200
WILLIAM STREIFER
Acknowledgements
.
. 266
References .
. 266
Appendix A-Calculations for the Birth Example of Section IVB3 .
. 261
Appendix B-Extensions of the Age-Size Specific Model
. 262
Appendix &The Critical Variable Equations.
.
. 264
PREFACE
In writing this paper I intended that it be read sequentially. However,
upon completion I find that much material of a rather general nature is
presented before any specific applications. For those readers who find
the discussion too general or vague for their tastes, I suggest reading
section VIIA on Daphnia pulex immediately after the subsection on live
births in IVB and reading section VIIB on Dugesia tigrina after the
subsection on fission reproduction. Section VIII on other applications
can be read at any time after section VII, and one can then return t o
subsection IVB to complete the paper.
I. INTRODUCTION
Models mathematically describe our conception of nature. The primary
requirement of models in ecology, as in other fields, is that they be
realistic, i.e. the mathematical predictions of total population, birth
rate, biomass (for example) should agree with one’s observations in the
field or in the laboratory.
In order that a population model be predictive it must represent the
demographic effects of the physiological processes at the level of
individuals. Furthermore, the dependences of these processes on the
presence of other members of the population, the presence of other
species, the food supply and the environment must be included, or the
model will be incapable of predicting the population dynamics. For
example, it is clear that if the ambient temperature were to change and
the death rate was not expressed as a function of temperature, the model
would yield unrealistic results (see Levins, 1966).
It is desirable to formulate general models which, for example, in the
case of single-species models would apply to many different species.
Generality, however, should not be confused with simplicity, for although
both are desirable, generality is the more important, and in fact the
requirement of generality demands some degree of complexity. If a
sufficiently general model is constructed to apply to several similar
species, only some of which are markedly sensitive to prevailing temperature fluctuations, that model would obviously have to be more complicated than a model which applied only to those species less sensitive to
temperature variations.
WILLIAM STREIFER
Acknowledgements
.
. 266
References .
. 266
Appendix A-Calculations for the Birth Example of Section IVB3 .
. 261
Appendix B-Extensions of the Age-Size Specific Model
. 262
Appendix &The Critical Variable Equations.
.
. 264
PREFACE
In writing this paper I intended that it be read sequentially. However,
upon completion I find that much material of a rather general nature is
presented before any specific applications. For those readers who find
the discussion too general or vague for their tastes, I suggest reading
section VIIA on Daphnia pulex immediately after the subsection on live
births in IVB and reading section VIIB on Dugesia tigrina after the
subsection on fission reproduction. Section VIII on other applications
can be read at any time after section VII, and one can then return t o
subsection IVB to complete the paper.
I. INTRODUCTION
Models mathematically describe our conception of nature. The primary
requirement of models in ecology, as in other fields, is that they be
realistic, i.e. the mathematical predictions of total population, birth
rate, biomass (for example) should agree with one’s observations in the
field or in the laboratory.
In order that a population model be predictive it must represent the
demographic effects of the physiological processes at the level of
individuals. Furthermore, the dependences of these processes on the
presence of other members of the population, the presence of other
species, the food supply and the environment must be included, or the
model will be incapable of predicting the population dynamics. For
example, it is clear that if the ambient temperature were to change and
the death rate was not expressed as a function of temperature, the model
would yield unrealistic results (see Levins, 1966).
It is desirable to formulate general models which, for example, in the
case of single-species models would apply to many different species.
Generality, however, should not be confused with simplicity, for although
both are desirable, generality is the more important, and in fact the
requirement of generality demands some degree of complexity. If a
sufficiently general model is constructed to apply to several similar
species, only some of which are markedly sensitive to prevailing temperature fluctuations, that model would obviously have to be more complicated than a model which applied only to those species less sensitive to
temperature variations.