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What is quantitative ecology and what lead to the quantitative trend in ecology?
 The application of mathematical and statistical tools to address questions in ecology
 The trend 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
 Formulate objectives/hypotheses
 Collect and analyze data
 Draw conclusions
 Evaluate hypotheses

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 satisfy your objectives and a statistician
 4. Some ecological questions are impossible to answer at the present time
 5. Decide on # of significant figures for continuous data prior to starting
 6. Never report an estimate without measure of possible error
 7. Be skeptical about the results of significance tests
 8. Never confuse statistical with biological significance
 9. Code all your data and enter it on a computer in some readable format
 10. Garbage in, garbage out

Why are preliminary and pilot studies important?
 Address simple questions of technique
 Determine sample sizes needed for a particular level of precision

What are the different scales of measurement in ecology?
 Nominal  attributes like sex or species
 Ranking  ranks attributes in relation to one another, but not a numerical value
 Interval/ratio  all characteristics of ranking, 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?
 Usually can not sample in random manner
 Hidden variables confound our interpretations
 Statistics can only deal with random error, not detecting biased data

Compare and contrast absolute abundance with relative abundance
 Absolute abundance  exact count of species
 Relative abundance  measure of dominance relative to coocurring species

What are the common measures of abundance used in ecological studies?
 Frequency  % of sampling points or quadrats with species
 Density  # of individuals per unit area
 Biomass  dominance (cover), production, number

What are the different ways that we measure abundance in animal populations?
 Markrecapture
 Removal/resight
 Distance

What is the Peterson estimate?
 Simplest markrecapture method to estimate population size
 Mark individuals once, release them, and then recapture to check for marks
 Tends to overestimate; bias is large for small populations

What are the assumptions of the Peterson estimate?
 Closed population
 Equal catchability
 Marking doesn't alter catchability
 Marks aren't lost between sampling
 All marks are reported upon discovery in second sample

What is the Seber modification of the Peterson estimate and why is it used?
Reduces the overestimation bias of the Peterson estimate

What is the Schnabel method, when is it used?
 Extension of the Peterson markrecapture estimate for population size
 Used for closed populations and multiple samples

What are the assumptions of the Schnabel method?
 Closed population
 Equal catchability
 Marking doesn't alter catchability
 Marks aren't lost between sampling
 All marks are reported upon discovery in second sample

What is the JolleySeber method?
 Markrecapture method for open populations
 Estimate of population size

When and how is the JollySeber method accomplished?
 3 or more markrecapture samples
 Individuals are marked to be specific for that sampling time
 Samples are usually point samples of short duration separated by a long duration from the next sample

What are the assumptions of the JolleySeber method?
 Equal catchability
 Equal survivability for marked individuals
 Individuals do not lose their marks and marks are not missed in sampling
 Sampling time is negligible in relation to the time between samples

What affects precision in the JollySeber method?
 Capture probability
 # of sampling intervals
 Survival rates

What removal/resight methods are used for exploited populations?
 Changeinratio
 Eberhardt's removal
 CatchEffort

What are the Changeinratio methods?
 Estimate of abundance/density from the change in sex ratio during a hunting season
 Assumptions:
 Composed of males/females and adults or young
 A differential change in the numbers of the two types of organisms occurs during the observation period

What is Eberhardt’s removal method and when is it used?
 If a population size index can be made before and after removal of a known # of individuals, we can use the indices to estimate absolute density
 Easier use of removal data
 Effective when >40% of the population is seen and >20% is removed

What are catcheffort methods and when are they used?
 Estimate population size by the decline in catchperunit effort over time
 Highly restricted because it only works well if a large fraction of population is removed so that there is a decline in the catchperuniteffort

What is the Leslie estimate and what is the theory behind the method?
 Catchperuniteffort is directly proportional to the existing population size
 Because the population must be declining time to time by an amount equal to the catch, a regression plot (accumulated catch vs. catchperuniteffort) should be a straight line
 Doesn't assume equal effort

What is the MoranZippen method?
 Two sample method of removal
 Assumes equal removal effort for both samples

What are resight methods and how do we estimate density in animal populations?
 Methods used to "resight" radiocollared/tagged individuals
 Maximum likelihood estimation for density

What is the boundary strip method?
 Used to estimate density
 Adds a "boundary strip" around the trapping area which is half the movement radius of the animals under study

What is the nested grids method and is it biased?
 If a large area is sampled you can break the data up into a series of nested grids to estimate density
 Large positive bias

What is a trapping web and why use this method?
 Used to estimate density
 Type of removal method, because each individual is counted only the first time and recaptures are ignored
 Trap density is lower as you move away from center
 Assumes every animal in the center is caught
 Individuals are not attracted to web from outside area

What is a quadrat and when is it used for sampling?
A measured area, of any shape and size, that is used as a sample area in a survey of plants or of sessile/sedentary animals.

What are the 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
 Small quadrats are more expensive than large based on number of objects sampled per unit time
 Coefficient of variation values are largest for small quadrats and sparse populations on average

What are quadrat shape effects?
 Rectangle quadrats are more accurate for aggregated populations because they typically include portions of aggregated and unoccupied patches in a single sample
 Circles are poor because they generally land completely within or outside of a patch
 Each quadrat shape tends to over estimate density parameters

What is an isodiametric quadrat?
 Quadrat has the same diameter (e.g., circle, square)
 These have fewer problems with parallax and moving around

What is simple random sampling?
A subset chosen entirely by chance from the entire population

What is meant by stratified random sampling?
 The population is divided into nonoverlapping subpopulations
 Once these strata are chosen, you sample each stratum separately

What are the benefits of stratification?
Means and confidence intervals can be estimated for each subpopulation

Can strata be given different weights?
Stratum weights can be assigned if subpopulations are unequal

What is meant by systematic sampling?
To regularly or systematically place samples

When and why is systematic sampling used?
 Simplicity of application
 Sample evenly across whole population or habitat

What is the statistical problem with using a systematic sample and how common is the problem in ecological systems?
 Systematic sampling is not random and may incorporate periodic variation
 Periodic variation rarely seems to occur in ecological systems

In our lab exercise which method of sample placement best estimated density?
Stratified > regular > random

How do we determine the appropriate size and shape of quadrat to use?
 Wiegert's method
 Hendricks' method
 N_{min }method
 Nested quadrats method
 Want normal distribution and high precision

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 in the sample at least occasionally
 Observe all parts of the quadrat with minimum personal movement
 Time for specified reliability should be minimized

What is Wiegert’s method?
 Determines quadrat size and shape
 Easy and fast
 Select quadrat size and shape that minimizes cost and variance (time = money)

What is Hendricks’ method?
 Determines quadrat size and shape
 More accurate, strict assumptions, but slower
 Variance decreases with larger quadrat size
 Time to read a quadrat is proportional to size (2m^{2} is twice as costly as 1m^{2})

What is the N_{min} method?
Determines adequacy and efficiency of sampling

What is the nested quadrats method?
 Determines quadrat size and shape
 Used to define a speciesarea curve for plant communities

What are quadrat size and shape effects?
 Rectangular quadrats are the best in heterogeneous habitats
 Circular quadrats work well with permanently marked points in sequential sampling (not in grasslands)
 Size and shape effects are not about biased abundance estimates as much as they are about efficiency
 Do pilot studies to determine optimal size and shape for your particular study (statistically, ecologically, and logistically)

Take home message on quadrat size and shape
 No single quadrat size or shape can be universally used
 Do a pilot study to gather means, variances, and costs

When can you ignore recommendations about size and shape of quadrats?
 If you want to compare your data with older data gathered with a specific quadrat
 If sampling several habitats, species, across seasons

How do we determine where to place quadrats?
There is no evidence that random placement of sample units gives better results than stratified or regular placement

How do we determine sampling strategy?
 Clearly specify the statistical population
 Decide your sampling units and your experimental units
 Select a sample and adopt a variety of sampling plans as necessary

What is sampling design?
Method of placement and # of samples must be decided before sampling

What is meant by adaptive sampling?
Take advantage of spatial pattern in the population to obtain more precise measures of abundance

What is an adaptive cluster sample?
Begins with normal random sampling but when an organism of interest is detected, additional quadrats in the vicinity of the original quadrat are added to the sample

What is meant by multistage sampling?
Used to describe any design where there are > 2 levels of sample selection

What is cover?
% of area (ground) covered by vegetation or other material

What are the four basic types of cover obtained in ecological sampling?
 Basal cover
 Canopy cover
 Foliar cover
 Ground cover

Why do we measure cover?
 Cover is an indicator of ecological processes
 Cover also serves as a management indicator for monitoring

How does cover measure dominance?
Cover is an ecological indicator of which species are dominating the site

What are the common methods for assessing cover?
 Simple quadrats (1m^{2} square)
 Line intercept
 Point quadrats
 Loop methods
 Ocular estimate method

What is the lineintercept method?
Assessment of the distance (and sometimes width) along a line that is intercepted by a plant species or type

What are point methods (to assess cover)?
Examination of many points on a site to estimate the proportion of "hits" of a species

What are ocular methods (to assess cover)?
Uses concept that even if it is not possible to accurately estimate precise cover for a given quadrat, it may be easy to estimate broad cover classes

From our lab exercise of estimating plant cover what are factors to consider prior to sampling?
 Time efficiency
 Vegetation type
 How to calculate variance and SD
 Sample consistency

In our lab of estimating plant cover which method best estimated cover?
Ocular > 1point > lineintercept > true mean > 10point

What is the difference between correlation and regression?
 Correlation  variables simply vary together
 Regression  variables vary together but there is evidence of a causal relationship

What is a contingency table?
Display format used to analyze the relationship between two or more categorical variables

What is a chisquare analysis?
 Used to determine if there is a difference between expected and observed frequencies in one or more categories
 Nonparametric

What is the chisquare formula?

How do you calculate expected frequencies for a chisquare analysis of a contingency table?

What are the types of ttests?
 Equal variance (parametric)
 Unequal variance (nonparametric)

What are ANOVAs?
 Analysis of variance that compares two or more means
 Parametric

What are plotless sampling procedures and when are they used?
 Another way of estimating abundance and density
 An alternative to mark/recapture and quadrats
 They are useful for plants and animals that do not move much or can be located before they move

How do plotless sampling techniques work?
 Based on the reciprocal relationship between density and nearness of individuals to one another
 Only necessary to know the distance between regularly spaced individuals to calculate density

What is line transect sampling?
 Method of estimating density
 An observer travels along a randomly positioned line, recording the distances and angles from the line to each organism detected

What are the assumptions of line transect sampling?
 Animals directly on the transect line will never be missed
 Animals do not move before being detected and are never counted twice
 Distances and angles are measured exactly
 Sightings of individual animals are independent events

What is the detection function of linetransect sampling?
Detectability will fall off with distance from the center line of the transect

What are the estimators for density using line transect sampling?
D = n/2La
 D = density of animals/unit area
 n = # animals seen on transect
 L = total length of transect
 a = half the effective strip width (a constant)

What are the two basic approaches to distance methods?
 Select random organism and measure distance to nearest neighbor
 Select random point and measure the distance from the point to the nearest neighbor

If an area has moderate to high density of sessile organisms and they are randomly dispersed, are distance methods or quadrats better?
Quadrats  less biased and do not overestimate density

If an area has low density of sessile organisms and they are randomly dispersed, are distance methods or quadrats better?
Distance methods  less costly in terms of money and time

What is random pairs?
 Both this and quarter method determine the average distance between organisms
 Measures distance between the object nearest to the sampling point and a second object that lies outside an exclusion angle of 180 degrees

What is nearest neighbor?
 Distance from an organism to the one closest to it
 Sometimes incorporates multiple neighbors

What is the pointquarter method?
 Plotless distance method to estimate density
 Quick, easy, and objective
 A series of random points is selected, often along a transect, with the constraint that points should not be so close that the same individual is measured at two successive points
 The area around each random point is divided into four quadrants and the distance to the nearest tree is measured in each quadrant
 Thus four pointtoorganism distances are generated at each random point to the first, second, third, and fourthnearest neighbors
 Overestimates density

What is the Bitterlich method?
 Plotless distance method to estimate density
 For tree basal area is very accurate and quick
 Use sighting scope
 Turn 360 degrees and only count objects that are greater than the crossbar
 Issues with parallax especially in grasslands

What is the Byth and Riply procedure and why is it used?
 Useful for large areas
 Set out 2n sampling points in study area
 Select half of the 2n points at random and measure distance to nearest organism
 Around other half of points set out plots that include about 5 individuals each
 Select n of these at random
 Measure distance from selected organism to its nearest neighbor

What is the TSquare method?
 Most robust estimator of density
 Measure distance from random points to nearest organism and then to its nearest neighbor
 Only used in randomly distributed populations

Compare all distance methods
 All distance methods are sensitive to spatial pattern (biased in clumped populations)
 Estimators based on point to organism are better in clumped
 Estimators based on organism to nearest neighbor are not so good in clumped

What are the three spatial patterns in nature and what gives rise to these patterns?
 Aggregated  some constraint on the population, environmental heterogeneity, gregarious behavior, reproductive behaviors
 Random  environmental homogeneity or nonselective behavioral patterns
 Uniform  negative interactions and competition

What are the two statistical distributions and their spatial patterns?
 Poisson  random pattern
 Negative binomial  aggregated

What is a community?
Associations of populations of many species that occupy the same geographical area

What are the historic community concepts?
 Organismic (holistic)
 Individualistic
 Intermediate

Who are Clements and Gleason?
Proposed the open community view and individualistic view

What is meant by ecotone?
 Transition area between two biomes
 It is where two communities meet and integrate

What is meant by open vs. closed communities?
 Closed have obvious ecotones between species distribution
 Open is overlapping

What is meant by interspecific associations and how do we test for this?
 Associations between two different species
 Test using a Chisquare

How are communities classified?
 Delineation of communities can be difficult unless the transition between adjacent communities is abrupt
 Often arbitrary
 Require statistical approaches such as ordination and cluster analysis

How do we determine where one community ends and another begins?
 Ordination
 Cluster analysis

What are measurements of community similarity?
 Binary coefficients
 Distance coefficients
 Correlation coefficients

What are binary coefficients?
 Used for presence/absence data
 Jaccard index
 Ochiai index
 Sorensens’ similarity index
 Dice index
 BaroniUrbani and Buser coefficient

What are distance coefficients?
 Measures of dissimilarity rather than similarity
 When a distance coefficient = 0, communities are identical
 Require some measure of species abundance in the community
 Euclidean distance, BrayCurtis measure, Canberra metric

What do binary coefficients of similarity deal with?
Simplest similarity measure that deals with presence/absence data

How many binary coefficients of similarity are available in the literature?
> 20 binary similarity measures

What is the Jaccard index?
 Binary coefficient of similarity in presence/absence data
 Deficiency  no significance test

What is the Ochiai index?
Binary coefficient of similarity in presence/absence data

What is the Sorenson’s index?
 Binary coefficient of similarity in presence/absence data
 Weights species composition matches between 2 samples more heavily than mismatches
 Deficiency  no significance test

What is the simple matching coefficient?
 Simplest binary coefficient of similarity in presence/absence data
 Makes use of negative matches as well as positive matches

What is the BaroniUrbani and Buser coefficient?
 More complex binary coefficient of similarity
 Makes use of negative matches

How do binary coefficients of similarity compare?
In general, the Sorenson’s coefficient yields the highest similarity whereas the Jaccard’s coefficient results in the lowest similarity

What is the BrayCurtis measure?
 Measure of community dissimilarity
 Weighs abundant species more heavily than rare species

Compare BrayCurtis and Canberra metric
 Both are particularly poor in diverse communities with large sample sizes
 Both are best used in situations with low species diversity and small sample size

What are the two types of correlation coefficients and when is each used?
 Pearsons product moment  used for parametric data
 Spearman’s rank  used for nonparametric data

What is percentage similarity?
Percent similarity between two communities

What is Ruzicka’s index?
 Similarity index for quantitative data
 Relatively unbiased
 Easy to compute

What is Morisita’s index?
 Similarity index for counts of individuals (not for other abundance estimates based on biomass, productivity, or cover)
 Also a dispersion coefficient

What is the simplified Morisita’s index?
Similarity index for proportional data (biomass, cover, or productivity)

What is Horn’s index?
 Similarity index
 Least sensitive to sample size and gives the best representation of similarity
 Can be calculated from raw data (numbers) or from relative abundances (proportions or percentages)

Describe the multivariate technique called cluster analysis?
Graphical way of portraying results from a large matrix of interspecific association (or similarity) indices

What is simple linkage clustering?
 Also called nearest neighbor method
 Simple to compute
 One inaccurate sample may compromise the entire process
 Tends to produce long, strung out clusters

What is complete linkage clustering?
 Farthest neighbor clustering method
 Opposite of single linkage
 Tends to produce compact clusters

What is average linkage clustering?
Consists of the Weighted Pair Group Method of Averaging and the Unweighted Pair Group Method of Averaging (UPGMA)

Compare and contrast the weighted and unweighted pairgroup methods of averaging (UPGMA)
 Weighted average procedure is more conservative than the unweighted method because it weighs the new addition to the cluster just as heavily as everything else
 Whereas the UPGMA assigns equal weights to each individual component within clusters

