I consider three explanatory strategies from recent systems biology that are driven by mathematics as much as mechanistic detail. Analysis of differential equations drives the first strategy; topological analysis of network motifs drives the second; mathematical theorems from control engineering drive the third. I also distinguish three abstraction types: aggregations, which simplify by condensing information; generalizations, which simplify by generalizing information; and structurations, which simplify by contextualizing information. Using a common explanandum as reference point—namely, the robust perfect adaptation of chemotaxis (...) in Escherichia coli—I argue that each strategy invokes a different combination of abstraction types and that each targets its abstractions to different mechanistic details. (shrink)

In the biomedical context, policy makers face a large amount of potentially discordant evidence from different sources. This prompts the question of how this evidence should be aggregated in the interests of best-informed policy recommendations. The starting point of our discussion is Hunter and Williams’ recent work on an automated aggregation method for medical evidence. Our negative claim is that it is far from clear what the relevant criteria for evaluating an evidence aggregator of this sort are. What is the (...) appropriate balance between explicitly coded algorithms and implicit reasoning involved, for instance, in the packaging of input evidence? In short: What is the optimal degree of ‘automation’? On the positive side: We propose the ability to perform an adequate robustness analysis as the focal criterion, primarily because it directs efforts to what is most important, namely, the structure of the algorithm and the appropriate extent of automation. Moreover, where there are resource constraints on the aggregation process, one must also consider what balance between volume of evidence and accuracy in the treatment of individual evidence best facilitates inference. There is no prerogative to aggregate the total evidence available if this would in fact reduce overall accuracy. (shrink)

Robustness is often presented as a guideline for distinguishing the true or real from mere appearances or artifacts. Most of recent discussions of robustness have focused on the kind of derivational robustness analysis introduced by Levins, while the related but distinct idea of robustness as multiple accessibility, defended by Wimsatt, has received less attention. In this paper, I argue that the latter kind of robustness, when properly understood, can provide justification for ontological commitments. The idea is that we are justified (...) in believing that things studied by science are real insofar as we have robust evidence for them. I develop and analyze this idea in detail, and based on concrete examples show that it plays an important role in science. Finally, I demonstrate how robustness can be used to clarify the debate on scientific realism and to formulate new arguments. (shrink)

Derivational robustness may increase the degree to which various pieces of evidence indirectly confirm a robust result. There are two ways in which this increase may come about. First, if one can show that a result is robust, and that the various individual models used to derive it also have other confirmed results, these other results may indirectly confirm the robust result. Confirmation derives from the fact that data not known to bear on a result are shown to be relevant (...) when it is shown to be robust. Second, robustness may increase the degree to which the robust result is indirectly confirmed if it increases the weight with which existing evidence indirectly confirms it. This may happen when it strengthens the connection between the core and the robust result by showing that auxiliaries are not responsible for the result. (shrink)

Robustness analysis is widespread in science, but philosophers have struggled to justify its confirmatory power. We provide a positive account of robustness by analysing some explicit and implicit uses of within and across-model robustness in evolutionary theory. We argue that appeals to robustness are usually difficult to justify because they aim to increase the likeliness that a phenomenon obtains. However, we show that robust results are necessary for explanations of phenomena with specific properties. Across-model robustness is necessary for how-possibly explanations (...) of multiply instantiated phenomena, while within-model robustness is necessary for explanations of phenomena with multiple evolutionary starting points. In such cases, the appeal of robustness is explanatory rather than confirmatory. (shrink)

Robustness may increase the degree to which the robust result is indirectly confirmed if it is shown to depend on confirmed rather than disconfirmed assumptions. Although increasing the weight with which existing evidence indirectly confirms it in such a case, robustness may also be irrelevant for confirmation, or may even disconfirm. Whether or not it confirms depends on the available data and on what other results have already been established.

Policy-makers face an uncertain world. One way of getting a handle on decision-making in such an environment is to rely on evidence. Despite the recent increase in post-fact figures in politics, evidence-based policymaking takes centre stage in policy-setting institutions. Often, however, policy-makers face large volumes of evidence from different sources. Robustness analysis can, prima facie, handle this evidential diversity. Roughly, a hypothesis is supported by robust evidence if the different evidential sources are in agreement. In this thesis, I strengthen the (...) case for the use of robustness analysis in evidence-based policymaking by answering open research questions about this inference technique. First, I argue that existing taxonomies miss a fruitful category of robustness reasoning, that is predictive stability. Second, I claim that derivational robustness analysis – the investigation of whether the results of different models are in agreement – can yield interesting insights even if not the entire relevant model space is covered by available models or if the model results are only partially in agreement. Third, I claim that expert knowledge is necessary to address questions that arise when one applies measurement robustness analysis – the investigation into whether multiple means of measurement yield the same result. Finally, I argue that, in situations where evidence from different measurements is not in agreement, it can be advisable to no longer take all of the evidence into account. This can be done in a rationally defensible way by choosing the most adequate theory or model underlying parts of the evidence set. I discuss examples from climate, medical, and economic policy-making to establish my claims. (shrink)

In addition to their core explanatory and predictive assumptions, scientific models include simplifying assumptions, which function as idealizations, approximations, and abstractions. There are methods to investigate whether simplifying assumptions bias the results of models, such as robustness analyses. However, the equally important issue – the focus of this paper – has received less attention, namely, what are the methodological and epistemic strengths and limitations associated with different simplifying assumptions. I concentrate on one type of simplifying assumption, the use of mega (...) parameters as abstractions in ecological models. First, I argue that there are two kinds of mega parameters qua abstractions, sufficient parameters and aggregative parameters, which have gone unnoticed in the literature. The two are associated with different heuristics, holism and reductionism, which many view as incompatible. Second, I will provide a different analysis of abstractions and the associated heuristics than previous authors. Reductionism and holism and the accompanying abstractions have different methodological and epistemic functions, strengths, and limitations, and the heuristics should be viewed as providing complementary research perspectives of cognitively limited beings. This is then, third, used as a premise to argue for epistemic and methodological pluralism in theoretical ecology. Finally, the presented taxonomy of abstractions is used to comment on the current debate whether mechanistic accounts of explanation are compatible with the use of abstractions. This debate has suffered from an abstract discussion of abstractions. With a better taxonomy of abstractions the debate can be resolved. (shrink)

The basic idea behind the Competitive Exclusion Principle is that species that have similar or identical niches cannot stably coexist in the same place for long periods of time when their common resources are limiting. A more exact definition of the CEP states that, in equilibrium, n number of sympatric species competing for a common set of limiting resources cannot stably coexist indefinitely on fewer than n number of resources. The magnitude or intensity of competition between species is proportional to (...) the degree of overlap in their niches or use of resources. Species that stably coexist do so because there are “important differences” in their niches or use of common limiting resources. (shrink)

This discussion paper describes the attempt of an imagined group of non-ecologists to determine the population growth rate from field data. The Modellers wrestle with the multiple definitions of the growth rate available in the literature and the fact that, in their modelling, it appears to be drastically model-dependent, which seems to throw into question the very concept itself. Specifically, they observe that six representative models used to capture the data produce growth-rate values, which differ significantly. Almost ready to concede (...) that the problem they set for themselves is ill-posed, they arrive at an alternative point of view that not only preserves the identity of the concept of the growth rate, but also helps discriminate between competing models for capturing the data. This is accomplished by assessing how robustly a given model is able to generate growth-rate values from randomized time-series data. This leads to the proposal of an iterative approach to ecological modelling in which the definition of theoretical concepts and model selection complement each other. The paper is based on high-quality field data of mites on apple trees and may be called a “data-driven opinion piece”. (shrink)