Chapter 1 – Ecological Data Ground rules 1. Ask a question! Based on personal observations Discussions with other ecologists Published research It is good if the question is focused enough so that it can be framed in terms of hypothesis testing and applied to repeatable investigations. 2. The question should be focused enough so that only pertinent data are collected – you can’t get all.

3. Collect data using a well-designed sampling protocol; well-designed experiments are useful; collect an adequate sample size. Garbage in = garbage out. Know your experimental design before you start – do not go to a statistician and then ask: What can I do with it? 4. There are logistical constraints in all forms of ecological research, particularly large-scale fieldwork. In regards to {3}, if you cannot collect an adequate sample size it may not be work doing the work.

II. Types of data Scales Nominal scale – variable that possesses a particular attribute, e.g., gender or species. 2. Ranking or ordinal scale – variable on a numerical scale, the value between observations cannot be quantified. Letters may be better to use than numbers; contain more information than data collected on a nominal scale. 3. Interval scale – constant intervals but no true zero. E.g., circular data and time of day. 4. Ratio scale – measurement scales having a constant interval and true zero, i.e., in relation to something physical. E.g., height of plant.

B. Distribution Continuously distributed data – there are an infinite number of possibilities. E.g., body weight: 28 g, 28.02 g, 28.7278 g. 2. Discrete data – variables that can only take on certain values. E.g., gender; also, in theory, the number of leaves on a tree. In practice, however, the latter can take on a continuous distribution.

III. Precision, bias, and variance. Always include some measure of variability with data. E.g., variance, stand deviation, standard error of the mean.

IV. Statistical significance does not necessarily mean biological significance and vice-versa.  does not have to equal 0.05. 0.1 for ecology?

V. Data recording, transcribing, and coding. Develop a standard protocol for data collection. Keep transcribing data to a minimum to help reduce error. E.g., pit tags, satellite telemetry, data loggers. All data must be coded for computer entry. *red-tail*

Chapter 6, Sampling In population ecology, it is important to distinguish between a statistical population and biological population.  = the mean of the statistical population and X = the mean of the sample of . Biological population – a group of individuals of one species in an area, though the size and nature of the area is defined, often arbitrarily, for the purposes of the study being undertaken.

It is usually not possible to census or enumerate an entire population, consequently it is sampled. Traditional parametric {and non-parametric} statistics, developed largely by Sir Ronald Fisher, assume random sampling. In theory, random sampling should always be employed; in practice, it may not always be feasible and/or the best approach. Alternative sampling approaches used in ecology: Accessibility sampling Haphazard sampling Judgmental sampling (sight/site matching) Volunteer (survey) sampling

Systematic Sampling .

Stratified random sampling The statistical population is divided {stratified} into non-overlapping subpopulations. Thus if   N, then N = N1 + N2 + N3 + NL, where L = the total number of subpopulations.

Construction of strata: As a generalization, the number of strata should not normally exceed six. 2. A sound knowledge of the ecological variability of a particular system is useful for determining strata. 3. Quantifiable techniques also exist for determining strata. Important: If random sampling is not used, make sure the sampling protocol is not correlated with some spatio-temporal pattern in nature.

Parameter estimation Parameter – the true population value of interest, expressed as a number. Estimator – an estimator is a mathematical expression that indicates how to calculate an estimate of a parameter from the sample data.

Chapter 7, Sequential Sampling Unlike the approaches outlined previously {and traditionally used in ecology}, sequential sampling does not assume an a priori sample size. Approach Sample Size Statistical Inference Traditional Fixed Two Possibilities: 1. accept null H0 2. reject null H0 Sequential Not Fixed Three Possibilities: 3. uncertain (additional)

Stopping rules: ns = [(Z + Z )S / (1 - 0)]2 , where 1 = the mean of the population postulated for H1 2 = the mean of the population postulated for H2  = likelihood of committing a type I error  = likelihood of committing a type II error {power} S = postulated standard deviation

Kuna Approach Based on fitting a quadratic equation. Again, requires preexisting data, either already collected by the investigator or by another investigator working on a similar system. Also requires a priori knowledge about the approximate density of the population of interest. Assumes the mean and variance of the data are correlated.

Sequential sampling can be expanded to test multiple hypotheses. Remember, power analysis can also be used for determining sample size when not using sequential sampling.

Chapter 8, Experimental Design Hierarchical, full 3-way factorial, blocked, repeated measures design. Model building – when different terms in an experimental design are retained or removed from the model depending upon their level of significance.

Hierarchical design, {nesting}. Involves subsampling of an experimental unit; i.e., it is extremely important to be able to correctly identify your experimental unit. Usually used in reference to space. Pseudoreplication – when subsamples are treated as independent observations. In such cases, the main effects d.f. are artificially inflated. Subsampling – can be useful for (1) providing a more realistic picture of the experimental unit and (2) removing the effects of significant variation within experimental units.

II. Factorial designs Useful for detecting interactions. Be able to distinguish between statistical and biological interactions. Factorial designs can test for synergy. Are the sum of the parts greater than the whole? Fractional factorial designs – do not contained all interaction terms.

III. Repeated measures When experimental units are resampled in time. Can result in a lack of independence and biased parameter estimation.

IV. Block design A block must contain one representative of each treatment. Each representative treatment must be positioned in the same general vicinity {usually adjacent to each other} to form a block. Blocking is particularly useful for removing the effects of spatial heterogeneity.

Spatial independence Each experimental unit should be independent in space. Pretreatment sampling Sampling units assigned to a treatment prior to the establishment of manipulations. Helps determine how “good” the replication is; can be used to remove preexisting differences.

Spatial Scale