La ley de Lotka
Alfred James Lotka es bien conocido por las famosas ecuaciones de Lotka-Volterra, usadas en ecología para determinar la dinámica de una población, u model predador-presa que describimos en la anterior entrada en este blog titulada Los tiburones de Vito Volterra. Pero este es sólo uno de sus logros, y la figura de Lotka merece sin duda que le dediquemos una entrada.
Lotka nació el 2 de marzo de 1880 en Lwów, entonces una ciudad del Imperio Austro-Húngaro, y hoy en día una ciudad de Ucrania. Sus padres, Jacques y Marie (Doebely de soltera) Lotka eran de origen polaco y norteamericanos de nacionalidad. Su educación fue muy internacional, y así consiguió su título de bachiller en la Universidad de Birmingham y finalizó su graduación en 1902 en la de Leipzig. Continuó su formación en la Universidad de Cornell y se doctoró en la original de Birmingham en1912.
Aunque a Lotka se le considera un matemático, su formación era mucho más amplia, y de hecho, en Birmingham y Leipzig estudió Química, y Química-Física; de hecho, en Leipzig recibió lecciones de Friedrich Wilhelm Ostwald, que recibió el Premio Nobel de Química en 1909 por sus trabajos sobre la catálisis. Esta formación en Química le permitió trabajar para la General Chemical Company, desde 1902 hasta 1908 y desde 1914 hasta 1919, ya que en el periodo 1909-1912 se dedicó a preparar su tesis doctoral en Birmingham.
Sus primeros trabajos fueron en el estudio de la dinámica de las mezclas de gases, y también comenzó su interés por los procesos demográficos. Después de interesarse por los modelos matemáticos para la malaria, publica en 1925 su gran obra Elements of Physical Biology, en el que propone una nueva aproximación a la teoría de la evolución. Su propuesta, muy influida por sus conocimientos de química, es que la energía desempeña un papel clave en la evolución, que, al final, resultaría de una lucha permanente de los organismos para hacerse con la energía disponible: los que sobreviven son los que mejor capturan y utilizan la energía disponible en su entorno. Esto supone un paso más en las ideas de D’Arcy Thompson’s en su obra On Growth and Form, tratando de incluir la física en la evolución (ver La vida es simétrica). Estas dos obras se consideran los fundamentos de la hoy llamada Biología matemática.
Las ecuaciones denominadas como de Lotka–Volterra fueron inicialmente propuestas por Lotka, en sus trabajos de 1910 sobre las reacciones químicas, partiendo de la ecuación logísitica obtenida por Pierre François Verhulst. En 1920 Lotka extendió el modelo a seres vivos (plantas y animales hervíboros. Vito Volterra llegó a las mismas ecuaciones motivado por una pregunta de su futuro yerno. Se sabe que Lotka y Volterra mantuvieron después una correspondecia sobre estos temas.
Un logro menos conocido de Lotka es la llamada Ley de Lotka, uno de los resultados pioneros en Bibliometría. Lotka obtuvo su ley analizando los nombres de los autores que aparecían en Chemical abstracts (una especie de Mathematical Reviews para los químicos), en el decenio 1907-1916. Dedujo, de manera empírica, una ley sobre la distribución de los autores según su productividad: el número de autores, An que publican n artículos sobre una materia es inversamente proporcional al cuadrado de n, es decir
An = A1/n2
dónde A1 es el número de autores que publican un solo artículo en ese tema. Esto está relacionado con la Ley de Zipf.
El propio Lotka explica la importancia de estas leyes bibliométricas: “Sería de interés determinar, si es posible, la parte en la que hombres de diferente calibre contribuyen al progreso de la ciencia.” La ley dice que la mayoría de los autores publican pocos artículos, mientras que unos pocos son los que producen la mayoría de ellos. Esto es cierto en todas las disciplinas y permite identificar grupos de investigación basándose en la coautoría del líder. Este link al artículo Lotka’s inverse square law of scientific productivity: Its methods and Statistics proporciona más información sobre esta contribución de Lotka.
Lotka se incorporó en 1922 a la universidad Johns Hopkins hasta 1924, año en el que comenzó a trabajar para una compañía de seguros, MetLife (Metropolitan Life Insurance Company), hasta su jubilación en 1947. Falleció en Nueva York el 5 de diciembre de 1949.
____
Manuel de León (CSIC, Fundador del ICMAT, Real Academia de Ciencias, Real Academia Canaria de Ciencias, ICSU).
Lotka’s law, named after Alfred J. Lotka, is one of a variety of special applications of Zipf’s law. It describes the frequency of publication by authors in any given field. … As the number of articles published increases, authors producing that many publications become less frequent.Wow! Thank this meaningful and helpful post! I am working as a creative consultant at online services that are mostly for dissertation writing service. Thanks a lot for the kind of perfect topic I have not a lot of information about it but I have got an extra unique info in your unique post.
[…] Matemáticas y sus fronteras -… […]
Excelente información. Gracias.
[…] Alfred James Lotka (1880-1949). Matemático, químico físico y estadístico. | Imagen: Madrid blogs. […]
Me sorprendió leer que Lotka nació en una ciudad que hoy es parte de Ucrania. Sus contribuciones, desde las ecuaciones Lotka-Volterra hasta la ley de Lotka en bibliometría, fueron fundamentales. Echoes of Aincrad Wiki tiene mucho que ofrecer sobre personajes y estrategias, igual como Lotka hizo con su ley. ¿Será que nos inspiran igual en nuestras búsquedas diarias, como encontrar el mejor lugar para un café?
This is a fascinating look at how mathematical principles can reveal patterns in something as seemingly chaotic as human creativity. It makes me wonder if similar power-law distributions apply to other fields, like software development or visual art. Thanks for the clear explanation.
This is a fascinating look at how mathematical principles can reveal patterns in human creativity. It makes me wonder if similar power-law distributions apply to other fields, like software development or visual art. Thanks for the clear explanation.
That’s interesting how Lotka’s Law can be applied to so many different fields, not just scientific publications. I wonder if the «author productivity» aspect is shifting with the rise of collaborative research and co-authorship becoming more common.
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The discussion about la ley de lotka raises some really valid points. This perspective is refreshing.
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The discussion about la ley de lotka raises some really valid points. This perspective is refreshing.
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Interesante artículo sobre la ley de Lotka. Es asombroso cómo un mismo principio matemático puede aplicarse tanto a
la ecología como a la bibliometría. Por cierto, si te gusta explorar patrones en datos, quizás te interese Gameilo, donde también se analizan tendencias en juegos.
I found the analysis of la ley de lotka particularly insightful. Could be valuable for anyone in this space.
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La explicación de la ley de Lotka ayuda a entender por qué una pequeña parte de los autores concentra gran parte de la producción científica. También es interesante la conexión con otras distribuciones de tipo potencia. Para recursos educativos con audio, https://playsoundboard.com puede complementar presentaciones de divulgación.
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