What can ecosystems learn? Expanding evolutionary ecology with learning theory
The structure and organisation of ecological interactions within an ecosystem is modified by the evolution and coevolution of the individual species it contains. Understanding how historical conditions have shaped this architecture is vital for understanding system responses to change at scales from the microbial upwards. However, in the absence of a group selection process, the collective behaviours and ecosystem functions exhibited by the whole community cannot be organised or adapted in a Darwinian sense. A long-standing open question thus persists: Are there alternative organising principles that enable us to understand and predict how the coevolution of the component species creates and maintains complex collective behaviours exhibited by the ecosystem as a whole?
Here we answer this question by incorporating principles from connectionist learning, a previously unrelated discipline already using well-developed theories on how emergent behaviours arise in simple networks. Specifically, we show conditions where natural selection on ecological interactions is functionally equivalent to a simple type of connectionist learning, ‘unsupervised learning’, well-known in neural-network models of cognitive systems to produce many non-trivial collective behaviours. Accordingly, we find that a community can self-organise in a well-defined and non-trivial sense without selection at the community level; its organisation can be conditioned by past experience in the same sense as connectionist learning models habituate to stimuli. This conditioning drives the community to form a distributed ecological memory of multiple past states, causing the community to: a) converge to these states from any random initial composition; b) accurately restore historical compositions from small fragments; c) recover a state composition following disturbance; and d) to correctly classify ambiguous initial compositions according to their similarity to learned compositions. We examine how the formation of alternative stable states alters the community’s response to changing environmental forcing, and we identify conditions under which the ecosystem exhibits hysteresis with potential for catastrophic regime shifts.
This work highlights the potential of connectionist theory to expand our understanding of evo-eco dynamics and collective ecological behaviours. Within this framework we find that, despite not being a Darwinian unit, ecological communities can behave like connectionist learning systems, creating internal conditions that habituate to past environmental conditions and actively recalling those conditions.
This article was reviewed by Prof. Ricard V Solé, Universitat Pompeu Fabra, Barcelona and Prof. Rob Knight, University of Colorado, Boulder.
Keywords: Evolutionary ecology, Alternative stable states, Lotka-Volterra dynamics, Theoretical ecology, Community assembly, Network structures, Ecological memory, Associative learning, Regime shifts, Community matrix
With ever-increasing anthropogenic pressure on natural systems, it is vital to understand how the ecosystems we depend upon have been conditioned by evolutionary processes in historical environments which may have been very different from those they experience in the present day, and how any such conditioning may shape these systems’ responses to new pressures. However, as ecosystems are not typically units of selection, we currently lack a framework linking adaptive pressures on individuals and populations to the dynamical properties of the systems they inhabit. In this article we investigate how systems above the Darwinian levels of selection may evolve collective behaviours, and observe a deep homology with emergent properties well understood in connectionist models of learning. We use this homology to develop theoretical analysis of emergent properties of natural selection in ecosystems, and explore the implications for community dynamics through Lotka-Volterra simulation.
The structure and organisation of ecological interactions within biological communities causes them to exhibit many complex behaviours that are not straight-forwardly attributable to the summative behaviour of the individuals they contain [1–5]. For example, the structure of the network of interactions in an ecosystem [6, 7] affects many of the system’s dynamical behaviours including succession dynamics and community assembly rules [8, 9], the stability, resilience and adaptive capacity of a community [10–14], the presence of alternative stable states [15–17], and the system’s susceptibility to regime shifts [18].
From some points of view these system-level behaviours exhibit the appearance of design and/or characteristics in common with organismic functions such as development and complex phenotypes [19–23]. However, an ecological community is not, in most cases, an evolutionary unit [4, 23, 24]; it is an assemblage of species each individually adapted to their biotic and abiotic conditions. Thus the complexity that an ecosystem exhibits is not the product of Darwinian adaptation at the community level [25]. Furthermore, at present we lack general organisational principles that can help us understand and predict how system-level organisation and function results from the many individualistic adaptations on which they depend [3, 19, 23, 26–30], in particular, the reciprocity between the ecological dynamics on the network and the evolutionary changes to the nodes, and hence, connections of the network [30–37]. In short, we do not know how the coevolution of the parts affects the organisation and subsequent behaviour of the whole, i.e. the ecosystem’s dynamical properties such as the location and number of its dynamical attractors; the trajectories it takes towards its these attractors (assembly rules); its stability during assembly and/or succession; and its sensitivity to initial conditions during assembly.
Characterising how evolution and coevolution of the parts affects community-level properties is vital to understanding the responses of ecological communities to changes in environment at all scales. This issue is particularly acute in microbial community research, including medical applications in gut flora, where rapid evolution [38] has the potential to alter the function of those communities we depend upon most intimately, and where there is significant interest in how parental effects create a footprint of community composition that may be remembered throughout life [39]. Coevolutionary processes in gut microbiota have shaped multiple alternative stable states (termed enterotypes) [40], but it remains unclear how the historical conditioning of different communities’ networks of interactions evolve in response to environmental changes in cases such as the use of antibiotics [41] and societal changes in diet [42], or how these changes affect the emergent properties of community networks [43] given the alternate enterotypes that act as attractors for these systems. At the macroscopic scale, Case et al. speculate that co-evolutionary processes maintain the distinct bird assemblages on the islands of Bali and Lombok, either side of Wallace’s line [44–46]. Although birds are relatively unimpeded by the short stretch of sea that has separated terrestrial species, each island maintains distinct avian communities, and the conjecture is that long periods of coevolution within each community has created ‘coevolved’ biogeographic provinces; each network maintains a stable state resistant to invasion by members of the other [44].
Yet, without a framework linking microevolutionary changes in interactions between species pairs to dynamical behaviours of whole communities, it remains unclear as to whether a network of coevolved interactions could be the explanation for the observed dynamical stability.
The need to characterise the evolutionary and historical determinants of ecological processes is identified as an important frontier in ecological research [29]. Understanding the evolution and adaptability of ecological interactions is necessary, for example, to characterise the response of an ecosystem to climate change or other perturbations [14, 15, 47, 48] and, more generally, to understand how the number and location of dynamical attractors (alternative stable states) are affected by the organisation of ecological interactions acquired over evolutionary time [17].
These issues connect deeply with the phenomenon of ecological memory [29, 49–51] defined by Thompson et al. [29] as “the result of past environmental conditions and subsequent selection on populations [which] is encoded in the current structure of biological communities and reflected in the genetic structure of species”. As an illustrative example, consider the phenomenon of character displacement, [52, 53] in which niche divergence between pairs of isomorphic competitors leads to (genetic) trait divergence and increased likelihood of future coexistance; subsequent communities’ distributions are shaped by the “memory” of past competition. Within ecosystems these genetic memories, distributed amongst multiple populations, influence assembly processes, stability, and resilience of the developing and mature ecosystem [29]. However, there remain many open questions about exactly how the microevolutionary modification of interspecific relationships by natural selection shapes any macroevolutionary memory at the community level [29, 54]. For example:
How do changes to interactions evolved in past environmental conditions alter the response of the community to future changes or perturbations in environmental conditions?
Is ecological memory merely a passive memory (like an imprint in clay) where the persistent effects of the most recent ecological states over-write or blend with those of older states, or can an ecological memory retain information about multiple distinct past states without just averaging them?
Can the assembly rules and succession dynamics of a community be systematically organised by selection in past environmental states?
How does the formation of an ecological memory affect the possibility of alternative ecological stable states, and regime shifts under subsequent environmental forcing?
The lack of a theoretical framework that links individual adaptations to collective behaviours leaves such questions unanswered. Our aim in this paper is thus to introduce such a framework. We do this by converting and exploiting theory that is already well-developed in another domain, namely, connectionist models of memory and learning. Below, we discuss the characteristics of connectionist models and their relationship to eco-evo dynamics. We then show a formal equivalence between these systems. We conclude that community-level organisation does not require community-level selection. The organisation of a community can be conditioned by past experience (collectively habituated to past environmental conditions) in the same sense, and with the same consequences for collective behaviours at the community level, as connectionist models of memory and learning. In order to demonstrate how making this general link between these disciplines leads to new insights about specific ecological behaviours, we then simulate mathematical models derived from this framework to address the above open questions about ecological memory.
Connectionism is an approach to modelling cognition, in particular using neural networks, that explains how complex system-level behaviours can arise via the appropriate organisation of many simple components. The first important contribution of these models is to show that although each unit in a network might be very simple (e.g. the activation level of a neuron is simply a non-linear sum of the weighted connections from other neurons [55–57]), if appropriately organised/connected, a network of such units can provide many remarkable collective behaviours, including: a) forming a distributed memory for one or more configurations; b) pattern recognition from partial stimulus; c) the removal of noise from corrupted compositions; and d) classification of ambiguous inputs [55–58]. It has been noted in many different domains that the collective behaviours that can be exhibited by neural networks are not exclusive to neural models and can be exhibited by other types of dynamical systems (e.g. gene regulation networks, immune systems, multi-agent systems, economic systems and social networks) [59–65]. This includes ecological networks (where the growth rate of a species is modelled as a non-linear sum of the weighted fitness-interactions with other species) [64–66].
A deficit in the analogy between neural networks and ecosystems is that whereas neural networks acquire the organisation necessary for their collective behaviours through learning mechanisms designed for that purpose, ecological connections are modified by individual-level natural selection with no such system-level purposes in mind. Although there are similarities with activation dynamics in neural networks, there has not been any reason to expect that both systems may be organised in a similar manner. However, connectionist models also show that network organisations sufficient for many collective behaviours can be generated via learning mechanisms that modify the strength of connections according to only very simple and local reinforcement principles – even by mechanisms that do not require any system-level reward or performance-based feedback. The full significance of this for the evolution of ecological networks has not been previously appreciated [67].
Learning mechanisms in neural network models have two basic types [67]. Supervised learning utilises an external reward signal, or error function, to direct incremental changes to connections. We have recently demonstrated a formal equivalence between supervised learning and the evolution of connections in a network that is selected (at the system level) to produce a particular target phenotype or phenotypes [60, 67]. However, in the absence of a group selection mechanism there is no “target” phenotype directing selection at lower levels within ecological communities; supervised learning does not occur at this scale.
The other type of learning in these systems is unsupervised learning (Fig. 1), which operates without a reward signal. This may seem counter-intuitive but, when learning correlations or associations, learning what things “often go together” has many useful properties that can be attained without a supervisory signal to indicate what things “should go together” [56, 57], (Watson, R.A., Szathmáry, E.: “Learning in evolution”, opinion article. Trends in Ecology & Evolution, forthcoming), [68]. Thus, whereas supervised correlation learning reinforces correlations that are good according to some external reward signal, unsupervised correlation learning changes connections simply to reinforce correlations that are frequent. Hebbian learning [69] is the simplest unsupervised correlation learning mechanism and is well-understood in neural network models of memory and knowledge representation [56, 57, 68]. Under Hebbian learning, the change in strength of a synaptic connection, Δωij, is proportional to the co-activation of the neurons it connects: i.e. Δωij=rxixj, where r>0 is a learning rate, and xk is the activation level of node k. This type of learning instantiates a very simple positive feedback principle between behaviour and connections, often paraphrased as “neurons that fire together wire together”. The effect of such changes is that correlation becomes causation, i.e. variables that happen to be both active at the same time (e.g., because they are stimulated by the same external conditions) become causally related by connections internal to the system, and thus their behaviour becomes more correlated in future. In this manner the network habituates to the perturbations it experiences by internalising information about the pattern of perturbation it has experienced into the organisation of its connections.
This simple principle is capable of producing many remarkable collective behaviours elucidated over more than 50 years of neural network research [56, 57, 68]. Famously, this includes the ability to develop of a distributed associative memory which can store and recall multiple patterns of activation in the organisation of synaptic connections [57], facilitating the use of these networks use in pattern recognition, noise reduction and classification (Fig. 1). A main contribution of this paper is to show that in ecological communities, given heritable variation in ecological relationships and certain conditions on ecological constraints, these positive feedback principles obtain from the action of individual natural selection [70]. Table 1 sets out the full analogy we make between connectionist learning in neural networks and eco-evo dynamics in ecosystems, starting with the previously recognised dynamical equivalence (Table 1a-f).
The biological evidence for positive feedback between ecological and evolutionary dynamics is entirely intuitive and already recognised in many areas where populations shape their future selective pressures (e.g. niche construction [71] and refs. within) but the full implications of this feedback have not been realised [72]. For example, this feedback is part of the backstory involved in “invasional meltdown” [73–75] where species that have been in prolonged contact with one another in one environment facilitate one-another’s invasion into a new environment because they “have had a long evolutionary time to develop a cosy relationship with each other” [73]. Notice the simple positive feedback involved; species that occur in high density at the same time and under the same environmental conditions coevolve to become less competitive with each other over time. In turn, this reduction in niche overlap makes it more likely that they will coexist in high-density together in future. Our first key result is to formalise this principle with population genetics and show its equivalence with unsupervised correlation learning (Table 1g). Then, to demonstrate how this opens-up a transfer of concepts and results between these domains, we use numerical simulation to show conditions where an ecosystem can acquire, hold and recall distributed information about past environmental conditions – i.e. form a distributed ecological memory. This demonstrates several phenomena that are well-understood in connectionist models of memory and learning (Table 1h-m).
The formal link between the disciplines does not depend on the specific scenarios relevant to investigating ecological memory nor on the simplifications that are necessary for the simulation models; for this reason we divide our work into two parts: I) an analytic model and results concerning the general equivalence, II) simulation methods and results concerning ecological memory.
We model an ecosystem state as a vector of population densities over all N species, X={x1,x2,…xN}, (xi≥0), and an interaction network, or “community matrix” [6], Ω, where each element, ωij, represents the fitness effect of species j on species i relative to i on itself (ωii=−1). We assume ∀i,j:ωij≤0, e.g. competitive (non-trophic) interactions such as via competition for resources. A Lotka-Volterra competition equation (Eq. 1) defines the rate of change of density of a species as a function of its intrinsic growth rate and a weighted sum of interactions with all other species [66]:
where xi is the density of species i, mi is the intrinsic net growth rate of species i, kie is the carrying capacity of species i in environment e (i.e. its density before interspecific competition), and N is the number of species in the network. The dynamical equivalence between models of this sort, where populations experience exponential growth asymptotically approaching a threshold, and those models used in neural networks of excitation/inhibition between neurons is well recognised ([64] and refs. within). We now turn our attention to the selective pressures on interspecific interactions, and make new comparisons with unsupervised learning in neural networks.
Each interaction coefficient summarises how a variety of structural, physiological and behavioural traits affect the degree to which one species impacts the population growth of another. Although subject to bio-physical constraints, e.g., stoichiometric constraints on resources, these interactions can often be modified by the evolved characteristics of the constituent species, e.g. traits that alter the overlap of habitat preference or resource utilisation profiles [76] or the time, effort or energy expended on a particular ecological resource or relationship.
We assume that only individual-level selection acts on these interactions. We do not model selection on whole ecosystems (e.g., via a population of ecosystems), nor on species. Thus only changes to traits that directly affect the growth rate of an individual compared to the rest of the individuals in the species can be selected. Individual selection acts to decrease the competitive effects from others by changing ωij; but note that an individual has no intrinsic interest in altering the growth rate of others by changing ωji. Changes that decrease the density of a competitor, for example, cannot be selected for under individual selection as (in the absence of group selection) such changes benefit all individuals in a species [77]. Therefore any changes to a species growth rate that occur as a side-effect of altering the density of some other species (e.g., via changes to ωji or via ecological trade-offs below) are not affected by individual selection (Appendix A).
We analyse the rate of accumulation of favourable mutations, v, in each interaction coefficient, ωij. In order to study the dynamical interaction between evolutionary and ecological dynamics, we are particularly interested in how the evolution of ωij is sensitive to the current species densities. The qualitative picture is as follows: Occasionally, mutants arise in species i that are identical to i except for the modification of an interaction coefficient with another species j’ in the ecosystem. The origin and establishment of such a mutant can be modelled by applying population genetics theory [78, 79] to the particular case. From the ecological dynamics it follows that the selective coefficient, s, conferred by the change, g, in the interaction coefficient ωij′, is the change in the invasion rate per capita of a mutant type of species i relative to the growth rate per capita of species i without the mutation:
(Simplified as s=mikiegxj henceforth). Since m, k and x are positive, a favourable mutation requires only g>0. Qualitatively, this means that a mutation to an individual of one species, e.g. a change in its habitat or resource usage, is selected for if the mutation reduces the negative influence of another species on its growth rate. We assume that in all species such mutations occur at rate μ per individual per generation. In general, the rate of accumulation of such mutations is equal to the product of the number of individuals, xi, the beneficial mutation rate, μ, and the average probability that a single new mutation will ultimately fix, P¯, such that: v=xiμP¯ [79]. In large sexual populations with linked loci, P¯ will depend on v, and in different ways depending on the type of recombination, recombination rate, population size, the mutation rate and magnitude of mutations [78, 79]. For unlinked loci, in small populations, or under strong selection and weak mutation where mutations occur serially, P¯ is proportional to the selection coefficient, s [79]. Since the effects we want to investigate do not depend on the effects of sexual recombination it is sufficient for our purposes to model the rate of adaptation in this simple manner. In this case, the rate of adaptation, vij, in an interaction coefficient, ωij, is given by: