discussion

Views:
 
Category: Entertainment
     
 

Presentation Description

No description available.

Comments

Presentation Transcript

Slide1: 

Boreal and Arctic Predator-Prey Dynamics in the Face of Global Climate Change A tutorial/discussion/free-for-all John Nagy1,2, Yang Kuang2,3, Hao Wang2, Irakli Loladze3,4 and whomever else we can recruit in the meantime… 1Department of Life Science, Scottsdale Community College 2Department of Mathematics and Statistics, Arizona State University 3Mathematical Biosciences Institute, The Ohio State University 4Department of Mathematics, University of Nebraska, Lincoln

Slide2: 

Boreal and Arctic Predator-Prey Dynamics in the Face of Global Climate Change Plan of attack: Nagy: Introduce the issue at hand; review what we already know Wang: Introduce a new predator-prey model; show its behavior and predictions; describe a hypothesis not generally known Loladze: Examine the consequences of stoichiometric constraints on predator-prey; attack an open problem—GCC’s effect on predator-prey dynamics through stoichiometry; nearly convince us all that we know just about everything Kuang: Return to the general problem; show beyond the shadow of a doubt that we really don’t know anything

Slide3: 

Published by AAAS G. A. Meehl et al., Science 307, 1769 -1772 (2005) Fig. 1. Time series of CO2 concentrations, surface air temperatures and sea level rise for various scenarios evaluated with a mathematical model of global climate change

Slide4: 

Published by AAAS G. A. Meehl et al., Science 307, 1769 -1772 (2005) Fig. 2. Surface temperature change for the end of the 21st century (ensemble average for years 2080-2099) minus a reference period at the end of the 20th century (ensemble average for years 1980-1999) from 20th-century simulations with natural and anthropogenic forcings

Slide5: 

The Phenomenon in the Boreal Forest

Slide6: 

The Phenomenon in the Arctic Picture from www.columbia.edu/~pjs2002/arctic/ Kaikusalo and Angerbjorn (1995) Picture from www.fjellrev.no/fakta Actually a lemming Lemmus lemmus

Slide7: 

The Problem in the Arctic “Climate is somehow involved in all the hypotheses of population cycles related to plant-herbivore interactions.” –Callaghan et al. (2004) “[T]he Arctic has an unusually high proportion of carnivorous species and a low proportion of herbivores. As herbivores are strongly dependent on responses of vegetation to climate variability, warming might therefore substantially alter the trophic structure and dynamics of Arctic ecosystems.”

Slide8: 

The Problem in the Boreal Forest –Dale et al. (2001)

Slide9: 

Typical Assaults on Predator Prey Dynamics 1) Continuous time, no spatial component (ODE): where M is a predator mortality function that includes “natural” and artificial (e.g., hunting) mortality; is prey-to-predator conversion efficiency; r and K are prey intrinsic rate of increase and carrying capacity sans predation, respectively.

Slide10: 

Typical Assaults on Predator Prey Dynamics A smorgasbord of predator functional responses to prey: Holling Type I: Holling Type II: Holling Type III: Kazarinov and Driessche’s generalization: Ivlev’s function: Gause, Rosenzweig:

Slide11: 

Less Typical Assaults on Predator Prey Dynamics Functional responses the depend on density of both prey and predator Beddington, DeAngelis et al.: Ratio dependent : Hassell, Varley variant: Crowley, Martin: after rescaling after rescaling

Slide12: 

Some Highlights from the Holling ODEs Consider Holling Type II Functional Response Predator-free Attractor (K = 1) Prey Density (x) Predator Density (y)

Slide13: 

Some Highlights from the Holling ODEs Consider Holling Type II Functional Response Coexistence with decaying oscillations (K = 1) Prey Density (x) Predator Density (y)

Slide14: 

Some Highlights from the Holling ODEs Consider Holling Type II Functional Response Decaying oscillations, long transient (K = 1) Prey Density (x) Predator Density (y)

Slide15: 

Some Highlights from the Holling ODEs Consider Holling Type II Functional Response Stable limit cycle (K = 1) Prey Density (x) Predator Density (y)

Slide16: 

Typical Assaults on Predator Prey Dynamics 2) Continuous time, continuous space (PDE): Model of an Algal Bloom A special case with no advection or diffusion, and Holling type III functional response. Time (t) Plankton Density Phytoplankton Zooplankton

Slide17: 

Typical Assaults on Predator Prey Dynamics 2) Continuous time, continuous space (PDE): Sufficient mixing causes the bloom to form a permanent pattern Hernandez-Garcia and Lopez (2006)

Slide18: 

Potential Effects of Global Climate Change 1) Continent-wide synchronization of cycles may disrupt food webs “If climate change results in … more shallow and icy snow pack, this will probably … expose small mammals to predators, … and thereby prevent peak abundances of lemmings and voles. For nomadic predators whose life history tactic is based on asynchronous lemming populations at a continental scale, [frequent large-scale] climatic anomalies that [induce] continental-wide synchrony is very likely to have devastating effects.” –Callaghan et al. (2004) Picture from www.columbia.edu/~pjs2002/arctic/ Kaikusalo and Angerbjorn (1995) Picture from www.fjellrev.no/fakta Actually a lemming Lemmus lemmus

Slide19: 

The “Moran Effect” Initiated by GCC Annual census data (simulated) from four geographically isolated vole populations spanning a continent-wide early spring thaw, which exposes voles to predation, in year 15. Vole populations were all equally affected in that year, resulting in synchronization of cycles thereafter. Early spring thaw Periods of vulnerability

Slide20: 

“Recently observed increased predation pressure on waterbirds in various Arctic regions might reflect a change of the lemming cycle in response to climate change with secondary effects on predators and waterbirds as alternative prey.” –Callaghan et al. (2004) Tremblay et al. (1997) Snowy owl from www.ronausting.com/birds/owls/snowy King Eider from www.greatnorthern.net/~dye/king_eiders Potential Effects of Global Climate Change 2) More general disruptions of food webs

Slide21: 

Potential Effects of Global Climate Change Potential Effects of Global Climate Change www.isleroyalewolf.org Increases in winter snow depth on Isle Royale associated with the North Atlantic oscillation result in grey wolves … hunting in larger packs. These larger packs reduce the population size of moose … which in turn allows higher productivity of balsam fir (Post et al. 1999). –McCarty (2001) 3) Unanticipated effects all the way up the trophic cascade

Slide22: 

Potential Effects of Global Climate Change From the perspective by Birks and Birks (2004) 4) Effects on soil chemistry…

Slide23: 

Potential Effects of Global Climate Change 4) …translate to altered stoichiometry at the origin of food webs

Slide24: 

References: Tremblay, J.P., G. Gauthier, D. Lepage, A. Desrochers. (1997) Wilson Bulletin 109:449–461. Callaghan, T.V. et al. (2004) Ambio 33:436–447. Kaikusalo, A. and A. Angerbjorn. (1995) Annales Zoologici Fennici 32:69–77. McCarty, J.P. (2001) Cons. Biol. 15:320–331. Post, E. et al. (1999) Nature 401:905–907. Dale, V.H. et al. (2001) BioScience 51:723–734. Birks, H.J.B. and H.H. Birks (2004) Science 305:484–485. Hernandez-Garcia, E. and C. Lopez. (2006) Underst. Complex Syst. ???:117–129.

authorStream Live Help