Modelling the flowering of four eucalypt species using new mixture transition distribution models

Abstract

The multivariate relationship between the probability of flowering, in relation to two discrete states of rainfall and of temperature (high/low), is investigated via a mixture transition distribution (MTD) analysis, which allows for a different transition matrix for each lag (up to 12 months backwards in time) to present flowering via a so-called MTDg analysis. The conventional mixture transition distribution (MTD) model considers the effect of each lag to the present independently, and uses equal transition matrices among different lags. Flowering data consisted of monthly flowering records of E. leucoxylon, E. microcarpa, E. polyanthemos and E. tricarpa (1940 and 1970). We extend the MTDg model to allow for interactions (between rain and temperature) to account for changes in the transition matrices amongst the differing lags. The MTDg model with interactions shows that the flowering of E. leucoxylon and E. tricarpa behave similarly with temperature (both flower at low temperature) and have a positive relationship with flowering intensity 11 months ago. Eucalyptus microcarpa behaves differently, in that it flowers at high temperature. MTDg analysis also found a highly significant interaction between mean temperature and rainfall for E. polyanthemos, in that E. polyanthemos does not tend to flower during the winter time (when it is cold and wet). Rainfall has a direct positive impact only on E. tricarpa. These four species are influenced by temperature (and to a lesser extent rainfall) and as a consequence their flowering phenology will possibly change in response to climate change.