61BL3313Population and Community Ecology

Lecture 02 Density dependent population growth Spring 2013

Dr Ed Harris

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Today

-lecture + lab + practice quiz

Announcements:

-R questions, issues (tutorial complete/confident/etc.)

-handbook (syllabus) updates?

-General comments?

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Last time

Last time we talked about a special case in the study of population growth, where generations are distinct and non-overlapping

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Generation

N

Scatterplot of N vs Generation

discrete growth

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Start here from last time

Exponential growth in populations with overlapping generations aka continuous population growth (but still density independent)

What happens when juveniles and adults occur together in the same generation and they interact?

(like a lot of animals, like humans, Paramecium, etc.)

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We need a different model

This model is for use when reproduction happens continuously and there is no distinct breeding season

However it is general enough that it CAN be used for seasonal breeders (like red deer) when a population exhibits a stable age distribution (fertility and mortality rates staying for a long time results in this condition)

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Scatterplot of N vs Generation

Continuous growth model

The basic form of this model we talked about last time

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Continuous growth model

The basic form of this model we talked about last time

where r is the intrinsic rate of increase

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Continuous growth model

We can use some simple calculus to solve this equation (don't worry, you won't have to)

which eventually becomes

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Continuous growth model

Remember

when r is positive, the population growth is exponential

when r is negative, the population is in exponential decline

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Continuous growth model

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Continuous growth model

we can also make this linear to aid us in visualizing growth (ln is the natural logarithm – that is, log base e, where e = 2.71828)

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Continuous growth model

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Population doubling time

A convenient measure that is intuitive to understand is called doubling time.

Unsurprisingly, this is the time it takes a population to double in size!

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Population doubling time

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Population doubling time

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Population doubling time

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Population doubling time

Thus, all we need to know to calculate doubling time is the intrinsic rate of increase

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Exponential growth in an invasive species

mute swan, Cygnus olor

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Exponential growth in an invasive species

Native to Europe, Asia

Introduced species in North America, Australasia

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Exponential growth in an invasive species

During a hurricane in 1962, five captive mute swans (Cygnus olor) escaped into theChesapeake Bay, in Maryland

Since they were pinioned and therefore flightless, their chance of survival during the winter was considered negligible and no attempt was made to cap- ture them

One pair, however, successfully nested. By 1975 the descendents of this original pair numbered approximately 200, and by 1986 totaled 264

By 1999 the estimated population of mute swans in the Chesapeake Bay was 3955 (Sladen 2003, Craig 2003)

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Exponential growth in an invasive species

In 2001 the Maryland Department of Natural Resources, in an effort to con-trol the swan population, began shaking (addling) mute swan eggs or covering them withcorn oil to terminate embryo development

Mute swans were also removed from Federal National Wildlife Refuges

The result was a decline to 3624 in 2002

Prior to these control efforts, the population was growing exponentially with an intrinsic rate of increase of 0.17 and a doubling time of four years!

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Exponential growth in an invasive species

During a hurricane in 1962, five captive mute swans (Cygnus olor) escaped into theChesapeake Bay, in Maryland

Since they were pinioned and therefore flightless, their chance of survival during the winter was considered negligible and no attempt was made to cap- ture them

One pair, however, successfully nested. By 1975 the descendents of this original pair numbered approximately 200, and by 1986 totaled 264

By 1999 the estimated population of mute swans in the Chesapeake Bay was 3955 (Sladen 2003, Craig 2003)

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Exponential growth in an invasive species

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Exponential growth in an invasive species

So what’s the problem?

Swans are considered graceful, even “majestic,” and are thought of as harmless by their admirers

However, mute swans, in addition to being a non-native species, have become permanent residents - that is, they do not migrate as do other swan species

Recent data show that an average adult swan eats 3.6kg of submerged aquatic vegetation (SAV) a day (Craig 2003)

This is occurring at a time when biologists are struggling to re-establish SAV in the Bay

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Exponential growth in an invasive species

Is it necessary to control the mute swan population? If so, how?

The Fund for Animals took the US Fish and Wildlife Service to court to stop its planto kill 525 swans in 2003 (Craig 2003).

The debate evidently will continue for the indefinite future

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Stochastic growth and PVA

Models so far have been deterministic, rather than stochastic

deterministic - specify conditions to exact outcome based on parameters in model

Stochastic - chance influences outcome

Important particularly in small populations

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Stochastic growth and PVA

Small populations are relatively prone to random effects

E.g., sex ratio

E.g., finding a mate

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Stochastic growth and PVA

demographic stochasticity

-the fate of individual animals

-some females may have 4 offspring in a given year

-some may have 0, some 8, etc.

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Stochastic growth and PVA

Popoulation Viability Analysis

-important tool in conservation

-based on stochastic models

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Stochastic growth and PVA

the biological variation is IMPORTANT

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Stochastic growth and PVA

the biological variation is IMPORTANT

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Stochastic growth and PVA

the biological variation is IMPORTANT

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Density dependent growth and intraspecific competition

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Density dependent growth and intraspecific competition

DD in populations with discrete generations

DD in populations with overlapping generations

non-linear dependence or birth and death rates / Allee effect

Time lags and limit cycles

Stochasticity

Lab and field data

Behaviour

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Density dependent growth and intraspecific competition

-philosophical divide between ecology and economics - application of ecological principles to self-limitation in human populations.

-K is the carrying capacity

-what is K for humans?

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Density dependent growth and intraspecific competition

what IS K for humans?

-answer may be tied to the logisitc growth equation

-a peek now, but we shall return...

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Density dependent growth and intraspecific competition

population growth in Paramecium

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Density dependent growth and intraspecific competition

population growth in Paramecium