Co-Evolved Balance
Evidence for this balance seen in introduced species as
Evolutionarily Uncoupled predators and prey:
chestnut blight, sea lamprey, synthetic chemicals
Lotka-Volterra predator-prey equations
Based on chemical principles of mass action:
Random encounters of enzymes and substates
Predator and prey responses proportional (linear responses) to their density
Paired equations for predator and prey\
Exponential growth and death
For prey:
dP/dt = rP prey growth
including predation losses: dP/dt= rP – a’CP
C = number of predators
a’ = attack frequency
For Predator: birth rate dependent on;
attack frequency (a’CP)
growth efficiency (f) (food converted to offspring)
dC/dt = fa’CP
including starvation from lack of prey: dC/dt = fa’CP – qC
q = preadator mortality rate
Running equations simultaneously develops cycles Fig 15.1 c, d
Assumptions:
Prey grow exponentially in absence of predators
Predator declines exponentially in absence of prey
Predators move randomly amoung randomly dispersed prey
Capture as a proportion of contact constant for all P & C
densities
# prey taken increases in direct proportion to prey increases
(linear)
no time lags for handling: instantaneous
energy intake immeadiately converted to offspring
Gause: Fig 15.4
Paramecium + Didinium: all eaten both die
Paramecium immigration + Didinium: cycles
Paramecium + Sediment+ Didinium:
Didium dies, refuge population explodes
Predator Functional and Numerical Responses
Functional Response: predator behavior to increasing prey
Holling”s type I, II, III Fig 15.7
Type I: linear increase with prey increase (Lotka Volterra assumption)
Fig. 15.8
Type II: decreasing increasing rate with increased prey: saturation
Fig 15.9 a, b, c, d
Identical to Michalis-Menton enzyme kinetics models
Handling time and Search time
For herbivores: biting and chewing
Chewing may compete with biting for intake rate (rabbit)
Type III: initial accelarated response followed by Type II
Fig. 15.9 e, f, g, h
Percent eaten is density dependent:
lower at low prey density, higher at high prey density
Ususally involve more than one prey type:
Refuge densities and Switching
Behaviors resullting in type III responses:
Changing preference to more abundant prey
Ignoring rare prey
Concentration on better patches of habitat
Search Images: education
Numerical Response: growth and immigration
Prey density dependent Aggregative responses Fig 15.12
Low & high density, no discrimiation
Predator interference at high density
Intermeadiate prey densities result in aggregative responses
Fig. 15.13. Low density of prey, scattered predators
Foraging Theory
Optimal Foraging: energetic efficiency, gain-loss
Suitable prey may have refuges in defence, time and space
Prey Selection
Optimum Size, Qualitative preference: Prey Prefence indices
Foraging Descisions
Where to look
Economic Models
Residence time in a patch should be related to
the density/quality of the prey (Fig 15.19)
the point at which prey depletion results in dreasing energy returns
the amount of time required to reach a new patch
Predators should “Give up” when time intervals between captures exceeds some threshold value
Whether to Pursue
Pursuit should be dependant on:
time required for pursuit relative to average pursuit time
search time between prey to pursue
energy reurn relative to pursuit time
If major expendature is for search, all items are pursued: insect/worm eating birds
If major expendature is for pursuit, selectivity for easily captured items: wolves, lions
Many animals have a territory or Home Place: Central Place Foraging
Should be more selective farther from nest/den to balance pursuit time
Exposure of the predator to predation, necessity to obscure central place
Is maximizing energy intake = minimizing time for acquisition of necessary energy
Risk Sensitive foraging
Time spent exploring unknown patches a risk
Predation risk