Speciation – the splitting of an evolutionary lineage into two descendant lineages – is a central topic in evolutionary biology (e.g. Coyne and Orr 2004), and one in which mathematical modeling has traditionally played a prominent role (Gavrilets 2004).

The reason is that speciation is a complex process that usually unfolds over long timescales, so that direct observations are difficult. Mathematical theory has been instrumental in determining the conditions for key components of speciation, such as adaptive divergence (e.g. Geritz et al. 1998), accumulation of genetic incompatibilities (e.g. Gavrilets …) and species-specific mate choice (e.g. Dieckmann and Doebeli 1999).

Here, we propose to develop mathematical models that will shed light on a topic of much recent interest: Whether speciation – and, in particular, speciation with gene-flow, can be facilitated by phenotypic plasticity.

A species is most commonly defined as a group inter-fertile individuals that cannot reproduce with members of other species (Mayr 1942). Thus, understanding speciation requires understanding the evolution of reproductive isolation.

According to the traditional view, speciation almost always requires a geographic barrier separating the range of an ancestral species (allopatric speciation). Two independently evolving subpopulations will then diverge between the nascent species (allopatric speciation) and become more and more incompatible, until they are recognized as separate species.

However, there is mounting evidence for the opposing view that speciation is also without a strict geographic barrier (parapatric or sympatric speciation). Such “speciation with gene-flow” (Smadja and Butlin 2011?) is theoretically challenging, because migration and hybridisation will counter-act genetic divergence, and because genetic recombination tends to destroy associations between sets of genes or characters. Most models of speciation with gene-flow assume a prominent role for divergent ecological selection pressures (Nosil 2012).

Phenotypic plasticity is the ability of organisms with identical genotype to produce different phenotypes in response to different environments (e.g. West-Eberhard 2003). It is pervasive in nature, and often is crucial in helping organisms cope with variable environments.

Recently, plasticity has been advertised by some as a centerpiece of an “extended evolutionary synthesis” (West-Eberhard 2003, Piggliucci and Müller 2009?), which aims to unify traditional population genetics with evolutionary developmental biology.

The main argument is that plasticity plays a leading role evolution (“genes follow development”), including diversification and evolutionary novelties (West-Eberhard 2003).

In the context speciation, plasticity is thought to facilitate phenotypic/ecological divergence as well as the evolution of reproductive isolation (West-Eberhard 2003, Pfennig et al. 2010, Pfenning and McGhee 2010, Fitzpatrick 2012). [Suggested mechanisms include …] In particular, several of the proposed examples imply speciation with gene flow (e.g., …).

However, many proposed scenarios rely on verbal models, and many details remain unclear. This is particularly true for scenarios involving plasticity in an ecological adaptation trait (but see Thibert-Plante and Hendry 2011).

As a first step, we will conduct a literature review with the aim of collecting and classifying the various mechanisms by which plasticity has been proposed to influence speciation/the evolution of reproductive isolation.

This will complement earlier reviews on the subject (West-Eberhard 2003, Pfennig et al. 2010, Fitzpatrick 2010).

This work will clarify previous arguments and underlying assumptions, and will guide future theory and empirical work.

It will also provide the student (who has a background in mathematics) with an opportunity to get to know the biological literature.

The main aim of this project is to develop models of speciation that will help answering the above questions.

Development of these models will be guided by insights gained during the literature review described above.

Most verbal descriptions of the process are vague with respect to the geographic setting (and the exact mechanism leading to reproductive isolation). In particular, the second phase may be imagined to happen anywhere on a continuum between allopatry and sympatry.

First scenario: Divergence phase (step 2) happens in allopatry

That is, plasticity evolves (or is already present), then two subpopulations continue to evolve in constant habitats, which should lead to a loss of plasticity and accumulation of genetic differences. Then, secondary contact is established, with selection for assortative mating.

Verbal models predict evolution of assortative mating and maintenance of genetic differentiation.

An alternative outcome might be a loss of genetic differentiation and a return to plasticity.

Here, we will study speciation without an allopatric phase

Nevertheless, environmental induction implies some sort of spatial structure

… and expression of plasticity may itself lead to a reduction in gene flow (plastic magic trait)

Previous models: Gavrilets and Vose 2007, Thibert-Plante and Hendry 2011

In contrast to Thibert-Plante and Hendry (2009), we will focus on scenarios that allow for the evolution of assortative mating

Methods: Population-genetics modeling, coupled with adaptive dynamics; stochastic individual-based simulations

The DPHS proposes that genetic divergence is preceded by the evolution of a purely plastic polyphenism.

This has a simple explanation if plasticity is the ancestral state of a lineage encountering a variable environment, but this then the question is why plasticity (and genetic polymorphism) evolved in the first place. Some advocates of the DPHS propose that novel phenotypes are generally more likely to arise by environmental induction (WE 2003, Uller and ???), but this is debated (Schwander and Leimar 2009, 2011).

A general framework for the evolution of environmental versus genetic control of phenotypic variation has been developed by Leimar et al. 2006. These authors envisage a developmental “switching device” that can take input from the the environment and the genome. The weighting of these two sources of information is evolvable. Environmental control should be favored when environmental cues are reliable and migration between different habitat types of common. However, this approach does not, per se, suggest a temporal sequence.

A different approach has recently been introduced by Draghi and Whitlock (2012?). These authors model plasticity via a developmental network (conceptually similar to a neural network) that takes input from the environment and whose structure is determined by genes (i.e. evolvable).

The DPHS assumes plasticity in an ecological trait (an character conferring ecological adaptation). Our aim will be to study how such plasticity influences the evolution of prezygotic reproductive isolation.

To our knowledge, the only model on this subject is by Thibert-Plante and Hendry (2009). These authors assume … Importantly, in one version of the model, the ecological trait also directly influences mate choice (i.e., it is a “magic trait”; Gavrilets 2004, Servedio et al. 2011).

However, the authors focus on parameter regimes with strong selection, in which most of reproductive isolation is due to immigrant inviability and little assortative mating evolves.

Here, we will …