Potentials and the Distributions of the Last Exit Times of Birth and Death Processes

0 .Introduction The mathematical eqnivalenoe of Brownian切otion and olaosioal poten七ialtheory has great imPulsed the study of Potentials of Markov Prooesse

The birth hour of mammals:insights from intra-specific variation in wild blue monkeys

While most mammals show birth hour peaks at times of the 24-h cycle when they are less active,there are exceptions to this general pattern.Such exceptions have been little explored,but may clarify evolutionary reasons for the diel timing of births.We investigated intraspecific variation in birth hour in wild blue monkeys Cercopithecus mitis stuhlmanni,a diurnal primate,to identify factors that differentiated daytime versus nighttime births.Behavioral and life history data from 14 groups over 14 years revealed that 4%of 484 births occurred during the day.Probability of daytime birth varied with mother’s age,peaking at 15.7 years.Births whose annual timing deviated most from the population’s peak birth months were 5 times more likely to occur during daytime than those that deviated less.There was no evidence that mother’s rank or infant sex influenced birth hour,and mixed evidence that daytime births were more probable in larger groups.Survivorship did not differ significantly for infants born during the day versus night.Prime-aged mothers may be able to handle the consequences of an unusual birth hour more successfully than mothers with less experience or those weakened by age.Daytime birth may be more advantageous in the off-season because nights are colder at that time of year.These findings are consistent with hypotheses relating birth hour to the risk of losing social protection in group-living animals,but are not consistent with those emphasizing risk of conspecific harassment.Patterns of within-species variation can help in evaluating evolutionary hypotheses for non-random birth hour.

Drastic changes in fertility level and timing in response to marriage and fertility policies: evidence from Shandong province, China

China’s“one-child policy”that had been in force between 1980 and 2016 evolved over time and differed widely between regions.Local policies in many regions also targeted the timing and spacing of childbearing by setting the minimum age at mar-riage,first birth and second birth and defining minimum interval between births.Our study uses data from the 120 Counties Population Dynamics Monitoring Sys-tem to reconstruct fertility level and timing in nine counties in Shandong province,which experienced frequent changes in birth and marriage policies.We reconstruct detailed indicators of fertility by birth order in 1986-2016,when policies on mar-riage and fertility timing became strictly enforced since 1989 and subsequently relaxed(especially in 2002)and abandoned(in 2013).Our analysis reveals that birth timing policies have fuelled drastic changes in fertility level,timing and spacing in the province.In the early 1990s period fertility rates plummeted to extreme low levels,with the provincial average total fertility rate falling below 1 in 1992-1995.Second births rates fell especially sharply.The age schedule of childbearing shifted to later ages and births became strongly concentrated just above the minimum pol-icy age at first and second birth,resulting in a bimodal distribution of fertility with peaks at ages 25 and 32.Conversely,the abandonment of the province-level policy on the minimum age at marriage and first birth and less strict enforcement of the policy on the minimum age at second birth contributed to a recovery of period fertil-ity rates in the 2000s and a shift to earlier timing of first and second births.It also led to a shorter second birth interval and a re-emergence of a regular age schedule of fertility with a single peak around age 28.