Introduction

This chapter provides an overview of the female reproductive system. Section 13.1 describes the basic internal anatomy of the female reproductive tract. A detailed review of the physiological mechanisms governing the development of eggs, from their origin in the ovaries as oogonia to their final release into the oviducts at ovulation is then provided in Sections 13.2 and 13.3; in Sections 13.4 and 13.5 the fertilization and oviposition of eggs are described, including a description of the female external genitalia that are involved in oviposition, and the role of female accessory glands in reproduction.

Anatomy of the internal reproductive organs

The female reproductive system consists of a pair of ovaries, which connect with a pair of lateral oviducts. These join to form a median oviduct opening posteriorly into a genital chamber. Sometimes the genital chamber forms a tube, the vagina, and this is often developed to form a bursa copulatrix for reception of the penis and/or spermatophore. Opening from the genital chamber or the vagina is a spermatheca for storing sperm, and, frequently, a pair of accessory glands is also present (Fig. 13.1).

THE BASIS OF an MCMC algorithm is the construction of a transition kernel (see Section 6.3), p(x, y), that has an invariant density equal to the target density. Given such a kernel, the process can be started at x0 to yield a draw x1 from p(x0, x1), x2 from p(x1, x2), …, and xG from p(xG–1, xG), where G is the desired number of simulations. After a transient period, the distribution of the xg is approximately equal to the target distribution. The question is how to find a kernel that has the target as its invariant distribution. It is remarkable that there is a general principle for finding such kernels, the Metropolis-Hastings (MH) algorithm. I first discuss a special case – the Gibbs algorithm or Gibbs sampler – and then explain a more general version of the MH algorithm.

It is important to distinguish between the number of simulated values G and the number of observations n in the sample of data that is being analyzed. The former may be made very large – the only restriction comes from computer time and capacity, but the number of observations is fixed at the time the data are collected. Larger values of G lead to more accurate approximations. MCMC algorithms provide an approximation to the exact posterior distribution of a parameter; that is, they approximate the posterior distribution of the parameters, taking the number of observations to be fixed at n.

Introduction

Insects typically have three pairs of jointed legs, one pair on each of the thoracic segments. The legs are moved by sets of extrinsic and intrinsic muscles, and are furnished with a range of sensory receptors, as well as with other mechanical structures such as hairs, spines and adhesive pads. In most insects, the primary function of the legs is to enable walking on land, but modifications of their structure allow them to be used in other kinds of locomotion, including jumping, swimming and walking on water. The legs are also specialized for a range of other tasks in different insects, including grasping, grooming, pollen collection and silk production.

This chapter is divided into five sections. Section 8.1 describes the structure of the legs, considering their segments, musculature, sensory apparatus and attachment devices. Section 8.2 discusses maintenance of stance and the movements and coordination of the legs in walking and running. Section 8.3 considers other mechanisms of terrestrial locomotion, including jumping and crawling. Section 8.4 describes the mechanism and function of the legs in aquatic locomotion, both in walking on the surface or the bottom, and in swimming. Section 8.5 discusses modifications of the legs for functions other than locomotion.

THE FIRST SECTION of this chapter discusses general properties of posterior distributions. It continues with an explanation of how a Bayesian statistician uses the posterior distribution to conduct statistical inference, which consists of learning about parameter values either in the form of point or interval estimates, making predictions, and comparing alternative models.

Properties of Posterior Distributions

This section discusses general properties of posterior distributions, starting with the likelihood function. It continues by generalizing the concept to include models with more than one parameter and goes on to discuss the revision of posterior distributions as more data become available, the role of the sample size, and the concept of identification.

The Likelihood Function

As you have seen, the posterior distribution is proportional to the product of the likelihood function and the prior distribution. The latter is somewhat controversial and is discussed in Chapter 4, but the choice of a likelihood function is also an important matter and requires discussion. A central issue is that the Bayesian must specify an explicit likelihood function to derive the posterior distribution. In some cases, the choice of a likelihood function appears straightforward. In the coin-tossing experiment of Section 2.2, for example, the choice of a Bernoulli distribution seems natural, but it does require the assumptions of independent trials and a constant probability. These assumptions might be considered prior information, but they are conventionally a part of the likelihood function rather than of the prior distribution.

THE MODELS DISCUSSED in this book are rather easy to program, and students are encouraged to do some or all of the exercises by writing their own programs. The writing of programs requires a complete understanding of the problem and is therefore the best way to ensure that the material has been mastered.

A number of excellent programs are suitable for programming the MCMC algorithms described in this book. At this writing, the most popular seems to be R, which is a free software environment for statistical computing and graphics. There are versions for UNIX, Windows, and MacOS, and it may be downloaded from your preferred CRAN mirror. R is explained in a large number of books and online material. An excellent general introduction is Maindonald and Braun (2010), and Springer publishes a large number of titles in its “Use R!” series, some of which cover Bayesian methods. Another important feature of R is the extensive set of packages that provide tools for specialized tasks.

Two useful packages for Bayesian model fitting in R are:

1. • MCMCpack is available at http://mcmcpack.wustl.edu; it contains some of the models discussed in this book as well as some additional measurement and ecological inference models of interest to political scientists. Its lead developers are Andrew Martin, Kevin M. Quinn, and Jong Hee Park.

2. MCMCpack utilizes the coda package (http://cran.r-project.org/web/packages/coda/ coda.pdf) to summarize the MCMC output by preparing summaries, computing convergence diagnostics, and making plots. Functions in the coda package can be used to analyze any MCMC output.

3. […]

THE MOTIVATION FOR this edition is the same as for the first: to provide a concise introduction to the main ideas of Bayesian statistics and econometrics. The changes, however, have made the book somewhat less concise. In particular, I have added a chapter on Bayesian nonparametrics and new sections on the ordinal probit model, item response models, factor analysis models, and time-varying variances. I believe that these additional materials make the book more useful to readers. Another difference is that this edition adopts the R statistics environment as the primary tool for computing.

In addition to those thanked in the preface to the first edition, without implicating them in any errors or omissions, I offer my sincere gratitude to John Burkett, Stephen Haptonstahl, Alejandro Jara, Kyu Ho Kang, Xun Pang, Jong Hee Park, Srikanth Ramamurthy, Richard Startz, and Ghislain Vieilledent.

I am grateful for the continued support of Lisa, Aida, my grandchildren, and Sylvia Silver and her family.

With sadness, I note the recent passing of my friends and colleagues Peter Steiner, Arthur Goldberger, and Arnold Zellner, and of my dear son Arthur, to whom I dedicate this edition.

Introduction

The mouthparts of insects comprise an intricate “toolkit” for feeding. The basic elements of the toolkit comprise the unpaired labrum in front, a median hypopharynx behind the mouth, a pair of mandibles and maxillae laterally and a labium forming the lower lip. These component parts have been modified into a remarkable diversity of forms that allow the insects as a group to exploit an extraordinarily wide range of food sources. This chapter begins by describing how the mouthparts have become modified to suit different feeding niches (Section 2.1). Next (Section 2.2) the mechanics of feeding are described, and in Sections 2.3 and 2.4 aspects of the regulation and consequences of feeding behavior are explained. The chapter ends with an extended consideration of the head glands and their various secretions, introducing, among other things, the world of saliva – the “salioverse” (Section 2.5).

Ectognathous mouthparts

In the non-insect hexapods, Collembola, Diplura and Protura, the mouthparts lie in a cavity of the head produced by the genae, which extend ventrally as oral folds and meet in the ventral midline below the mouthparts (Fig. 2.1). This is the entognathous condition. In the Insecta the mouthparts are not enclosed in this way, but are external to the head; the ectognathous condition. The form of the mouthparts is related to diet, but two basic types can be recognized: one adapted for biting and chewing solid food, and the other adapted for sucking up fluids.

Introduction

The central nervous system is ultimately responsible for producing behavior. It synthesizes inputs from arrays of sensory neurons that individually can only encode or represent tiny parts of the total environment and produces sophisticated representations of the outside world and the internal state of the insect. It is responsible for integrating these many different sensory inputs and deciding upon and organizing appropriate behavioral responses. It does this by coordinating the activity of the approximately 300 skeletal muscles that articulate the body in a precise temporal and spatial manner, all while monitoring the consequences of its own activity during ongoing behavior. The sensory systems are considered in Chapters 22–24, and the stomodeal system, regulating gut activity, is described in Section 3.1.7. In this chapter the basic cellular components of the nervous system, both nerve cells and the supporting glial cells, are described in Section 20.1. The means by which neurons carry signals and communicate with each other is covered in Section 20.2. In Section 20.3 the anatomy of the ventral nerve cord along with the structure and function of some of the different kinds of neurons found within are considered. Section 20.4 deals with the large-scale anatomy of the brain, together with some discussion of how different regions are specialized for different functions. Finally, in Section 20.5 a few examples of how networks of neurons work together to integrate and analyze sensory information, coordinate complex movements and learn new information are described.

Introduction

The lumen of the alimentary canal is a portion of the external environment over which the insect has great control, and this control is exerted predominantly by the gut epithelium. The principal functions of the alimentary canal are to process ingested food, mostly by chemical modification but also, in some insects, by mechanical disruption, and then to assimilate the products of digestion. The alimentary canal also comes into contact with toxins and microorganisms, including pathogens, associated with the food. Some of these microorganisms become resident in the gut and are beneficial to the insect. It therefore has to combine three capabilities: to mediate chemical transformations involving enzymes capable of degrading the insect's tissues; to provide an absorptive surface for the assimilation of nutrients and water; and to protect against pathogens and noxious compounds. These diverse capabilities are achieved through regional differentiation of the alimentary tract and integration of structure and function at both the molecular and whole-organ levels. Furthermore, the insect alimentary tracts include spectacular examples of adaptation in structural organization and function to different insect diets and habits.

This chapter is divided into four sections. Section 3.1 describes the structural organization of the insect alimentary tract. It is followed by Section 3.2 on digestion and Section 3.3 on absorption of nutrients, ions and water, and concludes with Section 3.4 on the gut as an immunological organ. Throughout the chapter the variation in structure and function with insect phylogeny and diet is addressed.

THIS CHAPTER CONCERNS data sets for which the assumption made about the exogeneity of covariates in Chapter 4 and subsequent chapters is untenable. Covariates that are correlated with the disturbance term are called endogenous variables in the econometrics literature. Three types of models are taken up in which endogeneity may be present: treatment models, unobserved covariates, and sample selection subject to incidental truncation.

Treatment Models

Treatment models are used to compare responses of individuals who belong either to a treatment or a control group. If the assignment to a group is random, as inmany clinical trials, the assignmentmay be regarded as independent of any characteristics of the individual. But in many economic applications and in clinical trials in which compliance is not guaranteed, whether an individual is in the treatment or control group is a choice made by the individual, and the choice may depend on unobserved covariates that are correlated with the response variable. Such unobserved covariates are called confounders in the statistical literature; in the econometrics literature, the treatment assignment is called endogenous when it is not independent of the response variable. As an example, let the response variable be wages and the treatment be participation in a job training program. You might expect that people with sufficient motivation to participate in training would earn higher wages, even without participating in the program, than those with less motivation. The problem may be less serious if individuals are randomly assigned to the training program, but there may still be confounding. For example, individuals assigned to the program may choose not to participate, and individuals not assigned to the program may find a way to participate.

Introduction

The insect abdomen is more obviously segmental in origin than either the head or the thorax, consisting of a series of similar segments, but with the posterior segments modified for mating and oviposition. In general, the abdominal segments of adult insects are without appendages except for those concerned with reproduction and a pair of terminal, usually sensory, cerci. Pregenital appendages are, however, present in Apterygota and in many larval insects, as well as in non-insectan hexapods. Aquatic larvae often have segmental gills, while many holometabolous larvae, especially among the Diptera and Lepidoptera, have lobe-like abdominal legs called prolegs. This chapter provides a general description of the insect abdomen (Section 11.1), followed by a discussion of the structure and function of abdominal appendages (Section 11.2).

Segmentation

Number of segments

The basic number of segments in the abdomen is 11, plus the postsegmental telson, which bears the anus (the telson is sometimes referred to as a 12th segment). Only in adult Protura and the embryos of some hemimetabolous insects is the full complement visible. In all other instances there is some degree of reduction. The telson, if it is present at all, is generally represented only by the circumanal membrane, but in larval Odonata three small sclerites surrounding the anus may represent the telson.

Introduction

Mechanoreceptors detect mechanical distortions that can arise from touching an object or from the impact of vibrations borne through the air, water or the substratum. They underpin the senses of touch and hearing, and monitor distortions of the body or limbs which arise from the stance or movements of the insect or from the force of gravity. Some mechanoreceptors are exteroceptors (which respond to external stimuli), some are interoceptors (responding to internally generated stimuli) and others are proprioceptors (which respond to body position and movement). Surprisingly, in some insects, mechanoreceptors even permit the detection of infrared radiation. Mechanoreceptors can have exquisite sensitivity and precise tuning to specific stimuli, permitting rapid and appropriate behavioral responses. Groups of similar mechanoreceptors often act together as “populations,” each member being tuned differently, so that their summed neuronal output can retain the benefit of high sensitivity while permitting the representation of a very wide range of possible inputs.

Three broad structural categories of mechanoreceptor are present in insects: cuticular structures with bipolar neurons, discussed in Section 23.1; subcuticular structures with bipolar neurons, known as chordotonal organs, described in Section 23.2; and internal multipolar neurons which function as stretch or tension receptors, detailed in Section 23.3. The descriptions of this chapter are broadly divided into discussions of structure and distribution, mechanisms of action and function. Roles of mechanoreceptors in the generation of motor patterns are detailed in Chapter 9, and their involvement in sound communication is considered in Chapter 26.

Introduction

Insects vary greatly in their reproductive anatomy, behavior and physiology. This chapter provides a general overview of the male reproductive system, including the mechanisms of copulation and insemination. It describes in Section 12.1 the basic elements of the internal anatomy, which include the testes that produce sperm, the vas deferens and seminal vesicles for their storage prior to ejaculation and the accessory glands that manufacture seminal fluids that mix with sperm to form the ejaculate and, in species in which insemination is indirect, the spermatophore in which the ejaculate is housed when passed to the female. Section 12.2 provides a detailed overview of the ultrastructure of insect spermatozoa and the processes of spermatogenesis. Section 12.3 describes the various means by which insemination is accomplished, covering a description of the male external genitalia, copulation and the transfer of sperm to the female reproductive tract. Finally, Section 12.4 discusses the various effects of mating on female nutrition and physiology that are brought about by accessory gland products that are transferred to females as part of the ejaculate.

Anatomy of the internal reproductive organs

The male reproductive organs typically consist of a pair of testes connecting with paired seminal vesicles and a median ejaculatory duct (Fig. 12.1). In most insects there are also a number of accessory glands which open into the vasa deferentia or the ejaculatory duct.