Tests of Occupancy Rates for Clustered Populations: Case Where the Cluster Sizes are Known

A modified chi-squared statistic Z is proposed for testing hypotheses about category occupancy rates for individuals distributed by clusters, when the cluster sizes are observed. This statistic is the Pearson chi-square statistic based on the individuals' counts divided by 1 + M* where M* is the mean number of other individuals per cluster per individual. The kind of alternative hypothesis for which the Z-based test compares favourably in power with the Pearson chi-square test based on the cluster frequencies is given. However, we prove that this latter test is more powerful than the former one as long as the equidistribution of the random choice vectors is assumed.     

基于GIS的稻田蜘蛛混合种群发生分析

在地理信息系统的支持下 ,对中国稻区 117个样点蜘蛛物种数与个体数进行空间插值 ,获得稻田蜘蛛混合种群数量专题地图和个体数量发生专题地图 .根据所得专题地图 ,分析了不同水稻种植区蜘蛛种群发生以及不同稻区的生态特征 .研究结果如下 :在北纬 35 .5°以南的水稻种植区域 ,蜘蛛种群与个体发生量较高 ,种群一般在 13种以上 ,个体数一般在每 10 0丛禾 10 0头以上 ;在北纬 35 .5°以北的水稻种植区域种群一般在 11种以下 ,个体数一般在每 10 0丛禾 47头以下 ;在北纬 35 .5°以南的水稻种植区域的年降雨量、年无霜期和 7月平均温度要高于在北纬 35 .5°以北的水稻种植区域 .在北纬 35 .5°以南的水稻种植区域的年日照时数要低于在北纬 35 .5°以北的水稻种植区域 .     

Some results of a survey of the macrobenthic fauna of the Ems-Dollard estuary (Eastern Dutch Wadden sea)

Summary The macrobenthic fauna of the Ems-Dollard estuary has been sampled in the tidal channels as well as on the tidal flats, by a method ensuring quantitative reliability. The size of the samples was such, that at least several specimens of the most abundant species would be cought. As far as possible, the sampling stations were laid out following a stratified random design.After treatment of the samples the following data were available: the species composition at every sampling station; the number of individuals of a certain species per unit area per sampling station and the ash-free dry weight of a certain species per unit area per sampling station.At the sampling stations in the southern and the western Dollard 8 parameters regarding the sediment were measured.To determine the structure of the macrobenthic fauna of the estuary three different cluster analyses were carried out. The first the presence/absence of species (all species being equally important); the second the number of individuals of a species per unit area, in which the abundant species play an dominant role, and the third using the ash-free dry weight of a species per unit area in which large animals play a dominant role as an input for the analyses.In general there was a good agreement between the structures resulting from the three analyses. The results of a factor analysis (used as a different grouping technique) carried out for sampling stations in the Dollard, confirmed the results of the cluster analyses.The overall structure of the macrobenthic fauna can be derived from maps in which the distribution of separate species is plotted. The estuary can be divided in two parts: a northern part, characterized by the occurrence of animals normally found in a more saline environment, and a southern part characterized by the occurrence of animals normally found in the more brackish parts of estuaries. The transitional zone lies between 53° 20 and 53° 25.The distribution pattern of several species permitted more detailed conclusions about the faunistic structure. These agreed well with the results of cluster and factor analysis. The two approaches to evaluate the data (plotting maps of distribution and pattern recognition analyses) appeared to confirm as well as to supplement each other.The almost completely absence of macrobenthic fauna in the S-E part of the Dollard could not be related to one or a combination of the 8 parameters measured, regarding the sediment. It was concluded that it is caused by factors related to the water, presumably by the waste water entering the estuary at Nieuw Statenzijl.A preliminary comparison with other estuaries reveals that the number of species and the actual species that were found during this investigation are normal for an estuary. The mean ash-free dry weight per unit area on the tidal flats in the northern part is low. This may be caused by the degree of exposition. In the middle part extremely low values occur, but the overall mean value (ca. 14 g/m²) is within the range of values normally to be expected. The mean value for the Dollard (ca. 5 g/m²) is lower than could be expected for this estuary.These conclusions are only preliminary and the items mentioned will have to be investigated more closely in future.     

Genetic structure and AFLP variation of remnant populations in the rare plant Pedicularis palustris (Scrophulariaceae) and its relation to population size and reproductive components

We investigated plant reproduction in relation to genetic structure, population size, and habitat quality in 13 populations of the rare biennial plant Pedicularis palustris with 3-28500 flowering individuals. We used AFLP (amplified fragment length polymorphism) profiles to analyze genetic similarities among 129 individuals (3-15 per population). In a cluster analysis of genetic similarities most individuals (67%) were arranged in population-specific clusters. Analysis of molecular variance indicated significant genetic differentiation among populations and among and within subpopulations (P < 0.001). Gene flow (N(e) m) was low (0.298). On average, plants produced 55 capsules, 17 seeds per fruit, and 42 seedlings in the following growing season. The number of seeds per capsule was independent of population size and of genetic variability. In contrast, the number of capsules per plant (P < 0.05) and the number of seedlings per plant (P < 0.05) were positively correlated with population size. The relation between population size and the number of seeds per plant was not significant (P = 0.075). The number of capsules and of seeds and seedlings per plant (P < 0.01) were positively correlated with genetic variability. Genetic variability was independent of actual population size, suggesting that historical population processes have to be taken into account, too. Stepwise multiple regressions revealed additional significant relationships of habitat parameters (soil pH, C:N ratio), vegetation composition, and standing crop on reproductive components. We conclude that populations of P. palustris are genetically isolated and that reproductive success most likely is influenced by population size, genetic variability, and habitat quality. Management strategies such as moderate grazing, mowing, and artificial gene flow should endeavor to increase population size as well as genetic variation.     

Termite colony ontogeny: supplemental data in the long-term assessment of reproductive lifespan, female neotenic production and colony size in Reticulitermes flavipes (Isoptera: Rhinotermitidae)

Reticulitermes flavipes (Kollar) colonies established by field-collected alates were reared in the laboratory for 11 years. Weights of members of each caste and full-colony censuses were performed regularly; the most recent 2003-2004 data are reported. Colonies averaged 11623.5 +/- 910 individuals, and with the exception of primary queens from one genetic lineage, mean weights for all castes had increased since 2001. Female replacement reproductives, or neotenics, developed to replace dead queens in clusters of either few, large individuals or many, small individuals. Regardless of cluster size, female neotenics comprised more reproductive biomass per colony than primary queens. The number and size of female neotenics was independent of colony size or time elapsed since a founding queen's death.     

岷江干旱河谷多苞蔷薇生长与繁殖特征

通过大面积野外踏查和样方调查,分析了岷江干旱河谷乡土灌木多苞蔷薇种群的分布、生长繁殖特征及其空间差异性.结果表明,多苞蔷薇广泛分布于岷江干旱河谷汶川绵褫至松潘镇江关约170 km长、海拔1 200～2 600 m的空间范围内,其株高、基径、年龄、冠幅、萌蘖株数和结实量的平均值分别为(123.33±3.13) cm、(12.49±0.40) mm、(3.34±0.16) a、(1.30±0.13) m²、(5.07±0.39)株/丛和(171.47±25.90)果/丛.随着海拔高度和纬度增加,其株高、基径、冠幅和结实量增加,而萌蘖株数没有显著变化.多苞蔷薇有性结实和无性萌蘖能力随环境空间变化的不匹配性与其生长密切相关,可能与多变环境下资源分配利用的平衡机制有关;以丛进行年龄统计,多苞蔷薇缺少幼龄个体,种群发展并不稳定,但随海拔高度升高,萌蘖株年龄结构均呈“金字塔”型,且较大龄级的萌株比例略增,显示出良好的种群持续性.综合分析发现,多苞蔷薇生长与繁殖的空间差异性是对干旱河谷长期适应的结果,既为种群持续提供了保证,也为种群扩大奠定了基础.     

Nuclear morphometry and AgNOR quantification: computerized image analysis on ovarian mucinous tumor imprints

OBJECTIVE: To determine the morphometric characteristics of nuclei and silver-stained nucleolar organizer regions (AgNORs) on cytologic imprints and their value in differential cytodiagnosis of benign, atypical proliferative (borderline) and malignant ovarian mucinous tumors. STUDY DESIGN: Forty-six mucinous ovarian tumor imprints (16 benign, 15 borderline, 15 malignant), were analyzed. Nuclear area, outline, "shape factor" and "form factor" were measured on Papanicolaou-stained smears. AgNOR quantification included 7 variables related to the number and area of single, cluster, total and relative AgNOR content per nucleus and the size distribution of AgNORs. RESULTS: Nuclear area and shape factor allowed distinguishing borderline and malignant tumors. The nuclear area in benign tumors was larger than that in borderline tumors; malignant tumors had the highest values. Single and cluster AgNORs were statistically significantly different in borderline tumors compared with malignant tumors, except for the cluster AgNOR area. The total AgNOR area, number and relative area increased from benign through malignant tumors, with statistically significant differences among all groups. By AgNOR size distribution, small AgNORs discriminate malignant from borderline and benign tumors. CONCLUSION: Combining nuclear morphometry and AgNOR analysis on cytologic imprints could be a diagnostically useful method in the assessment of mucinous ovarian tumors.     

Wintering areas predict age‐related breeding phenology in a migratory passerine bird

Understanding connections between breeding, stopover and wintering grounds for long‐distance migratory birds can provide important insight into factors influencing demography and the strength of carry‐over effects among various periods of the annual cycle. Using previously described, multi‐isotope (δ¹³C, δ¹⁵N, δ²H) feather isoscapes for Africa, we identified the most probable wintering areas for house martins Delichon urbica breeding at Badajoz in southwestern Spain. We identified two most‐probable wintering areas differing in isotopic signature in west Africa. We found that the probability to winter in the isotopic cluster two was related to age and sex of individuals. Specifically, experienced males (i.e. two years or older) winter in the isotopic cluster two with a greater probability than experienced females, whereas first‐year females winter in the isotopic cluster two with a greater probability than first‐year males. In addition, wintering area was correlated with breeding phenology, with individuals wintering in the isotopic cluster two initiating their clutches earlier than those wintering in the isotopic cluster one. For birds wintering in the isotopic cluster two, there was no relationship between age and clutch initiation date. In contrast, young birds wintering in the isotopic cluster one initiated their clutches earlier than experienced birds wintering in this area. There was no significant correlation between wintering area and clutch size or the number of fledglings produced. We hypothesize that the relationship among social status, population density and winter habitat quality should be the most important driver of the carry‐over effect we found for this population.     

Carabid beetle diversity and mean individual biomass in beech forests of various ages

Carabid beetle diversity and mean individual biomass (MIB) were analysed in three different successional stages of beech tree stands (60, 80 and 150 years old). Carabid beetles were captured using pitfall traps placed at nine sites (three per age class) in the Papuk Mountain of East Croatia during 2008. A cluster analysis identified three groupings that corresponded to the beech age classes. MIB values increased with stand age, ranging from 255 in 60-year-old stand to 537 in the oldest forests. The 80-year-old stand showed the highest species richness and diversity values. With respect to species composition, large species such as Carabus scheidleri and Carabus coriaceus were dominant only in the oldest forests. Furthermore, species that overwinter in the larval stage were more abundant in the oldest forests (45% of the total number of individuals from the 150-year-old stand) than in the younger ones (20% of individuals from 60-year-old, and 22% of individuals from 80-year-old stands). Our results showed that the analyses of species composition and life history traits are valuable for estimating the conservation values of older forests. Although the investigated sites form part of a continuous forested area and are only a couple of kilometres apart, MIB values detect significant differences associated with forest age and can be a useful tool in evaluating the degree to which a forest reflects a natural state.     

Gradients in the number of species at reef-seagrass ecotones explained by gradients in abundance

Gradients in the composition and diversity (e.g. number of species) of faunal assemblages are common at ecotones between juxtaposed habitats. Patterns in the number of species, however, can be confounded by patterns in abundance of individuals, because more species tend to be found wherever there are more individuals. We tested whether proximity to reefs influenced patterns in the composition and diversity ('species density' = number of species per area and 'species richness' = number of species per number of individuals) of prosobranch gastropods in meadows of two seagrasses with different physiognomy: Posidonia and Amphibolis. A change in the species composition was observed from reef-seagrass edges towards the interiors of Amphibolis, but not in Posidonia meadows. Similarly, the abundance of gastropods and species density was higher at edges relative to interiors of Amphibolis meadows, but not in Posidonia meadows. However, species richness was not affected by proximity to reefs in either type of seagrass meadow. The higher number of species at the reef-Amphibolis edge was therefore a consequence of higher abundance, rather than species richness per se. These results suggest that patterns in the composition and diversity of fauna with proximity to adjacent habitats, and the underlying processes that they reflect, likely depend on the physiognomy of the habitat.     

Sample design effects in landscape genetics

An important research gap in landscape genetics is the impact of different field sampling designs on the ability to detect the effects of landscape pattern on gene flow. We evaluated how five different sampling regimes (random, linear, systematic, cluster, and single study site) affected the probability of correctly identifying the generating landscape process of population structure. Sampling regimes were chosen to represent a suite of designs common in field studies. We used genetic data generated from a spatially-explicit, individual-based program and simulated gene flow in a continuous population across a landscape with gradual spatial changes in resistance to movement. Additionally, we evaluated the sampling regimes using realistic and obtainable number of loci (10 and 20), number of alleles per locus (5 and 10), number of individuals sampled (10–300), and generational time after the landscape was introduced (20 and 400). For a simulated continuously distributed species, we found that random, linear, and systematic sampling regimes performed well with high sample sizes (>200), levels of polymorphism (10 alleles per locus), and number of molecular markers (20). The cluster and single study site sampling regimes were not able to correctly identify the generating process under any conditions and thus, are not advisable strategies for scenarios similar to our simulations. Our research emphasizes the importance of sampling data at ecologically appropriate spatial and temporal scales and suggests careful consideration for sampling near landscape components that are likely to most influence the genetic structure of the species. In addition, simulating sampling designs a priori could help guide filed data collection efforts     

The prevalence of previously undiagnosed leprosy in the general population of northwest bangladesh

Background

The prevalence of previously undiagnosed leprosy (PPUL) in the general population was determined to estimate the background level of leprosy in the population and to compare this with registered prevalence and the known PPUL in different levels of contacts of leprosy patients.

Methodology and Principal Findings

Multistage cluster sampling including 20 clusters of 1,000 persons each in two districts with over 4 million population. Physical examination was performed on all individuals. The number of newly found leprosy cases among 17,862 people above 5 years of age from the cluster sample was 27 (19 SLPB, 8 PB2-5), giving a PPUL rate of 15.1 per 10,000.

Conclusions and Significance

PPUL in the general population is six times higher than the registered prevalence, but three times lower than that in the most distant subgroup of contacts (neighbour of neighbour and social contacts) of leprosy patients in the same area. Full village or neighbourhood surveys may be preferable to contact surveys where leprosy is highly endemic.     

A technique for quantitative estimation of small mammals traversing water obstacles

A new method for quantitative study of small mammals swimming across water obstacles was developed. A line of 25 traps was installed on either poles or boards (“rafts”) with anchors at a distance of 20–25 m from the bank and with 10-m distances between the items. The study was performed upstream along the Ilych River in August 2013. A total of 300 trap/day were accumulated. Twenty-four small mammal individuals of 8 species were captured. Their relative abundance was estimated as the number of individuals per 100 trap/day. It was found experimentally that floating poles neither repel nor attract animals. When an individual accidentally finds a floating pole, it climbs up and explores it for some time. The number of animals per total length of rafts per time unit can be suggested as an index of intensiveness of migration across a water obstacle. In the area studied, the number of small mammals of various species crossing the river was estimated at 26.7 individuals per 1 km/day. A length of 5 m for floating poles/boards and installation of two traps at the ends of an item is suggested to be used.     

One or two cameras per station? Monitoring jaguars and other mammals in the Amazon

Camera trapping has become a popular technique to monitor carnivore populations due to its usefulness in estimating abundance. Nevertheless, there are a number of problems associated with study design which are motivating researchers to search for a compromise that ensures improvement of precision while being cost-effective. We have used data from a capture?Crecapture study in a forested area in central Brazil to evaluate the effectiveness of using one versus two cameras per trapping station for determining jaguar (Panthera onca) density and capture rates of several other mammals. The capture rate for the jaguar and other species recorded with only one camera was lower than that with two cameras. The number of jaguars identified using photos from one camera ranged between six and seven animals, but reached ten individuals when two-camera sets were used where pictures of both flanks could be positively individualized. These differences, combined with different estimates of effective sampled area size, resulted in jaguar densities estimates ranging from 2.18 to 5.40 and 3.99?individuals/100?km² when one and two cameras were used per station, respectively (using the half-MMDM and Heterogeneity model). Based on our results, we recommend the use of two cameras per station for jaguar density monitoring to ensure reasonable levels of reliability and accuracy of estimates despite a small sample size.     

Source and sink dynamics of density-dependent otter (<Emphasis Type="Italic">Lutra lutra</Emphasis>) populations in rivers of central Finland

Long-term studies were carried out in central Finland between 1985 and 2003 to examine the temporal and spatial variation in the density of otter populations. Snow tracking was used to estimate the total population and the number of litters in the study area. In total 52 otters, including 16 cubs in 11 litters, lived in the study area (1,650 km²) in 2002–2003. The otter population clearly increased during the study period. The increase in density of the otter population was sigmoid, indicating that the population had reached the local carrying capacity. The density of the population was 0.12 individuals per river ha in 1985 and 0.29 individuals per river ha in 2002. The number of cubs per litter decreased when the density of the population increased. Density-dependent offspring production, together with the auto-correlation function of growth rate, indicates intraspecific competition in otter populations. Otters in a few river systems produced most of the cubs, creating several small source populations in the entire study area. Otters in secondary (sink) habitats had a low reproduction rate. Most otters lived in river systems with large lake surfaces. The number or area of lakes within the river system correlated positively with the total number of otters, litters and cubs in the river system. The six river systems (out of 16) with the largest water area of lakes produced 81.2% of all cubs born in the study area. However, the population growth rate per river hectare or per river kilometre was equal in all kinds of river systems. Thus, among local otter populations in central Finland, a source–sink system between different habitats seems to be prevalent.     

Evaluation of a mass screening program for lysinuric protein intolerance in the northern part of Japan

Lysinuric protein intolerance (LPI:MIM 222700) is an autosomal recessive disease characterized by defective transport of the dibasic amino acids. We recently reported a local cluster of LPI in the northern part of Japan (Koizumi et al., 2000). Mutational analysis of the LPI patients in this local cluster revealed they were exclusively homozygous for the R410X mutation. The effectiveness of early intervention with citrulline therapy (200 mg/kg per day) and protein restriction (1.5 g/kg per day) was confirmed in these patients. Mass screening was conducted in 4,568 newborn babies between 1999 and 2002, which was estimated to cover 100% of almost all newborns delivered in the screened area. Forty heterozygous newborns were found (0.88%), leading to an estimated incidence of LPI of 1:51,984. The number of people that required screening to detect one case was 51,984, and the cost for mass screening was 30 cents/person (a total of dollars 15,600). This is comparable to, or even less than, the cost of currently screened diseases in Japan. Therefore, we conclude that a mass screening program for LPI can be introduced effectively and economically into an area where an LPI cluster is located as the result of a founder mutation.     

A chromosome 8 gene-cluster polymorphism with low human beta-defensin 2 gene copy number predisposes to Crohn disease of the colon

Defensins are endogenous antimicrobial peptides that protect the intestinal mucosa against bacterial invasion. It has been suggested that deficient defensin expression may underlie the chronic inflammation of Crohn disease (CD). The DNA copy number of the beta-defensin gene cluster on chromosome 8p23.1 is highly polymorphic within the healthy population, which suggests that the defective beta-defensin induction in colonic CD could be due to low beta-defensin-gene copy number. Here, we tested this hypothesis, using genomewide DNA copy number profiling by array-based comparative genomic hybridization and quantitative polymerase-chain-reaction analysis of the human beta-defensin 2 (HBD-2) gene. We showed that healthy individuals, as well as patients with ulcerative colitis, have a median of 4 (range 2-10) HBD-2 gene copies per genome. In a surgical cohort with ileal or colonic CD and in a second large cohort with inflammatory bowel diseases, those with ileal resections/disease exhibited a normal median HBD-2 copy number of 4, whereas those with colonic CD had a median of only 3 copies per genome (P=.008 for the surgical cohort; P=.032 for the second cohort). Overall, the copy number distribution in colonic CD was shifted to lower numbers compared with controls (P=.002 for both the surgical cohort and the cohort with inflammatory bowel diseases). Individuals with < or = 3 copies have a significantly higher risk of developing colonic CD than did individuals with > or = 4 copies (odds ratio 3.06; 95% confidence interval 1.46-6.45). An HBD-2 gene copy number of < 4 was associated with diminished mucosal HBD-2 mRNA expression (P=.033). In conclusion, a lower HBD-2 gene copy number in the beta-defensin locus predisposes to colonic CD, most likely through diminished beta-defensin expression.     

Molecular simulation study of assembly of DNA-grafted nanoparticles: effect of bidispersity in DNA strand length

In this paper, we use molecular dynamics simulations to study the assembly of DNA-grafted nanoparticles to demonstrate specifically the effect of bidispersity in grafted DNA strand length on the thermodynamics and structure of nanoparticle assembly at varying number of grafted single-stranded DNA (ssDNA) strands and number of guanine/cytosine (G/C) bases per strand. At constant number of grafted ssDNA strands and G/C nucleotides per strand, as bidispersity in strand lengths increases, the number of nanoparticles that assemble as well as the number of neighbours per particle in the assembled cluster increases. When the number of G/C nucleotides per strand in short and long strands is equal, the long strands hybridise with the other long strands with higher frequency than the short strands hybridise with short/long strands. This dominance of the long strands leads to bidisperse systems having similar thermodynamics to that in corresponding systems with monodisperse long strands. Structurally, however, as a result of long–long, long–short and short–short strand hybridisation, bidispersity in DNA strand length leads to a broader inter-particle distance distribution within the assembled cluster than seen in systems with monodisperse short or monodisperse long strands. The effect of increasing the number of G/C bases per strand or increasing the number of grafted DNA strands on the thermodynamics of assembly is similar for bidisperse and monodisperse systems. The effect of increasing the number of grafted ssDNA strands on the structure of the assembled cluster is dependent on the extent of strand bidispersity because the presence of significantly shorter ssDNA strands among long ssDNA strands reduces the crowding among the strands at high grafting density. This relief in crowding leads to larger number of strands hybridised and as a result larger coordination number in the assembled cluster in systems with high bidispersity in strands than in corresponding monodisperse or low bidispersity systems.     

The life history of Ranunculus glacialis, an arctic-alpine perennial herb, in Finnish Lapland

Dynamics and performance of established individuals of Ranunculus glacialis at the time of peak flowering were monitored in a mountain area in Finnish Lapland for five years (1982–1986). The plants reproduced only sexually, and their spatial distribution in 40 1-m² quadrats was clumped. During the study period the mean density rose from 8.5 to 10.3 individuals m⁻². The mean annual growth rate and birth rate of the population was 4% and 8.5%, respectively. The mean annual death rate of established individuals was 3.7%. The estimated mean life expectancy of an established individual was 27 yr. Death rate per quadrat was positively related to R. glacialis density, but birth rate per quadrat was negatively related to the percentage cover of stones per quadrat. High R. glacialis density per quadrat had negative effects, but high nitrogen availability had positive effects on the number of leaves per individual. An important factor reducing flowering was small rodent herbivory. In the same genets, the correlation between the number of leaves per individual in year t and the number of flowers per individual in year t+4 was significant. The below-ground biomass of R. glacialis comprised about 70% of the total biomass, and there was a close correlation between the above- and the below-ground biomass of an individual. The individuals flowered abundantly each year and produced a great number of small-sized achenes.     

A general procedure for predicting rates of inbreeding in populations undergoing mass selection

Predictions of rates of inbreeding (DeltaF), based on the concept of long-term genetic contributions assuming the infinitesimal model, are developed for populations with discrete or overlapping generations undergoing mass selection. Phenotypes of individuals are assumed to be recorded prior to reproductive age and to remain constant over time. The prediction method accounts for inheritance of selective advantage both within and between age classes and for changing selection intensities with age. Terms corresponding to previous methods that assume constant selection intensity with age are identified. Predictions are accurate (relative errors < or =8%), except for cases with extreme selection intensities in females in combination with high heritability. With overlapping generations DeltaF reaches a maximum when parents are equally distributed over age classes, which is mainly due to selection of the same individuals in consecutive years. DeltaF/year decreases much more slowly compared to DeltaF/generation as the number of younger individuals increases, whereas the decrease is more similar as the number of older individuals increases. The minimum DeltaF (per year or per generation) is obtained when most parents were in the later age classes, which is mainly due to an increased number of parents per generation. With overlapping generations, the relationship between heritability and DeltaF is dependent on the age structure of the population.