Alfred J. Lotka
Encyclopedia
Alfred James Lotka was a US
mathematician
, physical chemist, and statistician
, famous for his work in population dynamics
and energetics
. An American
biophysicist best known for his proposal of the predator-prey model, developed simultaneously but independently of Vito Volterra
. The Lotka-Volterra model is still the basis of many models used in the analysis of population dynamics
in ecology
.
(now L'viv, Ukraine
). His parents, Jacques and Marie (Doebely) Lotka, were US
nationals and he was educated internationally. He received an B. Sc. in 1901 at the University of Birmingham
, England
, he did graduate work 1901-02 at Leipzig University, he received an M.A. in 1909 at Cornell University
and an D. Sc. at Birmingham University after his work here from 1909 to 1912.
Occupations
In 1935, he married Romola Beattie. They had no children.
Honors
He died in New York.
, Lotka was a bio-mathematician and a bio-statistician, who sought to apply the principles of the physical sciences to biological sciences as well. His main interest was demography
, which possibly influenced his professional choice as a statistician
at Metropolitan Life Insurance
.
Lotka published Elements of Mathematical Biology in 1925, the first book on mathematical biology
. He is also known for his energetics
perspective of evolution
. Lotka proposed that natural selection
was, at its root, a struggle among organisms for available energy; organisms that survive and prosper are those that capture and use energy
at a rate and efficiency more effective than that of its competitors. Lotka extended his energetic framework to human society. In particular, he suggested that the shift in reliance from solar energy to nonrenewable energy would pose unique and fundamental challenges to society. These theories made Lotka an important forerunner to the development of biophysical economics and ecological economics
, advanced by Frederick Soddy
, Howard Odum
and others
. His first book summarizes his previous work and organizes his ideas of unity and universality of physical laws, making his works accessible to other scientists. Although the book covered a large amount of topics, from energetics of evolution (see below) to the physical nature of consciousness, the author is primarily known today for the Lotka–Volterra equation of population dynamics.
in life sciences
.
Lotka proposed the theory that the Darwinian concept of natural selection
could be quantified as a physical law. The law that he proposed was that the selective principle of evolution was one which favoured the maximum useful energy flow transformation. The general systems ecologist Howard T. Odum
later applied Lotka's proposal as a central guiding feature of his work in ecosystems ecology
. Odum called Lotka's law the maximum power principle
.
-- the scientific study of scientific publications.
He teamed up with Louis Israel Dublin
, another statistician at Metropolitan Life, to write three books on demography and public health
: The Money Value of a Man (1930), Length of Life (1936), Twenty-five Years of Health Progress (1937).
Articles, a selection
Loth, A.J. (1926) “The Frequency Distribution of Scientific Productivity.” Journal of the Washington Academy of Sciences 16(1926):317-23.
About Lotka
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, physical chemist, and statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
, famous for his work in population dynamics
Population dynamics
Population dynamics is the branch of life sciences that studies short-term and long-term changes in the size and age composition of populations, and the biological and environmental processes influencing those changes...
and energetics
Energetics
Energetics is the study of energy under transformation. Because energy flows at all scales, from the quantum level to the biosphere and cosmos, energetics is a very broad discipline, encompassing for example thermodynamics, chemistry, biological energetics, biochemistry and ecological energetics...
. An American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
biophysicist best known for his proposal of the predator-prey model, developed simultaneously but independently of Vito Volterra
Vito Volterra
Vito Volterra was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations....
. The Lotka-Volterra model is still the basis of many models used in the analysis of population dynamics
Population dynamics
Population dynamics is the branch of life sciences that studies short-term and long-term changes in the size and age composition of populations, and the biological and environmental processes influencing those changes...
in ecology
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
.
Life
Lotka was born in Lemberg, Austria-HungaryAustria-Hungary
Austria-Hungary , more formally known as the Kingdoms and Lands Represented in the Imperial Council and the Lands of the Holy Hungarian Crown of Saint Stephen, was a constitutional monarchic union between the crowns of the Austrian Empire and the Kingdom of Hungary in...
(now L'viv, Ukraine
Ukraine
Ukraine is a country in Eastern Europe. It has an area of 603,628 km², making it the second largest contiguous country on the European continent, after Russia...
). His parents, Jacques and Marie (Doebely) Lotka, were US
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
nationals and he was educated internationally. He received an B. Sc. in 1901 at the University of Birmingham
University of Birmingham
The University of Birmingham is a British Redbrick university located in the city of Birmingham, England. It received its royal charter in 1900 as a successor to Birmingham Medical School and Mason Science College . Birmingham was the first Redbrick university to gain a charter and thus...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
, he did graduate work 1901-02 at Leipzig University, he received an M.A. in 1909 at Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
and an D. Sc. at Birmingham University after his work here from 1909 to 1912.
Occupations
- Assistant chemist for General Chemical Company (1902–1908, 1914–1919)
- Patent examiner for US Patent Office (1909)
- Assistant physicist for National Bureau of Standards (1909–1911)
- Editor of the Scientific AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
Supplement (1911–1914) - Staff member at Johns Hopkins UniversityJohns Hopkins UniversityThe Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
(1922–1924) - Statistician for the Metropolitan Life Insurance CompanyMetropolitan Life Insurance CompanyMetLife, Inc. is the holding corporation for the Metropolitan Life Insurance Company, or MetLife, for short, and its affiliates. MetLife is among the largest global providers of insurance, annuities, and employee benefit programs, with 90 million customers in over 60 countries...
, New YorkNew YorkNew York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...
(1924 until his retirement in 1947)
In 1935, he married Romola Beattie. They had no children.
Honors
- President of the Population Association of America (1938–1939)
- President of the American Statistical AssociationAmerican Statistical AssociationThe American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
(1942) - Vice president of the Union for the Scientific Investigation of Population Problems
- Chairman of the United States National Committee of the Union
- Fellow of American Public Health AssociationAmerican Public Health AssociationThe American Public Health Association is Washington, D.C.-based professional organization for public health professionals in the United States. Founded in 1872 by Dr. Stephen Smith, APHA has more than 30,000 members worldwide...
- Fellow of Institute of Mathematical StatisticsInstitute of Mathematical StatisticsThe Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world...
He died in New York.
Work
Although he is today known mainly for the Lotka–Volterra equations used in ecologyEcology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
, Lotka was a bio-mathematician and a bio-statistician, who sought to apply the principles of the physical sciences to biological sciences as well. His main interest was demography
Demography
Demography is the statistical study of human population. It can be a very general science that can be applied to any kind of dynamic human population, that is, one that changes over time or space...
, which possibly influenced his professional choice as a statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
at Metropolitan Life Insurance
Metropolitan Life Insurance Company
MetLife, Inc. is the holding corporation for the Metropolitan Life Insurance Company, or MetLife, for short, and its affiliates. MetLife is among the largest global providers of insurance, annuities, and employee benefit programs, with 90 million customers in over 60 countries...
.
Lotka published Elements of Mathematical Biology in 1925, the first book on mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
. He is also known for his energetics
Energetics
Energetics is the study of energy under transformation. Because energy flows at all scales, from the quantum level to the biosphere and cosmos, energetics is a very broad discipline, encompassing for example thermodynamics, chemistry, biological energetics, biochemistry and ecological energetics...
perspective of evolution
Evolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
. Lotka proposed that natural selection
Natural selection
Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....
was, at its root, a struggle among organisms for available energy; organisms that survive and prosper are those that capture and use energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
at a rate and efficiency more effective than that of its competitors. Lotka extended his energetic framework to human society. In particular, he suggested that the shift in reliance from solar energy to nonrenewable energy would pose unique and fundamental challenges to society. These theories made Lotka an important forerunner to the development of biophysical economics and ecological economics
Ecological economics
Image:Sustainable development.svg|right|The three pillars of sustainability. Clickable.|275px|thumbpoly 138 194 148 219 164 240 182 257 219 277 263 291 261 311 264 331 272 351 283 366 300 383 316 394 287 408 261 417 224 424 182 426 154 423 119 415 87 403 58 385 40 368 24 347 17 328 13 309 16 286 26...
, advanced by Frederick Soddy
Frederick Soddy
Frederick Soddy was an English radiochemist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also proved the existence of isotopes of certain radioactive elements...
, Howard Odum
Howard Odum
Howard Odum may refer to:* Howard W. Odum , American sociologist* Howard T. Odum , his son, ecologist...
and others
Elements of physical biology
While at Johns Hopkins, Lotka completed his book Elements of Physical Biology (1925) in which he extended the work of Pierre François VerhulstPierre François Verhulst
Pierre François Verhulst was a mathematician and a doctor in number theory from the University of Ghent in 1825...
. His first book summarizes his previous work and organizes his ideas of unity and universality of physical laws, making his works accessible to other scientists. Although the book covered a large amount of topics, from energetics of evolution (see below) to the physical nature of consciousness, the author is primarily known today for the Lotka–Volterra equation of population dynamics.
Energetics of evolution
His earlier work was centered on energetics and applications of thermodynamicsThermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
in life sciences
Life sciences
The life sciences comprise the fields of science that involve the scientific study of living organisms, like plants, animals, and human beings. While biology remains the centerpiece of the life sciences, technological advances in molecular biology and biotechnology have led to a burgeoning of...
.
Lotka proposed the theory that the Darwinian concept of natural selection
Natural selection
Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....
could be quantified as a physical law. The law that he proposed was that the selective principle of evolution was one which favoured the maximum useful energy flow transformation. The general systems ecologist Howard T. Odum
Howard T. Odum
Howard Thomas Odum was an American ecologist...
later applied Lotka's proposal as a central guiding feature of his work in ecosystems ecology
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
. Odum called Lotka's law the maximum power principle
Maximum power principle
The maximum power principle has been proposed as the fourth principle of energetics in open system thermodynamics, where an example of an open system is a biological cell. According to Howard T...
.
Demography and public health
In 1934 and 1939, Lotka published the two volumes of his Théorie Analytique des Associations Biologiques (Analytical Theory of Biological Associations) in French, which summarizes his works on demography.Bibliometrics
Within the field of bibliometrics, particularly that part devoted to studying scientific publications, Lotka is noted for contributing "Lotka's law." The law which Lotka discovered relates to the productivity of scientists. As noted by W.G. Poitier in 1981: "The Lotka distribution is based on an inverse square law where the number of authors writing n papers is l/n2 of the number of authors writing one paper. Each subject area can have associated with it an exponent representing its specific rate of author productivity." Lotka's work sparked additional inquiries, eventually seminally contributing to the field of scientometricsScientometrics
Scientometrics is the science of measuring and analysing science. In practice, scientometrics is often done using bibliometrics which is a measurement of the impact of publications. Modern scientometrics is mostly based on the work of Derek J. de Solla Price and Eugene Garfield...
-- the scientific study of scientific publications.
He teamed up with Louis Israel Dublin
Louis Israel Dublin
Louis Israel Dublin was a Jewish American statistician. As vice president and statistician of the Metropolitan Life Insurance Company, Dublin promoted progressive and socially useful insurance underwriting policies...
, another statistician at Metropolitan Life, to write three books on demography and public health
Public health
Public health is "the science and art of preventing disease, prolonging life and promoting health through the organized efforts and informed choices of society, organizations, public and private, communities and individuals" . It is concerned with threats to health based on population health...
: The Money Value of a Man (1930), Length of Life (1936), Twenty-five Years of Health Progress (1937).
See also
- Lotka–Volterra equations (for predation)
- Lotka–Volterra inter-specific competition equations
- Lotka's law (a special case of Zipf's law)
- Energy accountingEnergy accountingEnergy accounting is a system used within industry, where measuring and analyzing the energy consumption of different activities is done to improve energy efficiency.-Energy management:...
- Biophysical economics
- BioeconomicsBioeconomicsBioeconomics is closely related to the early development of theories in fisheries economics, initially in the mid 1950s by Canadian economists Scott Gordon and Anthony Scott...
- Energy economicsEnergy economicsEnergy economics is a broad scientific subject area which includes topics related to supply and use of energy in societies. Due to diversity of issues and methods applied and shared with a number of academic disciplines, energy economics does not present itself as a self contained academic...
Publications
- A.J.Lotka (1925) 'Elements of Physical Biology' [PDF] reprinted by Dover in 1956 as Elements of Mathematical Biology.
- Lotka, A.J. (1939) Théorie Analytique des Associations Biologiques translated in 1998 as Analytical Theory of Biological Populations. New York: Plenum Press.
- Lotka, A.J. (1989). Lotka on population study, ecology, and evolution. Population and Development Review, 15(3), 539–550.
- Lotka, A.J. (1998). Analytical theory of biological populations. New York: Plenum Press
Articles, a selection
- Lotka, A.J. (1907). Relation between birth rates and death rates. Science, 26: 121–130.
- Sharpe, F.R. & Lotka, A.J. (1911). A problem in age distribution. Philosophical Magazine, 21: 435–438.
- Lotka, A.J. (1919). A contribution to quantitive epidemiology. Journal of the Washington Academy of Sciences, 9: p. 73.
- A.J.Lotka (1922a) 'Contribution to the energetics of evolution' [PDF]. Proc Natl Acad Sci, 8: pp. 147–51.
- A.J.Lotka (1922b) 'Natural selection as a physical principle' [PDF]. Proc Natl Acad Sci, 8, pp 151–54.
Loth, A.J. (1926) “The Frequency Distribution of Scientific Productivity.” Journal of the Washington Academy of Sciences 16(1926):317-23.
About Lotka
- Haaga, J. (2000). Alfred Lotka, mathematical demographer. Population Today, 28(2), 3.
- Kingsland, S.E. (1985). Modeling nature: episodes in the history of population ecology. Chigago: University of Chicago.