecifics as covariates.We found compelling evidence that the population is under strong density dependence, despite being well below its historical population size. In the freshwater portion of the lifecycle, we found a negative relationship between productivity (offspring per parent) and peak winter flows, and a positive relationship with summer flows. We also found a negative relationship between productivity and releases of hatchery conspecifics. In the marine portion of the lifecycle, we found a positive correlation between productivity and the North Pacific Gyre Oscillation. Furthermore, harvest rates on wild fish have been sufficiently low to ensure very little risk of overfishing.Synthesis and applications.The evidence for density dependent population regulation, combined with the substantial loss of juvenile rearing habitat in this river basin, suggests that habitat restoration could benefit this population of at-risk steelhead. Our results also imply that hatchery programs for steelhead need to be considered carefully with respect to habitat availability and recovery goals for wild steelhead. If releases of hatchery steelhead have indeed limited the production potential of wild steelhead, there are likely significant tradeoffs between providing harvest opportunities via hatchery steelhead production, and achieving wild steelhead recovery goals.


2016 ◽  
Vol 50 ◽  
pp. 97-126
Author(s):  
Alfred Wong

Latvia has been suffering a substantial decrease in population since the early 1990s. There appears to have been little or no detailed analysis of the genesis of this decline in population. The major political event occurring at the beginning of the population decline was the rapid transitioning from socialism to capitalism. This study has revealed the causes of severe population decline to be a combination of steadily-declining birth rate, sharply rising high death rate, and mass emigration of people to wealthier European states. The cross-over of birth rate and death rate could be attributed to the tumultuous societal upheavals in the changeover from the socialistic protective-welfare system to a free-market capitalistic economic system. In particular, this traumatic event had probably affected the physical and mental health of many people to result in premature deaths from, among other things, consequential morbidity, accidents, homicides and suicides. Practicable remedies to arrest the continuing trend of precipitous decline in the population might include a) repairing the failures of the current modality of national health care, b) creating higher paying jobs in Latvia to entice prospective young emigrants to stay in Latvia, and c) repatriating of recent Latvian émigrés.


PEDIATRICS ◽  
1996 ◽  
Vol 98 (6) ◽  
pp. 1007-1019 ◽  
Author(s):  
Bernard Guyer ◽  
Donna M. Strobino ◽  
Stephanie J. Ventura ◽  
Marian MacDorman ◽  
Joyce A. Martin

Recent trends in the vital statistics of the United States continued in 1995, including decreases in the number of births, the birth rate, the age-adjusted death rate, and the infant mortality rate; life expectancy at birth increased to a level equal to the record high of 75.8 years in 1992. Marriages and divorces both decreased. An estimated 3 900 089 infants were born during 1995, a decline of 1% from 1994. The preliminary birth rate for 1995 was 14.8 live births per 1000 total population, a 3% decline, and the lowest recorded in nearly two decades. The fertility rate, which relates births to women in the childbearing ages, declined to 65.6 live births per 1000 women 15 to 44 years old, the lowest rate since 1986. According to preliminary data for 1995, fertility rates declined for all racial groups with the gap narrowing between black and white rates. The fertility rate for black women declined 7% to a historic low level (71.7); the preliminary rate for white women (64.5) dropped just 1%. Fertility rates continue to be highest for Hispanic, especially Mexican-American, women. Preliminary data for 1995 suggest a 2% decline in the rate for Hispanic women to 103.7. The birth rate for teenagers has now decreased for four consecutive years, from a high of 62.1 per 1000 women 15 to 19 years old in 1991 to 56.9 in 1995, an overall decline of 8%. The rate of childbearing by unmarried mothers dropped 4% from 1994 to 1995, from 46.9 births per 1000 unmarried women 15 to 44 years old to 44.9, the first decline in the rate in nearly two decades. The proportion of all births occurring to unmarried women dropped as well in 1995, to 32.0% from 32.6% in 1994. Smoking during pregnancy dropped steadily from 1989 (19.5%) to 1994 (14.6%), a decline of about 25%. Prenatal care utilization continued to improve in 1995 with 81.2% of all mothers receiving care in the first trimester compared with 78.9% in 1993. Preliminary data for 1995 suggests continued improvement to 81.2%. The percent of infants delivered by cesarean delivery declined slightly to 20.8% in 1995. The percent of low birth weight (LBW) infants continued to climb in 1994 rising to 7.3%, from 7.2% in 1993. The proportion of LBW improved slightly among black infants, declining from 13.3% to 13.2% between 1993 and 1994. Preliminary figures for 1995 suggest continued decline in LBW for black infants (13.0%). The multiple birth ratio rose to 25.7 per 1000 births for 1994, an increase of 2% over 1993 and 33% since 1980. Age-adjusted death rates in 1995 were lower for heart disease, malignant neoplasms, accidents, and homicide. Although the total number of human immunodeficiency virus (HIV) infection deaths increased slightly from 42 114 in 1994 to an estimated 42 506 in 1995, the age-adjusted death rate for HIV infection did not increase, which may indicate a leveling off of the steep upward trend in mortality from HIV infection since 1987. Nearly 15 000 children between the ages of 1-14 years died in the United States (US) in 1995. The death rate for children 1 to 4 years old in 1995 was 40.4 per 100 000 population aged 1 to 4 years, 6% lower than the rate of 42.9 in 1994. The 1995 death rate for 5-to 14-year-olds was 22.1,2% lower than the rate of 22.5 in 1994. Since 1979, death rates have declined by 37% for children 1 to 4 years old, and by 30% for children 5 to 14 years old. For children 1 to 4 years old, the leading cause of death was injuries, which accounted for an estimated 2277 deaths in 1995, 36% of all deaths in this age group. Injuries were the leading cause of death for 5-to 14-year-olds as well, accounting for an even higher percentage (41%) of all deaths. In 1995, the preliminary infant mortality rate was 7.5 per 1000 live births, 6% lower than 1994, and the lowest ever recorded in the US. The decline occurred for neonatal as well as postneonatal mortality rates, and among white and black infants alike. Sudden infant death syndrome (SIDS) rates have dropped precipitously since 1992, when the American Academy of Pediatrics issued recommendations that infants be placed on their backs or sides to sleep to reduce the risk of SIDS. SIDS dropped to the third leading cause of infant death in 1994, after being the second leading cause of death since 1980. Infant mortality rates (IMRs) have also declined rapidly for respiratory distress syndrome since 1989, concurrent with the widespread availability of new treatments for this condition.


1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff


1978 ◽  
Vol 15 (1) ◽  
pp. 187-191 ◽  
Author(s):  
John Haigh

A recent paper in Advances in Applied Probability (Siegel (1976)) considered the duration of the time Tmn for a linear birth and death process to grow from a (large) initial size m to a larger size n. The main aim was to show that, when the birth rate exceeds the death rate, Tmn is close to its mean value, log n/m, with high probability. This paper establishes this result using much simpler techniques.


Sign in / Sign up

Export Citation Format

Share Document