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\begin{document}

\title{Six strategies for framing theoretical research questions}



\author[1]{Allison Shaw}%
\author[1]{Ave T. Bisesi}%
\author[1]{Chris Wojan}%
\author[1]{Dongmin Kim}%
\author[1]{Martha Torstenson}%
\author[1]{Naven Narayanan}%
\author[1]{Peter Lutz}%
\author[1]{Ruby Ales}%
\author[1]{Cynthia Shao}%
\affil[1]{University of Minnesota}%


\vspace{-1em}



  
  \date{May 19, 2024}


\begingroup
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\sloppy


\section*{Abstract}

{\label{275422}}

Theory is a small but critical component of the biological research
process, and complements observational and experimental approaches.
However, early career biologists receive little training on how to frame
a theoretical question and, thus, how to evaluate when theory has
successfully answered the research question. Here we develop a guide
with six verbal framings for theoretical models in biology. These
correspond to different roles one might play as a theorist:
``Advocate'', ``Explainer'', ``Instigator'', ``Mediator'',
``Semantician'', and ``Tinkerer''. These are drawn from combinations of
two starting points (pattern or mechanism) and three foci (novelty,
robustness, or conflict). We illustrate each of these framings with
examples of specific theoretical questions, by drawing on recent
theoretical papers in the fields of ecology and evolutionary biology. We
show how the same research topic can be approached from slightly
different perspectives, using different framings. We show how clarifying
a model's framing can debunk common misconceptions of theory: that
simplifying assumptions are bad, more detail is always better, models
show anything you want, and modelling requires substantial math
knowledge. Finally, we provide a roadmap that early career researchers
can use to identify a framing to serve as a blueprint for their own
theoretical research projects.

\par\null

\section*{Keywords:}

{\label{627568}}

mathematical biology, methodology, narratives, pedagogy, scientific
writing, theoretical ecology

\par\null

\emph{Take the theorist personality quiz here:}
\href{https://z.umn.edu/theorypersonality}{\emph{https://z.umn.edu/theorypersonality}}

\section*{}

{\label{275422}}

\section*{Introduction}

{\label{275422}}

Theory is a critical component of how biology (and science broadly) is
conducted, and complements experimental and observational approaches.
Theory serves many purposes, including to explore logical consistency of
ideas, to identify the simplest model that can predict observed
phenomena, to demonstrate the complexity of a situation, to suggest ways
of looking at empirical data, to generate novel hypotheses, and to
explore possible ranges of behaviour of a system
\href{https://www.zotero.org/google-docs/?ugAoi5}{{[}1,2{]}}. Theory can
take a range of forms including verbal, conceptual, computational, and
mathematical. Broadly, theory serves as scaffolding
\href{https://www.zotero.org/google-docs/?Ykppb4}{{[}3{]}} that helps us
make sense of observations and experiments. Yet, papers with primarily
theoretical approaches make up a small portion of the overall biological
literature; only 18\% of papers in the most theory-heavy journals within
ecology and evolutionary biology presented primarily theoretical
findings \href{https://www.zotero.org/google-docs/?2PuDRw}{{[}4,5{]}}.
Perhaps due to this small representation, early career scientists in
biology receive little training on how to design and interpret theory
(particularly mathematical theory)
\href{https://www.zotero.org/google-docs/?s6KKXz}{{[}6{]}}, especially
compared to the amount of training they receive on experimental
approaches.

Lack of training could result from an absence of conversation among
biologists about best practices for designing and interpreting theory.
However, this is clearly not the case; for example, people have debated
how to do theory for as long as theoretical ecology has been a field.
Levins' seminal paper
\href{https://www.zotero.org/google-docs/?Z6tuRN}{{[}7{]}} argued that
the three key aims for models are realism, precision, and generality.
Since no model can accomplish all three aims simultaneously, we need
different sets of models to prioritise different aims so that we can
find true understanding at the point(s) where the results intersect
\href{https://www.zotero.org/google-docs/?7HWb8s}{{[}7{]}}. May
\href{https://www.zotero.org/google-docs/?bx2Hsg}{{[}8{]}} cautioned
against having an uneven balance of detail in models; including
extensive detail in some model aspects while keeping others vague can
convey a false sense of how much realism the model includes. In contrast
to Levins and May, some researchers have called for prioritising more of
one type of theoretical model over others. For example, Holling
\href{https://www.zotero.org/google-docs/?dXiFzt}{{[}9{]}} argued that
the field had enough of what he called `strategic' models (that
sacrifice precision to focus on generality), but needed more `tactical'
models. Evans et al.
\href{https://www.zotero.org/google-docs/?1dA67e}{{[}10{]}} similarly
called for embracing complex models as a means of achieving generality
through generating testable predictions. The opposite argument has also
been made: Marquet et al.
\href{https://www.zotero.org/google-docs/?8H6xhJ}{{[}11{]}} called for
the development of more `efficient' theories that have fewer parameters
and do not need to be precise. In addition, much has been written
arguing for the value of theory in biology as a whole, drawing parallels
between how theoretical and empirical studies are conducted in both
ecology \href{https://www.zotero.org/google-docs/?do5TaK}{{[}1{]}} and
evolutionary biology
\href{https://www.zotero.org/google-docs/?1XM4Qz}{{[}12{]}}. Yet,
conversations within these fields about designing and interpreting
theory have not translated into guidance for newcomers on how to conduct
and communicate theory. This lack of guidance creates a barrier for
scientists new to theoretical research.

In response, there have been a number of recent `how-to' guides aimed at
breaking down this barrier for early career researchers. For example,
recent guides on how to communicate theory to broad audiences include
suggestions like clearly stating context and assumptions, reducing
irrelevant complexities (adjusting math to the target audience), using
clear and standardised mathematical notation, and using analogies and
narratives to facilitate links between new and existing information
\href{https://www.zotero.org/google-docs/?j32v5q}{{[}13,14{]}}. In
another how-to guide, Edwards and Auger-M\selectlanguage{ngerman}éthé
\href{https://www.zotero.org/google-docs/?CXbCix}{{[}15{]}} provide
advice for choosing mathematical notation. There have also been recent
guides on how to read and use mathematical theory in ecology. Shoemaker
et al. \href{https://www.zotero.org/google-docs/?W7DqHl}{{[}13{]}}
suggest that readers spend extra time engaging with the math, including
breaking down equations into components and working through them with
peers, connecting specific equations to a general class of models, and
reconstructing models or exploring parameter space to get a better
handle on them. Other guides show how to use theoretical frameworks to
guide empirical lab and field work, use mathematical equations to make
empirically-based calculations, and test either the assumptions or
predictions of theory
\href{https://www.zotero.org/google-docs/?t1mLPp}{{[}16,17{]}}. Overall,
these suggestions provide guidance for researchers who are either
reading broadly before they start a project, or have completed a
theoretical research project and want to communicate it clearly. In
contrast, there is less guidance for the middle stage in the theory
development process: how to choose -- and frame -- a theoretical
research question. This is a critical gap. Even researchers who never
pose theoretical research questions themselves will use and evaluate
theory (e.g., as guides for experimental or observational work). Thus,
we all benefit from understanding how theory is framed in order to help
evaluate when theory has been successful.

Here, we fill this gap by providing guidance for how to frame
theoretical research in biology. Theoretical research often starts out
as a verbal model, using reasoning to set up an argument about what is
expected to occur. Verbal arguments can only get us so far, and relying
on common sense and intuition often leads us astray
\href{https://www.zotero.org/google-docs/?XNAChD}{{[}18{]}}. It is at
these points that turning the verbal (or narrative-based) argument into
a mathematical (or computational) form can provide clarity and help
extend a verbal argument
\href{https://www.zotero.org/google-docs/?sVZdc5}{{[}19{]}}. Here, we
argue that the converse is also true: a clear verbal framing can help
improve the usefulness of a mathematical or computational model. Below,
we present six ways to frame theoretical research, describing each as a
`personality type' or a specific role one might play as a theorist: the
``Advocate'', ``Explainer'', ``Instigator'', ``Mediator'',
``Semantician'', and ``Tinkerer''. We show that these roles are not
mutually exclusive; the same question or idea can be framed using
multiple roles. Finally, we demonstrate how the ways of thinking that we
present can be used to address common misconceptions about theory.

\par\null

\section*{Framing theory}

{\label{700921}}

Theoretical models (also called proof-of-concept models;
\href{https://www.zotero.org/google-docs/?pVdrVX}{{[}12{]}}) are
fundamentally about understanding the link between assumptions and
outcomes. Another way to view this is that models are about linking
`patterns' (outcomes of interest) to `mechanisms' (processes that can
generate those outcomes) (Figure 1). When a researcher starts developing
a theoretical model, they typically have a sense of both what
mechanism(s) they want to include and what pattern(s) to expect. The
core part of the modelling process is concretely stating the specifics
of patterns and mechanisms and determining the conditions under which
mechanisms and patterns are linked. Here, we propose that when writing
about theory for general readers (e.g., in grant proposals or
manuscripts), it can help to focus on either the pattern or mechanism as
a starting point and then connect it to the other. For example, a
theoretical project could start by describing a pattern and develop
theory to better understand the mechanisms that cause it (i.e.,
exploring causes). Alternatively, a theoretical project could start by
considering a mechanism and use theory to better understand the patterns
it can generate (i.e., exploring consequences). In addition to these two
starting points, we suggest that the goal of theory can be pitched with
a specific focus: novelty, robustness, or conflict. Taken together,
these two starting points and three foci lead to six different ways to
frame theory, or six different roles one might play as a theorist (Table
1).

\par\null\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.42\columnwidth]{figures/figure1/figure1}
\caption{{There are many possible links between pattern(s) and mechanism(s),
depending on whether one or more pattern(s) and mechanism(s) are
considered: (a) a novel link between one mechanism and one pattern, (b)
the robustness of one mechanism leading to multiple patterns, (c) a
relative importance of multiple mechanisms for one pattern, (d) the
reconciliation of multiple patterns with one mechanism, and (e) the
interaction among multiple mechanisms to generate multiple patterns.
{\label{743447}}%
}}
\end{center}
\end{figure}

Table 1. Overview of six different ways to frame theoretical models:
either start with a pattern or mechanism (rows) and focus on novelty,
robustness, or conflict (columns). For each framing, there is a
corresponding `personality type' or role one can play as a theorist.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
& \textbf{Novelty} & \textbf{Robustness} &
\textbf{Conflict}\tabularnewline
\textbf{Start with Pattern} & The ``Explainer'': Here's a pattern, can
-- and under what conditions does -- this mechanism generate it? & The
``Tinkerer'': Here's a pattern, how robust is it to changes in the
underlying mechanism(s)? & The ``Mediator'': Here are multiple
conflicting empirical data patterns, how do we reconcile them? Here are
multiple conflicting conceptual ideas, how do we reconcile them? Here is
a pattern in data that doesn't match the existing theory, how do we
reconcile this?\tabularnewline
\textbf{Start with Mechanism} & The ``Advocate'': Here is a mechanism
that has been overlooked, what are the consequences of including it?
Here is a mechanism at one scale, when does it affect patterns at
another scale? & The ``Semantician'': Here is a mechanism, how does its
effect on the pattern depend on how the mechanism is captured in a
model? & The ``Instigator'': Here are multiple mechanisms, what is their
relative importance for generating a pattern? Here are multiple
mechanisms, how might they interact to generate different
patterns?\tabularnewline
\bottomrule
\end{longtable}

These six roles form the core of our paper and we present them in
several different ways below. Our structure is motivated by the fact
that different people's brains work in different ways and that we
imagine that the same person may find it useful to come back to
different sections at different points in their project. In the
remaining text of this `Framing theory' section, we explain the six
different roles in detail. To illustrate each role, we give examples of
specific research questions, drawing on recently published theory in
ecology and evolutionary biology from three places: (i) searching for
theory papers from the year 2022 in journals from our field
(\emph{Ecology Letters, Evolution, Journal of Animal Ecology, Oikos,
Proceedings of the Royal Society B, The American Naturalist, Theoretical
Ecology}), (ii) looking at the set of theory papers analysed in Servedio
\href{https://www.zotero.org/google-docs/?Juw2ah}{{[}20{]}}, and (iii)
previous papers by ourselves (the authors). We expect this section may
be most useful for those new to the ideas presented here. In Table 1, we
organise the six roles by their starting point (pattern, mechanism) and
focus (novelty, robustness, conflict) and provide general ways to frame
research questions for each. This section may be useful for researchers
who want to brainstorm multiple different theoretical questions for
their research project. In Figure 1, we diagram the different
relationships between mechanism(s) and pattern(s), which depend on the
focus (novelty, robustness, conflict) and on whether there is one or
more of each pattern and mechanism. In Figure 2, we provide a decision
tree that a researcher can work through by answering a series of
questions, which lead to one of the six roles with examples of attitudes
one might have in each of these roles. This figure may be most useful
for researchers looking to narrow in on one particular way to frame
their question.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-2-shared/Figure-2-shared}
\caption{{Roadmap to help researchers choose a framing for their research
question. Images are from thenounproject.com, under a Creative Commons
Attribution 3.0 licence: ``debate'' icon by Surya Lesmana, ``Megaphone''
icon by Neneng Fadliyah, ``collision'' icon by Lars Meiertoberens,
``mediator'' icon by Setitik pixel, ``wrench and screwdriver'' icon by
Vectors Market, and ``text bubble'' icon by White Spaces Inc. Try out
this roadmap yourself here:~\url{https://z.umn.edu/theorypersonality}
{\label{880621}}%
}}
\end{center}
\end{figure}

\subsection*{}

{\label{903479}}

\subsection*{\texorpdfstring{\emph{Starting with pattern, focusing on
novelty (The
``Explainer'')}}{Starting with pattern, focusing on novelty (The Explainer)}}

{\label{903479}}

Theory can be motivated as providing a novel mechanism to explain a
particular pattern. In this role, one could frame a question like `Here
is a pattern, can -- and under what conditions does -- this mechanism
generate it?' For example, the pattern of species coexistence is often
viewed from a lens of competitive interactions between species
\href{https://www.zotero.org/google-docs/?L4kfaU}{{[}21{]}}. A recent
paper by McPeek et al.
\href{https://www.zotero.org/google-docs/?1Qm9ij}{{[}22{]}} explored how
the mechanism of mutualistic relationships could foster coexistence
between competitors by asking, `Under what conditions can mutualistic
relationships between two competitors lead to their coexistence?' As a
second example, consider the observed pattern that some spreading
populations fluctuate in how fast they spread over time, expanding
quickly in some years and expanding slowly (or even contracting) in
others. This pattern is often attributed to environmental heterogeneity
or stochasticity
\href{https://www.zotero.org/google-docs/?1vYRd8}{{[}23,24{]}}. Sullivan
et al. \href{https://www.zotero.org/google-docs/?PhFRRG}{{[}25{]}}
developed a model to show how the mechanism of deterministic internal
population dynamics alone could generate fluctuations in spreading
speed, by asking, `under what conditions can fluctuations occur in
deterministic models with spatially and temporally constant
environments?'

\subsection*{\texorpdfstring{\emph{Starting with pattern, focusing on
robustness (The
``Tinkerer'')}}{Starting with pattern, focusing on robustness (The Tinkerer)}}

{\label{670691}}

Alternatively, theory can be motivated by testing the robustness of a
particular pattern. In this case, the role of the theorist is to explore
the effects of tinkering with existing models. Questions with this
framing could be, `Here's a pattern, how robust is it to changes in the
underlying mechanism(s)?' This role is typically associated with
clarifying a mechanism (rather than proposing a new one), either by
making a verbal model more concrete, or by clarifying the conditions
under which a mechanism can generate a pattern. For example, Shaw et al.
\href{https://www.zotero.org/google-docs/?BVJxTn}{{[}26{]}} used one
type of modelling approach (ordinary differential equations) to study
the relative importance of insect life history and insect behaviour on
the spread rate of vector-borne plant pathogens (pattern). Following
this, Shaw et al.
\href{https://www.zotero.org/google-docs/?5wM3YD}{{[}27{]}} studied how
robust this pattern was to the modelling approach used by developing an
individual-based model to capture the same mechanisms of the same
system. Another instance of a ``Tinkerer'' style model comes from
Shoemaker and Melbourne
\href{https://www.zotero.org/google-docs/?rePakU}{{[}28{]}} who
developed a framework with multiple ecological mechanisms thought to
influence the pattern of spatial coexistence of species in competitive
metacommunities. Using their framework, they calculated the relative
contribution of these different ecological mechanisms in determining the
strength of coexistence (here, a species' low-density growth rate) for
different metacommunity paradigms.

\subsection*{\texorpdfstring{\emph{Starting with pattern, focusing on
conflict (The
``Mediator'')}}{Starting with pattern, focusing on conflict (The Mediator)}}

{\label{897476}}

Third, theory can be motivated by needing to reconcile conflicting
patterns -- within the empirical literature, between conceptual ideas,
or between theoretical and empirical results. The goal of this type of
theory is to mediate a conflict in patterns. Unlike the above two
(``Explainer'', ``Tinkerer''), this role is motivated by several
patterns rather than a single one. Questions here could be framed
accordingly, e.g., as `Here are multiple conflicting empirical data
patterns, how do we reconcile them?' For example, some empirical studies
find the pattern that migratory individuals typically have greater
parasite infection than resident individuals
\href{https://www.zotero.org/google-docs/?z9u6L5}{{[}29,30{]}}, while
other studies find the opposite pattern
\href{https://www.zotero.org/google-docs/?JaaYuS}{{[}31,32{]}}. Shaw et
al. \href{https://www.zotero.org/google-docs/?clhgfG}{{[}33{]}} used a
theoretical model to clarify the mechanism leading to these disparate
patterns: migration can simultaneously lead to a higher richness of
parasites and lower infection prevalence. Thus studies that use richness
as a metric find one pattern, while studies that use prevalence find the
opposite.

Questions could also be framed as `Here are multiple conflicting
conceptual ideas, how do we reconcile them?' For example, studies that
aim to understand sex-specific patterns of how individuals move to find
mates in sexually reproducing species have generated two contradicting
predictions. Theory that focuses on mate finding shows that when
individuals of one sex move more, individuals of the other sex should
move less, creating sex bias in dispersal
\href{https://www.zotero.org/google-docs/?mcepaE}{{[}34{]}}. In
contrast, theory that focuses on dispersal distance shows that when
dispersal affects the potential to find mates, selection favours both
males and females to have similar dispersal kernels, creating no sex
bias in dispersal
\href{https://www.zotero.org/google-docs/?Nymo5c}{{[}35{]}}. Shaw and
Kokko \href{https://www.zotero.org/google-docs/?YH1qEl}{{[}36{]}} built
a single model to resolve this contradiction, showing that the mechanism
details shape which results apply -- e.g. if females moving more brings
females closer to males (and thus males do not have to move) we get one
outcome whereas if females moving more leads to males being left behind,
we see the other outcome.

A final way that questions could be framed using this role is as `Here
is a pattern in data that doesn't match the existing theory, how do we
reconcile this?' For example, an observed empirical pattern is that
seabirds have a diversity of foraging strategies
\href{https://www.zotero.org/google-docs/?9LLVqW}{{[}37{]}}, which
conflicts with theory suggesting that there should be a single optimal
foraging strategy
\href{https://www.zotero.org/google-docs/?vdnZcP}{{[}38{]}}. Jeffries et
al. \href{https://www.zotero.org/google-docs/?8RvMax}{{[}38{]}}
reconciled this conflict by developing a model where seabirds have only
partial knowledge of the patchy food distributions in their environment
and showed that different foraging strategies are favoured by birds with
different personalities along the bold-shy continuum.

\par\null

\subsection*{\texorpdfstring{\emph{Starting with mechanism, focusing on
novelty (The
``Advocate'')}}{Starting with mechanism, focusing on novelty (The Advocate)}}

{\label{448111}}

In contrast to the three roles above (``Explainer'', ``Tinkerer'',
``Mediator''), theory can be framed as starting with a mechanism and
determining the consequences in terms of the pattern (or patterns)
generated. This kind of theory might result in advocating for an
overlooked mechanism to be included. Theory that aims to describe a
novel consequence of a mechanism could be framed as, `Here is a
mechanism that has been overlooked, what are the consequences of
including it?' For example, Yamamichi and Letten
\href{https://www.zotero.org/google-docs/?339Akq}{{[}39{]}} developed a
model with a new mechanism (rapid evolution in the face of temporal
fluctuations with a tradeoff between competitive ability and speed of
evolution) and determined how it affected the pattern of coexistence
between competing species.

This role can be particularly effective at connecting scales in ecology
by asking, `Here is a mechanism at one scale, when does it affect
patterns at another scale?' For example, linking the scales of
individuals to populations, Shoemaker et al.
\href{https://www.zotero.org/google-docs/?uzLd0t}{{[}40{]}} first used
experiments to measure how a pathogen changes the preferences of its
aphid vector for feeding on different host plants (mechanism). Then they
used a model to ask under what conditions these measured preferences
affected the spread of pathogens across a host plant population
(pattern).

\par\null

\subsection*{\texorpdfstring{\emph{Starting with mechanism, focusing on
robustness (The
``Semantician'')}}{Starting with mechanism, focusing on robustness (The Semantician)}}

{\label{440040}}

Just like the ``Tinkerer'' role above, theory that starts with a
mechanism can also have a focus on robustness by asking, `Here is a
mechanism, how does its effect on the pattern depend on how the
mechanism is captured in a model?' This role is fundamentally focused on
the semantics of a mechanism, that is, how the mechanism is expressed in
the model(s). For example, previous work has shown that species with
environmental sex determination are particularly sensitive to
environmental change
\href{https://www.zotero.org/google-docs/?fe0lxG}{{[}41,42{]}}. Crowley
and Labonne \href{https://www.zotero.org/google-docs/?6KPAWh}{{[}43{]}}
developed a model to ask, `how robust are these conclusions to how
evolutionary success (i.e., fitness) is encoded?' In this model, the
authors measured how environmental quality and habitat loss (multiple
mechanisms) could influence the fitness of populations (pattern) based
on whether the model was formulated in terms of growth rate (\emph{r})
or lifetime reproductive success (\emph{R}\textsubscript{0}). Thus, such
models can decipher how robust outcomes (or patterns) are to underlying
differences in descriptions of the same mechanisms in different models.

\par\null

\subsection*{\texorpdfstring{\emph{Starting with mechanism, focusing on
conflict (The
``Instigator'')}}{Starting with mechanism, focusing on conflict (The Instigator)}}

{\label{415660}}

Finally, theoretical models can be used to explore the consequences of
several mechanisms in combination. In this kind of framing, the theorist
instigates a potential conflict (or interaction) between multiple
mechanisms and investigates the outcome. The question here could be
framed in terms of relative importance, e.g., `Here are multiple
mechanisms, what is their relative importance for generating a pattern?'
For example, abundance of grazers can dramatically impact reef cover
dynamics \href{https://www.zotero.org/google-docs/?aMHflB}{{[}44{]}}.
Dispersal of coral and macroalgae between reefs seems likely to be
important for reef cover dynamics as well
\href{https://www.zotero.org/google-docs/?lgAWEP}{{[}45{]}}, yet it has
been less explicitly explored. Greiner et al.
\href{https://www.zotero.org/google-docs/?uhadrn}{{[}46{]}} built a
theoretical model to ask, `what is the relative importance of these two
mechanisms?'. Here the authors study the relative effects of grazer and
dispersal behaviour (multiple mechanisms) which interact to influence
spatial patterns of coral reefs (pattern).

Alternatively questions in this role could be framed as combining
several mechanisms that have previously been considered separately to
ask, `Here are multiple mechanisms, how might they interact to generate
different patterns?' For example, studies have examined how seed
dormancy \href{https://www.zotero.org/google-docs/?Zi7Vpe}{{[}47{]}} and
facilitation \href{https://www.zotero.org/google-docs/?kbLUtz}{{[}48{]}}
each separately shape plant populations and communities. Leverett and
Shaw \href{https://www.zotero.org/google-docs/?4yI5N2}{{[}49{]}}
developed a theoretical model with both mechanisms, in order to
understand how facilitation between seedlings interacts with dormancy in
seeds to shape patterns of plant population dynamics.

\par\null

\subsection*{\texorpdfstring{\emph{Other
perspectives}}{Other perspectives}}

{\label{171857}}

Although the six roles as described in detail above form the core of our
paper, we wanted to comment on a few other aspects of framing theory
that readers might find useful. First, one could start by asking how
many mechanisms and how many patterns they were interested in, and using
that to choose a role (Figure 1). A single mechanism and single pattern
would best fit one of the novelty roles of ``Advocate'' or
``Explainer''. A single mechanism with two (or more) patterns would fit
either robustness role (``Tinkerer'', ``Semantician'') or the
``Mediator'', while a single pattern with two (or more) mechanisms would
fit the ``Instigator'' role of looking at the relative importance of the
mechanisms. Multiple patterns and multiple mechanisms could also fit the
``Instigator'' role of aiming to understand the interaction among
multiple mechanisms.

Second, the process of model development can be seen as the act of
`translating' mechanisms from the complex language of biology to the
more abstract language of mathematics, analysing the model, and then
translating the results back again to understand the biological pattern
produced \href{https://www.zotero.org/google-docs/?JfHtnA}{{[}50{]}}.
Just like translation of text across different languages, there can be
multiple `correct' ways to translate between math and biology. For
example, a single biological system could be translated into e.g. a
differential equation model or into an individual based model.
Similarly, the same model result could be interpreted in the context of
e.g. metapopulations or in the context of disease dynamics. Viewing
theory development as translation, we can see that some of the roles
described above effectively compare multiple translations. For example,
one could start with a biological pattern and see if the pattern is
disrupted if the same biological mechanism is translated in two
different ways in the model (the ``Semantician''). Similarly, one could
start with a biological mechanism and vary how it is translated into a
model to see whether the details of translation affect the pattern
generated (the ``Tinkerer''). In contrast, the remaining roles (the
``Advocate'', ``Explainer'', ``Instigator'', ``Mediator'') are more
often about developing a single translation from biology to math and
back again.

\par\null

\section*{Flexibility in Framing}

{\label{703122}}

In the `Framing theory' section above, we described each research
project using a single role. However, the same project can often be
framed in several different ways. Indeed, many theoretical papers use
several roles when describing their study (e.g. in the abstract versus
the discussion). For other projects, the role used at the start of the
project may not be the same as the one used at the project's end. In
this section, we show how the same theoretical project can be framed
using multiple roles.

Different ways of framing theoretical projects might be best suited to
practitioners in different fields. For example, wildlife managers may be
interested in starting with patterns to frame a theoretical project
based on what they see in nature (e.g., observing the pattern that two
plant species X and Y often coexist in a community that is affected by
snowstorms). In contrast, developing a theoretical project starting with
a mechanism may be more relevant to ecologists who are interested in
understanding the effects of potential factors that influence ecological
systems (e.g., asking how the mechanism of snowstorms affects the
coexistence of plant species X and Y). By providing examples of
different ways to frame the same theoretical project, we hope to inspire
practitioners to continue asking their research questions using
different framings.

\par\null

\subsection*{\texorpdfstring{\emph{Multiple ways to start with pattern
(Sullivan et al. 2017,
PNAS)}}{Multiple ways to start with pattern (Sullivan et al. 2017, PNAS)}}

{\label{567024}}

First, consider a theoretical project that starts with a pattern of
interest and aims to understand the mechanisms underlying it. In
Sullivan et al.
\href{https://www.zotero.org/google-docs/?LLbMlT}{{[}25{]}}, the pattern
of interest was species invasion dynamics and the large variation in
speed of invasion (or range expansion) observed in many empirical
systems. Understanding variation in speed of invasive species spread is
crucial to devise strategies for their elimination or mitigation. In
order to explain the pattern of varying invasive speeds for species,
Sullivan and co-authors focused on two mechanisms: 1) a strong Allee
effect (where populations cannot grow from low density) and 2)
fluctuations in population size due to overcompensatory growth or
density-dependence in dispersal. By building spatio-temporal
mathematical models incorporating these mechanisms, the authors showed
how demographic and dispersal dynamics jointly produced fluctuating
invasion speeds as the population spread into new territory. Thus,
framing the research question as an inquiry into mechanisms responsible
for generating patterns of invasion speed variation led to novel
scientific insights (i.e., pattern/novelty framing -- the
``Explainer''). However, one could approach the same project with a
different framing: how robust is the pattern of variable invasion speeds
found in nature to the specific forms of population dynamics and
dispersal used in a model? Here, one could consider different existing
population dynamics models (e.g. logistic growth, Allee effect) and
study their interplay with different dispersal behaviours
(e.g.,dispersal propensity, dispersal distance). In this framing, the
model could be viewed as the ``Tinkerer'' role (i.e.,
pattern/robustness). Finally, one could frame a question in the role of
``Mediator'' (i.e., pattern/conflict) by noting that some invasive
species spread at relatively constant rates. Here the question could be:
how do we reconcile the fact that the spread rate of some species
fluctuates while the spread rate of others does not? While the methods
and results sections in both framings could remain identical, the
motivation for the study would appear significantly different based on
which above framing is used.

\par\null

\subsection*{\texorpdfstring{\emph{Multiple ways to start with mechanism
(Miller et al. 2021, Ecology
Letters)}}{Multiple ways to start with mechanism (Miller et al. 2021, Ecology Letters)}}

{\label{289269}}

Next, consider a theoretical project that starts with a mechanism of
interest and aims to understand the pattern(s) it can generate. Miller
et al. \href{https://www.zotero.org/google-docs/?KbrIHq}{{[}51{]}} used
a theoretical model to understand the effects of disturbance history (a
mechanism) on plant community structure and invasion outcomes
(patterns), given two resident plant species and an invader species
population (i.e., mechanism/novelty -- the ``Advocate''). However, the
most relevant way to define disturbance history in a model may depend on
what aspects of disturbance ecologists are interested in understanding.
For example, one may be interested in disturbance intensity (i.e., the
strength of the disturbance force)
\href{https://www.zotero.org/google-docs/?EMhPvj}{{[}52{]}}. In
contrast, one may be interested in disturbance frequency, which captures
the number of disturbed events that have occurred per specified time
period \href{https://www.zotero.org/google-docs/?KQGw72}{{[}51{]}}.
Given different possible definitions of disturbance history, one could
alternatively frame the project by asking how robust the model outcomes
are to how the mechanism of disturbance history is defined in the model
(i.e., mechanism/robustness framing -- the ``Semantician'').
Alternatively, if disturbance history is viewed as the sum of several
different elements, such as disturbance intensity and frequency, the
same theory can be framed by understanding how two different mechanisms
(disturbance intensity and frequency) combine to shape the dynamics of
species community structure (i.e., mechanism/conflict framing -- the
``Instigator''). Thus, this same theoretical project could be framed in
multiple ways that link these specific mechanisms to patterns in plant
communities.

\subsection*{\texorpdfstring{\emph{Changes in theoretical framing from
start to
finish}}{Changes in theoretical framing from start to finish}}

{\label{596773}}

Finally, the framing used by researchers might change throughout the
course of a research project. For example, a paper published in 2016
showed how migration from one environment to a second (migratory)
environment could be used as a strategy to escape and recover from
environmental-specific parasites in the first environment
\href{https://www.zotero.org/google-docs/?BlJnrc}{{[}53{]}}. When
presenting this research in talks, a common audience question was `what
about parasites that are present in the migratory environment?'. To
answer this, the authors built a model that included parasites in each
environment in order to understand how the costs/risks of having
parasites present in both environments shaped the evolution of
migration. Walking through our roadmap (Figure 2), this would be a case
of starting with mechanism (presence of parasites in the migratory
environment), so taking the left branch of the decision tree,
considering a single mechanism, and then advocating for the specific
mechanism (since the mechanism had not previously been included in
models). This leads to an ``Advocate'' (mechanism/novelty) role, i.e.,
what are the consequences of including parasites in the second
environment (which has previously been overlooked)? The results were
fairly intuitive: having parasites in the second environment narrows the
range of conditions where migration is favoured, and whether migration
is favoured or not comes down to the details of risk of infection (how
fast the different parasites are transmitted in each environment) and
the cost of infection (how costly the two parasites are compared to each
other). However, the authors also discovered that the model produced an
intriguing result: migrants typically had lower infection prevalence
while simultaneously having higher parasite diversity compared to
non-migrants
\href{https://www.zotero.org/google-docs/?h8xXLi}{{[}33{]}}. This result
replicated an ongoing conflict in the empirical literature (described in
the ``Mediator'' section above''), and they decided to revise the paper
framing accordingly. Revising the roadmap, this would now be a case of
starting with pattern(s) (pattern 1 is that some empirical studies find
that migrants have higher infection, and pattern 2 is that other studies
find the opposite), so taking the first right branch of the decision
tree. At the next step, they were exploring known mechanisms underlying
a set of patterns (since it is known empirically that parasites can be
present in several environments), and finally at the next step the focus
was on reconciling conflicting patterns. This leads to a ``Mediator''
role (pattern/conflict). The authors felt that a pattern/conflict
framing would allow their work to reach a broader audience than a
mechanism/novelty one, so they wrote the paper around the question: Here
are conflicting empirical data patterns, how do we reconcile them?

\par\null

\section*{Addressing misconceptions of
theory}

{\label{954269}}

By providing a roadmap for how to formulate specific theoretical
questions, we hope that our framework will pave the way for budding
theorists to develop successful modelling projects. However, wading into
theory can be daunting, particularly for empiricists, in no small part
because there are many misconceptions about modelling that may
discourage scientists from attempting their own theoretical work. Below,
we use our framework to address these misconceptions by considering the
example of R* theory -- a seminal, mathematically-derived hypothesis in
community ecology that suggests that coexistence between resource
competitors is possible when competitors are limited by different
resources \href{https://www.zotero.org/google-docs/?rqXOes}{{[}54{]}}.

\subsection*{\texorpdfstring{\emph{Misconception \#1: Simplifying
assumptions prevent models from being
useful}}{Misconception \#1: Simplifying assumptions prevent models from being useful}}

{\label{530862}}

A misconception that appears in almost any context in which theory is
discussed is the idea that models are not useful because they rely on
simplifying assumptions. No model can include every phenomenon at work
in a natural system, but we emphasise that this misconception
misunderstands the purpose of theory. Theoretical models are meant to
draw connections between informed assumptions and their outcomes. Models
cannot exist without assumptions, so this criticism is nonsensical. Our
framework focuses on the central modelling question rather than
belabouring what a model omits. This type of reframing can help
theory-wary scientists better understand the consequences of the
assumptions they make. For example, R* theory is concerned with
coexistence between species engaged in resource competition, and
therefore, in its most basic formulation, ignores the effects of other
types of competition like apparent competition
\href{https://www.zotero.org/google-docs/?tffYxg}{{[}54{]}}. While this
type of interaction may be important in many natural systems, the
predictions generated by R* remain useful for answering the central
question regarding resource competition. Focusing on these assumptions
as limitations of the model ignores the purpose of R*. If researchers,
after considering the central theoretical question, find that their
initial assumptions will prevent them from successfully addressing their
question, we encourage them to amend or alter those assumptions -- as
some theorists have indeed done with R*, using it to consider the
dynamics of apparent competition
\href{https://www.zotero.org/google-docs/?YTdrUd}{{[}55{]}}. This could
result in theoretical work that advocates for the importance of a change
in assumptions.

\par\null

\subsection*{\texorpdfstring{\emph{Misconception \#2: Adding more model
details always leads to predictive
improvements}}{Misconception \#2: Adding more model details always leads to predictive improvements}}

{\label{135344}}

The freedom to amend modelling assumptions is key to successful theory,
but that freedom often leads researchers to another misconception of
theoretical work: the idea that a model can always be made more useful
through the inclusion of additional details. It can be tempting to
believe that the addition of another mechanism will make a model ``truer
to life'' and improve results. In practice, additional details increase
mathematical complexity and make results harder to interpret. Expanding
a model also comes with the cost of time and energy. Empiricists face a
similar trade-off: while additional experiments can always be performed
(or more observations collected), more data is not worth the effort
spent if the central question is already answered by the data in hand.
We suggest to new theoreticians that models should only be expanded in
pursuit of the specific modelling question. Many such expansions would
fall under the role of ``Advocate'', and thus should address why
inclusion of novel mechanisms is important. When the aim of a model is
prediction, it is more likely to be important to include additional
phenomena \href{https://www.zotero.org/google-docs/?ZcnJG0}{{[}9,56{]}}.
For example, if one is interested in the robustness of R* coexistence
when resources follow seasonal fluctuations, the inclusion of these
dynamics would be justified
\href{https://www.zotero.org/google-docs/?GI5AdM}{{[}54{]}}.
Fluctuations in resource availability could also elucidate patterns of
coexistence across temporal scales that R* is otherwise not situated to
investigate \href{https://www.zotero.org/google-docs/?bW9s4C}{{[}54{]}}.
Adding a system detail is worthwhile if it has the potential to 1)
change the predicted link between a model's assumptions and its outcomes
or 2) open up additional avenues of study through development of a new
theoretical question. However, we emphasise that if the goal of a
project is to increase understanding of a system, adding details beyond
those sufficient to explain the pattern of interest will rarely improve
theoretical insights
\href{https://www.zotero.org/google-docs/?mOSt8u}{{[}9,56{]}}. For
example, adding spatial structure and consumers of competitors to R* for
the purpose of increasing biological realism could make the model
intractable without improving understanding of conditions of coexistence
between resource competitors
\href{https://www.zotero.org/google-docs/?Q1VoUn}{{[}54{]}}. We expect
that our framework will help scientists new to theory make informed
decisions about what to include and when to expand their models, though,
in general, we recommend that models are kept as simple as possible.

\subsection*{\texorpdfstring{\emph{Misconception \#3: You can make a
model show anything you
want}}{Misconception \#3: You can make a model show anything you want}}

{\label{264668}}

Making decisions about what to include in a model can occasionally lead
new practitioners of theory to believe that models can always be
constructed to generate positive results supporting their preferred
hypothesis. In some ways, this may be true: because theoretical models
link assumptions and outcomes, if it is possible to think of a way that
an assumption and an outcome can be connected, then a model can probably
be constructed to reflect that. Generally, cases where this does not
happen -- i.e. when the process of model-building uncovers a flaw in our
logic -- are not framed this way when published, which can contribute to
the sense that models always end up supporting our initial hypotheses.
However, a model that produces an intuitive result is often just a
starting point for addressing precise theoretical questions. For
example, the R* result that competitors can coexist on shared resources
may seem trivial until one frames a more precise question, which could
be done using any of the six framings. For example, using a
pattern/robustness framing (the ``Tinkerer''), one could ask ``under
what conditions is coexistence between competitors possible'' (rather
than just `is coexistence possible'). Second, one could scale the
understanding of this mechanism to an unlimited number of competing
species (mechanism/novelty framing, the ``Advocate''), and find that
coexistence is theoretically possible as long as species are limited by
different resources
\href{https://www.zotero.org/google-docs/?l1t0uT}{{[}54{]}}. We suggest
to new theoreticians that both getting precise on the question framing
and the thoughtful addition of system details can increase the range of
possible questions a model can answer, reducing how trivial a model
feels. Our framework supports scientists in extending their initial
assumptions into these types of precise, insightful questions.

\subsection*{\texorpdfstring{\emph{Misconception \#4: Successful
modelling requires extensive mathematical
background}}{Misconception \#4: Successful modelling requires extensive mathematical background}}

{\label{706449}}

Finally, a misconception that represents a major barrier to the greater
adoption of theoretical work in biology is the idea that extensive
mathematical background is essential to developing and evaluating
theoretical (especially mathematical) models. We believe that framing is
much more important to successful theoretical work than mathematical
acumen. This is because even practised theoreticians rarely have the
need to create new models from scratch since the same mathematical
representation can be translated into myriad biological meanings. Model
development instead tends to consist of combining and altering pieces of
existing models in interesting ways to answer new questions
\href{https://www.zotero.org/google-docs/?dHN1cP}{{[}17{]}}. Since
``most models are variants of previous models''
\href{https://www.zotero.org/google-docs/?ASXCwN}{{[}17{]}}, there are
many resources available to aid the mathematical evaluation of any
biological model, such as Otto and Day's ``A Biologist's Guide to
Mathematical Models in Ecology and Evolution''
\href{https://www.zotero.org/google-docs/?o809lA}{{[}57{]}} and similar
primers. Armed with these guides and the computational power of
platforms like MATLAB or R, new practitioners of theory will be able to
derive mathematically sound insights from models. However, because model
development relies on altering existing models, we suggest that framing
is essential to contextualise these models so that they can be
appropriately amended for a researcher's specific purpose. For example,
amending R* theory to consider different functional responses in
competing species would reflect the work of a ``Tinkerer'', asking how
robust the pattern of coexistence is to biologically relevant changes in
the way the underlying mechanism is translated into mathematical terms.
By understanding the framing of an existing model, researchers can
appropriately adapt models to answer their own questions without the
need for extensive mathematical training.

Theoretical modelling is an incredibly powerful research tool, one that
is made richer and more useful by the inclusion of scientists who
generally consider themselves empiricists. We hope that our framework,
by addressing common misconceptions of theory, can assuage many of the
anxieties that scientists new to theory may face and encourage them,
particularly those early in their research careers, to take informed
theoretical risks. As a final note, we emphasise that the utility of
models does not hinge on their validation by empirical experiments or
observation \href{https://www.zotero.org/google-docs/?kswd93}{{[}12{]}}.
Models do not require data to be proven, in the same way that it is
unnecessary to build a theoretical model to verify the results of an
experiment done in the lab. Modelling is one way of knowing in science,
most useful when paired with other types of investigation to improve our
understanding of a given phenomenon. It is our hope that our framework
helps scientists build generative questions to test with theory.
Clarifying theoretical questions as we do here will make it easier to
put modelling results in their proper context with findings from both
lab and field work.

\section*{Conclusion}

{\label{313417}}

Here, we have argued that developing a clear verbal framing is critical
when undertaking a new theoretical research project. Furthermore, we
posit that the verbal framing is even more important than the
mathematical framing when it comes to communicating the goal and results
of a theoretical model with non-theorists, echoing a point from Ou et
al. \href{https://www.zotero.org/google-docs/?EEFLuI}{{[}14{]}} on the
importance of emphasising the narrative reasoning behind models. Here,
we present six types of verbal framings of theoretical questions that
start with either a pattern or a mechanism, and that focus on novelty,
robustness, or conflict. Together, these lead to six roles that one
might play as a theorist: the ``Advocate'', ``Explainer'',
``Instigator'', ``Mediator'', ``Semantician'', and ``Tinkerer''. We
recognize that there are other ways to frame theory and hope this paper
inspires discussion among those with other perspectives on how to frame
theory in biology. We have shown that these framings also serve as tools
to help avoid misconceptions of theoretical research. Finally, although
our focus has been on the field of biology and the approach of
mathematical theory, we expect that some of these ways of thinking in
terms of being explicit about pattern and mechanism apply broadly to
other fields as well (e.g.
\href{https://www.zotero.org/google-docs/?YazBWw}{{[}58{]}}). In sum, we
hope the six roles we present here can serve as blueprints that
researchers who are relatively new to theoretical research can use when
developing their theoretical research questions.

\par\null

\section*{Acknowledgements}

{\label{426598}}

Thanks to Miao He, Kate Meyer, Matt Michalska-Smith, Maria Napolitani,
Aarcha Thadi, Jess Valiarovski, and Steph Varghese for helpful feedback.
And to many others for asking questions that inspired writing this
paper.

\par\null

\section*{Funding}

{\label{690814}}

We were supported in part by funding from the National Science
Foundation under Grant No. DEB-2109965 (for NN, PL, AKS), Grant No.
IOS-2019304 (for ATB), an INTERN supplement on Grant No. DEB-1654609
(for DK), and an REU on Grant No. DEB-1947406 (for CS); a Doctoral
Dissertation Fellowship (for DK) and a Torkse Klubben Fellowship (for
MT) from the University of Minnesota; and Startup Funds from the
University of Minnesota to AKS (for RA, AKS).

\par\null

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