Multi-Trophic Level, Pairwise Species Interactions:Predator-Prey, Parasitoid-Host & Parasite-Host

Relationships

“Nature red in tooth & claw”Alfred Tennyson (1809 - 1892)

Why study predation & parasitism?

A basic-science answer: All organisms are subject to various sources of mortality, including starvation, disease & predation; to understand population & community structure & dynamics requires knowing something about these processes

Predation & Parasitism

Photo from Greg Dimijian

Why study predation & parasitism?

A basic-science answer: All organisms are subject to various sources of mortality, including starvation, disease & predation; to understand population & community structure & dynamics requires knowing something about these processes

A utilitarian answer: Understanding how much natural mortality occurs, and why, in populations is critical to managing those that we exploit (e.g., fisheries, game animals, etc.), or wish to control (e.g., weeds, disease organisms or vectors, invasive species, etc.)

Photo from Greg Dimijian

Predation & Parasitism

Modeling predation: Lotka-Volterra model

Prey (victims) in the absence of predators:dV/dt = rV

Losses to predators are proportional to VP (probability of random encounters) and (capture efficiency – effect of a single predator on the per capita growth rate of the prey population)

Large is exemplified by a baleen whale eating krill, small by a spider catching flies in its web

Prey in the presence of predators:dV/dt = rV - VPwhere VP is loss to predators

V is the functional response of the predator (rate of prey capture as a function of prey abundance); in this case linear, i.e., prey capture increases at a constant rate as prey density increases

Predation

Predation

In the model’s simplest form, the predator is specialized on 1 prey species; in the absence of prey the predator pop. declines exponentially:

dP/dt = -qP P is the predator pop. size, and q is the per capita death rate

Positive population growth occurs when prey are present:dP/dt = ßVP - qP

ß is the conversion efficiency – the ability of predators to turn a prey item into per capita growth

Large ß is exemplified by a spider catching flies in its web (or wolves preying on moose), small ß by a baleen whale eating krill

ßV is the numerical response of the predator population – the per capita growth rate of the predator pop. as a function of the prey pop.

dV/dt > 0

dV/dt < 0

Equilibrium solution:

For the prey (V) population: dV/dt = rV - VP 0 = rV - VP VP = rV P = r P = r/

The prey isocline

P depends on the ratio of the growth rate of prey to the capture efficiency of the predator

^

Figure from Gotelli (2001)

The predator isocline

V depends on the ratio of the death rate of predators to the conversion efficiency of predators

Equilibrium solution:

For the predator (P) population: dP/dt = ßVP - qP 0 = ßVP - qP ßVP = qP ßV = q V = q/ß

dP/dt > 0dP/dt < 0

^

Figure from Gotelli (2001)

Combined graphical solution in state space:

The predator and prey populations cycle because they reciprocally control one another’s growth

Figure from Gotelli (2001)

Combined graphical solution in state space:

The predator and prey populations cycle because they reciprocally control one another’s growth

Figure from Gotelli (2001)

Prey limited by both intraspecific competition and predation:

dV/dt = rV - VP - cV2

VP due to predator cV2 due to conspecificsdP/dt = ßVP – qP

Now the prey isocline slopes downward, as in the Lotka-Volterra competition models

At this point, the prey population is self-limiting, i.e., no predators are required to keep the population from changing in size.

The predator and prey populations reach a stable equilibrium

What did this point represent in the competition models?

Figure from Gotelli (2001)

Satiation

Host-switching, developing a search image, etc.

Why might functional responses have these shapes?

R

ate

of p

rey

capt

ure

Victim abundance (V)

Figure from Gotelli (2001), after Holling (1959)

Functional Response Curves

Predators with either a Type II or Type III functional response:

Type II for prey:dV/dt = rV - [(kV) / (V+D)]P

Type III for prey:dV/dt = rV - [(kV2) / (V2+D2)]P

Where k = maximum feeding rate; D = half-saturation constant, i.e., abundance of prey at which feeding rate is half-maximal

The equilibrium in both cases (Type II & Type III functional responses) is unstable

Predator:dP/dt = ßVP – qP

Figure from Gotelli (2001)

An even more realistic prey isocline may be a humped curve:

In this case, the position of the predator isocline with respect to the maximum in the prey isocline determines dynamics

For example, imagine a combination of Allee effects, decreasing impact of predators with increases in prey numbers (e.g., Type II or III functional response), plus increasing impact of intraspecific competition

Figure from Gotelli (2001)

An even more realistic prey isocline may be a humped curve:

In this case, the position of the predator isocline with respect to the maximum in the prey isocline determines dynamics

For example, imagine a combination of Allee effects, decreasing impact of predators with increases in prey numbers (e.g., Type II or III functional response), plus increasing impact of intraspecific competition

Figure from Gotelli (2001)

An even more realistic prey isocline may be a humped curve:

In this case, the position of the predator isocline with respect to the maximum in the prey isocline determines dynamics

For example, imagine a combination of Allee effects, decreasing impact of predators with increases in prey numbers (e.g., Type II or III functional response), plus increasing impact of intraspecific competition

Figure from Gotelli (2001)

Coexistence with stable limit cycles

Coexistence at stable equilibrium

Unstable equilibrium

Figure from Gotelli (2001)

This idea developed out of a desire to warn against indiscriminate use of resource enrichment to bolster a population under management

Figure from Gotelli (2001)

Paradox of enrichment in predator-prey interactions(Rosenzweig 1971)

“control” conditions enriched conditions

This idea developed out of a desire to warn against indiscriminate use of resource enrichment to bolster a population under management

Figure from Gotelli (2001)

Paradox of enrichment in predator-prey interactions(Rosenzweig 1971)

“control” conditions enriched conditions

But is it only of theoretical interest?

See: Abrams & Walters 1996; Murdoch et al. 1998, Persson et al. 2001

In the real world enrichment generally fails to destabilize dynamics in this way, perhaps due to nearly ubiquitous occurrence of some invulnerable prey

Figure from Gotelli (2001)

Paradox of enrichment in predator-prey interactions(Rosenzweig 1971)

“control” conditions enriched conditions

R1 [N]

R2

[P]

A B

1 2 34

5

6

Resourcesupply point

Consumptionvectors

Slope of consumptionvectors for A

Slope of consumptionvectors for B

This is one way in which competitive interactions can also result in a paradox of enrichment

This idea also developed out of a desire to warn against indiscriminate use of resource enrichment to bolster a population under management

Imagine what happens when we fertilize with N

Paradox of enrichment in competitive interactions(Riebesell 1974; Tilman 1982, 1988)

Predator is a complete

specialist on the focal prey

Predator’s K depends on the abundance of

the focal prey

Predator uses multiple prey, so predator’s K is

independent of the focal prey; in this case predator has

low K

Where would the predator isocline be if the predator uses multiple prey and deterministically drives the focal prey extinct? Figure from Gotelli (2001)

Effect of changing the predator isocline(by changing the numerical response of the predator)

Tends to stabilizedynamics

Figure from Gotelli (2001)

Effect of prey refuges or immigration (rescue effect)

Experiment demonstrating the stabilizing influence of refuges

Six-spotted mite feeds on oranges and disperses among oranges by foot or by ballooning on silk strands

Predatory mite disperses by foot

See Huffaker (1958)

In experimental arrays, predators drove prey extinct in the absence of prey refuges; predator pop. then crashed

In large arrays with refuges (see fig.) predators & prey coexisted with coupled oscillations

Experiment demonstrating the stabilizing influence of refuges

Six-spotted mite feeds on oranges and disperses among oranges by foot or by ballooning on silk strands

Predatory mite disperses by foot

See Huffaker (1958)

Hare pops. cycle with peak abundance ~ every 10 yr;Lynx pops. track hare pops., with ~ 1 - 2 yr time lag

Canada Lynx & Snowshoe Hare exhibit synchronized oscillatory dynamics in nature (Elton & Nicholson 1942)

Figure from Gotelli (2001)

Lynx & hare

Hare populations are co-limited by food availability & predation (e.g., Keith 1983); hares rapidly deplete food quantity (principally buds & young stems of shrubs & saplings) & quality (hares stimulate induced defenses of food plants)

Low food availability increases susceptibility to predation (lynx, weasels, foxes, coyotes, goshawks, owls & etc.)

Simple Lotka-Volterra model is not a complete explanation; e.g., cycles are broadly synchronized, even on some Canadian islands w/o lynx

Sun spot cycles and their influence on climate & food plants are also implicated (e.g., Krebs et al. 2001)

At any rate, the lynx-hare cycle is more complex than suggested by the superficial resemblance to Lotka-Volterra models

Lynx & hare

How might the evolutionary advent of phenotypic plasticityalter predator-prey dynamics?

Agrawal (2001), Fig. 1

Phenotypic Plasticity & Predation

Mean-field assumption: all prey are the same (size, etc.)

Small prey may escape detection, or resources expended in capturing and handling them may exceed resources obtained by their consumption (the “celery bind”)

Size-dependent predation

Large prey may escape consumption owing to mechanical constraints on feeding, e.g., Paine (1966) found that the gastropod Muricanthus becomes too large for Heliaster starfish to handle

Brooks and Dodson (1965) proposed that size-dependent predation by fish determines the size structure of freshwater zooplankton

Observations:

Lakes seldom contained abundant large zooplankton (>0.5 mm) & small zooplankton (<0.5 mm) together

Large zooplankton were not found with plankton-feeding fish

Size-dependent predation

Crystal Lake, ConnecticutNo planktivorous fish

Large plankton

Crystal Lake 22 yr after introduction of

Alosa aestivalis (Blueback Herring)

Size-dependent predation

Brooks and Dodson (1965) proposed that size-dependent predation by fish determines the size structure of freshwater zooplankton

Observations:

Lakes seldom contained abundant large zooplankton (>0.5 mm) & small zooplankton (<0.5 mm) together

Large zooplankton were not found with plankton-feeding fish

Hypotheses:

Large zooplankton are superior competitors for food (phytoplankton) because of greater filtering efficiency

Planktivorous fish selectively consume large-bodied, competitively superior plankton

Size-dependent predation

Detailed analyses of the mechanisms of change showed that:

Fish do indeed selectively remove large-bodied zooplankton

But, large-bodied zooplankton do not competitively exclude small- bodied zooplankton… they eat them (intra-guild predation)!

Size-dependent predation

In some cases brood parasitism represents“predation” and parasitism combined

Davies 1992, pg. 217

Brood Parasitism

Microparasites – parasites that reproduce within the host, often within the host’s cells, and are generally small in size and have short lifespans relative to their hosts; hosts that recover often have an immune period after infection (sometimes for life); infections are often transient; examples include: bacterial, viral, fungal infectious agents, as well as many protozoans

Macroparasites – parasites that grow, but have no direct reproduction within the host (they produce infective stages that must colonize new hosts); typically much larger and have longer generation times than microparasites; immune response in hosts is typically absent or very short-lived; infections are often chronic as hosts are continually reinfected; examples include: helminths and arthropods

Parasitoids – insects whose larvae develop by feeding on a single arthropod host and invariably kill that host; e.g., Nicholson-Bailey models

Conceptual models of parasitism(usually categorized by function rather than taxonomy)

Susceptible hosts (X)

Infected hosts (Y)

Immune hosts (Z)

Birth

Death

a a a

b α + b b

β v

dX/dt = a(X+Y+Z) - bX - βXY + Z dY/dt = βXY - (α+b+v)Y dZ/dt = vY - (b+)Z

Coupled differential equations, one for each type of host

What is βXY? Combined encounter & infection rate

See: Anderson & May (1979); May (1983)

Modeling microparasite-host dynamics

Red grouse (U.K.) and their nematode parasites (Dobson & Hudson 1992)

Grouse: dH/dt = (b-d-cH)H - (α+)P Incorporates reduction in survival (α) & reprod. ()

Free-living stages (eggs and larvae) of the worms: dW/dt = P - W - βWH

Adult worm population (within caecae of grouse): dP/dt= βWH - (+d+α)P - α(P2/H)(k+1/k) Final term represents aggregation among hosts (smaller k more aggregated)

Parameter values estimated in the field Scotland (wetter) – model predicted observed 5-yr cyclesEngland (drier) – model predicted observed lack of cycles (possibly owing to higher mortality of free-living stages)

Modeling macroparasite-host dynamics

Standardized S of parasitesin native range

Sta

ndar

dize

d S

of

para

site

sin

intr

oduc

ed r

ange

0 0.5 1.00

0.5

1.0

molluscscrustaceansamphibians & reptilesfish

mammalsbirds

Parasite species richness (shown below) and parasite prevalence (% infected hosts) showed similar patterns

1-to-1

line

Redrawn from Torchin et al. (2003)

Parasite-host interactions & invasive species

Evolutionary trajectories of virulence…

Some key results:

Horizontal vs. vertical transmission (see Ewald 1994) Horizontal transmission generally leads to greater virulence than vertical transmission

Greater virulence usually results from higher transmission rates in general

Degree of alignment of reprod. interests (see Herre et al. 1999) The tighter the dependence of parasite reproduction on host reproduction, the less virulent parasites tend to become

Parasite-host interactions through evolutionary time

Darwinian Agriculture & Medicine make good use of these observations (see R. F. Denison; G. C. Williams & R. M. Nesse)

Co-cladogenesis and other macro-evolutionary processes…

Parasite-host interactions through evolutionary time

Cospeciation Host switch Duplication

Missing the boat Extinction

Host

Failure to speciate

Parasite

Coexistence

Which are most likely under strictly vertical transmission?From J. Weckstein (2003)

??

All else being equal, will host-switches preferentially occur onto more common potential hosts?

All else being equal, will host-switches preferentially occur onto potential hosts that are more closely

related to the current host?

?

?

What patterns do we expect in communities in which parasites (predators, parasitoids) have multiple potential “choices”?

?

? ?

Ghosts of Predation Past

Photos from: http://www.hoothollow.com

North American Cheetah (Miracinonyx) went extinct ~11,000 yr ago;even so the Pronghorn Antelope remains the fastest land animal in N. Am.

Miracinonyx was similar toextant Acinonyx jubatus