Table 1 Mechanistic equivalence between evo-eco dynamics and learning neural networks, and a map for the comparisons and analogies made in this paper

Activation dynamics

Population dynamics

a)

Neural activation level

Species density, x _i

b)

Neural activation pattern

Ecological state, X={x _i ,x ₂,...x _N }

c)

Synaptic connection strength, ω _ij

Inter-species fitness interaction, ω _ij

d)

Neural network (weight matrix, W).

Ecological network (community matrix, Ω).

e)

Neural activation dynamics: a non-linear weighted sum of inputs from other neurons (and external inputs).

Ecological population dynamics (Eq. 1): species growth is a non-linear function of the sum of weighted fitness interactions from other species (and environmental changes to carrying capacities).

f)

External input patterns

Environmental forcing

(aka. ‘training set’).

(in multiple environmental conditions)

Correlation learning (unsupervised)

Evolution of interactions (individual selection only)

g)

Positive feedback between activation strengths and connection strengths – aka. neurons that fire together wire together. Unsupervised correlation learning mechanism, Hebb’s rule: Δ ω _ij =r x _i x _j , where r>0 is a learning rate.

Positive feedback between ecological densities and connections – or species that occur together wire together. Direct effects of individual natural selection on interactions: v _ij =r x _i x _j , where \(r = \frac {m_{i}}{k_{\textit {ie}}} g \mu \) describes the available mutation (Eq. 3).

Collective behaviours in neural networks (arising from e.g., Hebbian learning, Fig. 1 )

Collective behaviours in ecosystems (arising from individual selection acting upon interspecific correlations)

h)

Memory formation (Fig. 1, top panel) Hebb’s rule organises synaptic connections to reinforce the state of the system, decreasing sensitivity to changes in input.

Ecological memory formation(Fig. 3): natural selection organises ecological relationships in a manner that reinforces the current ecological state, decreasing sensitivity to changes in environmental conditions. (Attractors due to environmental variables become attractors of community dynamics [17].)

i)

Distributed associative memory facilitates a memory of multiple patterns (Fig. 1 a): the capacity to store multiple patterns of activation in the organisation of synaptic connections and recall patterns from any initial conditions via activation dynamics.

Formation of alternative stable states (Fig. 5 a): the creation of a distributed ecological memory in the network of species interactions results in a system with attractors that mimic past ecological states.

j)

Pattern reconstruction (Fig. 1 b): the recall of a complete pattern from a partial stimulus.

Ecological assembly dynamics (Fig. 5 b): reconstruction of a particular community composition, from a subset of that community.

k)

Error correction (Fig. 1 c): the ability to remove noise from a pattern, repair imperfections and restore a complete pattern.

Ecological resilience (Fig. 5 c): the ability to recover from perturbations in species densities and restore the complete community.

l)

Recognition or classification of an input or stimulus (Fig. 1 d): return the nearest attractor from ambiguous initial conditions.

Ecological sensitivity to initial conditions (Fig. 5 d): the switch-like change in response to small variation in initial species densities.

m)

Holding state in dynamics: Hopfield networks and other recurrent networks have an internal state that allows them to display temporal dynamics (independent of input).

Ecosystems hold state in population dynamics (Fig. 6): in systems with multiple attractors this results in a communities capable of hysteresis with tipping points between states.