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Supplementary Information: Impact of climate change on larch budmoth cyclic
outbreaks
Sudharsana V. Iyengar1, Janaki Balakrishnan2,∗and J¨urgen Kurths3
1School of Physics, University of Hyderabad, Central Univ. PO, Gachi Bowli, Hyderabad 500 046, India.
2School of Natural Sciences & Engineering, National Institute of Advanced Studies (N.I.A.S.),
Indian Institute of Science Campus, Bangalore - 560012, India. and
3Potsdam Institute for Climate Impact Research, PO Box 601203, Potsdam 14412, Germany.
Description / Legends for video files:
1. (a) For Supplementary video-1 file (SI3a attract.mov) :
Video of bifurcation diagram of the larch budmoth (LBM) population density xwith respect to the climate
parameter sfor varying h.
For low hvalues the bifurcation diagram seems to move towards left, i.e, shifting towards lower svalues. At
h=0.048 one can see the creation of an attractive region which pulls points towards it from both sides. As h
increases the attractor moves towards higher values of s, though not strictly following an increasing trend. At
h= 0.071, the attracting region is roughly centred around s=0.04, when hincreases to 0.159, the attractor
occurs near s=0.18. In the screenshot in Fig.3(a) at h=0.722, the attracting region is centred around s=0.6
and it stabilises there despite any further increase in h.
2. (b) For Supplementary video-2 file (SI3b repel.mov) :
Video of bifurcation diagram of the larch budmoth (LBM) population density xwith respect to the climate
parameter sfor varying α. In the screenshot of the video (Fig.3(b)), at α=0.545 there is a repelling region
centered around s=0.41. The repeller begins at higher values of sand slowly moves towards the left (decreasing
s) as αincreases. For instance, at α=0.23 the repelling region is formed around s=0.75; as αincreases to 0.485,
the repeller shifts to s=0.6, shifting further to s=0.4 when α=0.555. The repelling and attracting regions
appear to be boundaries demarcating different stability regions in the phase space of the system. These sources
and sinks may be identified with climatic tipping points pushing the system into different stable states.
(c) Supplementary Figure S4 showing the predicted (but rare) 40 & 100 year cycles:
0 20 40 60 80 100110
0
0.05
0.1
0.15
0.2
0.25
0.3
Years between outbreaks
Relative frequency of Outbreaks
FIG. S4: Detail of the histogram showing relative frequency of budmoth outbreaks as obtained with our model, showing the
predicted (though rare) 40 and 100 year cycles both depicted with increased marker-sizes for visual clarity. Parameter values
of h=0.7, s=0.84 and λ=1.23, yield 40 year cycles while 100 year cycles result for h=0.76, s= 0.53 and λ=1.13.
∗Corresponding author. Electronic mail: janaki05@gmail.com