To determine what is lost or gained by using fewer age classes in a Leslie matrix model, I develop a novel method to reduce a Leslie matrix model to a …
To determine what is lost or gained by using fewer age classes in a Leslie matrix model, I develop a novel method to reduce a Leslie matrix model to a smaller one. An aggregated (“reduced”) Leslie matrix model inherits important properties of the original model. To illustrate the influence of aggregation on asymptotic and transient dynamics, I apply the aggregator to 10 Leslie matrices for populations drawn from a diverse set of species.
We give a very short proof of the Theorem: Suppose that $f(x) = a_1x + a_2x^2 + \cdots$ is a formal power series with coefficients in an integral domain, and …
We give a very short proof of the Theorem: Suppose that $f(x) = a_1x + a_2x^2 + \cdots$ is a formal power series with coefficients in an integral domain, and $a_1$ is a primitive $n^{\mathrm {th}}$ root of unity $(n \in {\Bbb N})$. If the $n^{\mathrm {th}}$ iterate $f^{(n)}(x) \equiv f\big (f(\cdots f\big (f(x)\big )\cdots \big )$ satisfies $f^{(n)}(x) = x + b_mx^m + b_{m + 1}x^{m + 1} + \cdots$, with $b_m \neq 0$ and $m > 1$, then $m \equiv 1 \pmod {n}$.