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## 61BL3313 Population and Community Ecology

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Title: 61BL3313 Population and Community Ecology

1
61BL3313 Population and Community Ecology
• Lecture 02 Density dependent population growth
• Spring 2013
• Dr Ed Harris

2
Today -lecture lab practice
quiz Announcements -R questions, issues
(tutorial complete/confident/etc.) -handbook
3
Last time Last time we talked about a special
case in the study of population growth, where
generations are distinct and non-overlapping
discrete growth
4
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.)
5
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)
6
Continuous growth model The basic form of this
model we talked about last time
7
Continuous growth model The basic form of this
model we talked about last time where r is
the intrinsic rate of increase
8
Continuous growth model We can use some simple
calculus to solve this equation (don't worry, you
won't have to) which eventually becomes
9
Continuous growth model Remember when r
is positive, the population growth is
exponential when r is negative, the population
is in exponential decline
10
Continuous growth model
11
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)
12
Continuous growth model
13
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!
14
Population doubling time
15
Population doubling time
16
Population doubling time
17
Population doubling time Thus, all we need
to know to calculate doubling time is the
intrinsic rate of increase
18
Exponential growth in an invasive species
mute swan, Cygnus olor
19
Exponential growth in an invasive species
Native to Europe, Asia Introduced species in
North America, Australasia
20
Exponential growth in an invasive species
During a hurricane in 1962, ?ve captive mute
swans (Cygnus olor) escaped into the Chesapeake
Bay, in Maryland Since they were pinioned and
therefore ?ightless, 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)
21
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 with corn 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!
22
Exponential growth in an invasive species
During a hurricane in 1962, ?ve captive mute
swans (Cygnus olor) escaped into the Chesapeake
Bay, in Maryland Since they were pinioned and
therefore ?ightless, 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)
23
Exponential growth in an invasive species
24
Exponential growth in an invasive species
So whats 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
25
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 plan to kill 525 swans in 2003 (Craig
2003). The debate evidently will continue for
the inde?nite future
26
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
27
Stochastic growth and PVA Small populations are
relatively prone to random effects E.g., sex
ratio E.g., finding a mate
28
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.
29
Stochastic growth and PVA Popoulation
Viability Analysis -important tool in
conservation -based on stochastic models
30
Stochastic growth and PVA the
biological variation is IMPORTANT
31
Stochastic growth and PVA the
biological variation is IMPORTANT
32
Stochastic growth and PVA the
biological variation is IMPORTANT
33
Density dependent growth and intraspecific
competition
34
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
35
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?
36
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...
37
• Density dependent growth and intraspecific
competition
• population growth in Paramecium

38
• Density dependent growth and intraspecific
competition
• population growth in Paramecium