In cmhoove14/DDNTD: Density Dependence in Neglected Tropical Diseases

knitr::opts_chunk$set(echo = TRUE)

require(knitcitations)
  cleanbib()
  cite_options(cite.style = "numeric",
               citation_format = "pandoc")

Simple ecological models fit to breeding population/offspring relationship

Applied to fisheries data

Where $S$ is spawner population size and $R$ is recruitment, simple ecological models such as the Myers model[ $R=(\alpha S^\delta)/(1+(S^\delta/K)) $] in which $\delta=1$ represents Beverton-Holt dynamics and $\delta>1$ implies presence of depensation or Allee effects.

Myers et al Science 1995

Fit Myers model above to fisheries data with >15 year time series with $\delta=1$ or $\delta$ as a free parameter then used likelihood ratio test to test for significance of $\delta\neq1$

Statistical models with penalized splines to estimate the shape of the relationship between pop size and pop growth rate

Stenglein and van Deelen 2016

The per capita population growth rate at time $t$ in population $i$ is estimated as $pgr_{i,t}=ln(N_{i,t}/N_{i,t-1})$. The shape of the relationship between $N_{i,t}$ and $pgr_{i,t}$ is then estimated via the regression:

$$pgr_{it}\sim N(\mu_{i,t},\sigma_i^2)\ \mu_{i,t}=\beta_i\times ln(N_{i,t})+\alpha_{i,t,k}\times Z_{i,t,k}$$

where $\alpha_{i,t,k}\times Z_{i,t,k}$ is the spline portion which provides flexibility in the shape between $\mu_{i,t}$ and $ln(N_{i,t})$. The authors claim that a hump-shaped spline function resulting from a fit to the data is evidence for an Allee effect

r citet("10.1371/journal.pone.0150535")

Commonly applied to fisheries data in which stock size and offspring population are measured. r citet(c("10.1098/rspb.2017.1284", ))