Predator-Prey Cycles and Effects of Climate Change Hao Wang Department of Mathematical and Statistical Sciences Centre for Mathematical Biology University of Alberta

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

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: 160-164)‏

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

Empirical Data lemming (prey) density stoat (predator) density (Olivier Gilg, Ilkka Hanski et al 2003, Science 302:866-868)‏

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.

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).

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

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.

Lemming-Stoat Delayed Model Hao Wang, John Nagy, Olivier Gilg, and Yang Kuang. The roles of predator maturation delay and functional response in determining the periodicity of predator-prey cycles, Mathematical Biosciences, Vol. 221: 1-10 (2009)

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.

Lemming-Stoat Delayed Model Hao Wang, John Nagy, Olivier Gilg, and Yang Kuang. The roles of predator maturation delay and functional response in determining the periodicity of predator-prey cycles, Mathematical Biosciences, Vol. 221: 1-10 (2009)

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.

Lemming-Stoat Delayed Model Hao Wang, John Nagy, Olivier Gilg, and Yang Kuang. The roles of predator maturation delay and functional response in determining the periodicity of predator-prey cycles, Mathematical Biosciences, Vol. 221: 1-10 (2009)

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

Lemming-Stoat Delayed Model Hao Wang, John Nagy, Olivier Gilg, and Yang Kuang. The roles of predator maturation delay and functional response in determining the periodicity of predator-prey cycles, Mathematical Biosciences, Vol. 221: 1-10 (2009)

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)‏

Empirical Data Fitting

Sensitivity Analysis

Compare the lemming cycle to the snowshoe hare cycle lynx hare

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.

1 10-year period 1976 1996

Sensitivity Analysis

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. 38-year moose cycle for moose-wolf interaction

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

Who knows the evolution direction?

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)‏

Lemming-Stoat Delayed Model predation rate increases with snow melt lemming stoat Hao Wang, John Nagy, Olivier Gilg, and Yang Kuang. The roles of predator maturation delay and functional response in determining the periodicity of predator-prey cycles, Mathematical Biosciences, Vol. 221: 1-10 (2009)

past present future

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.