Abstract
Periodic outbreaks of the larch budmoth Zeiraphera diniana population (and the massive forest defoliation they engender) have been recorded in the Alps over the centuries and are known for their remarkable regularity. But these have been conspicuously absent since 1981. On the other hand, budmoth outbreaks have been historically unknown in the larches of the Carpathian Tatra mountains. To resolve this puzzle, we propose here a model which includes the influence of climate and explains both the 8–9 year periodicity in the budmoth cycle and the variations from this, as well as the absence of cycles. We successfully capture the observed trend of relative frequencies of outbreaks, reproducing the dominant periodicities seen. We contend that the apparent collapse of the cycle in 1981 is due to changing climatic conditions following a tipping point and propose the recurrence of the cycle with a changed periodicity of 40 years – the next outbreak could occur in 2021. Our model also predicts longer cycles.
Highlights
Periodic outbreaks of the larch budmoth Zeiraphera diniana population have been recorded in the Alps over the centuries and are known for their remarkable regularity
Previous studies on larch budmoth (LBM) population cycles have established the presence of a third trophic level – parasitoids which prey upon budmoth larvae[6,7,8,9]
The current health of the plant which depends upon its nutrient supply and its previous state after the last budmoth infestation is captured well through a dimensionless Plant Quality Index (PQI) which is directly related to the needle length[9]
Summary
The general behaviour is expressed in terms of equilibria: stationary states, periodic solutions, etc. depending upon parameter values. Environmental changes following a climatic tipping point may affect the atmosphere, hydrosphere, biosphere, etc., which in turn are reflected in various ways such as changes in the home range of animals, changes in flowering and sprouting times, changes in population cycles, etc These changed conditions would be manifested as different phenomena in the resulting bifurcation diagrams with respect to the climate parameters. As the movies run, varied behaviour is seen: source and sink-like regions (attractors/repellors) are formed, bubble creation and destruction at specific s values, different chaotic bands, etc., converging from either side and merging, or getting repelled away from source These appear to be stability boundaries of basins in the phase space of the system, demarcating regions of differing stability. This suggests that source or sink-like regions seen in the bifurcation movies may be identified with climatic tipping points
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