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Multicentric reference values: shared reference limits.

In order to obtain shared reference limits, three laboratories in the same geographical area with a homogeneous population have developed a proposal to produce multicentric reference values. The strategy simulates a virtual laboratory, actually formed by the laboratories involved; the reference limits produced in the virtual laboratory are in fact derived from the blend of reference values obtained by each laboratory. Each laboratory has chosen its own reference sample and has measured the biochemical quantities under study. Reference individuals (n = 171) and 15 biochemical quantities among the most measured in clinical laboratories were selected. The reference values obtained in each laboratory were blended when permitted by the Harris & Boyd test (Clin Chem 1990; 36:265-70). The multicentric reference limits obtained by the virtual laboratory for each quantity were estimated according to the recommendations of the International Federation of Clinical Chemistry. For each quantity, each laboratory, with the results observed in their reference sample, estimated the diagnostic specificity, using as cut-off values the corresponding multicentric reference limits. Each observed value of diagnostic specificity was compared with the theoretical diagnostic specificity value, equal to 0.975, that should be observed when a reference limit is used as cut-off value. The multicentric reference limits obtained by the virtual laboratory are valid in all cases with the exception of the upper reference limit for the concentrations of calcium(II) and urate in serum in one of the laboratories.

Adult↗

Radical cystectomy: extending the limits of pelvic lymph node dissection improves survival for patients with bladder cancer confined to the bladder wall.

PURPOSE: We assess the influence of the limits of pelvic lymph node dissection on survival following radical cystectomy for bladder cancer. MATERIALS AND METHODS: From January 1990 to September 1997, 194 patients underwent radical cystectomy without prior treatment. Between March 1993 and September 1997, 126 consecutive patients underwent radical cystectomy with extended pelvic lymph node dissection beginning at the bifurcation of the aorta, including the common and external iliac vessels, presacral nodes and obturator fossa. Between January 1990 and March 1993, 68 consecutive patients underwent radical cystectomy, with limited pelvic lymph node dissection beginning at the bifurcation of the common iliac vessels, including the external iliac vessels and obturator fossa. The cystectomy procedure remained unchanged throughout this period and 1 surgeon performed all procedures. RESULTS: A total of 117 patients had tumors confined to the bladder wall (stage pT3a or less) and 77 had tumors penetrating beyond the bladder into perivesical fat or adjacent structures (stage pT3b or greater). The prevalence of patients with tumors penetrating the bladder was higher in the extended dissection group (42.9 versus 33.8% limited dissection). The incidence of lymphatic involvement was 26.2% and slightly higher in the extended than the limited dissection group. There was a modest improvement in the 5-year recurrence-free survival for the extended dissection group (62 versus 56% limited dissection, p = 0.33), and a substantial improvement for the subgroups with tumors confined to the bladder wall (tumor stage pT3a or less) (85 versus 64%, p <0.02) and without lymph node metastasis (stage pT3a or less, pN0) (90 versus 71%, p <0.02). Accordingly, extended pelvic lymph node dissection reduced the 5-year probabilities for pelvic and distant metastasis (2 versus 7% limited dissection, p = 0.17 and 10 versus 21%, p = 0.15, respectively) for patients with tumors confined to the bladder wall (stage pT3a or less). Survival was similar for patients with pT3b or greater tumor. CONCLUSIONS: This retrospective analysis suggests that extending the limits of pelvic lymph node dissection from the bifurcation of the common iliac vessels to the bifurcation of the aorta improves the recurrence-free survival rate for patients undergoing radical cystectomy for bladder cancer confined to the bladder wall (stage pT3a or less).

Adult↗

Biological monitoring and Biological Limit Values (BLV): the strategy of the European Union.

Occupational standards concerning allowable concentrations of chemical compounds in the ambient air of workplaces have been established in several countries worldwide. With the integration of the European Union (EU), there has been a need of establishing harmonised Occupational Exposure Limits (OEL). The European Commission Directive 95/320/EC of 12 July 1995 has given the tasks to a Scientific Committee for Occupational Exposure Limits (SCOEL) to propose, based on scientific data and where appropriate, occupational limit values which may include the 8-h time-weighted average (TWA), short-term limits/excursion limits (STEL) and Biological Limit Values (BLVs). In 2000, the European Union issued a list of 62 chemical substances with Occupational Exposure Limits. Of these, 25 substances received a "skin" notation, indicating that toxicologically significant amounts may be taken up via the skin. For such substances, monitoring of concentrations in ambient air may not be sufficient, and biological monitoring strategies appear of potential importance in the medical surveillance of exposed workers. Recent progress has been made with respect to formulation of a strategy related to health-based BLVs.

Air Pollutants, Occupational↗

Chronic kidney disease and functional limitation in older people: health, aging and body composition study.

OBJECTIVES: To assess whether chronic kidney disease (CKD) is independently associated with incident physical-function limitation. DESIGN: Prospective cohort study. SETTING: Two sites: Pittsburgh, Pennsylvania, and Memphis, Tennessee. PARTICIPANTS: Two thousand one hundred thirty-five men and women aged 70 to 79 without functional limitation at baseline from the Health, Aging and Body Composition Study. MEASUREMENTS: Functional limitation was defined as difficulty in walking one-quarter of a mile or climbing 10 steps on two consecutive reports 6 months apart (in the same function). Kidney function was measured using serum cystatin C. Estimated glomerular filtration rate (eGFR), using the Modification of Diet in Renal Disease formula (<60 versus > or =60 mL/min per 1.73 m(2)), was a secondary predictor. Muscle strength, lean body mass according to dual energy x-ray absorptiometry, comorbidity, medication use, and inflammatory markers were evaluated as covariates. RESULTS: Persons in the highest (> or =1.13 mg/L) quartile of cystatin C experienced a significantly higher risk of developing functional limitation than those in the lowest (<0.86 mg/L) quartile (hazard ratio (HR)=1.70, 95% confidence interval (CI)=1.40-2.07). The association between the fourth cystatin C quartile and functional limitation remained after adjustment for demographics, lean body mass, comorbidity, muscle strength, and gait speed (HR=1.41, 95% CI=1.13-1.75), although the association was attenuated after adjustment for markers of inflammation (HR=1.15, 95% CI=0.90-1.46). Similar results were found for eGFR less than 60 mL/min per 1.73 m(2), although the association with functional limitation remained after adjustment for inflammatory markers (HR=1.30, 95% CI=1.08-1.56). CONCLUSION: CKD is associated with the development of functional impairment independent of comorbidity, body composition, and tests of strength and physical performance. The mechanism may be related to a heightened inflammatory state in CKD.

Aged↗

Distinct expression of adhesion molecules on skin fibroblasts from patients with diffuse and limited systemic sclerosis. A pilot study.

OBJECTIVE: . Systemic sclerosis (SSc) is characterized by excessive production of collagen and other components of the extracellular matrix (ECM) by fibroblasts. The ECM receptors, integrins and CD44 (hyaluronan receptor), play a key role in the homeostasis of connective tissue and may also have a role in the pathogenesis of fibrosis. We investigated the expression of integrins and CD44 on skin fibroblasts from patients with limited and diffuse SSc. METHODS: We studied 13 patients with SSc, 8 with limited SSc, and 5 with diffuse SSc, and 8 control subjects. Fibroblasts were isolated and cultured from biopsies taken from the lesional skin of the second finger of the left hand. Cell-surface expression of beta1, beta3, alpha1-alpha6, alphav integrins, and CD44 was evaluated by immunofluorescence and flow cytometry analysis. RESULTS: Fibroblasts from limited SSc showed significantly decreased expression of alpha2, alpha3, alpha4 integrins, while diffuse SSc fibroblasts had significantly reduced expression of alpha5, alphav integrins, and CD44. Diffuse SSc also had significantly increased expression of alpha6 integrin on fibroblasts. In controls, the expression of alpha4 and alpha5 correlated positively, while in limited and diffuse SSc it did not. CONCLUSION: This is the first study evaluating separately the expression of adhesion molecules on skin fibroblasts from limited and diffuse subsets of SSc. We detected a distinct pattern of expression with decrease of collagen and fibronectin receptors in limited SSc, and downregulation of fibronectin and hyaluronan receptors in diffuse SSc. These results suggest that changes of fibroblasts/ECM interactions and mechanisms underlying the pathogenesis of fibrosis in SSc may differ in the single subset of the disease.

Cells, Cultured↗

Mobility limitation among persons aged > or =40 years with and without diagnosed diabetes and lower extremity disease--United States, 1999-2002.

Diabetes increases the risk for mobility limitation, especially among older persons. Lower extremity disease (LED), which includes peripheral arterial disease (PAD) and peripheral neuropathy (PN), also increases the risk for mobility limitation. To assess the prevalence of mobility limitation among persons with diagnosed diabetes, persons with LED, and persons with both or neither condition, CDC analyzed data from the National Health and Nutrition Examination Survey (NHANES) 1999-2002 for adults aged > or =40 years. This report summarizes the preliminary findings, which indicated that the national prevalence of mobility limitation is higher among persons with either diagnosed diabetes or LED than those without the conditions, and that adults with both conditions have a higher prevalence of mobility limitation than those with either condition alone. Monitoring the prevalence of diabetes, LED, and associated risk factors and identifying effective LED prevention strategies will help reduce the burden of mobility limitation in the United States.

Adult↗

Effect of alendronate on limited-activity days and bed-disability days caused by back pain in postmenopausal women with existing vertebral fractures. Fracture Intervention Trial Research Group.

BACKGROUND: Women with new vertebral fractures have an increased risk of back pain and functional limitation because of back pain. Alendronate sodium treatment reduces the risk of new vertebral fracture by 50% in postmenopausal women with osteoporosis. OBJECTIVE: To determine the effect of alendronate therapy on days affected by back pain in postmenopausal women with existing vertebral fractures. DESIGN: Three-year, placebo-controlled, randomized, double-blind study. SETTING: Fifteen university-based research clinics in the United States. PARTICIPANTS: A total of 2027 postmenopausal women aged 55 to 81 years with low femoral neck bone density and a preexisting vertebral fracture. INTERVENTION: Alendronate sodium (5 mg/d for 2 years and 10 mg/d for the third year) or placebo. MAIN OUTCOME MEASURES: Occurrence and severity of back pain, number of days with back pain, and number of days of bed rest or limited activity because of back pain during 3 years of follow-up. RESULTS: Irrespective of treatment assignment, women with new, clinically recognized vertebral fractures during follow-up had an increased risk of days of bed disability and days of limited activity because of back pain after the fracture. Women receiving alendronate reported an average of 3.2 fewer days of bed rest (P = .001) and 11.4 fewer days of limited activity (not including days of bed rest) because of back pain (P = .04) during follow-up than those receiving placebo. In the alendronate group, relative to the placebo group, there was a reduced risk of 1 or more bed-rest days (relative risk, 0.68; 95% confidence interval, 0.53-0.87), of 7 or more bed-rest days (0.44; 0.30-0.64), and of 7 or more limited-activity days (0.87; 0.76-0.99). There were no statistically significant differences between treatment groups in the frequency of days of back pain or increases in back-related disability between baseline and study end. CONCLUSION: In postmenopausal women with preexisting vertebral fracture, alendronate therapy for 3 years reduced the number of days of bed disability and days of limited activity caused by back pain.

Activities of Daily Living↗

Determining a 'safe' high-mass limit in matrix-assisted laser desorption/ionisation time-of-flight mass spectra of coal derived materials with reference to instrument noise

Three methods for determining a 'safe' estimate for high-mass limits of MALDI spectra of coal derived liquids were explored, using a sample of coal-tar pitch and its pyridine-insoluble fraction. Co-addition of increasing numbers of single-shot spectra (10, 30, 50 and 100 pulses) showed visually observable reductions in noise levels, consistent with robust and statistically meaningful signals. Three separate types of post-acquisition calculation were used to identify high-mass limits of the spectra. (i) A literature method indicated high-mass limits similar to those observed visually-as a shift from baseline at the highest masses, nearly 350 000 u for the coal tar pitch and about 390 000 u for its pyridine insoluble fraction. (ii) Comparing instrument signal with pre-selected multiples of the standard deviation, upper mass estimates of between 40-60 000 u for the coal-tar pitch and about 95 000 u for its pyridine-insoluble fraction were found. (iii) Calculation of the slope was used to identify 'lift-off' of the spectrum from baseline. The angle between the smoothed spectrum and the baseline was matched to a pre-selected value (e.g. 0.5 degrees and 1 degrees ). However, the arbitrary specification of the key parameter did not establish this last method on a firm basis. The choice of a criterion for estimating high-mass limits of MALDI spectra remains a semi-quantitative procedure; a reasonably conservative high-mass limit may be estimated by comparison of signal with five times the standard deviation. However, evaluation of size exclusion chromatograms of the present samples using polystyrene standards suggests that molecular mass distributions of pitch samples arrived at by MALDI mass spectrometry are, at least partly, determined by the limitations of available instruments. Copyright 1999 John Wiley & Sons, Ltd.

Journal Article↗

Limits of detection of polydimethylsiloxane in (29)Si NMR spectroscopy.

Limits of detection for neat poly(dimethylsiloxane) (PDMS), as detected via (29)Si NMR spectroscopy, were determined by the IUPAC, graphical, and propagation of errors methods from calibration curves obtained using a 7.05 Tesla superconducting magnet equipped with a magic angle spinning (MAS) NMR probe. Under conditions permitting full relaxation of the nuclear spins (recycle time >150 sec), the limit of detection with 128 transients was 1.7, 2.2, and 3.7 mg PDMS (23, 30, and 50 micromoles elemental Si) for the IUPAC, graphical, and propagation of errors methods, respectively. A higher limit of detection results when additional sources of uncertainty are considered. From the strict dependence of the limit of detection on the inverse of the square root of the number of transients signal-averaged, it is possible to extrapolate to a limit of detection of 183 microg PDMS (2.47 micromoles elemental Si) for a 24-hr signal averaging period. This limit of detection is 3 orders of magnitude higher than silicon levels found in human blood.

Biocompatible Materials↗

Are there more than cross-sectional relationships of social support and support networks with functional limitations and psychological distress in early rheumatoid arthritis? the European Research on Incapacitating Diseases and Social Support Longitudinal Study.

OBJECTIVE: To investigate whether greater social support and support network are cross-sectionally associated with less functional limitations and psychological distress in patients with early rheumatoid arthritis (RA); whether this association is constant over time; and whether increases in social support or support network are associated with less functional limitations and psychological distress. METHODS: Subjects were from the European Research on Incapacitating Diseases and Social Support cohort and had early RA. Social support, support network, functional limitations (Health Assessment Questionnaire), and psychological distress (General Health Questionnaire) were assessed annually. Variance and covariance analyses with repeated measures were performed. RESULTS: A total of 542 subjects were assessed for 3 years. On average, patients with a greater amount of specific social support or a stronger specific support network experienced less functional limitation and less psychological distress. Changes in a given subject's functional limitations and psychological distress did not depend on his or her baseline social support or support network. Neither social support nor support network change over time. CONCLUSION: There may be a cross-sectional link between specific social support or support network and functional limitations and psychological distress, but no longitudinal association could be evidenced.

Adult↗

Transient response of Enterobacter aerogenes under a dual nutrient limitation in a chemostat.

Utilizing a chemostat with a dual nutrient limitation of nitrogen and phosphate, we examined the transient response of the culture following a pulse of one of the limiting nutrients (ammonia). This method provided quantitative evidence that cells can be grown under dual nutrient limitation. Furthermore, the pattern of response was consistent with the hypothesis that phosphate limitation restricts nucleic acid synthesis in the cell and that nitrogen limitation restricts protein synthesis. The net result is that under a phosphate limitation there is a restricted biosynthetic capacity which we feel is closely associated with the RNA content of the cell.

Culture Media↗

Twenty-five years of clinical research for patients with limited-stage small cell lung carcinoma in North America.

BACKGROUND: To determine the changes in clinical trials and outcomes of patients with limited-stage small cell lung carcinoma (SCLC) treated on Phase III randomized trials initiated in North America between 1972 and 1992. METHODS: Phase III trials from 1972 to 1992 for patients with limited-stage SCLC were identified. Patients with limited-stage SCLC treated during a similar time interval were also evaluated in the Surveillance, Epidemiology, and End Results (SEER) database. Trends were tested in the number of trials, in the number and gender of patients entered on trial, and in survival duration over time. RESULTS: Thirty trials involving 6564 patients were eligible for analyses. Nineteen trials (61%) involving 3626 patients were initiated within the first half of this time period (1972-1981). The median of median survival times of all patients treated on the control arms of the Phase III trials initiated between 1972 and 1981 and between 1982 and 1992 were 12.0 months (range, 10-16 months) and 17.0 months (range, 11-20 months), respectively (P < 0.001). Of 26 studies available for survival analysis, 5 (19%) showed a statistically significant survival prolongation in the experimental arm compared with the control arm with a median prolongation of 3.4 months (range, 1-5.2 months). All five evaluated some aspect of thoracic radiation therapy. Over a similar time period, there was a 6.4-month increase in the median survival of limited-stage SCLC patients listed in the SEER database (P < 0.0001) and a more than doubling of the 5-year survival from 5.2% to 12.1% (P = 0.0001). CONCLUSIONS: Analyses of the patients with limited-stage SCLC treated on Phase III trials in North America initiated between 1972 and 1992 and those listed in the SEER database show significant improvements in median survivals. Furthermore, the 5-year survival of patients with limited-stage SCLC listed in the SEER database has more than doubled over the last 25 years. Further research will be needed to determine the relative contribution of improved therapy, supportive care, and stage migration to this prolongation in survival.

Adult↗

Isolation, characterization, and substrate properties of the external limiting membrane from the avian embryonic optic tectum.

The external limiting membrane of the avian embryonic optic tectum is isolated by mechanically separating the neuronal mesencephalon from the overlying mesenchymal tissue. The preparation consists of a basal lamina which is covered on its neural side by endfeet of neuroepithelial cells and has attached to it on its meningeal side a collageneous stroma, containing blood vessels. The external limiting membrane can be flat-mounted on a piece of nitrocellulose filter as mechanical support. It covers an area between 0.3 and 1 cm2, depending on the age of the donor embryo. The endfeet can be removed together with all cellular components of the meninges by treatment with 2% Triton-X-100 or with distilled water. The basal lamina itself is approximately 80 nm thick and consists of two laminae rarae and a central lamina densa. Immunohistochemical staining reveals that the basal lamina in the embryo, after isolation and after detergent extraction of the isolated preparation, contains type IV collagen, nidogen, laminin, and low density heparan sulfate proteoglycan as do other basement membranes. Antibodies against the neural cell adhesion molecule (N-CAM), chondroitin sulfate proteoglycan, and fibronectin fail to stain the external limiting membrane, but these proteins were clearly identified in the blood vessel-containing meninges or in the optic tectum. The flat-mounted external limiting membrane preparation was used as substrate to culture several different neural tissues of central and peripheral origin. Explants of neural crest cells, dorsal root ganglia, and sympathetic ganglia can be cultured on the external limiting membrane. All explants grow well on the basal lamina preparations whether the endfeet are attached or detergent-extracted prior to explantation; however, neurite outgrowth from sympathetic ganglia is reduced in the presence of the endfeet. Although the endfoot-lined external limiting membrane represents at least part of the immediate environment encountered by retinal axons as they invade the optic tectum and despite its excellent properties as a substrate for retinal axons in vitro, cues guiding the orientation of axons were not detected in the flat-mounted preparation.

Animals↗

Modeling of Random Formation of Microporous Material Following Thermodynamic Limitations.

The problem of pore formation in limited (small) volume has been considered. General equations describing the system in the continuous (many particles) and discrete (few particles) cases have been obtained. It has been shown that pore formation is not limited by nucleus genesis because of entropic reasons. Kinetic limitation leads to the auto-acceleration-like form of the dependence of the number of empty cells and the internal area functions. The percolation problem has been solved for 2- and 3-dimensional cases with comparison of systems obtained by traditional Monte Carlo and thermodynamic factors. The 3-dimensional situation leads to reduction of the percolation threshold. However, the difference in the values of percolation thresholds estimated by the ordinary Monte Carlo simulation and with thermodynamic limitation is not significant (less than the eventual error). The change of tortuosity was estimated. At the percolation threshold, the tortuosity decreases rapidly, then very slowly with an increase in microporosity, and only at very high microporosity (close to 1) the decrease in tortuosity is again sharp. The influence of the thermodynamic limitation on the regularity of the micropore cluster has been analyzed based on the consideration of behavior of free energy and surface area of the cluster. It has been found that both of these structural parameters significantly decrease if the thermodynamic limitation is imposed. Copyright 1999 Academic Press.

Journal Article↗

Evolutionarily Stable Reproductive Strategies in Sexual Organisms: III. The Effects of Lottery Density Dependence and Pollen Limitation

This paper extends our previous work on modelling, within a single framework, the allocation of resources to reproduction vs. survival and the male vs. female components of reproduction in perennial plants. We derive the evolutionarily stable strategy (ESS) results under pollen limitation for both hermaphroditic and dioecious plant populations held stable through density-dependent juvenile recruitment. Pollen limitation affects female reproductive allocation in our model because there is post-flowering provisioning of offspring. We find that pollen limitation is unimportant to the ESS reproductive allocation and sex allocation so long as there are enough seeds to fill the empty sites left by the death of adults. To the extent that the relationships between gamete output and resource investment are linear for both sexes or sex functions, the separate treatment of reproductive and sex allocation in modern life-history and sex-allocation theories is adequate. In such cases, the ESS sex allocation is exactly what is found in traditional sex allocation theory, and the ESS reproductive allocation of hermaphrodites or females in a dioecious species maximizes the amount of resources allocated to reproduction during an average lifespan, an analogue of the usual maximization principle in life-history theory modified to include the possibility of pollen limitation and extended seed maturation. The ESS reproductive allocation of males in a dioecious species maximizes lifetime pollen production, independent of pollen limitation and the female's resource allocation. Copyright 1997 Academic Press Limited

Journal Article↗

Modeling T-cell proliferation: an investigation of the consequences of the Hayflick limit.

Somatic cells, including immune cells such as T-cells have a limited capacity for proliferation and can only replicate for a finite number of generations (known as the Hayflick limit) before dying. In this paper we use mathematical models to investigate the consequences of introducing a Hayflick limit on the dynamics of T-cells stimulated with specific antigen. We show that while the Hayflick limit does not alter the dynamics of T-cell response to antigen over the short term, it may have a profound effect on the long-term immune response. In particular we show that over the long term the Hayflick limit may be important in determining whether an immune response can be maintained to a persistent antigen (or parasite). The eventual outcome is determined by the magnitude of the Hayflick limit, the extent to which antigen reduces the input of T-cells from the thymus, and the rate of antigen-induced proliferation of T-cells. Counter to what might be expected we show that the persistence of an immune response (immune memory) requires the density of persistent antigen to be less than a defined threshold value. If the amount of persistent antigen (or parasite) is greater than this threshold value then immune memory will be relatively short lived. The consequences of this threshold for persistent mycobacterial and HIV infections and for the generation of vaccines are discussed.

Antigens↗

Limits to steady-state lymph flow rates derived from plasma-to-tissue uptake measurements.

Upper and lower limits to basal lymph flow rates per unit tissue mass calculated from measurements of initial tissue uptake rates of 131-I albumin and steady-state lymph/plasma or interstitial fluid/plasma concentration ratios of endogenous albumin are compared with published measurements of lymph flow. The upper limit corresponds to purely convective transport of albumin, the lower to purely diffusive transport. Of a total of nine feasible comparisons, five show good agreement defined by the measured value falling at or between the calculated limits. These include two direct comparisons in the same or closely similar animal species and experimental conditions, and three cross-specific comparisons. Disagreement, with measured lymph flows much higher than the estimated upper limit, was observed in three comparisons, one of which was direct and conspecific and two that were cross-specific. In one instance, also cross-specific, reported lymph flows were below our minimal estimate. We suggest that estimates of lymph flow derived from tissue uptake measurements may be useful in setting limits to lymph turnover of fluid and plasma proteins in tissues and organs from which it is not feasible to collect lymph. They may also provide a means of evaluating experimentally induced disturbances of lymph drainage and over- or underestimation of the tissue mass from which lymph is collected, these being serious experimental problems associated with lymphatic cannulation and lymph collection. If both direct and indirect measurements can be made in the same tissue or organ under the same conditions, the relative contributions of convective and dissipative (diffusion and vesicular) transport processes to protein extravasation can be evaluated from the relation of the directly measured flow to the two calculated limits. These requirements were met for only two tissues among those surveyed: rat tail skin and rabbit leg muscles. For rat tail skin, our results suggest that approximately half the albumin transport is convective and half dissipative, and for rabbit muscle, about two-thirds is convective and one-third dissipative.

Albumins↗

Linkage disequilibrium and the infinitesimal limit.

Under the classical Fisher-Bulmer infinitesimal model of quantitative genetics, the within-family distribution for an additive trait with no environmental component is Gaussian with mean at the mid-parent value and a variance which is the same for all families. When an additive trait is determined by unlinked loci, the Fisher-Bulmer model can arise in the limit as the number of loci contributing to variation in the trait increases. However, a counterexample is presented where the Fisher-Bulmer model fails to arise in the infinite locus limit because there is too much linkage disequilibrium. An example is also presented where a degenerate form of the Fisher-Bulmer model arises. Under what conditions does the Fisher-Bulmer model arise in the infinite locus limit? It follows from the central limit theorem that the within-family distribution is Gaussian. But, under what conditions is the within-family distribution the same for almost all families in the population? An alternative population genetic derivation of the Fisher-Bulmer model is presented for a population at linkage equilibrium. This approach is then extended to allow many patterns of linkage disequilibrium. Diallelic models are used to illustrate the type of linkage disequilibrium allowed. The results on the limiting behaviour of population genetic models with many unlinked loci can be regarded as special cases of a more general limiting property of sequences of random variables. A possible application of this more general result to models of cultural inheritance is suggested.

Genetic Variation↗