Robustness and complexity co-constructed in multimodal signalling networks

Abstract

In animal communication, signals are frequently emitted using different channels (e.g. frequencies in a vocalization) and different modalities (e.g. gestures can accompany vocalizations). We explore two explanations that have been provided for multimodality: (i) selection for high information transfer through dedicated channels and (ii) increasing fault tolerance or robustness through multichannel signals. Robustness relates to an accurate decoding of a signal when parts of a signal are occluded. We show analytically in simple feed-forward neural networks that while a multichannel signal can solve the robustness problem, a multimodal signal does so more effectively because it can maximize the contribution made by each channel while minimizing the effects of exclusion. Multimodality refers to sets of channels where within each set information is highly correlated. We show that the robustness property ensures correlations among channels producing complex, associative networks as a by-product. We refer to this as the principle of robust overdesign. We discuss the biological implications of this for the evolution of combinatorial signalling systems; in particular, how robustness promotes enough redundancy to allow for a subsequent specialization of redundant components into novel signals.

Figure 1

(a) The basic perceptron architecture illustrated with six nodes of a signaller (numbered black squares) and six corresponding channels used to convey a message generated by node activity to a receiver (white square numbered 0). (b) Patterns of correlated activity illustrated through connections among signaller nodes. Two sets of three nodes show highly correlated activity: nodes 1–3 are highly correlated and nodes 4–6 are highly correlated. Each correlated cluster is referred to as a modality. (c) Representation of the receiver integrating inputs from the six channels constituting two signalling modalities.

Figure 2

The robustness value as a function of channel number. At low levels of duplication, individual channels increase the robustness by lowering the exclusion dependence. At high levels of duplication, individual channels make very low contribution to function and thereby lower the robustness value. The figure illustrates that systems of large non-integrated elements should not be deemed robust as channel removal does not influence behaviour. For increasing numbers of channels to increase robustness, we need more than duplication, we require the emergence of correlated modules or statistical modalities. Parameter α=10⁻³.

Figure 3

(a) Correlation matrix indicating by the size of black squares the magnitude of correlation or mutual information between pairs of nodes of the signaller. Here, all nodes are perfectly correlated in their activity. (a(i)) The perceptron connectivity corresponding to the correlation matrix (a). (b) Signaller nodes are only weakly correlated with each other and constitute approximately independent channels (b(i)) for the receiver to integrate. (c) Channels form correlated clusters of activity, with weak correlations among clusters. This corresponds to a two-modality signalling system (sets of channels M1 and M2). The two-modality case is both more robust and more complex. Robustness derives from insensitivity to channel occlusion through channel redundancy coupled to high information flow through weak modality decoupling.