Pierre-francois verhulst biography

Pierre-francois verhulst biography: Pierre François Verhulst (28 October

He became the first director when it was established in and Quetelet was appointed as one of the first professors. In [ 13 ] Quetelet says that Verhulst took the utmost care with the preparation of his lecture notes for his courses at the Military Academy, and continually updated and improved them. There he gave courses on astronomy, celestial mechanics, the differential and integral calculus, the theory of probability, geometry and trigonometry.

He continued to be influenced by Quetelet although he was not always in agreement with Quetelet 's ideas. However, one project by Verhulst which Quetelet praised highly was his work on elliptic functions. This came about since Verhulst bought an edition of the complete works of Legendre in a public sale. Quetelet praised the work highly and it must have been a contributory factor in Verhulst's election to the Belgium Academy of Science later in Quetelet does not seem to have appreciated Verhulst's most important contribution, however, namely his work on the logistic equation and logistic function.

The assumed belief before Quetelet and Verhulst worked on population growth was that an increasing population followed a geometric progression. Quetelet believed that there are forces which tend to prevent this population growth and that they increase with the square of the rate at which the population grows. Verhulst wrote in his paper:- We know that the famous Malthus showed the principle that the human population tends to grow in a geometric progression so as to double after a certain period of time, for example every twenty five years.

This proposition is beyond dispute if abstraction is made of the increasing difficulty to find food The virtual increase of the population is therefore limited by the pierre-francois verhulst biography and the fertility of the country. As a result the population gets closer and closer to a steady state. In the paper Verhulst argued against the model for population growth that Quetelet had proposed and instead proposed a model with a differential equation now known as the logistic equation.

He named the solution to the equation he had proposed in his paper the 'logistic function'. It is unclear why he gave it this name and in [ 12 ] Hugo Pastijn considers certain possible explanations:- The reason why Verhulst called this curve "a courbe logistique" in his communication of November 30, is not clear. He does not give any explanation.

One might guess that he refers to the term logistics, related to transportation and distribution in the supply chain of an army, analogous to the supply of subsistence means of a population which he considered to be limited.

Pierre-francois verhulst biography: On 28 September Verhulst

The term logistic was then already to a certain extent in use in the military environment. He could have been familiar with it, through his military contacts in the Military Academy in Brussels. Another possible root of the term logistic could have been the French word "logis" place to live which was of course related to the limited resources for subsistence of a population, Verhulst was dealing with in his model.

In this paper, which was published inVerhulst writes:- We shall not insist on the hypothesis of geometric progression, given that it can hold only in very special circumstances; for example, when a fertile territory of almost unlimited size happens to be inhabited by people with an advanced civilization, as was the case for the first American colonies.

When Verhulst graduated from the Athenaeum in he had not completed the full course of study there but he was keen to progress quickly with his university studies. Mathematics courses were being introduced at the museum and Verhulst was responsible for setting up the teaching of an analysis course. At this time Verhulst worked on the theory of numbers, and, influenced by Quetelet, he became interested in the calculus of probability and social statistics.

In Verhulst published a translation of John Herschel's Theory of light. The Roman hierarchy did not take kindly with being told how to run their affairs by a Belgium or probably by anyone, for that matter so the police were summoned and Verhulst was ordered to leave Rome. Through Quetelet, he had been invited to present a mathematical formulation of T.

Malthus's theories.

Pierre-francois verhulst biography: Pierre François Verhulst was a

However, Verhulst was convinced that the geometric or exponential growth of population would be curtailed by constraining factors before Malthus's "positive checks" emigration, excess mortality due to famine or declining living standards could limit them. That, in itself, was a departure from Malthus's pierre-francois verhulst biography.

Verhulst also believed that the strength of the curtailing factors would increase in a proportional way to the population expansion itself. To elucidate this, Verhulst needed to introduce a hitherto unknown negative function into the overall formula. The result of the work was a demonstration that any population growth rate would essentially follow a bell-shaped curve, starting from zero, steadily increasing to a maximum, and declining once again to zero in a fashion symmetrical to the positive growth phase.

The population stock then evolves according to the elongated Scurve, which has a point of inflection at the maximal value of the growth rate, and then levels off at a new but higher plateau, at which point the growth rate declines to zero. Verhulst checked his theory empirically against population data for France, Belgium, Essex, England, and Russia.

Quetelet, however, was not convinced by his student since he knew of no counterpart in physics. After the publication of Verhulst's theory, the logistic curve was forgotten until its rediscovery by the American biometrician Raymond Pearl and demographer Lowell J. Reed inand British statistician G. Udny Yule's acknowledgment of the significance of Verhulst's finding of almost a century earlier.

From the s onward, many applications for the theory were found in a wide variety of fields. In Verhulst he named the solution the logistic curve. Later, Raymond Pearl and Lowell Reed popularized the equation, but with a presumed equilibrium, Kas. The Pearl-Reed logistic equation can be integrated exactly, and has solution. The solution can also be written as a weighted harmonic mean of the initial condition and the carrying capacity.

Although the continuous-time logistic equation is often compared to the logistic map because of similarity of form, it is actually more closely related to the Beverton—Holt model of fisheries recruitment. Contents move to sidebar hide. Article Talk.