density-dependent factors


Summary: populations/mortality


• Variety of sources

• Can occur at any age (many young and old)

• Reproduction: females most important

• Age specific fecundity

• Fecundity patterns differ depending on evolution of reproductive strategies

• Managing for the gains and control the loses.

• Ok so that’s the additions and subtractions to a population.

• One thing to say they die and list the possible causes, but need more detail on those causes

• How important are they?

• In a management mode, can they be managed?

Population regulation and fluctuation (chap 8)

• Now turn our attention to the observation that energy capture of populations changes.

• Not how but


• Why does sometime N>M and other N<M?

Population regulation, fluctuation

(Chap 8)

• The myth of stability!

• Many people believe populations can remain relatively stable even if, they show a lot of fluctuation!!!??

• “stable within limits (190-1150!!)

Stability vs fluctuations

• Yet consider others to not be stable

• House mice in


• Fluctuated from <20 to 100/ 100 trap nights!

• Stability is often a matter of scale!!!

• Why is one “stable” and the other a fluctuation population??

• A lot of it is “faith based” science.

• We think they are stable because we want to believe in stability!!!

• With this belief we develop our models.

• Need to look at this all

Confusing terms!

• Because it is faith based, as with any religion, a lot of confusing/conflicting/contradicting terms and concepts arise.

• What they consider:

• Inputs: births and immigration

• Outputs; deaths and emigration

Density dependent and density independent

• Density dependent: proportion of the population dying increases or proportion entering as births decreases with increasing density:

rate dependent

• Density independent: proportion dying

(usually) or being born, not related to density:

Not rate dependent; random

Density dependent

• Underlying causes for changes in birth/death rates:

density-dependent factors

• Will tease out later but for now lump together.

Density dependent/density independent

Mathematical possibilities

• K raises its head!!


• Usually deal with death rates because birth rates often are density independent

(don’t change much)

• So will mainly be looking at density dependent mortality factors

Limitation versus regulation

• Another confusing concept!

• Limiting: an example

• Assume

density independent

(b) birth rate

• Assume some amount of

density independent

mortality (d


) shortly after birth

• Reduces birth rate to b



• Next comes density dependent mortality rate d


• This dd rate results in a K


• If d

1 did not occur, pop would have reached K


• If dd rate higher (d


), different set of Ks!

• Lets see this on a graph!!

Graphed out

Next comes density dependent mortality rate d


This dd rate results in a K


If d

1 did not occur, pop would have reached K


If dd rate higher (d


), different set of Ks!

Lets see this on a graph!!

What does this mean??

• Both density dependent and independent mortality


the “equilibrium” point.

• Thus “Limited” the population to a given

(albeit differing) size.


: process of determining the size of the equilibrium population

Limiting factors

: factors that affect that equilibrium point

any factor that causes mortality or affects birth rates



• IF there is an equilibrium at K, populations can be disturbed from it by


changes in limiting factors.

• E.g. severe winter, drought, influx of predators (from where, who knows?) could reduce it.

• Mild winters might increase it.

• After such temporary changes, population will “tend” to return to original K


• This “tendency” is supposedly due to effect of



• Called


• Defined: process whereby a densitydependent factor

tends to

return a population to its equilibrium

Tends to return…

is a failsafe to cover when population may continually be disturbed!!

Is a population ever stable?

• Begs the question as to whether or not any population is ever “stable” or is always

“continually disturbed”!!

• But lets continue…

• Contend that population fluctuates around random variations in density dependent and independent mortality

• This then gives range of K

Graphed out

• When density dependent mortality is strong (a), range of K is small

• When dd mortality is weak, range of K is large.

• Note: dd mortality is setting K!!

Point to note

• dd mortality is setting K!!

• But K is the factor that is suppose to affect the intensity of the density dependent factors!

• The closer to K, the more dd mortality BUT

• DD is the driver NOT K???

What does it mean?

• Can adjust graph for whatever we find in field: If we find high level of fluctuations, conclude dd mortality “weak” and what?

Population is not regulated??

• Assumes density independent factors random and within limits: not often the case.

• If VERY weak dd mortality, then K can go from 0 to Infinity!!

• Ok so the math is kind of confusing and maybe involves some circular reasoning.

• The basic question is: Is there evidence for some type of regulation?

So is there evidence for regulation?

• If population returns to equilibrium after a perturbation: assume some regulation.

• Most are like this where population

“leveled out” fluctuation between 900,000 and 1,300,000! That is what I call stable!


• Say if separate and independent populations at “natural carrying capacity” plotted against a resource index are related, indicates regulation.

• Given as evidence of positive relationship!

Stability, cycles, and chaos

• Ok, again data don’t fit well

• Do we discard regulation myth?

• No we make it more complex!

• “paradoxically, the same densitydependent processes that are responsible for natural regulation can also induce population fluctuations….”!!!

• Finding excuses for when it does not fit!

Deterministic chaos!

• What a name!

• This is for populations that do not increase smoothly over time and level off at a carrying capacity (most I think!).

• Rather they fluctuate erratically over time with no apparent repeated pattern!!

• Cause of this “deterministic chaos”??

Deterministic chaos

• Overcompensation!!!

• Overshoots carrying capacity

• Once above cc, net recruitment is negative

• Population declines rapidly

• Repeats this boom-bust pattern of fluctuations

• Kind of like this:

• But how does this differ from this?

• In the first case: 600-1750 (change of

1150 animals

• In the second: 900,000 to 1,300,000!


• Again, it is often a matter of scale!

• And what we want to believe!

• Believers never question that regulation is real or not, they accept it

• Start with the assumption of regulation and then try to make all fit!

Variations in the theme

• Acknowledge is not as simple and a lot of field data don’t fit their pre-determined conclusions: nature didn’t fit the models!!

• Often found lag periods in response to food declines

• Proposed

Delayed Density-dependent factors

Delayed density dependent factors

• Predators: often lag behind decline in prey

– “caused by the delayed action of starvation”!

• But lag can be 4 years! Takes 4 years to starve??

• Obviously more is going on!

Delayed density dependent factors

• In 34 year study of deer found that population rate change and rate of growth of juveniles are “dependent” on population size SEVERAL years earlier!!!

• May be correlated but



• Again, more is going on than meets the eye!

Inverse density-dependent or



• Biggest scam yet! Try to show that predation has a


effect on prey populations

• Again, faith based:

• 1) Predators kill decreasing % of prey as they increase, leads to faster increases!

• 2) as prey decline, predators take increasing % of prey, “driving” the prey down even faster toward extinction!!


What is wrong with this?

• First, assuming lethal effect of predators

(killing prey) is sufficient to affect prey numbers

– go through the numbers, just does not make sense

• Second: assumes that predators can find the last prey: no change in “catchability of prey as they decline. Will see later this is not often the case.

Go to presentation.

What is the problem?

• Believers admit there are problems with the concepts of regulation and density dependence.

• One is concept of carrying capacity!

The myth of carrying capacity

• The problem they see is in its definition!

• There are many!

• Ecological carrying capacity: (K of logistic equation). “natural limit of a population set by resources in a particular environment.

• Go on to say it can be affected by a variety of factors (brief changes or long term) that can change K

– moving target!!

• Looses its sense of a “natural limit”!!

Ecological Carrying capacity

• Because of all the things that can “briefly affect it” randomly AND

• Other factors such as predators, parasites, disease, etc. that can produce other possible “equilibria”

• If there is an “Ecological carrying capacity” it varies so much that it becomes a rather worthless concept.

Economic carrying capacity

• Population level that produces maximum

(or sustainable)


• First who came up with this word?

Oftake? Sounds like we are skimming extra ice cream from the top of the cone!

• Harvest is another!!

Back to the subject!

• This is ranching! Will see the connection later but it came from the concept of livestock carrying capacity!

Other meanings?

• Sociological defined carrying capacities

• - zero for predators: IF you are a cattleman

• - something higher if you receive millions of $$ from people who want to hear a wolf!

• So we see, difficult to define AND determine!!

Other problems?

• Book lists 3 main ones

• 1) confusion between limiting and regulating factors: Sometimes used synonymously, sometimes switched!

• This is a problem of semantics!

• But… does point out the fact that any factor any factor can affect an “equilibrium point” and so any factor affecting births and deaths is a limiting factor!

What does this do?

• Makes it a trivial question whether a certain cause of mortality limits a population, it has to or.. They all do!!

• Makes the whole concept trivial!

2) Regulation requirements

• Regulation requires the action of densitydependent factors (can limit AND regulate!)

• Density dependence is necessary for regulation but may not be sufficient to do it!!??

• Huh??

Regulation requirements

• One may be too weak and other unknown ones are assumed to be doing it!

• Others may be too strong and cause fluctuations rather than an equilibrium!!

• This is all too convenient!

3) Demonstration of density dependence

• Just demonstrating density dependence at some stage does not indicate the cause of regulation!!??

• Example: If a deer population is regulated through dd juvenile mortality, not sure of real cause of the mortality!

• Correlation with population size does not imply cause and effect, just an association!

Demonstration of density dependence

• So not a demonstration of density dependence but density relationship.

• Still not sure of causes of mortality and whether they are density dependent or independent!

A fourth factor

• Is it density dependent or density independent?

• The big question is: what are density dependent and density independent mortality factors?

• Many mortality factors are used interchangeably: Food resources: they set by climate

–definitely a density independent factor, but…

• This means food availability in any given year is set independent of density, yet…

• Food resource levels are often given as the factor setting the Ecological carrying capacity and competition for this resource the density dependent factor

• But changing food independent of density

• Will alter effect of competition!

• Lots of food, no competition

• Less food, same density, competition!

• So density independent factor is

“regulating” regulatory factor!!!


• Start with the assumption of regulation and then try to make all fit!

• In none of this is the behavior of the animals!!!!


All limiting factors

Den. Indep.

No regulation,

Random effects

Density Dependent


Too Weak

No regulatory affect


IF K is stable, within reason

Too strong

Cycles or chaos, No real regulation

No behavior!


No evidence of real regulation

Where does this leave us?

• Not as simple as limiting/regulating or density dependence/independence… so.

• Not talk about regulation vs limitation

• Not talk about density dependent and density independent

• Talk about what matters.

What does matter?

• Lets look at factors that matter.

• Givens:

• There IS a limit to food supply: can measure total biomass of an area and translate that to x # of individuals.

• That food supply can VARY over time, seasonally, yearly.


Rarely does a species use all of the food resources!

• Slobodkin, Smith, and Hairston:

Questioned; why is the world so green?

• What keeps herbivores from eating it all?

• What keeps predators from eating all their prey?


• There are factors that affect access to this food: competition-predation-weather

• There ARE mortality factors, lots of them.

• So

death and access

big factors!

Lets look at each

• Without regard to whether they are limiting, regulating, density dependent, density independent, blah, blah, blah!

• Where to begin?


Climate and populations

• Ultimately it is the climate that affects


food supply to wildlife.

• What is the


food source is later….

• So, how does climate affect food supply?

• Saw first week, depends on where you are on planet

• Determines temperature, rainfall, evaporation, etc.

– primary productivity

Closer look

• Here we want to get a feel for how these factors interact.

• First precipitation:

• Look at examples – we saw snow…





% of maximum harvest

% of maximum snowfall












65 70 75 80 85


90 95 00

20 40 60 80

Snow in December-Jaunary (cm)


• Deer and Moose



• Rodents to deer, amount of rainfall affects numbers.







P = 0.028



= 0.68



Shrubland November/previous annual rainfall


100 120 140 160 180 200 220 240 260 280 300 320

Rainfall (mm)

Ok there is a relationship, why??

• Through vegetation.

• Rainfall – productivity

• Tibet/Mexico








Y = -3.16 + 0.019 * precipitation r2 = 0.70, P = 0.003


Y = -3.24 + 0.018 * precipitation r2 = 0.74, P = 0.002










Figure 2


Y = 0.66 + 0.04 * X r2 = 0.34, P = 0.05


200 250 300

Precipitation (mm)

350 a



• Lack of access to existing food

• Related to snow depth

• Also, snow depth increases energy expenditures.

• Snow can protect small mammals.

How does it work?

• How previous weather can affect survival?

• Red deer example

Reproductive potential

• Affects the amount of young being born

Weather effects and predation

• Now know affects amount and access to food

• How about predation?

• Snow:

• Plus or minus

• Concentrates and decreased mobility

• Can use snow to hid under, small mammals

Rain and predation

• Prey have to concentrate at waterholes!

• Ok know weather affects or is related to numbers: but what affects weather?

• El Nino (ENSO)

• Brings us back to ocean currents!

Not just El Nino!

• NPO, NAO, etc

Related to wildlife?

Effect on predators?

• Predators respond to increase in prey.


- More concentrated

- Less mobile

Climate does matter!

• Usually considered a random density independent factor

• El nino, etc., cyclic

• In management need to consider impacts of climate on species of concern.

• Usually have historical patterns to help.

• One of the major factors affecting K!

Importance to you?

• Will be first generation of wildlife ecologists facing global climate change!

• Unpredictable effects

• More snow, less snow, more rain, less rain?

• Major changes/minor changes?

• Will face major challenges

How do you manage climate?

• You can’t!!!

• This is what upsets managers

• Hired to manage but can’t

• Why they look for scapegoats

• Usually predators….

International Herald-Tribune

US plans more lion hunts in effort to save deer

What can you do?

• As a manager who knows weather can have an effect, you can only inform, inform, inform, inform, the public.

• It’s the weather! Live with it, good times will come back.

• It is hunting….NOT shopping!


• Ok, climate sets potential food supply

• Also can affect actual supply available

• Snow e.g.

• Now turn our attention to other factors that affect actual supply

• First is


Competition defined

• When individuals are using a common resource that is in short supply,

or if not in short supply, harm each other in process of seeking it.

• Last part added because hard to show a resource is in short supply!!

• LOT of controversy around competition!

Interspecific competition

• Can talk about intra and interspecific competition

• Here we will deal only with interspecific.

• The general idea behind competition is that the food source is now being shared!

• But by how much?

• What determines degree of overlap?

Quick review

• Just touch on some key aspects of competition and then see how pertains to wildlife ecology and management.

• Basis comes from

niche theory

, which in itself is controversial!

• Each species with its n-dimensional hyper volume.

• Come into competition if they overlap

L-K equations

• All standard crap

• Mathematically possible but biologically not!

• K is a key to it and we know that K is really a worthless concept.

• Has led to idea of

competitive exclusion

, idea that two similar species cannot coexist!

• BUT: one outcome

IS coexistence!!

• And many do!!

Competitive exclusion

• So… many similar species do coexist!

• How do we explain it? Must be that they are not similar enough!

• Such things as using different microhabitats, different components of prey, different ways of feeding, different….

• This then allows them to coexist!

Limiting similarity

• Leads to the question: is it possible for any two species to be close enough to result in exclusion?

• Answer is:

limiting similarity


• There should be a limit to the similarity of niches allowing co-existence, beyond that limit (more similar), exclusion will occur.

Limiting similarity

• Logical question of limiting similarity is:

• Just how similar must two species be before one will exclude the other?

• Lets consider


in a population

• Maintained by degree of reproductive segregation

• Have many of these differences previously mentioned.


• Does one morph exclude others?

• Rarely

• So…. For exclusion to occur, two species would have to be more similar than two morphs of the same species!!!

What is wrong with all this?

• Concentrating on the similarities of niches!

• Similarities of niches DO bring them into competition: totally separate ones, no competition.

• But given that they do have similarities and are likely competing, it is the

DIFFERENCES that produce the outcomes!

Two identical species

• IF we could have two identical species, they would not exclude each other, how could they??

• But can’t have, not even a species is monomorphic!

• So there will always be differences between species

Consider outcomes

• Exclusion: Say that two similar species can’t coexist BUT it is the DIFFERENCES that produce the outcome.

• One species has an advantage because of a difference, not the similarity!

• This in fact, is what they always point to!


• Co-existence: Already saw that we contribute that to DIFFERENCES in niches that allow each to seek out aspect of niche where they are superior!

• Does it reduce competition?

• NO Don’t make “deals”!

• Results in competition being a more active evolutionary force driving two species apart as they concentrate on differences.

It’s the Differences!!!

• So Differences in niches decide if one species excludes another and it is differences that enable them to co-exist.

• Only role similarity has is it brings them into the initial competition.

And Wildlife management?

• How is this all important to wildlife management?

• Often have similar species in the same area.

• How do we manage them??

• IF we want to enhance one and not the other

• If we want to enhance both.

• If we concentrate on the differences, then we can see how we can tip competitive edge to species of desire

• Or how we can enhance the different resources that they use to support both.

Don’t dwell on similarities

• So they compete for a resource

• Look how they approach using that resource differently.

• Resource partitioning and habitat selection are part of that

• A more recent one is anti-predator ability.

Resource partitioning

• Books full of examples of how species divide up resources, because of

DIFFERENT abilities!

• One big resource often divide is habitat

• Examples.

Anti-predator ability

• Have mentioned, some areas more dangerous than others

• This is because of predator abilities

• These areas are DIFFERENT for each prey species, even for the same predator

• Reason: Differences in “niche” antipredator abilities

How affect competition/coexistence?

• Separate out the two species into respective safe habitats

• Poorer competitor now has a “refuge” from competition in area of high risk for superior competitor.


• From book: Wildebeest and buffalo in


• Co-existence when wildebeest can use grass area where reduced risk from lions

• Buffalo can use shrub area because can defend from lions.

• Both can use both areas but separation is because of predation risk.

Example continued

• When wildebeest were forced out of grassland, likely could have out-competed buffalo (faster growth rate, etc)

• BUT because of increased predation risk, lions eliminated them!!

• Book calls this Apparent competition; resource partitioning appears to be from competition but is because of other source. I have a better name for it!

• What this demonstrates is that it is difficult to separate out just competition factors without incorporating others such as predation risk, not predation but the mere risk of it.

• This we will deal with in the next chapter.

Why important to wildlife ecology?

• Competition exists and can affect access to resources (scramble, interference).

• Identifying the differences in resource use provides a valuable management tool.

• Can be used to try and enhance differences of one at the expense of another.

• Resolve wildlife/domestic stock conflicts

Deer and cows

• Identify not only those differences but the temporal pattern of the differences.

• Here winter is critical

• Note: contradicts idea that should be less overlap when resources are limiting!


• Competition theory is a MESS!!

• If one reads carefully, see a lot of contradictory ideas, circular reasoning, patch work ancillary hypotheses, etc.

• Two main reasons for the problems

• 1) concentrates on similarities rather than differences

• 2) Again, little behavior.

Predation (Chap 10)

• From bad to worse!

• Now we get into the real embarrassment of ecological theory, ecology, and wildlife management!

• First the one thing we know for sure: a predator kills its prey.

• How we interpret that leads us down a slippery road!

How predation is viewed

• Our ecological treatment of predation is, unfortunately, based on how we view predator and prey.

• Over-riding cultural views.

• So first, we need to take a historical view

Historical views of predatorprey relations

Prey as the “victim”

Predator as the “bad guy”

Literature treatment of predators

• Children’s stories:

• Wolves are bad, evil, cunning and are looking for any opportunity to kill innocent animals and humans!

Literature treatment of prey

• Children’s stories:

• Cute, cuddly, not too bright but lovable.

• And as we saw, victims of predators, and in the case of Bambi, man!

Adult literature

• Same tone, predators to be feared, hated, and most of all KILLED on sight.

Basic perceptions

• It must be understood that predation must be addressed for wildlife to be abundant for viewing or hunting.

The predator is to wildlife what weeds are to the farmer or gardener.

You cannot have abundant wildlife with abundant predators any more than you can have a fruitful garden or crops with abundant weeds.


• By T. R. Mader, Research Director

• Copyright, 1995, T. R. Mader.

• Permission granted to quote from or reprint if full credit is given to the source.

Early practices: Europe

• Game animals protected, cultured for the hunt.

• Predators killed

• As long as animals have been domesticated, people have been killing wild predators in their defense. At least

2,500 years ago, Athenian statesmen offered bounties on wolves. (pay to kill incentives)

Early practices: Euro American

• In America, bounties on predators date from the time of European colonists.

• Plymouth Colony placed the



bounty on

the wolf in 1630

• New York: first bounty on cougars $20 –

1882 (Wolves: $30)

Wildlife Conservation Timeline

Pennsylvania Game Commission


• 1683 - Hunting permitted on all lands under William Penn's Charter.

First bounty offered on wolves -- 10 and 15 shillings.

• 1721 - Pennsylvania's first Game Law enacted.

1749 - Squirrels (red and gray) were classed as predators.

• 1867 - Last native elk killed in Pennsylvania about this time.

• 1869 - Deer season set: September 1 to December 31.

1885 - So-called "Scalp Act" passed, creating bounties for weasels, hawks, and all but three species of owls.

• Elk disappeared not because of wild predators!!

Basic practice

• Humans declared war on predators – of all types.

• Treated prey species as domestic animals

• Wildlife management models come directly from animal husbandry models.

Impacts on predators:

• “Between 1937 and 1970, federal employees…killed 7,255 cougars; 23,830 bears; 477,104 bobcats; 50,283 red wolves;

1,744 lobo wolves; 2,823,000 coyotes; and millions of other animals.”


In addition to these efforts, many states offered bounties on animals they deemed to be “undesirable predators,” particularly the mountain lion.

Between 1907 and 1978, nearly 50,000 mountain lions were killed in the United


Current views?

It's a fact, predators kill pheasants.

Pheasants and


• It's a fact, predators kill pheasants.


Management Problems and Solutions


• Predators have historically been and will continue to be the principle


factor for pheasant nests and adult birds, as they are for

all other small game species


Pretty clear as to how predators are viewed!!

So the killing goes on

• Federal government started control operations in


• 1931

Animal Damage Control Agency

formed to control problem animals, mainly predators

• Later changed name to Wildlife Services, different name same job

Wildlife Services (WS)

• Provides Federal leadership and expertise to resolve wildlife conflicts and create a balance that allows people and wildlife to coexist peacefully:

means kill predators

Fiscal 2007

• 2,333 Red Fox

• 2,276 Grey Fox

• 2,090 Bobcat

• 90,326 Coyotes

• 336 Mountain lions

• 12,643 Raccoons

• 340 Wolves

• 511 Black Bears

• > 100,000 predators killed to “protect”

American wildlife and agriculture!

Current headlines

• Nevada Plans to Kill More Cougars to

Increase Deer Population 2-16-09

• Predators kill deer. Thus, if you want to protect your investment in the deer herd where you hunt, you should reduce the number of predators, right?

Current views

• So on a society level, little has changed on how we view predators:

• How many of you favor reintroducing cougars into NY?

• If not, why not? Most say they are afraid of them, the rest say they would

“decimate” the deer population.

• So it is within this cultural backdrop that ecological theory developed regarding predation!

• At the time early, and still persistent, models were developed, it was a GIVEN that predation was bad!

• Added to that was the mass action mindset of ecologists.

Ecologist’s view of predation

• One ball killing another, the end!

subconsciously, set out to demonstrate that predation was a


ecological force.

• So lets look at the development of the theory and see where it leads.