Chapter 4: The Graduation of Survivorship Data

1973 ◽  
Vol 27 ◽  
pp. 17-22
Author(s):  
Kenneth M. Weiss
Keyword(s):  
Life Table ◽  
Curve Fitting ◽  
Data Sets ◽  
Age Classes ◽  
Human Mortality ◽  
Age Class ◽  
Age Limits ◽  
Source Populations

The mortality between adjacent age classes can be estimated from the survivorship schedules derived in Chapter 3. The data, however, differ in each case in the number, size, and age limits of the age classes; therefore, it is not possible to derive strictly comparable information from the data sets. Further, it is not yet possible to define the internal mortality structure of each age class which must be known for the computation of many elements of the life table.If we assume, as is commonly done in demography, that human mortality patterns follow some function of age, then we can fit our 50 source populations to that function and assume that deviations from that fit are merely stochastic. This process of curve fitting is called graduation, and it is a powerful and useful smoothing operation for mortality or survivorship data.

Root sprouting in American beech: production, survival, and the effect of parent tree vigor

1987 ◽  
Vol 17 (6) ◽  
pp. 539-544 ◽  
Author(s):  
Robert H. Jones ◽  
Dudley J. Raynal
Keyword(s):  
Life Table ◽  
Mortality Rates ◽  
Beech Bark Disease ◽  
Age Classes ◽  
American Beech ◽  
Parent Tree ◽  
Age Class ◽  
Per Capita ◽  
Individual Parent ◽  
Annual Mortality

Root sprout age-class distributions around American beech trees were measured to characterize production of sprouts under closed canopies. Annual mortality of root sprouts was estimated by static and cohort life table analyses. Sprouts around parent trees with and without beech bark disease were compared to test for effects of lowered parent vigor on sprout production and vigor. Age-class distributions were highly variable, indicating episodic production of sprouts. Trends in the data suggested that (i) for individual parent beech trees, the number of sprouts per age-class decreased exponentially as sprout age increased; and (ii) parent trees with larger diameters had more sprouts, more sprout age-classes, but greater variability in age-class distribution. Life table analyses indicated uniform per capita mortality rates for clumps of sprouts but decreasing mortality with age for individual sprouts within clumps. Low parent vigor, due in part to beech bark disease, was weakly correlated with reduced sprout production, but diseased trees maintained populations of older sprouts that differed little from sprouts associated with nondiseased trees.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals Slenderness of trees in black locust stands

2018 ◽  
Vol 79 (2) ◽  
pp. 113-117
Author(s):  
Szymon Bijak ◽  
Katarzyna Orzoł
Keyword(s):  
Standard Deviation ◽  
Black Locust ◽  
Robinia Pseudoacacia ◽  
Habitat Type ◽  
Stand Age ◽  
Age Classes ◽  
Breast Height ◽  
Age Class ◽  
Crown Length ◽  
Research Material

Abstract This paper investigates the slenderness of black locust (Robinia pseudoacacia) trees in relation to the biosocial status of the trees, stand age class, crown parameters and habitat type. The research material was collected on 35 research plots in the Sława Śląska, Sulechów and Głogów forest districts in western Poland and comprises 1058 trees. For each tree, we measured height (h) as well as diameter at breast height (d) and determined its biosocial status (Kraft class), crown length (CL) and relative crown length (rCL). The age class and habitat type were assessed at the plot level. Because the obtained values for slenderness (s=h/d) diverged significantly from the normal distribution, we used Kruskal-Wallis and Mann-Whitney tests to investigate the influence of the above-mentioned parameters on the h/d ratio. Black locust slenderness ranged from 0.31 to 1.95 with an average of 0.91 (standard deviation 0.24). It furthermore differed significantly between Kraft classes (the higher the biosocial status, the lower the slenderness) and age classes (the older the trees, the lower their slenderness). We also found a significant effect of the habitat type (in oligotrophic sites trees formed more slender trunks than in mesotrophic sites) and crown parameters on the h/d ratio (decreasing with increasing crown length and relative crown length). The obtained results suggest that the slenderness of black locust does not differ substantially from native broadleaved trees in Poland.

scholarly journals The accuracy and relative efficiency of Landsat data and orthophotos for determining area and volume of spruce.

1985 ◽  
Vol 33 (2) ◽  
pp. 141-150
Author(s):  
D.A. Stellingwerf ◽  
S. Lwin
Keyword(s):  
Principal Components ◽  
Relative Efficiency ◽  
Field Work ◽  
Data Sets ◽  
Landsat Data ◽  
Age Classes ◽  
Upper Austria ◽  
Components Analysis ◽  
Total Forest Area ◽  
Area And Volume

Comparative estimates were made for a 12 841-ha area of Upper Austria comprising areas of pure or mixed Norway spruce and beech, young stands and non-forest. The Landsat data, classified by principal components analysis, gave very inaccurate differentiation of species, age classes and smaller non-forest areas, although the total forest area was reasonably accurate. Stand vol. of spruce was estimated by 2-stage sampling of both data sets followed by field work on sample plots. The Landsat method required 53% more primary (first-stage sampling) units, 23% more man-days and higher extra costs than the orthophoto method for the same accuracy. (Abstract retrieved from CAB Abstracts by CABI’s permission)

4. The entrance of statistics and mathematical models

2018 ◽  
pp. 24-34
Author(s):  
Sarah Harper
Keyword(s):  
Mathematical Models ◽  
Life Table ◽  
19Th Century ◽  
21St Century ◽  
Parametric Model ◽  
Scientific Investigation ◽  
International Union ◽  
Human Mortality ◽  
Demographic Methods ◽  
The 19Th Century

By the 19th century the study of demography had developed from John Graunt’s primitive life table to the complex statistical laws and theories of Benjamin Gompertz and William Makeham. ‘The entrance of statistics and mathematical models’ describes the Gompertz–Makeham law of mortality, the first parametric model of human mortality that is still valid today, and the formation of the International Union for the Scientific Investigation of Population Problems in 1927. It also outlines the contributions of William Farr, Francis Galton, Karl Pearson, Sir Ronald Aylmer Fisher, Leonard Henry Tippett, Ansley Johnson Coale, William Brass, and John ‘Jack’ Caldwell to the development of demography and demographic methods and analysis from the 19th century to the 21st century.

Timber production versus old-growth preservation with endogenous prices and forest age-classes

2004 ◽  
Vol 34 (6) ◽  
pp. 1296-1310 ◽  
Author(s):  
Olli Tahvonen
Keyword(s):  
Environmental Values ◽  
Timber Harvesting ◽  
Timber Production ◽  
Forest Age ◽  
Forest Land ◽  
Age Classes ◽  
Old Growth ◽  
Class Distribution ◽  
Age Class ◽  
Long Run

This study combines timber production and environmental values, applying a dynamic forest-level economic model with any number of forest age-classes. The model includes endogenous timber price or nonlinear harvesting costs and various possibilities to specify the dependence of environmental values (related e.g. to species persistence) on the forest age-class structure. The nonlinearities in the net benefits from timber production have the consequence that fluctuations in optimal timber harvesting may totally vanish or at least become smaller than in forest scheduling models without ad hoc even flow constraints. If environmental values are specified to depend on the fraction of forest land preserved as old growth, the optimal long run allocation between timber production and old growth is represented by an equilibrium continuum. Thus the optimal long run allocation depends on the initial age-class distribution. The continuum and the dependence of initial age-class distribution vanish when the rate of discount approaches zero. If the environmental values of age-classes increase smoothly with age, the long run equilibrium may simultaneously include multiple rotation periods. The model determines the optimality of producing timber and environmental values separately at different parts of the forest or at the same piece of forest land. Numerical computation suggests that the optimal solution always converges toward some optimal long run stationary age-class distribution.

scholarly journals FURTHER INVESTIGATIONS ON THE ORIGIN OF TUMORS IN MICE

1915 ◽  
Vol 22 (6) ◽  
pp. 713-731 ◽  
Author(s):  
A. E. C. Lathrop ◽  
Leo Loeb
Keyword(s):  
Tumor Incidence ◽  
Age Classes ◽  
Age Class ◽  
The Difference ◽  
Different Strains

1. In crossing strains known to diner in their tumor rates, the hybrids show in a considerable number of cases a tumor rate corresponding to the parent with a high tumor incidence; in some cases the offspring have the tumor rate of the parent with the low tumor incidence; in certain cases the tumor rate of the offspring is intermediate between those of the parents. That these results are not accidental follows from the fact that we could show in some cases that two sisters crossed with the same strains or with the same male give similar offspring, and in other cases we could show that the same individual crossed successively with two strains that behave similarly produces hybrids with a similar tumor incidence. 2. There exists some evidence for the conclusion that different strains in being crossed with other strains differ in their power to impress their tumor rate upon the crosses. Thus the English strain and the I and II daughters of No. 10 have the tendency to transmit to the offspring a high tumor rate, while Cream, Silver, and some European other than 151 have a tendency to transmit a low tumor rate. While crosses of these daughters of No. 10 with European 151 or with No. 8½ show the high tumor rate of the mothers, the crosses of one of the same females with Cream or Silver show an intermediate tumor rate. 3. We find further evidence for our conclusion previously stated that age class, of the tumors and tumor rate are not dependent on the same factor. The age class enters into the crosses as a factor independent of the tumor rate. Thus we find in the crosses between the first daughter of No. 10 and Cream, and in the crosses between the same female and English Silver a similar tumor rate, but the age classes differ in conformity with the difference in the age classes of the parents. We find, furthermore, that while in some cases a tumor rate and an age class that correspond to each other (high tumor rate, early tumors—low tumor rate, late tumors) are transmitted to the offspring, in other cases tumor rate and age class transmitted to the crosses diverge. 4. It seems that certain strains with very late tumors if mated with strains with earlier tumors have a tendency to transmit to the offspring their own tendency to very late tumors. With a certain strain lateness of the tumors seems to be dominant, while a low tumor rate is not necessarily dominant in the same crosses. This was noticeable in the crosses into which the strain European ± 102 or 103 entered as one of the parents. 5. If both parents have a similar tumor rate the offspring have usually a similar tumor rate. There was, however, one exception to this rule in the case of the German ± Carter mice, in which the offspring showed a much lower tumor rate and higher age class than either of the parent strains.

Testing the accuracy of using peroxidase activity to indicate stigma receptivity

1987 ◽  
Vol 65 (1) ◽  
pp. 107-111 ◽  
Author(s):  
Candace Galen ◽  
R. C. Plowright
Keyword(s):  
Peroxidase Activity ◽  
Pollen Germination ◽  
Age Classes ◽  
Stigma Receptivity ◽  
Age Class ◽  
Stigma Surface ◽  
Hand Pollination ◽  
Flower Age ◽  
Adhesion Rate ◽  
Pedicularis Canadensis

Stigma peroxidase activity was tested in flowers of Pedicularis canadensis and Clintonia borealis at discrete age-classes during the course of anthesis. For recipient flowers of each age-class pollen adhesion, rate of pollen germination, and total number of grains germinating on stigmas were scored following hand-pollination. In P. canadensis, the onset of detectable peroxidase activity occurred at the transition from the juvenile to pollen-dehiscing age-class. Concurrently, the stickiness of the stigma surface and total number of grains germinating on the stigma increased significantly. Stigma peroxidase was present to some degree throughout anthesis in C. borealis. However, the percentage of the stigma surface in which peroxidase was detectable increased significantly between straight-sided and medium-curled flower age-classes. Again, corresponding increases occurred in the stickiness of the stigma surface and total number of grains germinating. Results suggest that for both species stigma peroxidase activity is a reliable indicator of receptivity.

The Use of Graphical Methods to Estimate Demographic Parameters

1989 ◽  
Vol 69 (2) ◽  
pp. 367-371 ◽  
Author(s):  
Alastair Grant
Keyword(s):  
Undergraduate Students ◽  
Size Structure ◽  
Size Variation ◽  
Demographic Parameters ◽  
Graphical Methods ◽  
Age Classes ◽  
Size Frequency Distribution ◽  
Age Class ◽  
Frequency Histogram ◽  
Size Frequency

The demographic parameters of a population (the number of age-classes present; growth rates; mortality as a function of age and recruitment levels) are of considerable interest to marine biologists. If individuals can be aged from growth rings in their hard parts, then the estimation of demographic parameters is relatively straightforward. If this is not possible, the next best alternative is to tag or mark individuals and use data on the recapture of these to give the information required. For many marine invertebrates, neither of these options is practical and we must resort to estimating the demographic parameters by making assumptions about recruitment and the size variation between individuals of the same age and then infer the age structure of the population from its size structure. This was first done by Petersen (1891) who interpreted each mode on a size/ frequency histogram as representing a single age-class. More recently, extensive use has been made of methods which assume that the sizes of individuals of the same age will be normally distributed. The size/frequency histogram can then be decomposed into a number of normal distributions, each of which represents a single age-class. This can be done graphically (Harding, 1949; Cassie, 1954; Bhattacharya, 1967) or with computerbased numerical methods (Macdonald & Pitcher, 1979). The graphical methods seem to be the most popular and are frequently taught to undergraduate students. The same methods can be used to dissect a size/frequency distribution into components other than age-classes (Harding, 1949), but the principles are the same.

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