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Predator Isocline = Neutral Stability, Stable Equilibrium Or Prey Extinction Depending on Intersection Point Changing the Predator Numerical Response

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Predator Isocline = Neutral Stability, Stable Equilibrium Or Prey Extinction Depending on Intersection Point Changing the Predator Numerical Response Predation model predictions • Simplest Lotka-Volterra. Linear functional response no K = neutral stability • L-V model with K = stable equilibrium • No K, type II or III functional response = unstable • Hump shaped prey isocline, vertical predator isocline = neutral stability, stable equilibrium or prey extinction depending on intersection point Changing the predator numerical response: Have so far assumed the predator numerical response βV (per capita growth rate of predators as function of prey abundance) is a linear function of prey abundance But predators may have carrying capacities determined by factors other than prey availability. - In state space, a carrying capacity will bend the predator zero growth isocline to the right (more prey does not increase predator numbers) - This will generate a stable equilibrium along the horizontal part of the predator isocline Predator carrying capacity: predator can no longer drive prey to extinction. Stable coexistence What happens if a predator has multiple prey? Outcome will depend on whether prey species cycle in concert If prey abundances are not strongly positively correlated then as one prey species becomes scarce, the predator can continue to feed and increase its population size. Unstable equilibrium predators drive prey to extinction Predator carrying capacity and multiple prey species: Predator isocline with a positive slope is stable (damped oscillations) Any factor that rotates the prey or predator isocline in a clockwise direction (ie predator carrying capacity) will tend to stabilize interactions Conclusions: predation models • Simple predation models generate a variety of behaviors - neutral stability, stable limit cycles, and equilibrium stability. • Adding predator or prey carrying capacities tends to stabilize models whereas incorporating non-linear functional responses and time lags generally leads to instability. • Multiple prey species can destabilize populations if it allows predators to over-exploit prey, but predation may also facilitate prey coexistence (discussion paper) - depending on predator preference and competitive interactions among prey species Refugia and Dispersal Predator-prey interactions are difficult to study in the lab because lab conditions do not capture the spatial extent and complexity of natural habitats: Gause (1934) set out to look for evidence of population cycles between Paramecium (prey) and Didinium (predator) in a microcosm experiment. - Didinium quickly consumed all the Paramecium and then went extinct. -When sediment was placed in the bottom of the microcosm Paramecium was able to hide, Didinium went extinct and Paramecium population recovered. Huffaker (1956, 1958) Experiments with predator prey dynamics using mites Cyclamen mite (Tarsonemus): pest of strawberries Predatory mite (Typhlodromus): feeds on cyclamen mite and could potentially control population Growing house experiment: Two treatments 1. Strawberry plants + predator and prey mites 2. Parathion insecticide (p) = kills predator but not prey Predator! present! No predator! Mite predator and prey dynamics mirror observations in the field New strawberry fields are over-run by cyclamen mites first year - then controlled second year. Prey better dispersers?? Application of parathion in fields led to cyclamen mite outbreak. Why do predators control prey in this system? 2 key features • High reproductive rate r of the predator • Alternate food source for predator (can maintain high pop. density when cyclamen mite is rare. Dispersal - refuges in time? Dispersal of prey away from predators can also help stabilize predator-prey dynamics by preventing prey extinction… Huffaker’s (1958) oranges experiment Six-spotted mite (prey); Typhlodromus mite (predator) Dynamics on arrays of oranges and rubber balls Initial experiments: Add 20 prey mites (parthenogenic females) Prey population increased to 5-8,000 individuals and levelled off Add 2 predator female mites Predators increased - prey wiped out. Speed of extinction depended on dispersion of habitat (oranges) because takes time for predators to arrival Under what circumstances could predator and prey coexist? Coexistence achieved by helping prey dispersal (launch pads), while hindering predators (vaseline) Black spots= predators. Orange color=low density; red=high density of prey mites Classical predator-prey dynamics Gilg et al. (2003, 2006) finally explain what really happened to the lemmings… Lemming populations cycle with a clear four-year periodicity Cyclic dynamics of the arctic collared lemming Gilg et al. (2003, 2006) Lemmings live in high arctic tundra (NW Greenland) 4 predators: stoats, snowy owl, skua and fox Measured lemming densities, over several years, along with food availability and predation rates (observations, skat samples, pellet samples, lemming fur in borrows) No evidence that food or space limits lemming pop. growth Skua Fox eaten/day Lemmings response Functional Lemming density (indiv/ha) What kind of functional response is this? Skua Fox Numeric response Numeric produced/yr Young Stoat Stoats always use lemming nests in winter. Only predator to show a delayed response - highest number year after lemming pop peak response Numeric Observed data Squares = lemmings Circles = nests Model prediction Conclusions: 1. No space or food limitation for lemmings i.e., no intrinsic prey density-dependence (resource limitation) 2. Only one specialist predator drives lemming population cycles 3. Dynamics generated by destabilizing predation by the stoat (time lag effects) 4. Delayed numerical response of stoat driving force for numerical fluctuations 5. Can use the model to examine effects of removing one or more predators on prey population dynamics Apparently Gilg (2006) not the last word on lemmings… Menyushina et al. (2012) found lemming cycles on Wrangel Island, where there are no stoats. -Cycles are different at Wrangel (longer periodicity 5-8 yrs), and higher minimum lemming densities. -Suggested that cycles may be changing across the arctic – may represent climate change – warmer conditions lead to rainfall then icing? What about examples where food does become limiting? • Most famous example is cycling of Canadian lynx and snoe-shoe hare (Elton and Nicholson 1942, Journal of Animal Ecol 11:215) • Hare populations cycle with peak abundance ~ every 10 yr • Major source of hare mortality is predation • Lynx populations appear to closely track hare populations often peaking 1-2 years after the hare peak Classic example of Lotka-Volterra neutral stability? Snowshoe hare and lynx pelts collected by trappers for the Hudson Bay Co. Various hypotheses: Elton - variation in solar radiation resulting from periodic sunspot activity Keith (1963) Wildlife’s ten year cycle. Univ Wisconsin Press: Starvation/disease at high population sizes or predation? Lemming-style predator-prey model does not work: - On Anticosti Island, Quebec there are no lynx but hare populations cycle anyway… Keith (1983,1984) Oikos 40:385-395; Wildlife Monog. 90:1-43 looked at the cycle in detail and concluded: Hare populations are co-limited by food availability and by predation from many sources (goshawks, owls, weasels, foxes, Coyotes). Hare population growth rates are sufficient to produce rapid depletion of food resources (principally buds and stems of shrubs and saplings). Furthermore, induced defenses of hare forage results in additional declines in food availability. Definitive(?) study of snoeshow hare dynamics in Yukon (Krebs et al. 1995) Recognized that can only understand system with manipulation experiment -1 km2 plots. Monitoring of populations for 8 years -Fertilizer to increase plant growth (N,P,K) -Electric fences to keep large predators out (permeable to hares) -Food addition treatments -Predator exclusion = 2x hare density -Food addition = 3x hare density -Predator exclusion x Food addition = 11 x hare density Some unresolved questions: mechanism? Why hares low so long? What’s grousing the red grouse?? (apart from being shot that is…) Number of grouse shot (solid line) is a good measure of grouse abundance (dashed). Some years grouse are very scarce Number of grouse shot (solid line) is a good measure of grouse abundance (dashed). Some years grouse are very scarce Grouse population growth rate is strongly negative correlated with intensity of infection of nematode parasites Nematodes affect adult survivorship Control population Grouse treated once with worm medicine Grouse treated twice with worm medicine Effect of nematocide on population cycling Proportion treated 20 % 10 % 5 % none Nematodes can explain population cycling, but not synchronicity of population cycling among populations Cattadori et al. (2005) 91 grouse populations Harvest records 1839-1994 High population synchronicity was correlated with climate: Warm dry May impede egg development followed by wet cold July inhibited nematode transmission. Predation escape through predator satiation If predation rates decline at high prey densities (type II and III functional responses) then predator satiation may allow prey species to maintain their populations. Many examples: Janzen suggested that seed predation is a major selective force favouring ‘masting’ (massive super-annual seed production) e.g. Janzen (1976) Why bamboos wait so long to flower. Ann. Rev. Ecol. Syst. 7:347-391 Bamboos are the most dramatic mast fruiters, with many species Fruiting at 30-50 yr intervals and some much longer e.g. Phyllostachys bambusoides fruits at 120 year intervals! Williams et al (1993) Predator
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