New Zealand Journal of Ecology (1981) 4: 45- 51

Graphical Analysis of Lag in Population Reaction to Environmental-Change

Research Article
F. H. Wood 1,2
Marion A. Foot 1
  1. Entomology Division, DSIR, Private Bag, Auckland, New Zealand
  2. Present address: Ruakura Research Station, Ministry of Agriculture and Fisheries, Hamilton, New Zealand

A method of graphical analysis which accounts for cause/effect lag between biological populations and environmental factors is presented. The method involves analysis of ellipsoid curves generated by delayed population responses to cyclic environmental variables. Six ellipse types are distinguished which determine the type of relationship involved and provide a key to equations for calculating the lag interval. The equations are based on the formula τ = Lθ/360, where θ = either arcsin x' /x" or 90+ arccos x' /x", x' and x" are measurements taken from the ellipse, τ = lag and L = independent cycle length.

The method is constrained to populations where generation time is small relative to duration of the independent cycle (L), and where lag is no greater than half L. Sampling interval should be short relative to L.

Examples are cited to demonstrate application of the method, and interpretation of biological relationships from it is discussed.