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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
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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
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