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Unformatted text preview: Lecture 7: Lecture Population ecology III. Announcements: Announcements: Next week’s section will be outdoors. Wear appropriate clothing. Bring binoculars if you have them. Will announce on Monday where to meet. Questions for Lecture 6 Questions
Assessing population status:
3. Matrix modeling (age or stage based) What are the basic elements of a matrix What model? What two matrices (and associated pieces of information) do you need to do population projection ? population How does a matrix model differ from cohort How analyses? What kinds of questions can you explore with What matrix modeling in addition to pop. growth? matrix Potential exam essay question: Potential
Compare and contrast the different types Compare of information you can gain from (1) cohort analyses, (2) static age structure analysis and (3) matrix modeling. Tortoise study: goal was to enhance tortoise populations. Broom study: goal was to control pest population. used transition matrix to see where to focus management to increase survival to create positive pop. Growth (lambda) Used transition matrix to identify where to decrease survival or decrease fecundity to decrease broom lambda Today (lecture 7) Today Exponential versus logistic growth equations. equations. Density dependence –what is it? Density Usefulness of exponential and logistic Usefulness growth models. growth Scotch Broom -Population growth very high in some populations When species have no competitors and lots of resources then growth may be exponential Traditional population biology built around exponential population growth curves growth dN dN = r * N dt r= intrinsic rate of increase (birth-death) Population size (N) Time (t) Population Growth
• dN = (instantaneous) rate of change in population dt size r = maximum/intrinsic growth rate (varies with the species) N = population size (number of individuals) • • Projecting Population Size
Nt = N0ert
N0 = initial population size Nt = population size at time t e ≈ 2.7171 r = intrinsic growth rate t = time r determines growth curve If we wanted to use this equation to predict growth for desert tortoise or scotch broom…. scotch What do we need to measure ?
r = birth rate - death rate How would you define birth rate for broom ? Was actual birth rate in the d. tortoise model? Which of our two species would have higher r ? Why don’t we use these models to project population growth ? They contain almost no biology. They do not tell us about ‘vital rates’ They make unrealistic assumptions about They populations. populations. Assumptions of the exponential model:
• Populations are closed (no immigration, Populations emigration) emigration) • There are unlimited resources • No genetic structure (all individuals reproduce No equally) equally) • No age/size structure • Continuous growth with no time lags (individuals become reproductive instantly) When is exponential growth a When good model for a species population growth? population Small organisms with no pre-reproductive Small period (microbes in a closed envir. or guppies introduced into a fishless pond ?) guppies Environment has unlimited resources Environment also has no predators, Environment competitors or disease competitors Population size (N) What should this curve look like to be more representative of pop growth in nature ? Time (t) Introduce Carrying capacity =K • Logistic growth =
• • • Symmetrical S-shaped curve with an upper asymptote (=K) Assumes that density-dependent factors affect population Growth rate should decline when the population size gets towards limits of resources How do you model logistic growth? How do you write an equation to fit that S-shaped curve? Start with exponential growth dN = r * N dt 5.22 Townsend Add a term to show population is reaching Add carrying capacity carrying N dN/dt = r * N (1 – ) K K = max. number of individuals a site can support N 1= dampening term 1K Population growth is being dampened as individuals use up resources (take some of the “K”) of What does (1-N/K) mean? Unused Portion of K If white box represents total resources (=carrying capacity=K), and green area represents current population size… IMAGINE K can support 100 individuals, and N = 15 individuals (1-N/K) = (1-15/100)= 0.85 ⇒ population is growing at 85% of the growth rate of an exponentially increasing population N dN/dt = r * N (1 – ) dN/dt = r * N (1 – ) K Reduces rate of growth as a function of how much of K is used up. =DENSITY DEPENDENT GROWTH Useful points of this sort of modeling modeling Demonstrates mathematically how Demonstrates population density influences population growth. =density dependent growth. growth. Forces you to think about value of K and Forces proximity of N to K. How does K vary with environment ? As population approaches K, As INTRASPECIFIC competition becomes important. Growth slows. Do you see this? important. Low productivity High productivity (more food) Which lake should have higher K ? How might r vary across lakes ? Assumptions of Logistic Growth Model:
• • • • • • Closed population (no immigration, emigration) No genetic structure No age/size structure Continuous growth with no time lags Constant carrying capacity (is this reasonable?) Population growth governed by density-dependent competition for resources. • An equilibrium with K will be reached So do species show logistic growth? growth? Lactobacillus (bacteria) Juncus (wetland sedge) Salix (Willow) What can we do with these models? models?
1. Figure out when to harvest a species Figure relative to its growth curve. Harvest when population is at max growth Population growth rate (dN/dt) is slope of the S- curve Maximum value occurs at ½ of K
SO IF YOU KNOW K harvest when pop. Is halfway to K This concept is used to establish maximum sustainable yield (MSY) in fisheries in Problems with this approach to fisheries management ? fisheries
How do we know when fish populations are at peak growth ? Do we have any idea if K concept is Do relevant to each fishery ? What is fish population size and growth is What stochastically determined ? (this model is deterministic…what does that (this mean ?) mean 2. Allows hypothesis generation regarding population regulation regarding Estimate r, and K then see if populations Estimate are behaving as predicted are If not, explore why. If 3. Compare r values across species. species. Allows quick comparison of GROWTH Allows potential if there were no regulation of growth (r in exponential model) growth 4. Does a species tend to behave (in terms of pop. growth) as if growth was driven by r or by K? This has resulted in classification of organism life histories into two categories categories
‘r selected species’ selected 2. ‘K-selected species’ 2. K-selected
K species Where on this curve do species life histories and traits seem to fit ? r species Traits of r and k species Traits
r species (spend most species of of their lives in nearexponential exponential phase of growth) growth) K species (spend most of species lives in K dominated growth growth phase) Early reproduction High High allocation to reproduction reproduction High population turnover Little Little investment in long term term structures Poor Poor competitors for resources resources Later Later age at first reproduction reproduction Lower birth rates Less Less total allocation to reproduction Slower growing Longer lived Good Good at competing for resources resources Environments of r vs K species Environments
r species species Disturbed Disturbed (newly opened) opened) Temporary Temporary high resource resource pulses Ephermal K species species Crowded environments Constant environment Little Little opportunity for rapid rapid growth Ended here Ended Is this categorization valuable ? Is Provides a framework to think about types Provides of selective pressures that might have brought about a species life history traits brought Provides an expectation of sorts of Provides species you will see under different disturbance regimes disturbance Alternatives to r vs K categorization Alternatives Treat life history traits as a continuum from Treat extreme r-selected to extreme K with lots of in between of Conduct multivariate statistical analysis of Conduct all species in a region to see if they split out into clear categories out (Australian scientist found 17 discrete (Australian grouping of life history traits. YIKES!) grouping Use terms more descriptive of species Valuable for extremes Opportunists vs. Competitors Population boom and bust cycles Not very competitive Rapid development Early reproduction Small body size Single reproductive effort Short lifespan Do well in predictable climate Lower mortality rates Population in equilibrium near carrying capacity Good competitors Late reproduction Large body size Repeated reproduction Longer lifespan ...
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- Fall '08