Week 4: Predator Prey Dynamics + Functional Responses and Host-Parasite Dynamics

Enemy - Victim Dynamics

• Winner (predator, prey, parasitoid)

• Loser (prey, host)

Conversion efficiency

how many prey needed to produce one predator offspring

Zero growth isoclines

what is the condition for the growth of prey/ predator to be 0

Prey ZGI

Zero growth when predation = population growth

Zero growth when predator density = ratio of prey growth (BR) to attack rate

• essentially when births and deaths balance

Predator ZGI

Zero growth when gains from predation = losses from death

• Mathematics gives the density of prey at which this occurs

4 phase predator-prey population cycle

1. Increase in prey

2. Predators consume more –abundance increases

3. Prey become depleted

4. Predators then crash due to lack of food

How do predator-prey dynamics work with host-parasite relationships?

If ε = 1

• host-parasite, host-pathogen, or host-parasitoid model

In host-pathogen/parasite models:

• N = disease free (susceptible) individuals

• C = infected individuals

• a = disease transmission rate

• Death rate of infected usually increases

  • -(q+d)C

Issues with the hare-lynx example

• numbers of hare and lynx relate to numbers of individuals shot for fur pelts

• same number of hunters going out for the same time each year? → No → different sampling intensity

Is hare-lynx even predator-prey?

• Predator-prey or herbivore-plant

Hare –restricted by grass growth

foraging → out + vulnerable

Lose condition

• Higher predation rate?

• Extra toxins in grass: 2/3 years→ under high herbivory pressure, toxins persist for 2-3 years (about 1/4 of the 8-12 yr cycle)

• ¼ of hare cycle

Driven by predator(s)? Or grass?

Plant-herbivore cycles?

Other predators

Self-Limitation

Limitation in predators→

• Competition

• Territoriality

• Disease: canine distemper virus spread from pet dogs→ purple bands → outbreaks of virus → pop crashes

Generally: self-limitation in predator or prey stabilizes

• Negative density dependence

What are 3 stabilising processes that help prevent predator boom/ bust?

• Generalist predators (switch from rare to common species); more constant predation pressure

• Predator/prey Territoriality; limitation

• Spatial heterogeneity (predator-free refuges)

What affects predator-prey cycles?

• So far → linear relationship assumed (type 1 functional response)

1. Handling time?→ how long they have to handle the prey e.g in marine ecology, crabs having to break into the shells of their food

2. Satiation?

3. Saturation of predators

Functional Response

intake rate of a consumer as a function of food density

Type 2 functional response

Intake of prey always decelerating

• predator's rate of prey consumption begins to slow down as prey density increases and then plateaus when satiation occurs

• most common functional response

• destabilising effect on prey → low prey densities have high mortality

Switching prey species

• Consumers may select some resource items over others

  • Preference for one type

  • Ignore other types

• Switching

  • Preference for more common resource

  • Ignore rare resource

• Search image in head → initially hard to spot a species even if there are many around → after a while, become easier to find/ spot

Type III Functional response

• S shaped curve on graph

• Hard to detect and differentiate from Type II because main difference is at low prey densities

• common/ high density = over-eaten

• low density - prey ignored

• stabilising effect on prey

Microparasites

• Direct reproduction in hosts

• Large numbers within host

• Small size, fast generation times

• Recovered hosts acquire immunity→ immunity may wear off/ be lifelong

• Usually consider infected and non -infected individuals.

• Evolution within hosts?

Examples of microparasites

• Viruses: e.g. measles, chicken pox

  • Lifelong immunity acquired.

• Bacteria: e.g. tuberculosis

  • Immunity neither complete nor life-long.

• Protozoa: e.g. malaria

  • Persistent, chronic disease, antigenic variation leads to repeated infections.

Macroparasites

• No direct reproduction within the definitive host

• Typically larger and have longer generation times than microparasites.

• The immune response often depends on the past and present number of parasites in the host, and tends to be of short duration.

• Thus, macroparasite infections tend to be persistent in nature.

• This category embraces parasitic helminths and arthropods.

Example of macroparasite

Schistosoma → Platyhelminth/ flat worm

Life Cycle

1. Eggs or gravid proglottids in feces are passed into environment

2. Cattle (T.saginata or beef tapeworm) and pigs (T.solium or pork tapeworm) become infected by ingesting vegetation contaminated by eggs/ gravid proglottids

3. Oncospheres hatch → penetrate intestinal wall → circulate to musculature

4. Oncosphere develop into cysticerci in muscle (infective stage)

5. Humans infected by ingesting raw/ undercooked infected meat

6. Scolex attaches to intestine

7. Adults → small intestine

→ involvement of intermediate hosts

Microparasite-Host dynamics: Phases of Infection

1. Latent period – the time between a host being infected and it becoming infectious.

2. Infectious period – the time during which parasite transmission can occur.

3. Incubation period – time from infection to the appearance of symptoms.

4. Recovery period – the time when hosts are immune, often lifelong.

What 4 categories can the host population be divided into? (SEIR MODEL)

1. Susceptible

2. Exposed

3. Infectious

4. Recovered

Often (1), (3),(4) are modelled.

Sometimes only (1) and (3). Depends on the parasite

Terms in SEIR Model Equations

• N = S+E+I+R (total population size)

• m: birth rate

• b: contact rate

• d: death rate (1/d is average lifespan)

• a: rate of becoming infectious (1/a is the latent period)

• g: recovery rate (1/g is the infectious period)

• might not include BR if over short periods of time- assume pop doesn’t change much

• dR assumes lifelong immunity but can move into susceptible pool

R₀

Average number of secondary infections caused by the introduction of an infected host into a completely susceptible host population

= abS / (a+d)(g+d)

What R₀ do we need for an infection to spread/ invade a susceptible population?

R₀ > 1

What can b (contact rate) depend on?

• season

• location

• behaviour

What decreases the chance of a disease to spread/ the threshold density?

Fast recovery + low contact late

critical proportion that must be immunised for eradication

p_c = 1 - (1/ R₀)