What can ecosystems learn? Expanding evolutionary ecology with learning theory

In more complex cases, where there is interference between alleles at different loci, vij may not be linearly proportional to xixj as it is in Eq. 3, but in all cases, the rate of evolutionary change in an interaction coefficient increases with the product of xi and xj since mutations must be both created and selected in order for an interaction coefficient to evolve. This is robust to the choice of underlying model (Appendix B). This is entirely intuitive: a) if suitable heritable variation in relationships is available, natural selection always acts to reduce the negative effects of others, and b) the rate of adaptation of the interaction coefficient between two species, e.g. by character displacement, is driven by their co-occurrence [54].

This is our first key result, describing how selection acts on inter-species relationships as a function of the current ecological state (Table 1g). Equation 3 tells us that the rate of adaptation on inter-species relationships is proportional to the co-occurrence of the species involved: Hence, species that occur together (arise in high density at the same time and under the same conditions), “wire” together (and there will be selection for changes to interactions that makes those species more likely to co-occur in future) - as per the principle of unsupervised correlation learning. (Correlation learning can be produced either by a reduction in negative interactions, as here, or by an increase in positive interactions, with the same effect on system dynamics, i.e. either will increase the future co-occurrence of the species that have co-occurred in the past.) We now investigate the consequences of this finding for collective behaviours in an ecological community, using ecological memory as a case study.

In general, Eq. 1 may exhibit unstable or even chaotic behaviour. In the following investigations we restrict our simulations to interactions that are symmetric (∀i,j:ωij=ωji) as per competition for shared resources or for competition coefficients estimated from utilisation functions [80], in which case the dynamics have only fixed point equilibria [81]. During simulation we allow the ecological dynamics to equilibrate at each time step (over τ iterations of Eq. 1). Then all interaction coefficients are updated according to the direct effect of natural selection in proportion to the rate of adaptation (Eq. 3). Then ecological constraints are applied to these interactions as follows, and the process is repeated.

In ecosystems where niche space is saturated, the capacity of natural selection to alter interactions is subject to inevitable ecological constraints and evolutionary trade-offs that prevent selection from eliminating all competition. Individuals with traits that cause them to avoid competition with one species may be forced to compete more with others. Thus the interaction between two species is more generally governed by a) the evolvable characteristics of the species as described by Eq. 3, and b) evolutionary trade-offs or ecological constraints applied by the physical properties of the environment (e.g., energy spent on exploiting one resource cannot also be spent exploiting another). Here these trade-offs are represented by normalisation conditions that conserve the sum of interactions to and, by symmetry, from each species. Specifically, for all species i and j (j≠i), ∑j=1Nωij(t)=Qi and ∑j=1Nωji(t)=Qj, where Qi=Qj<0 is a constant (the sum of interaction terms in row/column i at time t=0) (see Appendix C). Such normalisation represents ecological niches that resist change in width more than change in location, e.g. individuals can more easily change which resources they depend on than how dependent they are overall [82].

Although natural selection always acts to reduce competitive impacts from others, the fact that the rate of adaptation is greater for some competitive interactions than others (Eq. 3), together with these normalising evolutionary trade-offs, will mean that the competition between some species will increase. When the interaction, ωij, from some species j to a given species i is, for example, made less competitive (decreased in magnitude) by the evolution of heritable traits, all the other interactions involving i, i.e., ωih (h≠j) and ωhi (h≠i), are made more competitive by these normalising evolutionary trade-offs. This, in turn, leaves all interactions not involving i relatively less competitive. Self-interactions are not modified by either evolutionary or normalisation mechanisms (ωii=−1).

To investigate ecological memory we are interested in how the evolution of ecological interactions is influenced by past ecological states. To model the evolution of an ecosystem under varying environmental conditions that force or drive the ecosystem to adopt different ecological states, we define two environmental conditions, E1 and E2, that have differing effects on the carrying capacities of the species (Appendix C). Relative to a default environment E0, environment E1 increases the carrying capacity of some species and decreases others, whilst in E2, a different subset of species is increased/decreased. E1 and E2 may represent hot-dry and cold-wet climates, for example; or high/low levels of some key broadly-utilised resource such as phosphorous input rates for a lake habitat [48]. Given that individuals from each species experience both conditions over evolutionary timescales, these conditions could vary in space (e.g. geographic localities, [33]), rather than in time (e.g. seasonal change). To make the effects of these two conditions on community composition easily identifiable we utilise environmental forcing patterns corresponding to two arbitrary but easily identifiable pictograms (Fig. 2). Here the hot and cold pictograms describe two different configurations of species densities representing, for example, hot dry savannah and cold wet/temperate ecological states, respectively. The environment is switched between E1 and E2 every T evolutionary updates.

Model parameters of the simulations and methods used for assessing ecological attractors are described in Appendix C.

We use the series of four open questions concerning ecological memory listed above to exemplify some of the implications of our general result.

Experiment 1 investigates how evolution in fixed environmental conditions changes the ecological dynamics of the community. Before the evolution of interactions, during the ecological phase of simulation, the ecosystem arrives at a stable equilibrium corresponding to the pattern prescribed by the current environmental forcing (Fig. 3a and b). Inter-species interactions are then evolved in environment E1, i.e., without changes to the environmental forcing during evolution. The process is repeated for 800 ecological and evolutionary cycles. We then assess how evolved interactions have altered the sensitivity of the ecosystem to subsequent environmental forcing. We find that the ecosystem now arrives at a stable equilibrium corresponding to the E1 pattern (the pattern it experienced when interactions were evolving) even when the environmental forcing is subsequently changed to E0 or E2 (Fig. 3c). Experiment 1 thus shows that the effect of evolving ecological interactions by individual natural selection under fixed environmental conditions is to create a stable attractor for the specific ecological state experienced in that past environment, reducing the responsiveness of the ecosystem to respond to subsequent environmental forcing, and increasing the adaptive capacity of the system to withstand changes to environmental conditions or perturbations to population densities. This behaviour demonstrates the basics of an ecological memory, but only a memory of one pattern. Even passive systems can remember one pattern, e.g. an imprint in clay, but connectionist models show that a dynamical network is capable of storing and recalling multiple patterns.

In Experiment 2 varying environmental conditions are applied to cause the ecosystem to adopt two different ecological states (E1 and E2) repeatedly whilst inter-species interactions are evolving. The effect of these evolved changes plus normalising evolutionary trade-offs are illustrated in Fig. 4. We see that their evolution is identical to Hebbian learning (again this is robust to the choice of underlying model, Appendix D).

After evolution we find that, in the absence of further environmental forcing, the ecological dynamics have two stable attractors corresponding to E1 and E2, reached from any initial species densities (Fig. 5a, Appendix C). An ecological memory can thus retain information about multiple distinct past states without just averaging them or blending them (for example, the system does not have an attractor for the union of both patterns).

After evolution in the varying environment (Experiment 2) either of the two patterns can be completely recalled or assembled from an initial subset of species. That is, when the initial species densities have just a few species present in a density that matches one of the previous patterns, the ecological dynamics act to recreate the full pattern to which that ‘partial stimulus’ belonged (Fig. 5b). This experiment also reveals more about how the stability and resilience of the community is affected by the presence of multiple memories. When the initial conditions are ‘corrupted’ versions of a previous pattern, the complete pattern is restored, even when the corruption is severe (Fig. 5c.) (thus maintaining/re-creating the current ecological pattern), and when the initial species densities partially resemble both patterns, the population dynamics ‘break symmetry’, causing all species to adopt the pattern to which the initial conditions are closest (thus ‘choosing’ between two ecological states - not blending them).

Figure 6 examines the response of the ecosystem to patterns of environmental forcing that change linearly from E1 to E2. Before the evolution of interactions, the response of the ecosystem is proportional to the environmental forcing applied (Fig. 6a). In contrast, after the evolution of interactions (Experiment 2), the response of the system is discrete or switch-like and exhibits significant hysteresis (Fig. 6b). That is, as the pattern of environmental forcing moves incrementally from E1 to E1, the response of the system is to stay on E1 considerably past the mid-point and then suddenly switch to E1. Conversely, when the environmental forcing is reversed, the ecosystem retains a configuration matching E1 considerably past the mid-point before switching back to E1. The dynamics underlying this hysteresis loop are shown by the vector field of species densities changes (Figs. 6c, 9a). This also shows that the response of the population dynamics to perturbations in species densities slows down near the critical transition (consistent with early-warning signals for a tipping point [83, 84]). Figure 6d. shows how the response of the ecosystem to forcing changes over evolutionary time. Around generation 470, the ecosystem exhibits non-linear but non-catastrophic transitions [18]. The catastrophic regime change is not a general instability property of the evolved system – it only occurs when the environmental forcing is similar to a past state that is remembered by the ecosystem – unstructured forcing results in a linear response (Appendix E).

These observations demonstrate a conversion of one type of ecological alternate stable state into another. Beisner et al. [17] describe the “ecosystem” perspective on alternate stable states, which involves changes driven by abiotic environmental conditions, and the “community” perspective, which involves multiple attractor states that can exist under fixed environmental conditions. Figure 6 shows a system that converts alternate “ecosystem states” into alternate “community states”; thus converting patterns from past environmental states into ecological memories.

Figure 10 shows a ‘bestiary’ of ecological attractors changing over evolutionary time, showing some diversity before settling down to the two-attractors shown in Figs. 5 and 6. During long-term simulation we find that, as the forcing used to switch the system between attractors is of fixed value, while the effect of the evolved changes to interactions is ever-increasing, eventually the level of forcing applied is insufficient to shift the system from its current attractor. When this happens, the system becomes ‘stuck’ at one attractor, effecting a breakdown in observed behaviour (Appendix F, Figs. 10 and 11).

Our results formalise the intuitive idea that individual selection on ecological interactions produces positive feedback on species co-occurrence. By recognising an equivalence between this feedback and principles of unsupervised correlation learning we are able to use concepts from connectionist models to understand and illustrate the consequences of these changes for system-level behaviours. This makes several contributions to our understanding of evo-eco interactions:

Evo-eco dynamics have predictable consequences for collective behaviours. The worked example developed in our simulations converts informal notions about the evolutionary and historical determinants of ecological processes into a model that makes specific predictions about how past ecological conditions alter the selective pressures on the component species and hence modifies their future ecological behaviours. This presents a specific model for non-trivial ecological memory that can be empirically tested (Appendix G). From this model we better-understand the necessary conditions for a distributed ecological memory to form, such as the presence of evolutionary trade-offs that cause species to become more dependent on other species [85] rather than just becoming less competitive with them (Appendix H).

Ecological communities can exhibit organised collective behaviours. Under certain conditions, memories of past ecological states can be stored in a distributed way in the organisation of evolved ecological relationships. Such memories are not simply the summative or average result of multiple species each with individually alternate stable states. The connections that produce these behaviours are organised not by evolutionary adaptation at the community level, but rather by evolutionary adaptation at the individual level and ‘past experience’ of historic environmental conditions. The organisation of the system is thus conditioned by past environmental conditions, causing it to collectively habituate to the patterns of perturbation it has experienced [47].

Community assembly rules can be organised to re-assemble specific past states. The assembly of complete and specific past ecological states may be triggered by partial environmental cues or a small number of founders (as in invasional meltdown) (Fig. 5b) or, similarly, the system can recover each specific state from corruptions of that state (Fig. 5c). The learned assembly rules result in a system that ‘classifies’ initial compositions according to their similarity to past ecological states and will return community composition to the state that most closely resembles initial conditions (Fig. 5d). Ecological memories can thus direct subsequent community assembly to recreate multiple past ecological states in a complex and collective, but predictable, manner.

Stability and resilience tends to increase but instability and regime shifts are also predictable. We find that evolutionary pressures on ecological interactions tend to increase ecosystem resilience (recovery after perturbations to species densities) (Fig. 3) and adaptive capacity (robustness to environmental forcing) (Figs. 3 and 6) [10, 11, 13, 16, 47]. However, if the evolutionary history of an ecosystem has included a multi-modal distribution of environmental conditions, then this can result in alternative stable states (rather than universal stability) and may exhibit critical transitions in changing from one state to another [10]. This switch-like change in the community (Fig. 6) is only exhibited when the forcing that is applied is similar to past forcing – when arbitrary forcing is applied the response may remain linear (Appendix E, Fig. 9). Critical transitions between alternate stable states may thus reflect memories of specific past states and are not necessarily arbitrary non-linear responses to the current forcing pattern. Past experience of distinct environmental conditions (e.g. temperatures) may thus make future responses to related forcing (e.g. climate change) more likely to exhibit discrete changes in ecological states, critical transitions or tipping points [15, 18]. This suggests that critical transitions are not necessarily the arbitrary failure of an ecological community but can be a matter of ‘recalling’ alternate states familiar from past conditions.

Future work should explore the ultimate equilibrium of these evo-eco feedbacks (Appendix F, Figs. 10 and 11), and investigate relaxation of some of the simplifying assumptions utilised in the memory behaviours illustrated here (Appendix H). In particular, this paper has not investigated the effect of evo-eco feedbacks on trophic (e.g. predator-prey) interactions or mutualisms, nor have we investigated the ecological analogues of other behaviours that can be produced by unsupervised learning in more general neural networks (e.g. with multi-layered or asymmetric connection structures). Some intriguing further research directions are also suggested:

Do brains learn in the same way that ecosystems evolve? We have shown that ecosystems evolve in the same way that brains learn, but recognising evo-eco dynamics and connectionist learning models as different instantiations of the same underlying adaptive mechanisms also sheds light in the other direction, i.e. on cognitive processes [86, 87].

Can an ecosystem gain from experience? The idea of sequential selection, where non-arbitrary organisation arises in a system over evolutionary time without selection being applied at the system level [21, 88] suggests that a biological community “may gain from experience” by using “a system ‘memory’ carried in the gene pool” [19]. Our work in other domains has shown that the more specific sense of system memory demonstrated in the current paper can improve the ability of an adaptive network [32] to solve constraint problems or optimise resource allocation problems (without an external reward signal) [58]. This suggests that adaptation at the ecosystem level is possible in a formal sense without group selection; not adaptation in a Darwinian sense, but rather in the same sense and by the same mechanism as connectionist models of organismic adaptation [60].

Similarly, demonstration that ecosystems exhibit collective adaptive behaviours without being units of selection prompts inquiry as to whether these systems are capable of more complex computational tasks. For example, natural ecosystems are under very many constraints that limit species abundance (e.g. phosphate availability). Does selection on individuals improve a system’s ability to resolve these constraints? Hopfield networks are known to be able to solve complex constraint satisfaction problems [89]. Do these abilities translate to ecological networks?

We have introduced the framework of connectionist learning as a tool to expand our understanding of evo-eco dynamics and collective ecological behaviours. Within this framework we find that, despite not being an evolutionary unit, an ecological community can behave like an (unsupervised) learning system, creating internal organisations that collectively habituate to past environmental conditions, and actively recalling past responses to those conditions.

Previously there have only been two choices in how to interpret collective behaviours in ecosystems – i.e. either they have no system-level organisation or some mechanism of group selection must be involved. Our findings demonstrate that there is a third possibility. Ecological organisations that produce collective behaviours can arise from the positive feedback of individual natural selection and ecological population dynamics without invoking group selection. Specifically, given the presence of evolutionary trade-offs, the effect of individual-level natural selection acting on interspecific relationships is dynamically equivalent to a mechanism of unsupervised correlation learning and ecosystems can thereby exhibit organised collective behaviours via the same principles of connectionist learning that apply to neural networks. What is it that ecosystems learn? We find that they have the potential to learn where to go (i.e. evolved ecological attractors recreate past ecological states, where an attractor may be the climax community resulting from a successional process [90]), how to get there (i.e. the successional or assembly process) and how to stay there (i.e. the relationships that increase the resilience and stability of those mature ecological states). Of course, interpreting evo-eco dynamics as a connectionist learning system is not obligatory. A description in terms of individual natural selection and ecological population dynamics only is entirely compatible – indeed, we have provided this level of description for all the results in this paper. But recognising the equivalence with connectionist models enables us to convert and exploit well-understood concepts and results from this discipline to understand the organisation of ecological communities in new ways, and thereby to recognise the potential for predictable collective behaviours.

Reviewer 1: This is a rather intriguing paper, suggesting a novel view of ecosystems as a special class of neural-like networks. The underlying idea is that several relevant features of ecological networks, as well as the assembly dynamics of ecosystems and their resilience against different classes of perturbations, can be understood in terms of the attractor dynamics associated to unsupervised neural networks. Such a connection would make possible to rethink community dynamics and the emergence of complex ecosystems as connectionist objects.

Reviewer 1: The authors make a detailed comparison between both classes of networks and the key dynamical features shared by both. Some of the reported similarities are rather generic. They include the presence of attractor dynamics or the robustness against stochastic changes. These are almost inevitable components of most complex adaptive systems. Due to their dissipative behaviour, attractors are expected to occur, and given the nature of the interactions among neurons or species (described by connectionist models sharing several structural properties) multiple attractors are inevitable.

Authors: Yes, the existence of multiple attractors is indeed a generic property of dynamical systems. However, it is not the attractors per se that we claim are interesting – it is their location with respect to the history of the system. The emergence of attractor states that resemble past ecological states is not a property of complex adaptive systems in general.

Reviewer 1: The list of mechanistic equivalences given in table I is systematic, and several specific ingredients are very valuable and non-trivial. This is the case, for example, of the weights of trophic (or mutualistic) interactions among species. Could these connections incorporate some class of learning driven by evolutionary forces?