Download Predation model predictions

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
Fox
Functional response Lemmings eaten/day
Skua Lemming density (indiv/ha)
What kind of functional response is this?
Numeric response
Young produced/yr
Skua Fox
Numeric response
Stoat
Stoats always use lemming
nests in winter. Only
predator to show a delayed
response - highest
number year after
lemming pop peak
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 satiation by periodical cicadas
Ecology 74:1143-1152
Magicicada spp emerge once every 13 or 17 yrs up to 4 million/
ha= 4 tonnes of cicadas/ha - the highest biomass of a natural
population of terrestrial animals ever recorded!
Monitored Cicada populations in N. Arkansas
Estimated emergence rates by capturing insects in traps on the
ground as they came out of the soil
Captured dead adults in traps and determined predation rate by
birds by counting discarded wings
- Estimated 1,063,000 cicadas emerged in 16 ha
- 50% of population emerged on just four nights
- Birds killed a large proportion of the first emergents when Populations were low, but only killed 15 % of the population overall
Prey may escape consumption by virtue of size
e.g., Paine (1966) Gastropod Muricanthus eventually becomes too
large for Heliaster starfish to feed on them.
Perhaps more often, small prey escape detection, or resources
expended in capturing them exceed those obtained by their
consumption
If there is size selection of prey by predators across a community
then this may be an important determinant of community structure
Example of a trade-off: the ‘size-efficiency hypothesis’
Brooks and Dodson (1965) Predation, body size, and
composition of plankton
Proposed that size-dependent predation by fish determines the size structure of freshwater zooplankton
Observations:
- lakes seldom contained abundant large zooplankton (>0.5 mm)
and small Zooplankton (<0.5 mm) together
- large zooplankton did not coexist with plankton feeding fish
Hypotheses:
Large zooplankton assumed to be superior competitors for food (phytoplankton) because of greater filtering efficiency
Planktivorous fish thought to selectively consume large-bodied,
competitively superior plankton
Crystal lake Connecticut.
No planktivorous fish (Alosa)
Large plankton
Crystal lake 22 years later after introduction of Alosa