A set of core concepts has organized the contents of this book, providing a perspective on the science of hormones, brain, and behavior. One of these is the notion that underlying many behaviors carried out by animals, including ourselves, are central motive states that are influenced by hormones acting on the brain (Lashley, 1938; Beach, 1942; Stellar, 1954). That is, hormones induce and sustain central states that prepare an animal to perceive the world in characteristic ways and then act accordingly.

Recall the Introduction: Hormonally facilitated central motive states can be divided into two phases. The first is the appetitive phase – searching for what is desired (e.g., sodium) and avoiding what is aversive (e.g., a predator). The second is the consummatory phase, in which the animal satisfies its desire (e.g., by ingesting sodium or by feeling safe). The organization of the behaviors is reflected in the functional roles that hormones play in the brain to generate behaviors that will maintain the internal milieu and respond to problems in the external world. Steroid and peptide hormones activate and sustain central motive states.

Herbert (1993) has produced a beautiful monograph depicting different contexts in which steroids and peptides interact to regulate behavior (see also Hoebel, 1988). Most of these have been discussed in this book. They range from ingesting food, water, and sodium to maternal behavior, fear, and aggression. Being economical, nature uses the same hormones to generate a variety of different central states.

Introduction

One of evolution's most successful adaptations is the self-generated rhythmicity (endogenous rhythmicity) with which organisms adjust to periodic influences in their environments, including diurnal, lunar, seasonal, and tidal cycles. By measuring the passage of time, endogenous biological clocks regulate both behavior and physiology, with one complementing the other. There are several kinds of biological clocks, and their anatomic locations and functions vary across species.

In most species, a behavior alternates between an active phase and a restful phase. Recall that during active periods the concentrations of hormones such as cortisol are elevated. The active phase reflects energy use, and the rest phase energy conservation. However, hormones such as melatonin, which is secreted at night, can be elevated during the active phase or the rest phase, depending upon the presence of light/darkness. In rodents, two oscillators have been hypothesized: One oscillator is synchronized to dusk, and the other to dawn, and the two are entrained to one another (e.g., Pittendrigh and Daan, 1976).

In most animal species, sleep is regulated both by circadian (daily) mechanisms and by mechanisms that maintain homeostasis. One mechanism monitors time, while the other monitors the need for sleep. In some cases the circadian clock may facilitate wakefulness against the opposing homeostatic need to remain asleep (Edgar et al., 1992). Sleep deprivation acts on the homeostatic mechanisms for sleep; within limits, the more sleep an animal loses, the more it will need to make up.

Introduction

In this Chapter we discuss methods for estimating the time spent in different behaviors. The Chapter is intended primarily for researchers who collect behavioral data, and we have therefore felt justified in discussing practical problems in some detail. We also assume a moderate familiarity with the goals of behavioral sampling and the practical difficulties often encountered. Lehner (1996) and Martin and Bateson (1993) discuss many other aspects of measuring and describing behavior as well as some of the points discussed here.

By ‘sampling behavior’ we mean that one or (usually) more types of behavior have been defined, and the objective is to estimate how often they occur. ‘How often’ may mean any of the following: proportion of time spent in the behavior, frequency of the behavior (e.g., number/hour), average duration of the behavior. All three estimates might be of interest for some behaviors (e.g., fights with intruders) while for other behaviors this might not be true. For example, it might be feasible to count the number of pecks/minute but difficult, due to the speed with which a peck occurs, to estimate either the average duration of a peck or the proportion of time spent pecking.

Defining behaviors and bouts

A first task in designing the sampling plan is to define the behaviors. The definitions should be specific enough that different observers would interpret them the same way and that they can be explained clearly. Defining positions of the body (head up/head down), type of movement (walking, running, flying), and different types of vocalizations generally meet these criteria better than broader terms such resting, feeding or scanning for predators.

Introduction

The phrase ‘capture–recapture methods’ refers to studies in which a sample of animals is marked and then some, but usually not all, of them are recovered on one or more subsequent occasions. Goals of capture–recapture studies include estimating population size, survival, and certain other variables discussed in this Chapter and studying associations between these and other variables such as how survival rates vary with age or across years. In this Chapter we review the basic concepts that underlie capture–recapture studies, identify major branches of the field, and describe recent developments. Although the methods were originally used primarily to estimate population size and survival rates, contemporary methods provide a rigorous approach for studying a wide variety of other issues of interest in behavior, ecology, and evolution (Nichols 1992). The methods, however, are complex and new refinements appear constantly. We therefore suggest consulting a specialist in capture–recapture methods before undertaking work in this field, and we do not attempt to provide a comprehensive guide to the methods.

Rationale

The basic rationale in capture–recapture methods is to estimate what fraction of the animals marked and present in the study area was counted during each sampling period. This fraction is then used to estimate quantities of interest. Two general approaches might be distinguished for estimating the fraction. First, suppose we can assume that all animals (marked and unmarked) present at the start of the study are still present on each recapture occasion. We will also assume that the marked and unmarked animals, in a given cohort, have the same recapture probabilities.

Introduction

We begin this Chapter by reviewing the meaning of tests and statistical significance and providing guidance on when to use one- and two-tailed tests in behavioral ecology. Confidence intervals are then discussed including their interpretation, why they provide more complete information than tests, and how to decide when to use them. We also discuss confidence intervals for the ratio of two random variables such as estimates of population size in two consecutive years. Sample size and power calculations are then reviewed emphasizing when and how they can be most useful in behavioral ecology. The rest of the Chapter discusses procedures for carrying out tests. We first discuss parametric methods for one and two samples including paired and partially paired data. A discussion is included of how large the sample size must be to use t-tests with data that are not distributed normally. The Chapter ends with some simple guidelines for carrying out multiple comparisons.

Statistical tests

Carrying out hypothesis tests to determine whether a parameter is different from a hypothesized value, or to determine whether two parameters are different from each other, is undoubtedly the most common statistical technique employed by behavioral ecologists. Understanding what these tests reveal is thus important, but is also surprisingly difficult. In this section we review some general principles briefly and identify a few subtleties that are easily overlooked in behavioral ecology. These principles are introduced in the context of testing hypotheses about a proportion.

Introduction

Consider the following sampling problem, taken from a real consulting session we encountered. A biologist was studying the density of a large mammal in different habitats in a large study area. He had defined eight habitat types. The species was always close to water bodies, so the biologist viewed water bodies as the sampling unit. He had delineated the habitats along each water body in the study area. During each of three field seasons, aerial surveys of most or all of the study area were flown two to four times per year. Individual animals were plotted on maps and the habitat each was in, at the time it was sighted, was subsequently determined. The biologist wished to determine which habitats were used disproportionately. More specifically, he wished to estimate density in each habitat and then test the null hypothesis that actual density was the same in each habitat. Ideally, this step would be carried out using a comprehensive test. If the null hypothesis was rejected, then pairwise comparisons would be made as explained in Section 3.7.

This example presents us with a host of problems from an analytical standpoint. Habitat patches varied in size and care must be taken in defining the population units if density is the characteristic of interest. It is problematic whether we have a random sample of habitats since the entire study area was covered in at least some of the surveys. The variable, number of individuals, was recorded at specific times so the population unit is an areatime, but we do not have a simple random sample of area-times within each year because there were only two to four surveys per year.

Introduction

Several statistical methods not previously discussed are briefly described in this Chapter. Our goal is to introduce the methods and indicate where more information on them may be found rather than to present in-depth discussions of the techniques. The first three Sections discuss relatively new methods that have not been widely used in behavioral ecology, or at least some of its subdisciplines, but that may be useful in a variety of applications. The subsequent three Sections discuss other branches of statistics with well-developed methods that we have not had space in this book to cover in detail.

Adaptive sampling

In conventional survey sampling plans, such as those discussed in Chapter Four, the sampling plan and sample size are determined before collecting the data and, in theory, all of the population units to be included in the sample could be identified before data collection begins. This approach, however, is sometimes unsatisfactory when the population units are uncommon and clumped in space and/or time. For example, suppose we are estimating the proportion of trees in an orchard damaged by rodents, and the damage occurs in widely scattered patches. We select rows of trees to inspect. Most trees are undamaged but occasionally we encounter an area in which most trees are damaged. Under conventional sampling plans we can only include trees in the selected rows in our sample. Yet we may be able to see that the damage extends to nearby rows and feel that some way should exist to include those trees in the sample as well.

This book describes the sampling and statistical methods used most often by behavioral ecologists. We define behavioral ecology broadly to include behavior, ecology and such related disciplines as fisheries, wildlife, and environmental physiology. Most researchers in these areas have studied basic statistical methods, but frequently have trouble solving their design or analysis problems despite having taken these courses. The general reason for these problems is probably that introductory statistics courses are intended for workers in many fields, and each field presents a special, and to some extent unique, set of problems. A course tailored for behavioral ecologists would necessarily contain much material of little interest to students in other fields.

The statistical problems that seem to cause behavioral ecologists the most difficulty can be divided into several categories.

1. Some of the most difficult problems faced by behavioral ecologists attempting to design a study or analyze the resulting data fall between statistics – as it is usually taught – and biology. Examples include how to define the sampled and target populations, the nature and purpose of statistical analysis when samples are collected nonrandomly, and how to avoid pseudoreplication.

2. Some methods used frequently by behavioral ecologists are not covered in most introductory texts. Examples include survey sampling, capture–recapture, and distance sampling.

3. Certain concepts in statistics seem to need reinforcement even though they are well covered in many texts. Examples include the rationale of statistical tests, the meaning of confidence intervals, and the interpretation of regression coefficients.

4. Behavioral ecologists encounter special statistical problems in certain areas including index methods, detecting habitat ‘preferences’, and sampling behavior.

5. […]

Introduction

This Chapter reviews methods for studying the relationship between two or more variables. We begin with a brief description of scatterplots and simple summary statistics commonly calculated from them. Emphasis is given to examining the effect of outliers and influential points and to recognizing that measures of association such as the correlation coefficient only describe the linear (i.e., straight line) relationship. Simple linear regression is then described including the meaning of the slope, the basic assumptions needed, and the effects of violating the assumptions. Multiple regression is then introduced, again with emphasis on quantities of direct value to behavioral ecologists rather than on the analytical methods used to obtain these results.

We make a slight notational change in this Chapter. In prior Chapters, we have used lower-case letters for quantities associated with the sample and upper-case letters for quantities associated with the population. In discussions of regression, upper-case letters are generally used for individual values and their means regardless of whether they are associated with the sample or population. Regression coefficients for the population are generally identified by the symbols β (e.g., β0, β1 …) and the corresponding sample estimates are denoted b0, b1 and so on. These practices are so well established in the statistical literature that we follow them in this Chapter even though it introduces some inconsistency with other Chapters.

Scatterplots and correlation

Among the simplest and most commonly used methods for studying the relationship between two quantitative variables are scatterplots and correlations.

Introduction

This Chapter provides an overview of how statistical problems are formulated in behavioral ecology. We begin by identifying some of the difficulties that behavioral ecologists face in deciding what population to study. This decision is usually made largely on nonstatistical grounds but a few statistical considerations are worth discussing. We then introduce the subject of making inferences about the population, describing objectives in statistical terms and discussing accuracy and the general ways used to measure it. Finally, we note that statistical inferences do not necessarily apply beyond the population sampled and emphasize the value of drawing a sharp distinction between the sampled population and larger populations of interest.

Specifying the population

Several conflicting goals influence decisions about how large and variable the study population should be. The issues are largely nonstatistical and thus outside the scope of this book, but a brief summary, emphasizing statistical issues insofar as they do occur, may be helpful.

One issue of fundamental importance is whether the population of interest is well defined. Populations are often well defined in wildlife monitoring studies. The agencies carrying out such studies are usually concerned with a specific area such as a State and clearly wish to survey as much of the area as possible. In observational studies, we would often like to collect the data throughout the daylight hours – or some portion of them – and throughout the season we are studying.

Sampling throughout the population of interest, however, may be difficult for practical reasons. For example, restricting surveys to roads and observations to one period of the day may permit the collection of a larger sample size.

Introduction

Survivorship, the proportion of individuals surviving throughout a given period, may be estimated simply as p = x/n where n = the number alive at the start of the period and x equals the number alive at the end of the period, or it may be estimated using capture–recapture methods as discussed in Chapter Nine. Two additional issues, however, often arise in behavioral ecology. One is that in many studies a measure of overall survival across several periods, each having a separate survival estimate, may be desired. The second issue is that in studies of nesting birds or other animals, information is often incomplete because many nests are not discovered until well after they have been initiated and may not be followed to completion. In this Chapter we discuss methods developed to handle both of these cases. We focus on telemetry studies, which raise the first issue, and studies of nesting success which raise both issues.

Telemetry studies

In telemetry studies, transmitters are attached to animals which are then monitored for various purposes, including the estimation of survival rates. The simplest case arises when all transmitters are attached at about the same time and animals are checked periodically at about the same times until they die or the study ends. Cohorts based on age, sex, or other factors may be defined.

Data of this type are basically binomial (White and Garrott 1990; Samuel and Fuller 1994). On any sampling occasion, t, the proportion of animals still alive is the appropriate estimator of survivorship to that time.

Introduction

We use the phrase resource selection to mean the process that results in animals using some areas, or consuming some food items, and not consuming others. In some studies, resources are defined using mutually exclusive categories such as ‘wooded/nonwooded’ in a habitat study or ‘invertebrate/ plant/bird/mammal’ in a diet study. In other studies, resources are defined using variables that are not mutually exclusive and that define different aspects of the resource such as elevation, aspect, distance to water, and cover type. In some studies, only use is measured. In many others, availability of the resources is also measured and analyses are conducted to determine whether the resources are used in proportion to their availability or whether some are used more – and some less – than would be expected if resources were selected independently of the categories defined by the investigator. In this Chapter, we concentrate on methods in which resources are assigned to mutually exclusive categories because this approach has been by far the most common in behavioral ecology. However, studies in which resources are defined using multivariate approaches are discussed briefly, and we urge readers to learn more about this approach since it can be formulated to include the simpler approach but offers considerably more flexibility.

The investigator has great flexibility in defining use. In the case of habitat studies use may mean that an area is used at least once during the study or (less often in practice) used more than some threshold number of times, or used for a specific activity (e.g., nesting). When the population units are possible prey items, used items might be those attacked, consumed, partly consumed, etc.

Introduction

The term pseudoreplication was introduced by Hurlbert (1984) to describe analyses in which ‘treatments are not replicated (though samples may be) or replicates are not statistically independent’. In survey sampling terms, the problem arises when a multistage design is employed but the data are treated as a one-stage sample in the analysis. For example suppose m secondary units are selected in each of n primary units. In most cases the nm observations do not provide as much information as nm observations selected by simple random sampling. The correct approach is to base the analysis on the means per primary unit.

The initial point made by Hurlbert and soon thereafter by Machlis et al. (1985) was incontrovertible. When multistage sampling is employed, ignoring the sampling plan and treating the data set as though it is a simple random sample can lead to gross errors during interval estimation and testing. This point is emphasized in survey sampling books, and calling attention to the error, which was quite common at the time, was a service to the discipline. Subsequently, however, cases began to appear in which the proper analytical approach was more difficult to agree on. These cases often did not involve large, clearly described populations, and well-defined sampling plans. Instead, they usually involved some combination of incompletely specified populations, nonrandom sampling, nonindependent selection, and small sample sizes. As noted in Chapter Four these issues are inherently difficult and full agreement on the best analytical approach and most appropriate interpretation cannot always be attained. Nonetheless, we believe that progress may be attainable in some cases by applying the ideas developed in Chapter Four.