In de 18e eeuw werd algemeen aangenomen dat de toename van een populatie dieren kan worden beschreven met behulp van een meetkundige rij. Een model uit die tijd is:
\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{model }1\right.\left\{\begin{array}{l} P_{n}=r \cdot P_{n-1} \\ P_{0}=c \end{array}\text { model } 1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l}P_{n}=r\cdot P_{n-1}\\ P_0=c\end{array}\text{ model }1\right.\left\{\begin{array}{l} P_{n}=r \cdot P_{n-1} \\ P_{0}=c \end{array}\text { model } 1\right. model 1
In dit model geldt:
•P_{n}$\quad P_{n}is de populatiefractie na$njaar. Dat is de grootte van de populatie als deel van de maximale populatie.$P_{n}is dus een getal tussen 0 en 1.
•c$\quad cis de startpopulatiefractie. Ook dit getal wordt uitgedrukt als een deel van de maximale populatie (en dus geldt$0<c<1).
•r$\quad ris de reproductiefactor: een getal dat aangeeft hoe snel een populatie zich per jaar uitbreidt.