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

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2 Today -lecture + lab + practice quiz Announcements: -R questions, issues (tutorial complete/confident/etc.) -handbook (syllabus) updates? -General comments?

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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

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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.)

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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)

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6 Continuous growth model The basic form of this model we talked about last time

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7 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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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

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9 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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10 Continuous growth model

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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)

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12 Continuous growth model

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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!

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14 Population doubling time

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15 Population doubling time

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16 Population doubling time

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

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18 Exponential growth in an invasive species mute swan, Cygnus olor

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19 Exponential growth in an invasive species Native to Europe, Asia Introduced species in North America, Australasia

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20 Exponential growth in an invasive species During a hurricane in 1962, ﬁve captive mute swans (Cygnus olor) escaped into the Chesapeake 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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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!

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22 Exponential growth in an invasive species During a hurricane in 1962, ﬁve captive mute swans (Cygnus olor) escaped into the Chesapeake 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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23 Exponential growth in an invasive species

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24 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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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 indeﬁnite future

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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

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27 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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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.

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29 Stochastic growth and PVA Popoulation Viability Analysis -important tool in conservation -based on stochastic models

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30 Stochastic growth and PVA the biological variation is IMPORTANT

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31 Stochastic growth and PVA the biological variation is IMPORTANT

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32 Stochastic growth and PVA the biological variation is IMPORTANT

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33 Density dependent growth and intraspecific competition

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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

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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?

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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...

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37 Density dependent growth and intraspecific competition population growth in Paramecium

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38 Density dependent growth and intraspecific competition population growth in Paramecium

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