Height cycles in the 18th and 19th centuries

Spectral analysis of the physical stature of Americans and Europeans in the 18th and 19th centuries reveals a cyclical structure similar to the traditional view of the business cycle: a longer cycle with a length of 7-10 years, and a shorter cycle with a length of 3-5 years. The correlation between height cycles and cycles of economic variables such as grain prices indicates an influence of economic cycles on physical stature. The phase shift between the cycles indicates that economic conditions are especially important for growth in infancy. In part, this result is due to a cumulative effect: born into a recessionary period, a child is likely to face several cyclical downturns during the growing years.     

Linkage disequilibrium in a population undergoing periodic fragmentation and admixture

Glacial and interglacial cycles are considered to have caused the fragmentation and admixture of populations in many organisms. A simple model incorporating such periodic changes of the population structure is analysed in order to investigate the behaviour of neutral genetic variation at one and two loci. The equilibrium is reached very quickly in terms of cycles if the length of a cycle is long, as would be expected of the glaciation cycles. Heterozygosity and linkage disequilibrium are shown to depend on the length of time of the fragmented and admixed phases, population sizes, and number (n) of subpopulations in the fragmented phase. If the population size is small in the fragmented phase and its duration is long, the squared correlation coefficient of two loci (a measure of linkage disequilibrium) just after the admixture is approximated by 1/(n-1) for n > 1. After admixture, the correlation decays at a rate of approximately twice the recombination rate. Therefore, if post-glaciation admixture created linkage disequilibrium, we expect to observe linkage disequilibrium even between moderately linked loci, and its decay pattern along the chromosome is very different from that in a random mating population at equilibrium. This is especially true in organisms with long generation times such as trees.     

Evidence of ovulation in goats (Capra hircus ) with short estrous cycle and its occurrence in the tropics

The influence of season and exposure to buck on the length of the estrous cycle were determined in 32 normally cycling native goats of different ages and parity. The estrous cycle durations were classified as short, medium and long. Ten goats (31%) exhibited medium length estrous cycles; 22 animals (69%) exhibited a combination of short, medium and long estrous cycles. Of the 155 estrous cycles studied, 15% were short, 72% were medium and 13% were long. Short estrous cycles were significantly shorter (P < 0.01) in estrus duration than medium or long estrous cycles. Significant differences (P < 0.05) for estrous cycle length and estrus duration were found between does but not within does. The presence of a buck for 8 to 16 h showed no significant effect on the length of the estrous cycle or on estrus duration, but a 24-h exposure period to a buck yielded shorter estrous cycles and estrus duration than found in the unexposed control group. Estrous cycles were significantly shorter (P < 0.01) in October, when rainfall is 57.9% of the annual total, and significantly longer (P < 0.01) in February, when rainfall is low at 0.2% of the annual total. A negative linear relationship (r = -0.87) was observed between estrous cycle and rainfall. Twenty-eight (90.3 %) of the short estrous cycles were ovulatory. The short cycles had a relatively lower ovulation rate than medium and long estrous cycles. The results indicate that the short estrous cycle in goats is associated with ovulation, and its occurrence in the tropics is related to rainfall.     

A longitudinal study of estrous cyclicity in aging C57BL/6J mice: I. Cycle frequency, length and vaginal cytology

Cycle frequency, length, and vaginal cytology were measured longitudinally in three cohorts of singly housed virgin mice staggered across a 3-year interval. The age profiles of these parameters were qualitatively similar, but quantitatively different, among cohorts. Cycle frequency was initially low (Phase I), due to prolonged cycles and late-starting cycles, and did not peak (Phase II) until mice were 3-5 months old. Phase II lasted for 7-10 months, depending on the cohort. Thereafter cycle frequency declined steadily (Phase III). The average age of cessation of cyclicity varied among cohorts, occurring between 13 and 16 months of age. Age changes in cycle length paralleled those of cycle frequency. During Phase II, median cycle length was less than 5 days and variance was lowest. During Phases I and III, variance was about twofold greater and median cycle length was greater than 5 days. Although median cycle length remained stable for several months during Phase II, the peak period of 4-day cycles was much shorter. In all cohorts, 4-day cycles did not peak until 7-8 months of age and began to decline by 9 months. The decrease in 4-day cycles was associated with a progressive lengthening of cycles-first from 4 to 5 days, then to longer cycles. The fraction of cycles with extended cornification (greater than 2 days) increased with advancing age from less than 0.35 during the initial period of cycle lengthening to a maximum of 0.60. The observation that the initial phase o cycle prolongation was not usually associated with extended cornification is consistent with earlier evidence that this period is characterized by a delayed, rather than prolonged, preovulatory rise of estradiol. However, the increased fraction of prolonged cycles with extended cornification at later ages suggests that the preovulatory elevation of estradiol may ultimately be prolonged.     

Modeling menstrual cycle length using a mixture distribution

In reproductive health studies, epidemiologists are often interested in examining the effects of covariates on menstrual cycle length which is a convenient, noninvasive measure of women's ovarian and reproductive function. Previous literature (Harlow and Zeger, 1991) suggests that the distribution of cycle length is a mixture of a major symmetric distribution and a component featuring a long right tail. Motivated by the shape of this marginal distribution, we propose a mixture distribution for cycle length, representing standard cycles from a Normal distribution and nonstandard cycles from a shifted Weibull distribution. The parameters are estimated using an estimating equation derived from the score function of an independence working model. The fitted mixture distribution agrees well with the distribution estimated using nonparametric approaches. We propose two measures to help determine whether a cycle is standard or nonstandard, developing tools necessary to identify characteristics of the menstrual cycles that are biologically indicative of ovarian dysfunction. We model the effect of a woman's age on the mean and variation of both standard and nonstandard cycle lengths using multiple measurements of women.     

Human axillary secretions influence women''s menstrual cycles: The role of donor extract from men

Menstrual cycle lengths of 29.5 +/- 3 days ("normal cycles") are more frequent in women who have weekly coital activity than in women who do not. In order to investigate potential mechanisms controlling the association between heterosexual activity and menstrual cycle length, and in light of the nonhuman literature suggesting that a chemical signal from males could be involved, menstrual cycle lengths of nulliparous women were evaluated following regular application of axillary extract from donor males. Compared to controls receiving only blank/ethanol applications, women receiving axillary extracts for 12.5 to 14.5 weeks showed the following changes: a reduced incidence in variability of cycle lengths; and a reduced proportion of aberrant length cycles.     

Menstrual cycle characteristics and predictability of ovulation of Bhutia women in Sikkim, India

Although a woman's menstrual history can have significant implications for health outcomes, few studies have examined menstrual cycle variability in non-western, non-clinically based populations. This study presents menstrual cycle characteristics from Bhutia women living in Gangtok, Sikkim, India. The Bhutia are one of two indigenous populations residing in this small, northeastern state of India. A total of 1067 cycles were recorded by 200 Bhutia women over the course of 12 months. Mean cycle length in this population was similar to reported mean cycle lengths for populations in the U.S (30 days vs. 28 days). Menstrual cycles in this sample were highly variable with most women experiencing more than one short or long menstrual cycle. The frequency of irregular menstrual cycles experienced by individuals also varied significantly by season. A body mass index (BMI) above or below the WHO defined normal range was associated with higher rates of irregular cycles. Leutenizing hormone (LH) and follicle stimulating hormone (FSH) levels were also determined from urine samples collected just before mid-cycle, based on median cycle lengths. Although menstrual cycles in this sample were highly variable, median cycle length was still useful in predicting timing of the pre-ovulatory hormone surges of LH and FSH. Frequency of irregular cycles did impact the successful capture of the LH and FSH peak values.     

Distributions of positive signals in pyrosequencing

Pyrosequencing is one of the important next-generation sequencing technologies. We derive the distribution of the number of positive signals in pyrograms of this sequencing technology as a function of flow cycle numbers and nucleotide probabilities of the target sequences. As for the distribution of sequence length, we also derive the distribution of positive signals for the fixed flow cycle model. Explicit formulas are derived for the mean and variance of the distributions. A simple result for the mean of the distribution is that the mean number of positive signals in a pyrogram is approximately twice the number of flow cycles, regardless of nucleotide probabilities. The statistical distributions will be useful for instrument and software development for pyrosequencing and other related platforms.     

Length distribution of sequencing by synthesis: fixed flow cycle model

Sequencing by synthesis is the underlying technology for many next- generation DNA sequencing platforms. We developed a new model, the fixed flow cycle model, to derive the distributions of sequence length for a given number of flow cycles under the general conditions where the nucleotide incorporation is probabilistic and may be incomplete, as in some single-molecule sequencing technologies. Unlike the previous model, the new model yields the probability distribution for the sequence length. Explicit closed form formulas are derived for the mean and variance of the distribution.     

Relations between apical structure and growth patterns in Pinus halepensis Mill,seedlings

Abstract

The process of primary growth in 2-year-old seedlings of 11 populations of Pinus halepensis Mill. is described. At the end of the first growing season one type of apical structure was observed: type-1, a tuft of primary needles placed close together, surrounding and protecting a meristematic apex.

At the end of the 2nd growing season, three types of apical structure were observed: type-1; type-2, a terminal winter bud; and type-3; a «bud» with characteristics of both type-1 and type-2.

Morphological observation along with an anatomical examination of the winter bud led to the conclusion that the definitive growth pattern in juvenile P. halepensis is monocyclic with a variable number of summer shoots. This growth pattern is reached by some P. halepensis populations in 3–4 years, by contrast, in other pine species two years are usually needed.

The populations studied differed both in growth potential (differences in number of cycles, ratio of first cycle to total growth, growth rates) and in the developmental stages of the apical meristem.

Four groups could be identified: (i) Morocco and Spain, (a limited growth, few cycles, a high ratio of 1st cycle to total growth, and growth in 2nd season almost entirely due to free growth); (ii) Algeria and Greece, (moderate to low growth, a large number of cycles, a low ratio of 1st cycle to total growth, and very early formation of apical structure with preformed primordia); (iii) Israel and Central Italy (a high growth, a large number of cycles, a medium ratio of 1st cycle to total growth, and early formation of apical structure with preformed primordia); (iiii) Greece, France and Italy, which was intermediate between group (i) and the other 2 groups.     

Effects on reproduction of estrous cycle variations, rectal temperatures and liveweights in mated Brahman cross heifers

Estrous cycle variations and the association of rectal temperature with reproductive measurements and liveweight were examined in 25-month-old 1 2 and 3 4 Brahman heifers (n = 88). The mean cycle length was longer in the 1 2 Brahmari (24.3 days) than in the 3 4 Brahman heifers (21.3 days) due to the length of estrus-metestrus, but the overall difference was not statistically significant. Cycle length was not influenced by cycle number or liveweight. Cycles were classified into 6 types: normal, short, long, anovulatory and those involving embryonic nortality and prolonged diestrus. Only 33.6% of 1 2 Brahman cycles and 36.1% of 3 4 Brahman cycles were of normal duration (18 to 24 days), and 13.3% of 1 2 Brahman and 11.6% of 3 4 Brahman cycles were classified as embryonic mortality cycles. On an individual animal basis, 25.0% and 31.8% of 3 4 Brahman heifers, respectively, had cycles in which embryonic mortality was suspected. Heifers that became pregnant were significantly (P < 0.01) heavier throughout mating and had significantly (P < 0.05) lower mean rectal temperatures. Heifers in which embryonic mortality had occurred were lighter and had significantly (P < 0.01) higher rectal temperatures than heifers in which embryonic mortality had not occurred. Correlations between rectal temperature and ambient temperature were nonsignificant after eliminating the effect of genotype, but rectal temperature was significantly (P < 0.01) negatively correlated with liveweight.     

Ovarian follicular dynamics during the estrous cycle in buffalo (Bubalus bubalis)

The growth, selection, regression and ovulation of ovarian follicles was ultrasonically monitored in 30 Murrah buffalo throughout a spontaneous estrous cycle during the breeding season (autumn). Examinations revealed that follicular growth during the estrous cycle occurs in waves; the buffalo showed 1-wave (3.3%, n = 1), 2-wave (63.3%, n = 19) or 3-wave (33.3%, n = 10) follicular growth. The first wave began at 1.00, 1.16 +/-0.50 and 1.10 +/- 0.32 d in buffalo with 1, 2 and 3 waves, respectively (ovulation = Day 0). The second wave appeared at 10.83 +/- 1.09 and 9.30 +/- 1.25 d (P < 0.01) for the 2 and 3 wave cycle animals, respectively. The third wave started at 16.80 +/- 1.22 d. Structural persistence of the first dominant follicle was longer in the 2- than 3-wave cycles (20.67 +/- 1.18 vs 17.90 +/- 3.47 d ; P < 0.05). The duration of the growth and static phases of the first dominant follicle differed between the 2 and 3 wave cycles (P < 0.05), whereas there were no differences in linear growth rates (cm/d). Two and three wave cycles differed (P < 0.05) with respect to the maximum diameter of both the first dominant follicle (1.51 +/- 0.24 vs 1.33 +/- 0.18 cm) and the ovulatory follicles (1.55 +/- 0.16 vs 1.34 +/- 0.13 cm). No relationship was found between dominant follicle development and the presence of either a CL or a previous dominant follicle in either ovary. Two and three wave cycles also differed with respect to the mean length of intervals between ovulation (22.27 +/- 0.89 vs 24.50 +/- 1.88 d; P < 0.01) and the mean length of luteal phases (10.40 +/- 2.11 vs 12.66 +/- 2.91 d; P < 0.05). These results demonstrate that buffalo have estrous cycles with 1, 2 or 3 follicular waves; that 2-wave cycles are the most common; and that the number of waves in a cycle is associated with the luteal phase and with estrous cycle length.     

Extended postpregnancy estrous cycles in fernale lion-tailed macaques

Past studies of female primate reproduction have focused on regularly cycling females, and thus the reproductive characteristics of females in other reproductive states (e.g., pregnant, or lactating) have rarely been investigated. In this study, data were collected on estrous swellings and sexual and proceptive behavior in six female lion-tailed macaques during recovery from lactational amenorrhea for the first three to five postpregnancy cycles. For these females, the length of the first lactational recovery swelling cycle averaged 81 days, nearly three times the length of cycles exhibited by nonparturient, isosexually housed females Actual swelling durations were also nearly three times the length of those seen in nonlactating females, and occupied a larger proportion of the cycle For most females, cycle duration and sexual and proceptive behavior declined progressively over successive cycles. The alpha female in each group accounted for the majority of copulations in the first three cycles, and this effect was pronounced in the first cycle. Extended postpregnancy cycles in this species may be related to female reproductive competition and /or a tactic to attract extra-group males. © 1993 Wiley-Liss, Inc.     

Waves of follicle development during the estrous cycle in sheep

The pattern of ovarian follicle development in maiden cyclic lambs was characterized using the definition of a follicle wave as the changes in the number of follicles among the days of the estrous cycle, as originally defined in cattle by Rajakoski in 1960. We also examined the steroid content relationships among follicles on Days 5 (Wave 1) and 14 (Waves 2 and 3) of the estrous cycle. In Experiment 1, the ovaries of 20 cyclic lambs (40 to 45 kg) were examined daily using transrectal ultrasonography for 1 or 2 estrous cycles (n = 31 cycles). The number of small (2 and 3 mm in diameter), medium (4 and 5 mm) and large (> or = 6 mm) follicles were aligned with the beginning and end of the average length estrous cycle and then compared among days. Identified follicles were defined as those that grew to > or = 4 mm and remained at > or = 3 mm for > or = 3 d. The number of identified follicles emerging (retrospectively identified at 2 or 3 mm) per ewe per day was also aligned with the average length estrous cycle. In Experiment 2, ewe lambs were ovariectomized on Day 5 (n = 6) or 14 (n = 5) of the estrous cycle, then follicle diameters and follicular fluid concentrations of estradiol and progesterone were compared among follicles. Data were analyzed by repeated measures ANOVA and compared among days using Fisher's LSD. In Experiment 1, either 2 (n = 10 cycles), 3 (n = 20 cycles) or 4 (n = 1 cycle) periods of emergence of identified follicles occurred during individual cycles, with estrous cycle lengths of 15.6 +/- 1.6, 16.1 +/- 1.1 and 17 d respectively. In animals with 2 or 3 periods of emergence of identified follicles, the total number of small, medium and large follicles differed (P < 0.05) among days of the estrous cycle showing a wave-like pattern. In Experiment 2, a single follicle collected on each of Days 5 and 14 of the cycle (6.2 +/- 0.2 and 3.9 +/- 0.2 mm in diameter) had a higher (P < 0.05) concentration of follicular fluid estradiol (36.2 +/- 4.4 and 50.9 +/- 21.6 ng/mL) than other follicles collected on the same day (next largest follicle: 4.3 +/- 0.3 and 3.5 +/- 0.4 mm; 4.3 +/- 0.9 and 18.2 +/- 6.7 ng/mL estradiol). The results showed that 1) there was a synchronous emergence of follicles associated with fluctuations in the number and size of follicles during the estrous cycle; 2) within a wave there was a hierarchy among follicles for diameter and steroid content; 3) ovarian follicle growth in ewe lambs occurred in 2 or 3 organized waves during the estrous cycle.     

Contamination of livestock due to the operation of a small waste incinerator: a case incident in Skutulsfjörður,Iceland, in 2010

Background

Declining fertility is a major concern for dairy farmers today. One explanation is shorter and weaker expression of oestrus in dairy cows making it difficult to determine optimal time for artificial insemination (AI). Chemical communication is of interest in the search for tools to detect oestrus or to synchronise or enhance oestrous periods. Pheromones, used in chemical communication within species, can influence reproduction in different ways. The aim here was to investigate whether oestrous cycle length, and duration and intensity of oestrous expression in dairy heifers could be manipulated through exposure to pheromones in oestrual substances from other females.

Methods

Beginning on day 16 of two consecutive control oestrous cycles, ten heifers of the Swedish Red Breed (SRB) were exposed to water. During the two following cycles the heifers were exposed to urine and vaginal mucus, obtained from cows in oestrus. Cyclicity parameters were monitored through hormone measurements, oestrus detection and ultrasonographic examination.

Results

We found no difference in cycle length or in duration of standing oestrus between control and treatment. We did, however, find a tendency of interaction between type of exposure (control or treatment) and cycle number within type of exposure for cycle length (p = 0.068), with the length differing less between the treatment cycles. We also found a tendency of effect of type of exposure on maximal concentration (p = 0.073) and sum of concentrations (p = 0.063) of LH during the LH surge, with values being higher for the control cycles. There were also significant differences in when the different signs of oestrus occurred and in the intensity of oestrous expression. The score for oedema and hyperaemia of external genitalia was significantly higher (p = 0.004) for the control cycles and there was also a significant interaction between type of exposure and time period for restlessness (p = 0.011), with maximum score occurring earlier for treatment cycles.

Conclusions

No evidence of altered oestrous cycle length or duration of oestrus after exposure of females to oestrous substances from other females was found. Expression of oestrus, and maybe also LH secretion, however, seemed influenced by the exposure, with the effect of treatment being suppressive rather than enhancing.     

Ovarian activity during normal and abnormal length estrous cycles in the goat

Ovarian and behavioral cyclicity were studied during 3-5 estrous cycles in a group of 10 multiparous, Nubian does. Changes in ovarian morphology throughout the estrous cycle were identified and photographed laparoscopically. Forty-eight estrous cycles were observed during the study and of these, 21 were abnormally short in duration (mean +/- SEM, 6.5 +/- 0.5 days). Mean duration of the estrous cycle for the 27 normal length cycles was 21.5 +/- 0.8 days. Eighteen/21 (86%) of the short cycles and 6/27 (22%) of the normal cycles were initiated during early breeding season (between September 1st and October 15th). There were no differences (P greater than 0.05) in the duration of estrus for the short (mean, 2.9 +/- 0.3 days) and normal (mean, 2.8 +/- 0.8 days) cycle groups. A total of 6/11 (55%) of the short duration cycles examined laparoscopically appeared to be anovulatory, but ovulation was observed in all normal cycles examined. The number of corpora lutea (CL) observed during normal length and short estrous cycles was 3.1 +/- 0.2 and 2.2 +/- 0.2, respectively (P less than 0.01). The cumulative percentage of does that showed morphological evidence of ovulation by the first, second and fifth day after the onset of estrus was 30%, 60% and 100%, respectively. Based on distinct differences in morphology and development, 2 types of CL were identified. The maximum visible diameter of Type I and Type II CL was 9.4 +/- 0.6 mm and 5.1 +/- 0.5 mm, respectively. These data document ovarian morphology throughout the normal and abnormal duration estrous cycle of the goat and indicate that 1) short estrous cycles observed early in the breeding season are associated with prematurely regressing CL or anovulation and 2) the ovary produces 2 morphologically distinct types of CL which differ not only in size and appearance, but also potentially in postovulatory function and longevity.     

Cyclicity and gestation length ofMacaca fascicularis

Menstrual cycle records were kept on all of the females in the colony for a period of 14 months. The mean cycle length was 30.8 days; the median, 33 days; and, the mode, 28 days. Cycles ranging from 27 to 32 days in length comprised 66.4% of all cycles. Regular cycles were scored on the basis of menses beginning within 2 days of a projected date based on an average of 6 previous cycles. Regular cycles were observed in 6.24% of the cases. The mean cycle length for regular cycles was 29.2 days. Forty-five percent of all females had regular cycles at least 70% of the time. The duration of menstrual flow for 150 cycles averaged 2.8 days. Menses ranged from 1 to 8 days in length, with 90.7% of the cases ranging from 1 to 4 days in length. For a given duration of menses, the percentage of cases of light flow increased as the end of the menstrual period was reached. The mean gestation length of 3 pregnancies was 164.4 days, with implantation bleeding beginning on day 19 of pregnancy and lasting from 4 to 9 days.This work supported by National Institute of Child Health and Human Development, Center for Population Research Contract No. 70-2061; USPHS Grant No. 5-PO6-RR 00366-04, to the Center for Laboratory Animal Resources, and, NIH Career Development Award No. 1-K4-HD35, 306-01. Journal Series Article No. 5668. Approved by the Director, Michigan State University Agricultural Experiment Station.     

Proliferation of human-derived osteoblast-like cells depends on the cycle number and frequency of uniaxial strain

We tested the hypothesis whether the number of applied load cycles and the frequency of uniaxial strain have an effect on proliferation of human bone derived osteoblast-like cells. A new approach was developed in order to differentiate between the effects of frequency and the effects of cycle number and strain duration. Monolayers of subconfluently grown cells were stretched in rectangular silicone dishes with cyclic predominantly uniaxial movement along there longitudinal axes. Strain was applied over 2 days varying the number of applied load cycles (4-3600) at a constant frequency (1Hz) or varying the frequency (0.1-30Hz) at a constant number of applied cycles (1800) or at a constant strain duration (5min). At a constant frequency, proliferative response increases (103%) with the number of applied cycles until a cycle number maximum (1800 cycles) was reached. 3600 cycles reduced cell number (43%) in contrast to the maximum. The variation of the frequency of applied strain tended to result in slight differences with regard to cell proliferation when cycle number was left constant. However, combined with an appropriate number of cycles there was an optimal frequency (1Hz) as stimulus for bone cell proliferation (84%). A higher frequency (30Hz) in combination with a high cycle number (9000) reduced cell number to control level (4%). This study demonstrates a frequency and cycle number dependent proliferative response of human osteoblast-like cells. It could be shown that effects of the frequency should not be considered separately from the effects of the cycle number.     

The Dynamics of Conjunctive and Disjunctive Boolean Network Models

For many biological networks, the topology of the network constrains its dynamics. In particular, feedback loops play a crucial role. The results in this paper quantify the constraints that (unsigned) feedback loops exert on the dynamics of a class of discrete models for gene regulatory networks. Conjunctive (resp. disjunctive) Boolean networks, obtained by using only the AND (resp. OR) operator, comprise a subclass of networks that consist of canalyzing functions, used to describe many published gene regulation mechanisms. For the study of feedback loops, it is common to decompose the wiring diagram into linked components each of which is strongly connected. It is shown that for conjunctive Boolean networks with strongly connected wiring diagram, the feedback loop structure completely determines the long-term dynamics of the network. A formula is established for the precise number of limit cycles of a given length, and it is determined which limit cycle lengths can appear. For general wiring diagrams, the situation is much more complicated, as feedback loops in one strongly connected component can influence the feedback loops in other components. This paper provides a sharp lower bound and an upper bound on the number of limit cycles of a given length, in terms of properties of the partially ordered set of strongly connected components.     

The effective number of a population that varies cyclically in size. I. Discrete generations

We consider a dioecious population having numbers of males and females that vary over time in cycles of length k. It is shown that if k is small in comparison with the numbers of males and females in any generation of the cycle, the effective population number (or size), N(e), is approximately equal to the harmonic mean of the effective population sizes during any given cycle. This result holds whether the locus under consideration is autosomal or sex-linked and whether inbreeding effective population numbers or variance effective population numbers are involved in the calculation of N(e). If, however, only two successive generations in the cycle are considered and the population changes in size between these generations, the inbreeding effective population number, N(eI), differs from the variance effective population number, N(eV). The mutation effective population number turns out to be the same as the number derived using calculations involving probabilities of identity by descent. It is also shown that, at least in one special case, the eigenvalue effective population number is the same as N(eV).