Download Predator-prey interactions

We’ve considered various defensive adaptations, what
about adaptations that enhance a predator’s
abilities/success?
One obvious adaptation is in tooth compliment and
structure: herbivores have large grinding surfaces on their
molar teeth, and many are hypsodont, meaning that the
teeth keep growing through much of adult life. The
grinding would otherwise ‘wear out’ an animal’s teeth.
Animals that are hunters and meat eaters need to be able
to grasp and tear. They have sharp (the text calls them
‘knifelike’) incisors for tearing and canine teeth to grasp
and hold prey.
Here is a comparison of two mammalian herbivores and
a carnivore:
Note the lack of canines and the larger number and
prominence of premolars and molars in the herbivores.
Both horse and deer have incisors – horses have both
upper and lower incisors, deer only lower ones.
Adaptations in tooth structure are also useful in following
the evolution of species in response to their diet.
Microtus, the field vole, originally lived in grasslands with
only C3 grasses. Then the expansion of the range of C4
grasses from central Mexico into American prairies and
grasslands made for tougher chewing. The surface of the
molars evolved to become more complex (more ridges
and ‘triangles’) to effectively grind the new food source.
M. pennsylvanicus –
mostly C3 foods
M. ochrogaster – a
prairie vole that eats a
mixed C3/C4 diet
Some animals (e.g. snakes) swallow prey whole. Their
adaptations are in jaw structure and hinging to permit a
much larger gape. In snakes the hinge point for the lower
jaw is moved from the quadrate to the supratemporal
bone. This text figure indicates the expanded potential
(double entendre fully intended):
Different diets (herbivorous versus carnivorous) also
make differing demands on digestion. Plant tissues require
a much more prolonged digestion to extract nutrients and
calories – cell walls have to be crushed or broken down,
frequently requiring the ‘cooperation’ (mutualism) of gut
flora and fauna. The most obvious differences are in the
length of the small and large intestine…
And finally, it’s important to recognize that animal prey
also have defenses against predation. Those defenses
include:
1. crypsis (camouflage),
2. chemical sprays,
3. warning colouration (as an indicator of some type of
[usually] chemical defense),
4. mimicry (look like something that is well defended),
5. deceptive colouration
6. mobbing behaviour
Crypsis (or camouflage) is hiding in plain sight. The
organism has evolved to look similar enough to its
background to escape detection by predators.
The most famous example is the peppered moth, that
evolved changing camouflage rapidly in response to soot
darkened tree bark. Here we have a leaf-mimicking
mantid and a homopteran called a ‘lantern fly’
Chemical sprays – skunks are the obvious example,
especially with the increased numbers in Windsor.
However, there are many other examples, e.g. the
bombardier beetle in your text:
It sprays an almost boiling liquid very accurately toward
the eyes of an approaching predator.
Warning colouration (and mimicry) – organisms warn a
potential predator of their toxicity or unpalatability by
obvious colours. Typically the colours are orange, red and
yellow contrasted with black. Coral snakes are one
example. Here are three coral snake species patterns:
Only one of these two snakes is a poisonous coral snake;
the other one isn’t poisonous, but found in the same areas.
Would you take a chance on recognizing the difference?
In Batesian mimicry one species is toxic, and the other
species gains protection by looking like the toxic species.
How might this evolve?
We have evidence that the mimicry works. One of the
famous examples is the mimicry between Viceroy and
Monarch butterflies.
Here’s what happens when a bluejay eats the unpalatable
model, the Monarch…
In Müllerian mimicry, both the model and the mimic are
dangerous or unpalatable prey; each gets protection by
looking like a different toxic or unpalatable prey.
Deceptive colouration – imagine yourself as a bird
predator approaching this tasty moth, with its wings
folded. Suddenly, as you get near, it opens both front and
hind wings. What you see is the ‘eyes’ of a much larger
organism, perhaps it’s an owl??
Mobbing behaviour – large predators (like owls) are
much less maneuverable than their smaller prey, and
focus closely on a single prey item as they try to chase it.
Both single and mixed species flocks will mob an owl,
and prevent it from chasing any one prey without
confusion…
Before we move on to the theory of predator-prey (or
other consumer-resource) interactions, there is one last
group to consider: detritivores (or, in some texts,
saprophages) sometimes called decomposers. These
organisms feed on dead organic matter. They are critical
in ecosystems, but interactions with their food source
don’t influence the abundance of that food – it’s already
dead!
Since we’re interested in interactions and how they affect
the dynamics of interacting species, that is the first (and
probably the only) mention of detritivores.
Predator prey interactions in greater detail…
In the 1920s, ecologists reasoned that predator-prey
interactions would take the form of cycles in population size
of both predator and prey…
PREY INCREASE
PREDATOR
DECREASE
PREDATOR
INCREASE
PREY DECREASE
The result should be cycles – coupled oscillations in the
population sizes of predators and their prey. That is what
the Lotka-Volterra equations describing predator-prey
interactions predict. In abstracted form, here’s what we
expect they should look like:
Based on the logic of the interaction, ecologists searched for
evidence of cycles. They also did experiments to try to
produce cycles in laboratory populations.
One of the first series of experiments was Gause’s study of
the interaction between Paramecium and a predator,
Didinium.
Didinium
engulfing a
Paramecium
This is what Gause’s basic results looked like:
Predator efficiency was very high.
Predators could quickly exploit the prey population, driving
it to extinction. Without food, it followed its prey into
inevitable extinction.
This was not what the logic had led scientists to expect.
Gause then made the experiment slightly more realistic. He
gave the prey a refuge. By putting a straw infusion or
oatmeal sediment in the bottom of the flasks, the prey could
hide from the predator. (Were they really hiding, or did
chance allow the Paramecium who happened to move into
the infusion escape predation?)
Here’s what Gause then found…
Prey grows to its carrying capacity
N
With prey able to ‘hide’, predator
eventually goes extinct
TIME
Once the predator had consumed available prey it went
extinct. Then the prey that had been in the refuge were free
to increase to their carrying capacity.
This experiment, too, failed to produce cycles of predator
and prey populations. It failed to support the theoretical
prediction of cycles.
Gause tried one further complication. He generated
immigration by adding predators or prey when their number
neared extinction. Here’s what he then saw…
Gause’s results indicated that:
• closed systems (without immigration) are prone to
extinction
• cycles are only likely to occur when immigration is
involved in the dynamics of species
• refuges for prey prevent or delay its extinction
• high predator efficiency (in prey capture) is destabilizing
Gause’s difficulty in producing oscillation in predator and
prey populations were used to suggest that possibly
oscillations in natural predator and prey populations were
rare.
Huffaker, an ecologist at U.C. Berkeley, thought that the
problem might have been the simplicity of Gause’s system,
that his experimental system was ‘unrealistic’.
So, Huffaker created a more complex experimental universe
in the laboratory, one in which the environment was
‘patchy’.
His experiments used two species of mites: a six-spotted
mite, Eotetranychus, as the prey and another mite,
Typhlodromus, as the predator.
The universe consisted of oranges and tennis balls connected
by various bridges (paper strips, wires) to permit mites to
move from one ball to another. Here are a couple of his
‘environments’…
4 oranges connected by fine wires
120 oranges, trays linked by paper bridges, oranges mostly covered
by vaseline.
The six-spotted mite happily fed on the oranges, and the
predatory mite happily fed on the six-spotted mite. Here is
the basic result he got…
Huffaker was surprised. He was of a school that believed
‘complexity’ would confer ‘stability’ on his system and the
interaction. He thought that both predator and prey would
persist, that the spatial complexity would prevent the
predator from killing prey mites on all the oranges they
occupied at the same time.
This failure did not deter him. He created a yet more
complex system. The universe consisted of >200 oranges.
There were bridges, and each orange had vaseline barriers
that limited how much area the mites could use. Since prey
mites became crowded on the space of an orange rapidly,
they dispersed and colonized new oranges at a high rate.
In this system coupled oscillations were observed.
Here’s what the oranges looked like…
The numbered segments at the top divide the available area
to make it easier to count mites.
Here’s what the oscillations he observed looked like:
What had been learned by Gause’s and Huffaker’s
experiments in sum:
1. Cycles do occur in complex systems
2. Both experiments (but in different ways) establish that the
prey must have some advantage (refuges or an advantage
in the migration among patches)
3. While some local populations (mites on an orange) went
extinct, others were established by migration before
extinction could occur
4. What this has described is a metapopulation, a set of
component populations that exchange immigrants and
emigrants. In Huffaker’s experiment each orange was a
patch that could be occupied by a local population.
These classical experiments reveal that…
• Migration among patches is critical to persistence. In
Gause’s experiments, he generated the migration
artificially from outside the system.
• Metapopulation structure favors persistence of the regional
population (the entire metapopulation), though local
extinction (the mites on some specific oranges) may
occur
• Complex systems (more oranges, higher rates of prey
species immigration) are more likely to persist than
simpler ones (fewer oranges, less complex spatial
structure)
• Simpler systems lack ‘stability’
Even before Gause’s and Huffaker’s experiments, a
mathematical theory (equations) had been developed to
describe predator-prey dynamics. Alfred Lotka and Vito
Volterra developed differential equations (that is, in the same
form as the equation for continuous exponential or logistic
growth, developing functions to describe the rate of change
in the size of predator and prey populations) to model the
interaction.
Each species influences the growth rate of the interacting
species. The growth rate of the prey population is reduced
by interaction with predators. The growth rate for the
predators depends on (and increases with) interaction with
the prey.
Prey rate
of growth
= prey growth – death of prey
due to predators
Predator rate = growth due - natural death rate
of growth
to contact with
of predators
prey
Now we turn those word equations into proper differential
equations…
For the prey population:
dR
 rR  cRP
dt
where R is the size of the prey population
r is its intrinsic rate of increase for the prey
c is the predator’s efficiency (sometimes referred to
as capture efficiency)
P is the size of the predator population
The first term is the exponential growth rate of the prey in
the absence of predators. The second term is the removal of
prey by the predators.
When you use Populus to do next week’s lab, you will see
an equivalent equation with slightly different terms. Here’s
the equation in Populus:
dN
 r1 N  CNP
dt
N has replaced the R in the previous equation, r1 has replaced
r, and c has been capitalized to C. Meanings are identical.
The parallel equation for predators is:
dP
 acRP  dP
dt
Here P is the population size for predators
R is the population size for prey
c is once more the capture efficiency
a is the efficiency with which food (captured prey) is
turned into predator population growth
d is the per capita death rate for predators
Note that this terminology (as in the text) differs slightly
from that in the Populus models. Use this one.
Just to make sure, here is the Populus equation for predator
population dynamics:
dP
  d 2 P  gCNP
dt
Here d2 has replaced d, the R of the text equations has
become N (as in the prey equation), c has been capitalized to
C, but still is capture efficiency, and a from the text has been
renamed g, but still measures conversion efficiency.
Going on with solution…
As with previous differential equation models, we are
particularly interested in the equilibrium.
We set dR/dt = 0
If dR/dt = 0, then
rR = cRP
dividing each side by R,
Peq = r/c
… and we set dP/dt = 0
If dP/dt = 0, then
acRP = dP
dividing both sides by P,
Req = d/ac
This seems fairly simple; each species has an equilibrium
value, but only the joint equilibrium point is stable. If the
system diverges from this single value, it does not return to
that joint equilibrium. The equilibrium point is not what
theory calls an attractor. This is called neutral stability.
Instead, perturbation causes populations to oscillate around
the equilibrium in a continuous cycle. These are the cycles
of predator-prey theory.
The cycle even has a period:
2
T
rd
Note that the system oscillates faster when prey growth (r)
or predator death (d) occur at higher rates.
Here are what the cycles look like…
And here is the reason…
An error:
this is the
predator
isocline
If we combine the dynamics of predators and prey, we get a
pattern (a trajectory) usually diagrammed as a circle:
these lines that indicate 0 growth of predators and
prey respectively, are called equilibrium isoclines
Where dP/dt = 0, the number of prey is in balance with
predator growth. This is the predator isocline. To the left
(low prey #s) predators decline, to the right (high prey #s)
predators increase.
Here Req = d/ac. If the death rate of predators, d, increased
and either (or both) c or a decreased, the predator isocline
would move right; a larger prey population would occur at
equilibrium.
This horizontal isocline is set where dR/dt = 0. The prey are
at 0 growth. This is set by the predators, and is the prey
isocline. Below it (low #s of predators), prey numbers grow,
above it (high # predators), prey numbers decline.
Peq = r/c. Increasing r or decreasing c would raise the prey
isocline, i.e. the prey could support a larger number of
predators. They grow faster and/or are less efficiently
captured.
We can compare what this phase plane diagram is indicating
with a graph of the coupled oscillations in predator and prey
numbers:
Now let’s compare the predictions of Lotka-Volterra theory
with the observations of the classic experiments of Gause and
Huffaker…
Feature
Lotka-Volterra model
Experiments
Cycles
Predicted
Not seen in simple
systems
Refuges
Not a part of the model
Important for prey
persistence
K
Not set for prey or
predator
Yes, observed
System
Closed
Open – migration
makes persistence more
likely
Like all simple models, there are key assumptions built into
the Lotka-Volterra model. They are:
1. The parameters for prey growth rate, r, and predator death
rate, d, are constant.
2. The parameters for predator capture efficiency, c, and for
the efficiency with which captured prey are turned into
predator growth, a, are constant over the full range of prey
densities.
If these assumptions hold, we can describe the predation as
density independent. The dynamics of both are driven by
the interaction. There is no K for either species. The
growth of each is limited by the other. The model is of
continuous growth.
3. All responses are instantaneous, with no time lag for
handling and ingesting prey. Energy input to predators is
immediately converted to birth of predators.
Finally, this isn’t really an assumption, but rather the
character of the model equations:
4. Consumption of prey by predators is proportional to the
rate at which encounters occur. The number of prey
consumed increases linearly with number of predators.
What do we mean by “density-independent” predation?
An example:
Prey Number
Number eaten
% eaten
10
1
10%
100
10
10%
1000
100
10%....
That is what a constant capture efficiency means!
You can learn more about the models and
implications in preparation for the laboratory of
Oct.31 –