Infancy blossoms into childhood with the dramatic changes of the second and third years of life. These average changes from infancy to early childhood are so marked that one of the founders of developmental psychology, James Mark Baldwin (1894), suggested that, during the first year, infants possess only the properties of lower vertebrates; during the second year, they employ processes of higher vertebrates; not until the third year of life, however, do children begin to use cognitive processes characteristic of the human species. Although Baldwin's ontogeny-recapitulates-phylogeny interpretation of the changes from infancy to early childhood would find few adherents today, no one would deny that the average changes from infancy to early childhood are considerable. It is critical, however, to recognize that what we know about the transition from infancy to early childhood is limited primarily to average age differences rather than to individual differences.

This chapter discusses what is meant by developmental change in terms of individual differences rather than average age differences. Developmental change in terms of individual differences can be quite different from normative change because, as discussed in Chapter 2, the description and explanation of group differences are not necessarily related to individual differences. Indeed, it has been suggested that “there may be an inverse relationship between the suitability of a dimension as an expression of individual differences and its status as a dimension of major developmental change” (Wohlwill, 1973, p. 335).

Everything psychologists measure in the family environment is at least indirectly a measure of parental behavior. This is obvious for the two “superfactors” parental warmth and control, but it is just as true for physical aspects of the home environment such as number of books in the home. Consider, for example, the most widely used measure of the family environment, Caldwell and Bradley's (1978) Home Observation for Measurement of the Environment (HOME). Each of the 45 items clearly involves parental behavior; for example, the first item is “mother spontaneously vocalizes to child at least twice during visit.” The six scales of the HOME also indicate the behavioral nature of the HOME: emotional and verbal responsivity of the mother, avoidance of restriction and punishment, organization of the physical and temporal environment, provision of appropriate play materials, maternal involvement with child, and opportunities for variety in daily stimulation.

If measures of the home environment are viewed as indirectly assessing parental behavior, variations in such parenting measures can be studied from a quantitative genetic perspective. This perspective leads us to investigate the etiology of differences in childrearing behavior among parents and to consider genetic as well as environmental components of variance. Genetic variance can lead to variability on a measure of parenting for two reasons.

Teaching in Cambridge proved to be refreshing and stimulated my wish to write a new version of my earlier book, Das menschliche Gehirn (Hippokrates Verlag Stuttgart, 1968), drawing upon my experience and accumulated teaching material. This new book attempts, as did an earlier one (Experimental Neurology, Clarendon Press, Oxford, 1961), a combination of morphological data with physiological and neurological studies.

Being primarily a morphologist rooted in the concept of the evolution of structure I have placed the emphasis on structural organisation, but functional aspects, experimental research and clinical findings have been incorporated, broadening the interest for clinical students and for students of neurobiology.

I wish to thank Professor R. J. Harrison, FRS for his offer of a base in his department from which I could take part in departmental teaching and continue my research, supported by the Deutsche Forschungsgemeinschaft; and Dr J. Herbert, Fellow of Gonville and Caius College, and Professor W. J. Macpherson, President of the College, for making mean Associate Member of the College, enabling me to teach some of their medical students. I also wish to thank students from Gonville and Caius College, in particular Pak-Lee Chau, David Evans, Diane Hopper, John Williams and Kwong-Wai Man for their help in various ways. My thanks to Petra Schuba for her great illustrative skill, to Mrs F. Glees for her secretarial help, to Tim Crane and Dennis McBrearty for their expert technical assistance and to Herr G. Koch, Gesellschaf t für wissenschaftliche Datenverarbeitung, Göttingen, for help with the index. I am indebted to the staff of Cambridge University Press, for their patience and linguistic support during the preparation of this book.

The goal of this book is to explore the origins of individual differences in behavioral development during infancy and early childhood. A key phrase is “individual differences.” When developmentalists look at infancy and early childhood, they are usually absorbed by the dramatic changes that members of our species undergo during this fast-moving period of development. For example, Jean Piaget, the most influential figure in developmental psychology since the 1960s, described cognitive changes in terms of the transition from the sensorimotor actions of infancy to the representational abilities of early childhood, seen most clearly in the blossoming of language. However, Piaget was concerned only with average developmental trends, not with differences among children.

In contrast, when we look at children, we see children, not the child. That is, our interest centers on the development of individual differences among children rather than universal or normative (average) aspects of our species' development. A powerful theory of development must be able to explain individual differences, if for no other reason than that such differences exist – individual differences represent a major part of the phenomenon to be explained. There are, however, other reasons for studying individual differences: Descriptions and explanations of normative aspects of development bear no necessary relationship to those of individual differences; questions concerning the origins of individual differences are more easily answered than questions concerning the etiology of normative aspects of development; and the developmental issues of greatest relevance to society are issues of individual differences.

Introduction

In Chapter 3 the Lapicque model, in which a lumped circuit consisting of a resistance and capacitance in parallel, was employed to represent the entire nerve cell. Though that simple model is not without usefulness, when we cast our minds back to the anatomical facts we reviewed concerning motoneurons in Chapter 1, we realize that we must extend the model if we wish to incorporate the realities of neuronal structure.

For example, we might ask what is the relative effectiveness of synapses close to the soma, compared to those of the same strength on distal parts of the dendritic tree. Or we might wish to inquire how branching affects the integration of various inputs. The model developed in this chapter will help us answer these kinds of questions within a mathematical framework, which is not conceptually difficult, though it has a cumbersome nature when the geometry of the cell is complicated. The various portions of the dendritic tree and the axon are now regarded as passive nerve cylinders and the equations satisfied by the electric potential are the partial differential equations of linear cable theory. (The term passive here means that the membrane conductance is fixed.)

We will here bridge the gap between the simple lumped-circuit model of Chapter 3 and the more complicated Hodgkin–Huxley model considered later. It must be emphasized that in this chapter and the next we deal only with subthreshold responses: that is, levels of excitation less than those required to generate action potentials.

The central nervous system

Our brains and spinal cords contain specialized cells called nerve cells or neurons, which are collectively referred to as the central nervous system (CNS). At one time it was thought that the nervous system was continuous, but it is now firmly established that the neuron is the fundamental discrete unit of the CNS. The nervous system is extremely complex and estimates of the number of nerve cells in the human brain are on the order of 10 billion (i.e., 1010). In addition, there are closely associated cells, as numerous or more so, called glial cells or glia, that seem to play an important regulatory role. They have several properties in common with neurons but are nevertheless quite distinguishable from them.

From location to location in the CNS, nerve cells differ in their properties and functions. It is convenient, however, to envisage a paradigm, or typical nerve cell, with four basic components (see Figure 1.1). The components and their usual roles are as follows.

Cell body or soma

This is the focal part from which branching structures emanate. It roughly delineates the input or information-gathering parts of the cell from the output or information-transmitting parts.

Dendrites

There are usually several dendrites that may branch several times to form treelike structures–the dendritic trees. Over the dendrites occur many contacts from other cells at specialized sites called synapses, though these are also often found on the cell body.

Introduction

In the preceding chapter we showed how, in the framework of cable theory, the steady-state depolarization could be found either in a nerve cylinder or a whole neuron composed of soma, dendritic tree, and axon. To achieve that, we had to solve ordinary differential equations with given boundary conditions at terminals and branch points.

The steady-state solutions are of interest when they can be related to experimental results and can provide some relatively quick insights into the effects of various input patterns and various neuronal geometries. In the natural activity of a nerve cell, however, steady-state conditions will never prevail. In order to understand the dynamic behavior of nerve cells, we must therefore examine the time-dependent solutions.

To obtain the time-dependent solutions, we must solve the partial differential equation (4.25), or the dimensionless version (4.59), for the depolarization V(x, t) at position x at time t. The inclusion of the time variable makes obtaining solutions more difficult, though it may be said that if we are using the linear cable model, there is no problem that we cannot, in principle, solve.

We will begin by showing the usefulness of the Green's function method of solution for nerve cylinders. This extends the approach we used in the previous chapter, and the technique can be used for any spatio–temporal input pattern. We will then look at the case of a nerve cylinder with time-dependent current injection at a terminal.

Introduction

One fundamental principle in neural modeling is that one should use the simplest model that is capable of predicting the experimental phenomena of interest. A nerve-cell model must necessarily contain parameters that admit of physical interpretation and measurement, so that it is capable of predicting the different quantitative behaviors of different cells.

The model we will consider in this chapter is very simple and leads only to first-order linear differential equations for the voltage. However, when we employ the model in many situations of neurophysiological interest, we find that the mathematical analysis becomes quite difficult, due mainly to the nonlinearities introduced by the imposition of a firing threshold. This will become even more apparent in Chapter 9, where we consider stochastic versions of this model.

The model will be called the Lapicque model after the neurophysiologist who first employed it in the calculation of firing times (Lapicque 1907). Other names for this model, which have recently appeared in the literature are the leaky integrator or the forgetful integrate and fire model.

According to Eccles (1957) the resting motoneuron membrane can be represented by the circuit shown in Figure 3.1A. A battery with a potential difference equal to that of the resting membrane potential maintains that potential across the membrane circuit elements consisting of a resistor and capacitor in parallel. We call this a lumped model or a point model to indicate that the whole cell (with attention focused on the soma and dendrites) is lumped together into one representative circuit.

This is the first of two volumes dealing with theories of the dynamical behavior of neurons. It is intended to be useful to graduate students and research workers in both applied mathematics and neurobiology. It would be suitable for a one-quarter or one-semester course in quantitative methods in neurobiology.

The book essentially contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the last 30 years. Chapter 1, however, contains a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical development. A number of suggestions are made for further reading for the reader whose training has been primarily mathematical.

The remainder of the book is a mathematical treatment of nerve-cell properties and responses. From Chapter 2 onward, there is a steady increase in mathematical level. An attempt has been made to explain some of the essential mathematics as it is needed, although some familiarity with differential equations and linear algebra is desirable. It is hoped that physiologists will benefit from this method of presentation. Biophysicists, engineers, physicists, and psychologists who are interested in theoretical descriptions of neurons should also find this book useful.

From Chapter 2 onward, the theme is the systematic development of mathematical theories of the dynamical behavior of neurons. The fundamental observation is of the resting membrane potential. Hence Chapter 2 is mainly concerned with the passive properties of cells and is an exposition of the classical theory of membrane potentials (i.e., the Nernst–Planck and Poisson equations).

• MEASURING THE NEED FOR POWER

Practically every Student of personality, from Freud to McDougall to Murray and Cattell, has found that human beings are characterized by a need for power, aggression, or domination. Anthropologists, biologists, and philosophers like Nietzsche have all been impressed by human beings' aggressive urges.

The story of how a measure for the motive involved here was finally derived is considerably more complicated than it was for the achievement motive. An early measure patterned after the scoring System for n Achievement was discovered to have some limitations and was eventually modified, expanded, and refined into the measure generally used today. The account of its development illustrates how science proceeds by trial and correction and, once again, how crucial precise measurement is in science.

The original coding System for n Power was derived by Veroff (1957) from examining the content of stories written by Student candidates for office while they were waiting for election returns to be counted. The idea was that students seeking office would be more likely than others to want power and that their power need would be more apt to be aroused while they were waiting to see if they would get power than under more neutral conditions.

For historical reasons, as explained in Chapter 3, academic psychologists first conceived of motives as efforts to avoid discomfort and to reduce strong Stimulation, whether caused by hunger, thirst, pain, electric shock, conflict, or frustration. They found it easy to observe the effects of such strong Stimulation on their favorite subjects—namely, animals in the laboratory—and they believed that psychoanalysts working with patients had confirmed their view that anxiety reduction was a kind of master motive. From this point of view it did not make much sense to think in terms of different kinds of avoidance motives: Individuals simply learned different ways of reducing their anxiety, and these might be as varied as the number of people studied. Thus, one person might reduce his or her anxiety by chewing gum, another by jogging, and a third by going to the movies.

It did not make sense to try to define and measure a gum-chewing motive, a jogging motive, or a movie-going motive, so not much attention has been given to sophisticated measurement in this area such as has characterized the work on measuring n Achievement or n Power. In the beginning, scholars were satisfied with simple reports by individuals as to how anxious they felt.