Biology by numbers : an encouragement to quantitative thinking / Richard F. Burton.
Biologists are notoriously reticent about using mathematics. This textbook is both an introduction to quantitative biology and a guide for the number-shy. Richard Burton fosters a sense of the fundamental importance and usefulness of mathematical principles in biology, with a fascinating range of ex...
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| Format: | Electronic eBook |
| Language: | English |
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Cambridge ; New York, NY :
Cambridge University Press,
1998.
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Table of Contents:
- An introduction to quantitative biology. The fundamental importance and usefulness of mathematical principles in biology. Putting two and two together. Darwin's earthworms. An inordinate fondness for beetles. The extinction of birds on Hawaiian islands. Pollen and honeybees. Estimating the sizes of redwoods and whales. Plant productivity and use of solar energy. The number of cells in the human body. William Harvey and the circulation of the blood. How our kidneys work. Calcium, and the small litter sizes of bats. Conclusions concerning biological arithmetic. Units, formulae and the use of old envelopes: confronting some obstacles to quantitative thinking. Units of measurement. Checking formulae for consistency of units; avoiding errors in calculation. Identifying appropriate units for unfamiliar quantities. Dimensional analysis. Approximate arithmetic. Cultivating a feeling for magnitudes. Looking at an equation. Aspects of energy metabolism. Energy from food. Basal metabolic rate. Fat storage and the control of appetite. Birds' eggs and respiratory quotients. Getting things in proportion. Aspects of human heat and energy balance. Fat as an acid to buoyancy in water. Buoyancy in fish. Temperature, metabolism and buoyancy
- a general formula. Blood volumes of snails. Blood volumes and animal populations
- another general approach. Perilous percentages, dangerous ratios. Dangers in treating losses of body heat in terms of percentages. Organ mass as a percentage of body mass
- the gonosomatic index. An organ of variable composition
- the snail's albumen gland. The composition of milk. Building a trophic pyramid. The smaller mass of predators than of prey. Populations of grazers on grassland. The base of the pyramid. Sodium in animals and plants. Sodium in herbivorous insects. The puddling behaviour of moths. The importance of sodium in the diet of moose. The distribution of sodium in the human body. Exchanges of water and carbon dioxide. Transpiration and photosynthesis. The dependence of plant productivity on rainfall. Solar energy used in transpiration and photosynthesis. The role of breathing in mammalian water balance. Water balance in foraging bumblebees. A geometric series. More approximate arithmetic. Darwin, Linnaeus and Malthus. Ancestors and inbreeding. The penetration of sunlight through water. Fish and probabilities. The genetic code. Introduction to logarithms. Natural logarithms. Bringing logarithms to life. How do logarithms come into biology? How else do logarithms come into biology? The growth of insects. The sizes of New Guinea fruit pigeons. Logaritms and sensation. Exponential relationships. Basic mathematics. Exponential increase: pollen grains in a sequence of sediments. Exponential decrease: dung flies and the attractiveness of dung. Exponential decline: viability of seeds in soil. Other ways of viewing an exponential decrease. Aspects of allometry. Relative growth: the claw of the fiddler crab. Relative growth of gourds. Macrotritopus
- a problem of taxonomy. Stag beetles
- failure of the relationship. Graphical estimation of scaling exponents and scaling coefficients. Antlers. Eye size in mammals. More on allometry, and on quantitative patterns in nature. Surface area/ volume relationships. Body size and metabolic rate in mammals: the importance of surface area. Body size and metabolic rate: Kleiber's rule. Birds' eggs: metabolism and water loss. The mammalian skeleton. Tree height and trunk diameter. Wind-borne seeds and fruit. The energetic equivalence rule. The self-thinning rule
- and a general caution. Numbers of bird species on Pacific islands. How the abundance of food affects rates of feeding. Rates of predation and the abundance of prey. Food availability and the grazing rates of herbivores. The characterization of trees and other branching systems.