1. Predator-Prey Cycles and Effects of Climate Change
Hao Wang
School of Mathematical and Statistical Sciences
University of Alberta

2. Trends of Cycles Period Amplitude Incidence CO2 Predator-Prey Cycles
Temperature
Global Climate Change
Predator-Prey Cycles
Hypothesis
Trends of Cycles
Period
Amplitude
Incidence

3. Does climate change have strong
effects on predator-prey cycles?
What are the effects?
How about feedback?

4. Predator-prey cycles

5. Top-down regulation:
Prey limited by Predator
Bottom-up regulation:
“Predator” limited by “Prey”

6. Generic Predator-Prey System

7. Population Cycles Large groups 29% 204 694 All 33% 1 3 Bivalves
Gastropods
50% 6 12
Crustaceans
16% 13 79
Insects
43% 56
129
Fish
109
328
Mammals
13% 18
139
Bird
Fraction
Periodic #
Testing #
Taxon
Large
groups
(Bruce Kendall, John Prendergast and Ottar Bjornstad 1998, Ecology Letters, 1: )‏

8. Nearly 30% of testing populations are cyclic.
Cycles occur mainly in mammal and fish populations.
The incidence of cycles increases with latitude in mammals alone.
There is no latitudinal gradient in cycle period.
Cycle amplitude declines with latitude in some groups of fish.
(Kendall et al 1998, Ecology Letters)‏

9. For mammals, why does the incidence of cycles increase with latitude?
(Kendall et al 1998, Ecology Letters)‏

10. Why does the incidence of cycles increase with latitude only in mammals?
Many fish, birds and insects can mitigate the effects of seasonality by migration, but few of mammals do so.
(Kendall et al 1998, Ecology Letters)‏

11. Climate has strong effects on population cycles.
What’s the evolution direction of incidence and features of population cycles with climate change?

12. Population Cycles in a Small Mammal - Lemmings
brown lemming
in Alaska
collared lemming
in Greenland

13. Empirical Data
lemming (prey) density
stoat (predator) density
(Olivier Gilg, Ilkka Hanski et al 2003, Science 302: )‏

14. Lemming Background
The population numbers of lemming fluctuate greatly over a period of 3-4 years until now.
Ecologists suspect that such oscillations are controlled by a trophic mechanism.
Their principal summer foods are moss and vascular plants.
Lemmings are eaten by many animals, like weasels, arctic fox and a bigger number dies when they try to cross rivers, lakes or seas.

15. Trophic Mechanisms
Brown lemmings in Alaska: bottom-up regulation (P.Turchin et al 2000, Nature).
Collared lemmings in NE Greenland: top- down regulation (Olivier Gilg et al 2003, Science).

16. The lemming cycle driven by predators
Top-down Regulation
The lemming cycle driven by predators

17. For collared lemmings in NE Greenland, the
major sources of mortality are predation by
stoats, arctic foxes, snowy owls and long-tailed
skuas. Only the stoat is a specialist.

18. Lemming-Stoat Delayed Model
(Hao Wang, John Nagy, Olivier Gilg and Yang Kuang, Mathematical Biosciences)

19. Functional Response Test
(Olivier Gilg et al 2003, Science)‏
Predation by stoat is modeled with Holling Type III functional response, which was
used to incorporate a possible "refuge" for the lemming at very low densities. when
lemmings are so dispersed, then they must become very hard to locate for the stoat.

20. Lemming-Stoat Delayed Model

21. Stoat Maturation Delay
The stoat maturation delay is about 3 months.
The stoat juvenile/maturation death rate is chosen to be the maximum stoat death rate, 4/year.

22. Lemming-Stoat Delayed Model

23. Prey Dependent Death Rate
The stoat death rate depends on lemming density
This is tested by Olivier Gilg from field.

24. Lemming-Stoat Delayed Model

25. Modified Logistic Growth
Per capita growth rate
for the lemming
mammals
Population density x
(Richard M. Sibly et al and John D. Reynolds et al 2005, Science)‏

26. Empirical Data Fitting

27. Sensitivity Analysis

29. Compare the lemming cycle to the snowshoe hare cycle
lynx
hare

31. Hare-Lynx Delayed System
In general view, the snowshoe hare cycle is also controlled
by predators like collared lemming in NE Greenland.
Differences: (i) Holling Type II functional response;
(ii) constant lynx death rate.

32. 1
10-year period
1976
1996

33. Sensitivity Analysis

34. Goal: 4<10 Therefore the predator maturation delay is the key
Predation rate and conversion rate are comparable.
Lynx maturation death rate is less than that of stoat
which makes the period of snowshoe hare cycle
smaller than the period of lemming cycle.
Lynx maturation delay is 1.5 years, much larger
than the stoat maturation delay, 3 months. This
makes ‘4<10’ possible.
Therefore the predator maturation delay is the key
factor to generate different periods (4-year and 10-
year) of lemming and hare cycles.

35. Maturation Hypothesis
Climate change leads to variation
of predator maturation period.

36. Who knows the evolution direction?

37. Climate change results in more frequent
Snow Melt Hypothesis
Climate change results in more frequent
freeze-thaw events leading to a more
shallow and icy snow pack, which will
probably act to expose small mammals
to predators……
(Callaghan et al 2004, Ambio;
Callaghan et al 1995, Phil. Trans. R. Soc. Lond. A)‏

38. Lemming-Stoat Delayed Model
predation rate increases with snow melt
lemming
stoat

39. past
present
future

40. Observation
For collared lemmings in NE Greenland,
period of the cycle is decreasing and
amplitude is almost unchanged. Climate
change has different effects on lemming
cycles in different locations because of
different mechanisms triggering them.