Mimicry is exhibited in multiple scales, ranging from molecular, to organismal, and then to human society. 'Batesian'-type mimicry entails a conflict of interest between sender and receiver, reflected in a deceptive mimic signal. 'Müllerian'-type mimicry occurs when there is perfect common interest between sender and receiver in a particular type of encounter, manifested by an honest co-mimic signal. Using a signalling games approach, simulations show that invasion by Batesian mimics will make Müllerian mimicry unstable, in a coevolutionary chase. We use these results to better understand the deceptive strategies of SARS-CoV-2 and their key role in the COVID-19 pandemic. At the biomolecular level, we explain how cellularization promotes Müllerian molecular mimicry, and discourages Batesian molecular mimicry. A wide range of processes analogous to cellularization are presented; these might represent a manner of reducing oscillatory instabilities. Lastly, we identify examples of mimicry in human society that might be addressed using a signalling game approach.

Background: Mimicry, in which one prey species (the Mimic) imitates the aposematic signals of another prey (the Model) to deceive their predators, has attracted the general interest of evolutionary biologists. Predator psychology, especially how the predator learns and forgets, has recently been recognized as an important factor in a predator–prey system. This idea is supported by both theoretical and experimental evidence, but is also the source of a good deal of controversy because of its novel prediction that in a Model/Mimic relationship even a moderately unpalatable Mimic increases the ri Predator psychology, especially how the predator learns and forgets, has recently been recognized as an important factor in a predator–prey system. This idea is supported by both theoretical and experimental evidence, but is also the source of a good deal of controversy because of its novel prediction that in a Model/Mimic relationship even a moderately unpalatable Mimic increases the risk of the Model (quasi-Batesian mimicry). In Batesian mimicry, a palatable species (the Mimic) benefits from its resemblance to an unpalatable species (the Model), whose aposematic signal is therefore degraded in time; in this way, it is a parasitic relationship [1] , [5] , [8] . Müllerian mimicry involves two or more sympatric aposematic species, known as co-Mimics, that share the same or a similar warning pattern [2] , [5] , [8] . All of the unpalatable co-Mimic species benefit because they share the mortality costs of the predator learning process [2] , [reprinted in 9] . Many studies have suggested that the evolutionary consequences of these two types of mimicry are distinct [5] , [8] , [10] , [11] . In Batesian mimicry, a more abundant Mimic is expected to increase the predator attack rate on the Mimic as well as on the Model (negative frequency-dependent selection) and promote polymorphism in the Mimic, because an increase in the number of a certain type of Mimic is expected to decrease the fitness of that mimic [6] , [10] , [11] . In contrast, in Müllerian mimicry, the existence of co-Mimics is expected to reduce the per capita attack rate on both species, leading to number- or frequency-dependent selection and promoting monomorphism in the co-Mimics [6] , [10] , [11] . However, in some well-known examples of Müllerian mimicry, the co-Mimics are spectacularly polymorphic [12] . This type of mimicry is called quasi-Batesian [18] , [20] because even though both species are defended, the weakly defended species exploits the better-defended one in a parasitic, Batesian manner [18] , [20] . Support has been growing for this approach, because a quasi-Batesian relationship can explain the observed polymorphism of co-Mimics in nature [2] , [18 cf . 7] , [21] . However, this quasi-Batesian relationship, where even a defended Mimic raises the predation risk of its Model, would seem counterintuitive, and the prediction has stirred new controversy as to whether it really occurs in nature [7] , [9] , [21] . 23] ; in this case, the less unpalatable species raises the attack probability on the more unpalatable species. We propose here a mimicry model in which the Pavlovian predator system [18] , [20] is expanded by including alternative prey (other than the Model, the Mimic, or co-Mimics) and a predator that follows optimal foraging strategy ( = a Darwinian predator), because the existence of alternative prey to the aposematic prey species has a significant effect on mimicry [33] – [35] . This result reflects the definition of the classical dichotomy, which makes it inevitable that the relationship will emerge at a certain point along the palatability spectrum of the Mimic; that is, the two categories of mimicry should switch instantaneously across a ‘knife-edge’ [16] . Quasi-Batesian mimicry emerges only when the availability of alternative prey is very low (very low T ). Figure 2 The effect of the learning rate ( α ) and rule of the predator learning, and the availability of alternative prey ( T ), on Model–Mimic relationships. According to the predictions of our simulation, it was the tacit assumption of constant predation pressure rather than its extraordinary simplified predator psychology that prevented Huheey's mathematical formula [13] , [15] from predicting Müllerian mimicry (also see Predator psychology vs. alternative prey ). In Huheey's model [13] , [15] , the predator's attack probability on aposematic prey did not increase even after attacks on the Mimic, although the model predicted that a Mimic would always raise the predation risk to the Model. One controversy regarding the theory of Batesian mimicry centers around why Models do not simply evolve away from their Mimics [8] . [10] , [11] , [57] ), mimicry rings may be evolutionarily stable. It has been argued that the benefit of Batesian mimicry is negatively frequency-dependent on the Model/Mimic population because the presence of Mimics causes the attack rate to be higher on both species [1] , [6] , [10] , [11] . According to this view, negative frequency-dependent selection may prevent Mimics from outnumbering Models [1] , [6] , [10] , [11] , and promote polymorphism in Mimics. In contrast, our model predicted the absence of such selection pressure only when alternative prey are abundant. The relationships described by previous theories are predicted by our model to occur only when the availability of alternative prey is low (or the value of the Mimic is higher than that of alternative prey). Batesian Mimics have traditionally been viewed as having a parasitic relationship with their Models. Our model also suggests that Batesian mimicry is more often commensalistic than parasitic. This view may require a reconsideration of the simple Batesian–Müllerian dichotomy, along with the recent claim that the selective mechanisms of Müllerian mimicry may include the advergence of less-defended species toward the more-defended one [21] .

Current theory suggests that many signaling systems evolved from preexisting cues. In aposematic systems, prey warning signals benefit both predator and prey. When the signal is highly beneficial, a third species often evolves to mimic the toxic species, exploiting the signaling system for its own protection. We investigated the evolutionary dynamics of predator cue utilization and prey signaling in a digital predator-prey system in which prey could evolve to alter their appearance to mimic poison-free or poisonous prey. In predators, we observed rapid evolution of cue recognition (i.e. active

Prey often evolve defences to deter predators, such as noxious chemicals including toxins. Toxic species often advertise their defence to potential predators by distinctive sensory signals. Predators learn to associate toxicity with the signals of these so-called aposematic prey, and may avoid them in future. In turn, this selects for mildly toxic prey to mimic the appearance of more toxic prey. Empirical evidence shows that mimicry could be either beneficial (‘Mullerian’) or detrimental (‘quasi-Batesian’) to the highly toxic prey, but the factors determining which are unknown. Here, we use st