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What is quantitative ecology? What lead to the quantitative trend in ecology?
The application of mathematical and statistical tools to questions in the field of ecology. The trend of quantitative ecology reflects the demand to interpret larger and more complex data sets. Also in response to criticism from other scientific disciplines for ecologists to use more quantitative approaches.

What are the 5 steps in ecological research?
 make observations
 form objectives/hypothesis
 collect data
 analyze data
 make conclusions
 reject hypothesis

What are Krebs’ rules for ecological methodology?
 1. not everything that can be measured should be measured
 2. find a problem and state your objectives clearly
 3. collect data that will achieve your objectives and make a statistician happy
 4. some ecological questions are impossible to answer at the present time
 5. with continuous data, save time and money by deciding on the number of significant figures needed in the data before you start the experiment
 6. never report an ecological estimate without some measure of its possible error
 7. be skeptical about the results of statistical tests of significance
 8. never confuse statistical significance with biological significance
 9. code all your ecological data and enter it on a computer in some readable format
 10. garbage in, garbage out

Why are preliminary and pilot studies important?
 critical in both field and lab experiments
 they help address simple questions of technique
 they help determine the sample sizes needed for a particular level of precision

What are the different scales of measurement in ecology?
 Nominal scale: attributes like sex or species. Can only determine if one object is different from another. Common in ecology, only formal property is equivalence
 Ranking scale: ranks things, but not a numerical value, just ranked in relation to one another.
 Interval or ratio scales: have all characteristics of ranking scale, but know distance between classes. Data may be discrete or continuous

Compare and contrast accuracy and precision.
 accuracy  measure of bias
 precision  measure of spread

Why is statistical inference difficult in ecology?
Just because something is statistically significant, does not mean its biologically significant, and the reverse is true. Statistics can only deal with random error; biased data is hard to detect.

What are the common measures of abundance used in ecological studies? Compare and contrast absolute abundance with relative abundance.
 Frequency  percentage of sampling points or quadrats where species occur
 Density  number of individuals per unit area
 biomass
 dominance  cover
 production
 numberrelative/absolute  absolute is an exact count of species? relative abundance is another measure of dominance

Measuring abundance in animal populations: Mark recapture techniques. What is the Peterson (Lincoln) estimate? What are the assumptions of using this estimate? What is the Seber modification of the Peterson estimate? Why is it used?
 Peterson
 closed population
 single marking, single recapture
 based on probability: estimated size of pop at time of marking (N) = (total number captured in second sample (C )* number marked in first sample (M) ) / number recaptured (R)
 widely used
 produces biased estimates  tends to overestimate, bias is large for small populations, several formulas to reduce bias
 Assumptions:
 closed population
 all animals have an equal chance of getting caught
 does not alter catchability
 must randomly sample marked and unmarked individuals
 animals do not lose marks b/t sampling
 successive samples must be taken in same life history stage
 sampling must not span periods of increased mortality or emigration
 Seber Modification:
 unbiased if (M+C) > N and nearly unbiased if there are at least 7 recaptures of marked animals

What is the Schnabel method? When is it used? What are its assumptions?
 extension of petersen method for multiple samples
 assumptions:
 same for petersen’s estimate
 easier to pick up violations of the assumptions

What is the JolleySeber method? When and how is it accomplished? What are the assumptions? What affects precision in the JollySeber method?
 mark recapture samples are taken on three or more occasions
 individuals are marked to be specific for that sampling time
 can know when individual was last captured
 samples are usually point samples of short duration separated by a long duration from the next sample
 bonus:
 can estimate probability of survival
 can estimate addition rate (dilution rate) and loss rate for the population
 assumptions:
 every individual has same chance of being caught
 every marked individual has same probability of surviving
 individuals do not lose their marks, and marks are not missed in sampling
 sampling time is negligible in relation to the time between samples
 Precision increases when:
 capture probability goes up
 number of sampling times increases
 survival rates are higher

How do we test for equal catchability?

What are removal and resight methods for estimating animal abundance? What techniques are used for exploited populations? What are the change in ratio methods? When are they used?
 developed so wildlife managers could get estimates of populations under harvest
 Methods for exploited population techniques:
 change in ratio:
 estimated from field data on the change in sex ratio during a hunting season
 assumptions:
 composed of 1. male and female and 2. adults or young
 the differential change in the numbers of the two types of organisms occurs the observation period

What is Eberhardt’s removal method? What are catcheffort methods? When are each used?
 Animal Abundance:
 Eberhardt’s removal method:
 easier use of removal data
 as with markrecapture, works best when a high fraction of the population is seen and a high fraction is removed
 percentage seen must be >40%, percentage removed must be >20% to be precise
 catcheffort methods:
 estimate population size by the decline in catchperunit effort with time
 highly restricted in its use because it will only work well if a large fraction of population is removed so that there is a decline in the catch  peruniteffort
 assumptions:
 pop is closed
 equal catchability
 probability of each being caught in a trap is constant throughout the experiment

What is the Leslie estimate? What is the theory behind the method? What is the MoranZippen method?
 Animal Abundance:
 Leslie estimate
 catchperuniteffort is directly proportional to the existing population size
 pop must be declining time to time by an amount equal to the catch, accumulated catch graphed against catchperuniteffort will be a straight line
 Moran Zippen
 not really sure it fits in in the above samples
 2 sample method
 assumes equal effort for both samples
 See lab exercise*

What are resight methods? How do we estimate density in animal populations? What is the boundary strip method? What is the nested grids method? Is it biased? What is a trapping web? Why would you use a trapping web?
 resight methods are used for radiocollared/tagged individuals, uses maximum likelihood estimation
 boundary strip method
 boundary strip is ½ the movement radius of the animals under study
 1. calculate the average home range size
 2. compute the ratio of grid size to area of average home range
 3. computer simulation with elliptical
 home ranges allowed to overlap
 nested grid method
 large positive bias
 trapping web
 type of removal  recaptures are ignored
 trap density is lower as you move away from center
 assume everyone in the center is caught
 assumes that distances from center of web to each trap are measured accurately
 individuals are not attracted to web from outside area

What is a quadrat? When is a quadrat used for sampling? What are the requirements for using quadrats?
 Quadrat  a measured area, of any shape and size, that is used as a sample area in a biological survey, particularly a survey of plants or of sessile and sedentary animals.
 Requirements for using quadrats:
 area (or volume) counted is known
 organisms are immobile during counting

What are quadrat size effects?
Small quadrats require larger sample sizes for a specified level of adequacy than larger quadrats. Smaller quadrats are more expensive than large based on number of objects sampled per unit time. Coefficient of variation statistics are directly related to sample size needed for specified levels of adequacy, the C.V. values are largest for small quadrats and sparse populations on average.

What are quadrat shape effects? What is an isodiametric quadrat?
 Rectangle quadrats are more accurate for aggregated populations because they have a greater chance of including portions of aggregated and unoccupied patches in a single sample. The circle estimated density the worst because it had the greatest chance of falling completely within a patch or completely out of a patch.
 Isodiametric quadrats (same diameter: circle or square), have fewer problems with parallax and moving around.
 All shapes overestimated density because the edge has low density and we excluded much of the edge because the samples that run over the edge are excluded.

What is simple random sampling?
A simple random sample is a subset chosen entirely by chance from the entire population. Each individual sample must have the same probability of being chosen. Simple random sampling is different from random sampling and should be completely unbiased. Replacement sampling (two samples are independent; the first sample does not affect what we get on the second sample) is usually more accurate than sampling without replacement.

What is meant by stratified random sampling? What are the benefits of stratification? How define strata? Can strata be given different weights?
 In stratified random sampling, the population is divided into subpopulations that do not overlap. Once these strata are chosen, you sample each stratum separately. Benefits of stratified random sampling: Means and confidence intervals can be estimated for each subpopulation
 Often results in a gain in precision of parameters of entire populations
 Stratum weights can be assigned if subpopulations are unequal. Often stratum weights are proportions and must add up to 1. Boundaries between strata can be determined by the cumulative square root of frequency of quadrats method.

What is meant by systematic sampling? When and why is it used? What is the statistical problem with using a systematic sample? How common is the problem in ecological systems?
 To regularly or systematically place (or take) samples
 Used for simplicity of application
 Used to sample evenly across whole population or habitat
 The problem with systematic sampling is that it is not random and may incorporate periodic variation
 Periodic variation rarely seems to occur in ecological systems

How do we determine appropriate size and shape of quadrat to use?
 How to determine appropriate size:
 Need to minimize edge effects in small quadrat sizes
 Want to get values with normal distribution
 Cost: Minimum number of quadrats required for adequate sample
 Want a quadrat size that gives highest precision (Lowest SE, narrowest CI).
 How to determine appropriate shape:
 Edge effects: circle<square<rectangle
 Long, thin quadrats are better than circular or square ones in heterogeneous habitats
 Circular quadrats work better with permanently marked points in sequential sampling
 Quadrat size and shape effects are not about biased abundance estimates as much as they are about efficiency.
 Simplest approach: Go to the literature and use the same size and shape that everyone else uses
 Better approach: Do pilot studies to determine optimal size and shape for your particular study (Statistically, ecologically, and logistically).

What criteria should be met in determining adequate quadrat size and shape?
 No species should occur (or be equally abundant) in all quadrats
 All important species should be included in the sample at least occasionally
 Be able to observe all parts of the quadrat with minimum personal movement
 Time required to achieve a specified reliability should be minimized

Quadrat size and shape: What is Wiegert’s method?
(easy and fast) Pick quadrat size and shape that minimizes relative cost and relative variance (time=money)

Quadrat size and shape: What is Hendricks’ method?
 (not as quick, more accurate, strict assumptions)
 Assumptions:
 Variance decreases with larger quadrat size
 Log of variance will fall linearly with the log of the quadrat size
 slope of the line is between 0 and 1 (if not, this method cannot be used)
 Time to read a quadrat is proportional to size (2m2 is twice as costly as 1m2)

Quadrat size and shape: What is the nested quadrats method?
 Used to define a speciesarea curve for plant communities
 Then can be used to define quadrat size
 Can be any shape

Take home message on quadrat size and shape
 No single quadrat size or shape can be universally used
 Best to do a pilot study to gather means, variances, and costs
 Pilot studies should be part of every experimental design
 When to ignore recommendations: If you want to compare your data with older data gathered with a specific quadrat, if sampling several habitats, species, across seasons.

