exploitation.txt

UNIT 7: Predation

----------------------------------------------------------------------

EXTRA Look into FIGHFIG

----------------------------------------------------------------------

TSEC Introduction

	Exploitation is when interactions between two species are good for
	one species and bad for the other

		Typically, the ``exploiter" is taking resources from the other
		species

	Exploitation is widespread and highly diverse

----------------------------------------------------------------------

Examples

	Antelopes graze on trees

	Lions eat antelopes

	Ticks feed on lions

	Swallows eat ticks

	Bacteria reproduce inside the swallow

	Viruses infect the bacteria ...

----------------------------------------------------------------------

PSLIDE Exploitation examples

WIDEFIG webpix/antelope.jpg

---------------------------------------------------------------

PSLIDE Exploitation examples

WIDEFIG webpix/tiger_antelope.jpg

---------------------------------------------------------------

PSLIDE Exploitation examples

FIGHFIG webpix/tick.jpg

---------------------------------------------------------------

PSLIDE Exploitation examples

FIGHFIG webpix/figbird.jpg

---------------------------------------------------------------

PSLIDE Exploitation examples

FIGHFIG webpix/tb.jpg

---------------------------------------------------------------

PSLIDE Exploitation examples

FIGHFIG webpix/phage.jpg

---------------------------------------------------------------

Types of exploitation

	These words are usually not used precisely, and I'm not going to
	test you on them

		{\it Predation}: a {\it predator} kills and eats {\it prey}

		{\it Parasitism}: a {\it parasite} lives on or in a {\it host}
		and makes use of host resources

			Many parasites are {\it pathogens}, meaning that they cause
			disease

		{\it Parasitoidism}: a {\it parasitoid} develops inside a host,
		but must kill the host to complete development

		{\it Grazing}: a {\it grazer} takes food from another organism
		(typically a plant), and moves on

----------------------------------------------------------------------

Borderline cases

	The categories listed above are useful, but not precise -- and not
	used precisely

		Do rabbits predate small plants, or graze them?

		Are small insects on large trees grazers, or parasites?

		Do intestinal worms in healthy people count as pathogens?

		Anthrax is usually referred to as a parasite (or predator!),
		but should probably really be a parasitoid

----------------------------------------------------------------------

Our course

	This unit will focus mostly on predation; also relevant for grazing

	The next unit (disease) will focus on micro-parasites: things that have
	populations inside individual hosts

----------------------------------------------------------------------

Exploiters and resources

	In this unit, I will often refer to the species being exploited as the {\bf
	resource species}

		There is a strong analogy between resource species, and {\bf abiotic}
		resources like water, light and nitrogen

			Both benefit the species that use them

			Both may, or may not, be depleted significantly by the activities
			of the species in question

----------------------------------------------------------------------

TSS Balance and equilibrium

	In an exploiter-resource system, each species has an indirect,
	negative effect on itself. Why?

		ANS As resource species population grows, the number of
		exploiters should increase, which is bad for the resource species

		ANS As exploiter population grows, the population of the resource
		species should decrease, which is bad for the exploiter

	Since each species has a negative effect on itself, these systems
	have a {\em tendency} to come to equilibrium

		Equilibrium may be reached, or we may cycle around it

----------------------------------------------------------------------

Equilibrium questions

	What factors determine the equilibrium levels of a
	resource-exploiter system?

	What factors determine whether neither, one or both species survive?

	What happens if people perturb the system (e.g., by eating a lot of
	one or the other species)?

	The equilibrium is of interest even if it is not reached:

		if there are cycles, the equilibrium is what the system cycles
		around.

----------------------------------------------------------------------

Reciprocal control

	Imagine a pair of exploiter and resource species whose population
	densities are mostly regulated by each other

		The per capita growth rate of the exploiter population depends
		mostly on the density of the resource species

		The per capita growth rate of the resource population depends
		mostly on the density of the exploiter species

	POLL What will determine equilibrium values? What determines equilibrium number of rabbits?

		ANS For equilibrium, each species must be at the density
		required to keep the \emph{other} species balanced

		ANS We should have about as many foxes as required to control the rabbit
		population, and about as many rabbits as required to keep the fox
		population about constant.

----------------------------------------------------------------------

TSS Tendency to oscillate

	In an exploiter-resource system, each species has an indirect,
	negative effect on itself

	This effect is delayed in time: it takes time for each species to
	respond to the other

	This means these systems have a tendency to oscillate

		RESTING The same idea as from our population models, but with an explicit
		mechanism for delay

	RESTING There is a simple intuition for how these systems oscillate:

		ANS Exploiter goes up \rec Resource goes down \rec Exploiter goes
		down \rec Resource goes up \rec Exploiter goes up \ldots

----------------------------------------------------------------------

ONSLIDE Persistence of oscillations

	Resource-exploiter systems have a \emph{tendency} to oscillate

	In the simplest possible models, oscillations are \textbf{neutral}

		e.g., they don't get larger or smaller

	In more realistic models, large oscillations will tend to get smaller

		If small oscillations also tend to get smaller, we say that
		oscillations are \textbf{damped}

			Oscillations which are not damped are \textbf{persistent}

		If small oscillations tend to get larger, the system (usually)
		approaches a \textbf{limit cycle}

----------------------------------------------------------------------

ONSLIDE Damped oscillations

DOUBLEFIG exploitation/pp.sim.Rout-2.pdf exploitation/pp.sim.Rout-0.pdf

----------------------------------------------------------------------

ONSLIDE Neutral cycles

DOUBLEFIG exploitation/neutral_cycles.sim.Rout-4.pdf exploitation/neutral_cycles.sim.Rout-5.pdf

----------------------------------------------------------------------

ONSLIDE Neutral cycles

FIG exploitation/neutral_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

ON PSLIDE Neutral cycles

FIG exploitation/neutral_cycles.sim.Rout-4.pdf

----------------------------------------------------------------------

ON PSLIDE Limit cycles

FIG exploitation/pplimit.sim.Rout-7.pdf

----------------------------------------------------------------------

ON PSLIDE Limit cycles

FIG exploitation/pplimit.sim.Rout-5.pdf

----------------------------------------------------------------------

ONSLIDE Limit cycles

DOUBLEFIG exploitation/pplimit.sim.Rout-5.pdf exploitation/pplimit.sim.Rout-7.pdf

----------------------------------------------------------------------

ONSLIDE Limit cycles

FIG exploitation/pplimit.sim.Rout-3.pdf

----------------------------------------------------------------------

ONSLIDE Neutral vs.\ limit cycles

	POLL  What is the difference between neutral cycles and limit cycles?

		ANS Neutral cycles have no tendency to get larger or smaller

			ANS Large cycles stay large, small cycles stay small

		ANS Limit cycles converge to a limit

			ANS Large cycles get smaller, small cycles get larger

----------------------------------------------------------------------

ON PSLIDE Neutral cycles

FIG exploitation/neutral_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

ON PSLIDE Limit cycles

DOUBLEFIG exploitation/pplimit.sim.Rout-2.pdf exploitation/pplimit.sim.Rout-0.pdf

----------------------------------------------------------------------

ON REPSLIDE Limit cycles

DOUBLEFIG exploitation/pplimit.sim.Rout-5.pdf exploitation/pplimit.sim.Rout-7.pdf

----------------------------------------------------------------------

ON PSLIDE Limit cycles

FIG exploitation/pplimit.sim.Rout-3.pdf

----------------------------------------------------------------------

TSEC A simple model

	We can investigate exploiter-resource systems using simple
	models

	Resource-species growth rate may depend on density of exploiter, or
	resource species, or both:

		$\frac{dN_f}{dt} = r_f(N_e, N_f) N_f$

	Exploiter growth rate may depend on density of exploiter, or
	resource species, or both:

		$\frac{dN_e}{dt} = r_e(N_e, N_f) N_e$

	At equilibrium:

		ANS $r_e = r_f = 0$

		ANS $r_f = N_e = 0$

		ANS $N_e = N_f = 0$

		ANS If $N_f =0$, what happens to $r_e$?

----------------------------------------------------------------------

Interactions 

	What makes this a resource-exploiter system?

		$\frac{dN_f}{dt} = r_f(N_e, N_f) N_f$

		$\frac{dN_e}{dt} = r_e(N_e, N_f) N_e$

	ANS We expect the resource species to be good for the exploiter
	($r_e$ goes up as $N_f$ goes up)

	ANS We expect the exploiter to be bad for the resource species
	($r_f$ goes down as $N_e$ goes up)

	Mnemonic: $e$ for exploiter, $f$ for food.

----------------------------------------------------------------------

Simplest model

	The simplest model of resource-exploiter interaction is when their
	per-capita growth rates only respond to each other.

		$\frac{dN_f}{dt} = r_f(N_e) N_f$

		$\frac{dN_e}{dt} = r_e(N_f) N_e$

	This is a pure \textbf{reciprocal control} model: resource growth rate depends only on exploiter density, and vice verse

----------------------------------------------------------------------

PSLIDE Resource-exploiter interactions

WIDEFIG webpix/shark_fish.jpg

----------------------------------------------------------------------

PSLIDE Resource-exploiter interactions

FIGHFIG webpix/gm_defoliation.jpg

----------------------------------------------------------------------

Ratios

	This model assumes:

		The rate at which individual fish get eaten depends on the
		total number of sharks

		The rate at which individual sharks eat fish depend on the total
		number of fish

	The ratio of sharks to fish does not matter directly

	Does this make sense? What happens in the model if there are too many
	sharks, for example?

		ANS The number of fish will go down

		ANS \emph{Then} the number of sharks will go down

		ANS Then the number of fish will go up ...

----------------------------------------------------------------------

SS More detailed models

----------------------------------------------------------------------

PSLIDE How do populations affect their own growth rates?

FIG webpix/fish_schools.jpg

----------------------------------------------------------------------

Resource populations

	POLL  Why might we expect resource population to affect per-capita growth rate of the resource species?

		ANS Competition for food, territory, mates (density
		dependence)

		ANS Co-operation for protection, food-gathering (Allee effects)

		ANS Protection by numbers (predator satiation, co-operation)

----------------------------------------------------------------------

Exploiter populations

	Why might we expect exploiter population to affect per-capita growth
	rate of the exploiter species?

		ANS Competition for resources, territory, mates (density
		dependence)

		ANS Co-operation for food-gathering, competing with other exploiters
		(Allee effects)

----------------------------------------------------------------------

Types of cycles

	The simplest models of reciprocal control lead to neutral cycles

		Cycles starting from any starting point will go back through that
		starting point

		These seem unrealistic; why should there be no tendency to
		spiral out or in for any cycle?

	To take the next step, we ask what factors will tend to:

		make cycles get smaller (approach equilibrium)?

		make cycles get larger (move away from equilibrium)?

----------------------------------------------------------------------

PSLIDE Neutral cycles

FIG exploitation/neutral_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

TSS Reciprocal control 

	In this model, what happens to the \emph{equilibrium} of this system if we
	reduce $r_f$, without changing $r_e$ (for example, we start catching a lot
	more cod)?

		ANS The equation for change in $N_e$ stays the same, so the
		equilibrium value of $N_f$ must stay the same. 

			ANS Unless

			ANS \ldots\ $N_e$ goes to zero!

		ANS The value of $r_f$ has gone down, so we must increase it

			ANS by decreasing the number of exploiters

----------------------------------------------------------------------

Reciprocal control 

	In this model, what happens to the \emph{equilibrium} of this system if we
	are at equilibrium, and then we reduce $r_e$ without changing $r_f$ (for
	example, we start killing sharks):

		ANS $r_f$ doesn't change, so $N_e$ must stay the same

		ANS $r_e$ has gone down, so we must increase it

			ANS $N_f$ must increase 

		ANS If we can't increase $r_e$ enough

			ANS sharks go extinct

			ANS fish increase to infinity.

----------------------------------------------------------------------

PSLIDE People and the ocean

FIG webpix/fish_harvesting.jpg

----------------------------------------------------------------------

Harvesting response

	Species under reciprocal control may respond to change in unexpected
	ways

	Imagine a community of sharks and large fish whose densities are
	primarily controlled by their exploitative interactions (the sharks
	eat the fish)

	What will happen to these populations in the \emph{short term} if
	people start fishing on a large scale (and catching large numbers of
	both sharks and fish)?

		ANS Populations will go down, because people are catching them

----------------------------------------------------------------------

Harvesting equilibrium 

	What will happen to happen to these reciprocally controlled
	populations of sharks and fish in the \emph{long term} if people
	start fishing on a large scale?

		ANS Shark population will go down (less sharks are needed to keep
		the fish in balance)

		ANS Fish population will go up (more fish are needed to keep the
		sharks in balance)

----------------------------------------------------------------------

Real implications

	Until fairly recently, almost all species in the oceans were
	controlled primarily by interactions with other ocean species

		Fishing food fish had little or no effect on the equilibrium
		number of fish at that \textbf{trophic level}

			ANS Decreased the number of sharks

		Catching sharks directly had little or no effect on the number of
		sharks

			ANS \emph{Increased the number of food fish}

	As fishing increases, this link is eventually broken

		ANS Fishing becomes an important regulator of ocean fish
		populations

		ANS Further increases in fishing can cause rapid declines in fish
		populations

----------------------------------------------------------------------

SEC Adding details

----------------------------------------------------------------------

PSLIDE How do populations affect their own growth rates?

FIG webpix/fish_schools.jpg

----------------------------------------------------------------------

Resource density-dependence

	The most unrealistic aspect of the current model is that, in the
	absence of the exploiter, the resource species increases without
	limit

		In reality, we would expect it, eventually, to be regulated.

	We can change our equations to allow the resource species to have a
	(negative) effect on itself:

		$\frac{dN_f}{dt} = r_f(N_e, N_f) N_f$

		$\frac{dN_e}{dt} = r_e(N_f) N_e$

----------------------------------------------------------------------

Predator satiation 

	Another conceptual problem with the model is the idea that exploiter
	feeding is proportional to size of the resource population

	What is the effect on feeding rates if the density of the {\em
	resource species} increases?

		From the point of view of the exploiter?

			ANS Per-capita feeding goes up

		From the point of view of the resource species?

			ANS Per-capita feeding goes down

		Predator satiation means the resource species density can sometimes have
		a \emph{positive} effect on its growth in the short term

----------------------------------------------------------------------

SS Dynamics

----------------------------------------------------------------------

Prey density dependence

BC

	Reduces prey reproduction the most when prey numbers are highest

	Tends to pull cycles towards the middle

	Makes cycles get smaller, leading to \textbf{damped} cycles

NC

SIDEFIG exploitation/dd_cycles.sim.Rout-0.pdf

EC

----------------------------------------------------------------------

PSLIDE Neutral cycles

FIG exploitation/neutral_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

PSLIDE Prey density dependence

FIG exploitation/dd_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

Prey density dependence

DOUBLEFIG exploitation/neutral_cycles.sim.Rout-0.pdf exploitation/dd_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

Predator density dependence

BCC

	POLL  If we go back to neutral cycles, and add predator density dependence, do we expect cycles to spiral out, or spiral in? | Cycles should spiral: out; in

NCC

SIDEFIG exploitation/neutral_cycles.sim.Rout-0.pdf

EC

----------------------------------------------------------------------

Predator density dependence

FIG exploitation/int_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

PSLIDE Predator density dependence

DOUBLEFIG exploitation/neutral_cycles.sim.Rout-0.pdf exploitation/int_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

Predator density dependence

BC

	Density dependence in the predator (exploiter species) has what
	effect on cycles?

		ANS Reduces predator reproduction when predators are the highest

		ANS This is not the same time as when prey are the highest,
		although we intuitively think that it is

		ANS Tends to cause damped cycles

NC

SIDEFIG exploitation/int_cycles.sim.Rout-0.pdf

EC

----------------------------------------------------------------------

Predator satiation

	POLL The fact that predators can consume only limited amounts of prey has
	what effect on cycles? | Cycles should spiral: out; in

		ANS Compared to neutral case, reduces predator reproduction when
		prey are the highest

		ANS Tends to make cycles get bigger

		ANS Without density dependence, makes cycles get bigger
		forever 	(oscillations increase to $\infty$)

----------------------------------------------------------------------

PSLIDE Neutral cycles

FIG exploitation/neutral_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

Predator satiation

FIG exploitation/nolimit.sim.Rout-0.pdf

----------------------------------------------------------------------

PSLIDE Prey density dependence

FIG exploitation/dd_cycles.sim.Rout-0.pdf

----------------------------------------------------------------------

Satiation with prey density dependence

	What sort of oscillations do we expect?

		If density dependence is relatively strong?

			ANS Damped oscillations

		If density dependence is relatively weak?

			ANS Close to equilibrium, we expect oscillations to increase

			ANS Far from equilibrium, density dependence takes over
			(prey cannot increase beyond their predator-free equilibrium)
			and oscillations decrease

			ANS We reach a ``limit cycle" where the population oscillates

----------------------------------------------------------------------

Density dependence plus predator satiation

FIG exploitation/pplimit.sim.Rout-3.pdf

----------------------------------------------------------------------

Density dependence plus weak predator satiation

FIG exploitation/ppweak.sim.Rout-0.pdf

----------------------------------------------------------------------

Oscillation summary

	\emph{Neutral} cycles repeat from any starting point

	\emph{Damped} cycles spiral in to the equilibrium.

	\emph{Unstable} cycles spiral out forever 

		Biologically unrealistic

	A \emph{limit cycle} is approached by spiralling out from near the
	equilibrium, and by spiralling in from far away

	Any oscillations that are not damped are called \textbf{persistent} --- they don't go away


----------------------------------------------------------------------

REPSLIDE Neutral vs.~limit cycles

DOUBLEFIG exploitation/neutral_cycles.sim.Rout-0.pdf exploitation/pplimit.sim.Rout-3.pdf

----------------------------------------------------------------------

Oscillations in a complex system

	All resource-exploiter systems have a tendency to oscillate

	It often takes a long time for damped oscillations to die out, or for
	stable oscillations to converge

	Other stuff is going on at the same time

		Other interactions

		Environmental perturbations -- weather, fire, people

----------------------------------------------------------------------

Real-world implications

	If a resource-exploiter system is tightly linked, we expect to see
	some sort of noisy oscillations, with exploiter following resource
	(i.e., resource species goes up or down first)

	If the basic interaction leads to damped oscillations, we expect to
	see relatively small oscillations in reality

	If the basic interaction leads to stable oscillations, we expect
	to see relatively large oscillations in reality

----------------------------------------------------------------------

CUTOFF Harmless unless .cut notes are requested

----------------------------------------------------------------------

SS Equilibria

----------------------------------------------------------------------

Prey density dependence

	Imagine that the resource species has a negative effect on its own growth rate

		$\frac{dN_f}{dt} = r_f(N_e, N_f) N_f$

		$\frac{dN_e}{dt} = r_e(N_f) N_e$

	What happens to the equilibrium if we start catching fish?

		ANS $r_e$ doesn't change, so $N_f$ can't change

		ANS $r_f$ goes down and must be balanced by less sharks

	What if we start catching sharks?

		ANS $r_e$ goes down, so $N_f$ must go up

		ANS Increasing $N_f$ decreases $r_f$, so $N_e$ must go down

----------------------------------------------------------------------

Predator satiation

	What if we also consider ``satiation'' -- there is some limit to how
	much a predator can catch (or eat)

		$\frac{dN_f}{dt} = r_f(N_e, N_f) N_f$

		$\frac{dN_e}{dt} = r_e(N_f) N_e$

	What happens to the equilibrium if we start catching fish?

		ANS $r_e$ doesn't change, so $N_f$ can't change

		ANS $r_f$ goes down and must be balanced by less sharks

	What if we start catching sharks?

		ANS $r_e$ goes down, so $N_f$ must go up

		ANS Satiation:  More fish means higher $r_f$ means more sharks at
		equilibrium!

		ANS This is the opposite of what we see for density dependence, so we would have to ask which is the stronger effect in particular circumstances.

----------------------------------------------------------------------

Examples

	Is reciprocal control realistic?

		In the long term, catching fish isn't bad for fish populations?
		Feeding grouse doesn't improve long-term grouse populations?

	POLL  What happens \emph{first} in this model if I start feeding grouse? What happens first?

		ANS First we get more grouse \ldots

		ANS then we get more foxes, then we get less grouse, \ldots

	POLL  What happens \emph{eventually} in this model if I start feeding grouse? What happens eventually?

		ANS Population eventually approaches (or orbits around) a new
		\emph{equilibrium}, with more foxes, and the same amount of
		grouse as before

----------------------------------------------------------------------

PSLIDE Harvesting dynamics

FIG exploitation/fish_harvest.sim.Rout-2.pdf

----------------------------------------------------------------------

PSLIDE Harvesting dynamics

FIG exploitation/fish_harvest.sim.Rout-0.pdf

----------------------------------------------------------------------

Harvesting dynamics

DOUBLEFIG exploitation/fish_harvest.sim.Rout-2.pdf exploitation/fish_harvest.sim.Rout-0.pdf

----------------------------------------------------------------------

PSLIDE Harvesting dynamics

FIG exploitation/shark_harvest.sim.Rout-2.pdf

----------------------------------------------------------------------

PSLIDE Harvesting dynamics

FIG exploitation/shark_harvest.sim.Rout-0.pdf

----------------------------------------------------------------------

Harvesting dynamics

DOUBLEFIG exploitation/shark_harvest.sim.Rout-2.pdf exploitation/shark_harvest.sim.Rout-0.pdf

----------------------------------------------------------------------

PSLIDE Harvesting dynamics

FIG exploitation/both_harvest.sim.Rout-2.pdf

----------------------------------------------------------------------

PSLIDE Harvesting dynamics

FIG exploitation/both_harvest.sim.Rout-0.pdf

----------------------------------------------------------------------

Harvesting dynamics

DOUBLEFIG exploitation/both_harvest.sim.Rout-2.pdf exploitation/both_harvest.sim.Rout-0.pdf

----------------------------------------------------------------------

TSEC Who controls whom?

	These results tell us that how ecosystems respond to perturbation
	depends not only on the perturbation, but on how the ecosystems are
	regulated

	What controls populations of large fish in the ocean?

		Sharks that eat them?  Small fish that they eat?

	Studies of snowshoe hares

		Very simple ecology:  a few food species, one major predator

		Food availability?  Food edibility?  Predators?  Diseases?

	It's never a simple question

----------------------------------------------------------------------

PSLIDE What controls ecosystem-level balance?

BC

SIDEFIG webpix/green_forest.jpg

NC

SIDEFIG webpix/blue_ocean.jpg

EC

----------------------------------------------------------------------

What controls ecosystem-level balance?

	POLL  Why is the earth green and the ocean blue? What does that question _mean_?

		ANS The ocean could be green, and the earth could be brown

		ANS Why does the earth seem to be covered by plants, and the
		ocean doesn't?

	The question is: what trophic levels provide the primary control for
	which other trophic levels?

		Top-down control theory: on land, herbivores are mostly controlled
		by carnivores, rather than by food

		Plants fight back theory: plants invest enough in ``defense" to
		escape herbivore control and compete with each other

	For each case, we can ask why the ocean is different

----------------------------------------------------------------------

PSLIDE What controls ecosystem-level balance?

BC

SIDEFIG webpix/overgrazing.jpg

NC

SIDEFIG webpix/green_ocean.jpg

EC