Introduction

An empirical model is based only on data and is used to predict rather than to explain systems. In ecology, such models often consist of mathematical functions like linear or nonlinear regressions which describe the trend of data.

The word empiricism comes from a mixture of the Greek and Latin words experientia from where we get experience and empiric referring to an ancient Greek doctor Sextus Empiricus whose methods came from experiences rather than relying on instructions from theories. In more modern philosophy, John Locke formed in the seventeenth century the doctrine of empiricism as considering the human mind as a 'tabula rasa' (clean slate) where experiences can be registered. Humans have no innate ideas - all we know has come from experience. Consequently, we also call empirical models as 'black box' models or 'input-output' models.

Empirical models are successfully used in ecology as the predictive part of the scientific process in the public phase of the hypothetico-deductive method of theory building (Figure 1). They can be used to describe the behavior of parts of ecosystems and can be used in combinations to describe whole ecosystems. There are a lot of actors in ecosystems, and both complicated models and assemblages of more simple, empirical models are necessary for surveying the systems and revealing the system's properties. In opposition to, for example, physical sciences, it is not possible to reduce observations of the behavior of ecosystems to simple laws of nature formulated with universal constants. The irreducibility of ecosystems makes it necessary to develop more complicated and 'soft' models consisting of submodels which can be empirically derived. By comparing uncertainties among such empirical submodels, we can carry out sensitivity analyses and assess further research priorities among subsystems. Since 1980, several theories for whole ecosystem behavior based on modeling have appeared as Odum's theory on maximum power, Ulanowicz' theory on ascendency, and various theories for structural dynamic models based on thermodynamic principles. To get an overview of how the analysis of structures and functions work together with the synthesis in holistic ecosystem behavior, a matrix for lake-ecosystem research has been proposed:

Reductionistic/ analytical

Holistic/integrative

In-depth

Parts and

Dynamic modeling

single case

processes,

linear

causalities

Comparative

Loading-trophic

Trophic topology and

cross-

state, general

metabolic types,

sectional

plankton

homeostasis,

model, etc.

ecosystem

behavior

A similar way to show the role of empirical models in lake ecosystem research was done for the Mirror Lake study by grouping in four approaches:

1. empirical studies where bits of information are collected and an attempt is made to integrate and assemble these into a complete picture;

2. comparative studies where a few structures and a few functional components are compared for a range of ecosystem types;

3. experimental studies where manipulation of a whole ecosystem is used to identify and elucidate mechanisms; and

4. modeling and computer simulation studies.

Synthetic or private phase:

Informal interaction and testing

Analytic, public, or Popperian phase:

Critical or formal tests

Previous observations

Perceived problem

Insight

Belief

Existing theory Working hypotheses

Concept

Formal hypotheses

Deduction

Prediction

Confirmation {_

Falsification _*

Comparison — with observation -

Figure 1 A schematic diagram of the hypothetico-deductive method, indicating the separation of private and public phases of theory building. From Peters RH (1991) A Critique for Ecology. Cambridge: Cambridge University Press.

Here we can see that empirical models and submodels are important instruments on all levels from reductionistic single case and cross-sectional behavior and as parts and backgrounds for holistic descriptions of lake ecosystems. Similar matrices and lists of approaches can be developed for terrestrial and coastal ecosystems, but for oceanic systems they are probably not as applicable due to the scales and the availability of data.

Popperianists drew lessons from physics and rejected increased instrumentalization of science on account of theory development. They declared that improved theories bring us closer to reality and automatically generate better predictions. But they admitted that this view was not testable. For the development of ecology as a science, a list of criteria for judgment of scientific theories can be made: goal definition, relevance, immediacy, operationalism, accuracy, generality, precision, quantification, and economy of effort, and further into a number of social criteria referring to the implied scientists: practicability, simplicity, consistency, and heuristic power. We can add a set of criteria that identify the success for the theories to be adopted by the audience - the theories have to be conceptually simple and consistent. Almost all of these criteria are relative but the predictive power is absolute, and since empirical models have their strength in predictive power their use in ecology is widespread. The predictive power also makes empirical models extremely popular as management tools.

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