Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

A succinct mathematical account of the co-evolution of defence and signalling of that defence (also known as aposematism) has been a long standing problem of ecology. The completion of the single-species game-theoretic model of Broom et al (2006) and its extension to the two-species case will have impact in a range of disciplines: from mathematical ecology and experimental biology (see for example Cortesi and Cheney 2010, Lee et al. 2010 and Lee et al. 2011, in the bibliography section) to game theory and complex systems theory. The specific aims of the proposed project are to1. Carry out an extensive review of the relevant literature (included in the Bibliography section); 2. Complete the one-species case (by uncovering the complete list of ESSs and characterising these in terms of their stability); 3. Develop the general model for the treatment of prey populations consisting of two species; 4. Determine the ESSs for two-species case (and characterise these in terms of their stability) for the case in which there is convergence in appearance (also known as two-point solution); and 5. Produce a model for Batesian mimicry (with strong emphasis in specific models of this). Background Prey species invest in constitutive and induced defences against attackers in order to increase their fitness. For attacks that occur over short time-scales constitutive defences admit the dominant mech-anism to avoid predation and may be classified as primary or secondary (Broom et al. 2006). The aim of the former is to reduce the rate at which prey species are attacked whereas the aim of the latter is two-fold: to reduce the probability that a mounted attack results in death (K) and to increase the aversive information (I) that predators have on similar looking prey. Investment in secondary defences may not be easily evaluated by predators ( as is the case with chemical defences) and is often coupled with a warning display which signals a prey species' investment in these defences (Broom et al. 2006). For the remainder of this discussion we will consider those secondary defences that require signalling in order for them to be evaluated by predators (Broom et al. 2010, Broom et al. 2013, Ruxton et al. 2009). The aim of the project that we are proposing is to complete the work on aposematism byroom et al. (2006) for the one-species case and to develop the general model for the two-species case. The latter will open up the possibility for studying particular models of Batesian mimicry (a form of mimicry in which harmless prey resemble harmful prey in order to increase their fitness) that are of interest in biology (Broom and Rychtar 2013, Cortesi and Cheney 2010, Lee et al. 2010 and Lee et al. 2011). Literature Review The co-evolution of secondary defences and signals of those defences have received certain, but not significant theoretical attention ( compared with studies on the mechanisms of action of these defences - Broom et al. 2006). A game-theoretic model of this co-evolution was first devised by Leimar et al.(1986) and continues to constitute dominant work in aposematism (Broom et al. 2006). Despite its novelty, this model is unable to account for the possibility of predators increasing their attack proba-bility towards prey species due to the presence of an ever-increasing inhibitory gradient. Additionally, many of the results rely on certain restrictive functional forms, which make it difficult to assess the generality of the model (Broom et al. 2006). In contrast with Leimar et al. (1986), which considers a set of (initially) naive predators (Broom et al. 2006), the (also game-theoretic) model of Broom et al. (2006), considers a set of predators modelled as a group in equilibrium for states of learning, hunger etc. and prey species (with average local relatedness a:) consisting of residents and mutants playing one of two distinct strategies. Of key importance to this model are evolutionarily stable strategies (ESSs) which are

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

Doctoral Training Partnerships: a range of postgraduate training is funded by the Research Councils. For information on current funding routes, see the common terminology at https://www.ukri.org/apply-for-funding/how-we-fund-studentships/. Training grants may be to one organisation or to a consortia of research organisations. This portal will show the lead organisation only.