2. Some main points What defines a population? How do we measure numbers in a population? Populations change Populations increase exponentially under good conditions Density dependent factors can limit growth Environmental conditions can limit growth There are tradeoffs in reproductive strategies

3. Population = group of individuals that form a gene pool ?? Are the following populations? If you think not, what prevents them from being a gene pool, i.e. interbreeding? all large mouth bass in North America all copepods of species W in the Pacific Ocean all lake trout in a stratified 100 m deep, 40 k wide lake all rotifers in a stratified 100 m deep, 40 k wide lake rotifer, ~ 50  m http://www.pbrc.hawai i.edu/~petra/aetideopsi s.html calanoid copepod, ~ 2 mm

4. Sampling: so we don’t have to count or measure them all!! Population/universe: the entire group about which you want to draw conclusions ex. All the yellow perch in Lake Erie, all the water penny beetles in 10 m creek, all lake trout in North America Sample: subset that you measure to draw conclusions on the population

5. How do you estimate population size? It’s simple if your organisms don’t move 1m if mussel density = 10/m 2, pond has 1,000 m 2 bottom area, then population = 10 x 1,000 = 10,000

6. mobile benthic animals Enclose portion of sediment, many designs, must be heavy for hard substrate Grab closing trap doors Core tubes

7. plankton know diameter & depth, calculate volume filtered net, column integrateddepth specific bottle

8. running water drift: know time and depth of water to calculate volume filtered bottom invertebrates: disturb substrate in front of net, know area flow 1 m

9. For rare organisms may need to swim transects unionid clams stream fish marine mollusks (conchs) 50 m

10. Measures of Central Tendency Describing the middle of a distribution X =  X i n sum of values of all observations total number of observations sample mean = ‘X bar’ Arithmetic mean Sample mean provides an estimate of the population mean, .

11. Other descriptions of the center “other means” e.g. geometric or harmonic Median = the middle measurement in a ranked list of values, half the values are below the median and half are above. (same as mean for symmetric distribution) Mode = the most frequent value (most fashionable) IQ of college professors frequency of occurrence mean median mode Symmetric and unimodal distribution

12. Estimating Dispersion 0 10 20 30 40 A B same mean and range, but have different patterns of dispersion (variability)

13. Variance Variance (s 2 ) = n-1  (X i – X) 2 Deviation from the mean = difference between each point and the mean (sums to zero)

14. Variance Variance (s 2 ) = n-1  (X i – X) 2 Sum of squares = square the deviation of each data point from the mean added together

15. Variance Variance (s 2 ) = n-1  (X i – X) 2 Variance ~ ~ mean sums of squares

16. Standard Deviation =positive square root of variance of a sample sd = s 2 -same units as the original data - it does not vary with sample size

17. variance and SD visualized X XiXi X ii X i - X X ii - X Total sum of squares n-1 = ~Mean SS =variance I side =SD freq 2 2 If you don’t square them, they add to zero

18. Coefficient of variation = standard deviation relative to the mean sd X CV=

19. M = number of individuals marked in first sample C = number of individuals captured in second sample R = number of marked individuals in second sample N= CM R Estimating population with mark - recapture study 1) sample once, mark all individuals caught 2) sample again, count number of marked and unmarked individuals (may repeat this several times) 3) calculate total population based on ratio of marked to unmarked

20. How many fish are there in a pond? 1) Set nets and capture 20 fish, mark with a fin tag 2) Next week, set nets again, catch 50 fish, 6 w/ tags N= CM R N= 50 x 20 6 N=167 this is a little bit of a simplification of how ‘professionals’ do this, but the same basic idea

21. Population variability occurs across space and time Spatial distribution and scale Time scales: seasonal: phytoplankton, zooplankton, larval fish see Fig 6.3 long-term trends: can depend on environmental conditions cycles: common in fish see Fig 6.4

22. Spatial Distributions random little control over movement or settlement, no strong habitat influence even things w/ negative effects on each other, net spinners & tube builders clumped heterogeneous habitat, common in benthos & plankton

23.  How does does distribution affect quadrat sampling?  quadrat size  number of samples

25. Population Size through time Decrease reproduction & import mortality & export Increase probably both happening, net change in population numbers depends on balance of both processes

26.  growth rate = change in number per individual over time r = dNdN dtdt N  Suppose each individual produces 2 in next generation, begin with 10 G 0 = 10 G 1 = 20 G 2 = 40 G 3 = 80 G 4 = 160 G 5 = 320 0 80 160 240 320 012345 number in population generations or cohorts Eq. 6.5

27. Exponential growth describes fast population growth, for example…….. - when conditions are good - parthanogenic reproduction (Daphnia etc…..)

28. N t = N 0 e rt # in pop @ time t initial # in pop exponential growth rate Time number in population N0N0 0 t NtNt slow increase at first pop goes to infinity Integrate eq. 6.5

29. 0 400 800 1200 1600 0510152025 Time Total number in population r = 0.01 r = 0.05  ‘small’ difference in growth rate results in big differences in population size over time. Both populations start w/ 100, at t=10 slower growing population has 173, where faster growing has 1,564

30. r = b - d In a population without much immigration or emigration  birth can be measured in lab experiments  death usually calculated as r - b

31. Time population size rapid (exponential) growth resources become limiting K Carrying capacity (K) = upper limit of population size due to limits of available resources (space, nutrients, food, water….) Density dependent regulation

32. Why does rate of growth slow as population size increases? less to eat = lower reproductive rate = poor health = starvation  good conditions for parasites and disease  attract predators, or increase their population growth rate  crowding  resource limitation

33. R 2 = 0.631 P=0.0001 0.01 0.02 0.03 0.04 0.05 0100,000200,000300,000400,000 Number Early Juvenile / Ha Individual growth (g/day) Pre-Zebra Mussel Post-Zebra Mussel Density Dependence in Early Juvenile Y Perch

34. Density independent regulation: factors external to the population can limit numbers. ex. If a pond dries up, all fish will probably die, regardless of how many are there. Resting eggs: an adaptation to adverse conditions

35. http://www.ncbi.nlm.nih.gov/books helf/br.fcgi?book=daph&part=ch2 http://www.novaquatis.eawag.c h/media/20090310/index_EN Eggs that will hatch into live daughters Resting Eggs that can withstand bad conditions in the sediment and hatch years later Read egg bank model pg153

36. Allocation of energy: different reproductive strategies energy Immediate reproduction: offspring can have more babies growth & defense; affects future reproduction Resting eggs: can hatch later when conditions are good

37. Some main points What defines a population? How do we measure numbers in a population? Populations change Populations increase exponentially under good conditions Density dependent factors can limit growth Environmental conditions can limit growth There are tradeoffs in reproductive strategies