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Adaptive foraging of pollinators fosters gradual tipping under resource competition and rapid environmental change
Fig 2
Species persistence collapses for high rates of environmental change within environmental ranges that are otherwise presumed safe.
(A) Three scenarios are represented for communities without adaptive foraging, perturbed to start with a low initial species abundance (out of equilibrium). (Inset) Stress in communities increases over time as the driver of decline increases at different rates, λ, up to a maximum value, 
. The black line represents the point of collapse above which a fixed value of the driver of decline leads to the collapse of all communities and below which some communities are sustained. The maximum value of the driver of decline in each simulation is denoted by the fraction θ of the point of collapse 
. (A) Dotted orange line represents an increase in the driver of decline up to 90% of the critical value, 
, dot-dashed green line an increase up to 50%, and dashed pink an increase up to 20%. In this panel, species persistence is calculated as the fraction of pollinator species alive relative to the number of species alive at the lowest rate of change measured (λmin = 10−4). (B) The persistence of species decreases as a function of the maximum value of the driver of decline, represented as a fraction θ of the point of collapse, for a fast rate of change (λ = 1). Communities without adaptive foraging see a critical transition in species persistence when the driver of decline increases to a value close to, but lower than, the point of collapse 
at a fast enough rate. In this panel, species persistence is calculated as the fraction of pollinator species alive relative to the number of species alive at θ = 0 (no external stressor). Initial species abundance Sinit = 0.1 for all simulations. The results are averaged over 100 feasible networks, for which all 15 plant and 35 pollinator species survive under no stress, with the bands representing the first to third quartile ranges. Other parameters in Table A in S1 Text.
doi: https://doi.org/10.1371/journal.pcbi.1011762.g002