Impact of colonization history on the composition of ecological systems

Abstract

Observational studies of ecological systems have shown that different species compositions can arise from distinct species arrival orders during community assembly-also known as colonization history. The presence of multiple interior equilibria in the positive orthant of the state space of the population dynamics will naturally lead to history dependency of the final state. However, it is still unclear whether and under which conditions colonization history will dominate community composition in the absence of multiple interior equilibria. Here, by considering that only one species can invade at a time and there are no recurrent invasions, we show clear evidence that the colonization history can have a big impact on the composition of ecological systems even in the absence of multiple interior equilibria. In particular, we first derive two simple rules to determine whether the composition of a community will depend on its colonization history in the absence of multiple interior equilibria and recurrent invasions. Then we apply them to communities governed by generalized Lotka-Volterra (gLV) dynamics and propose a numerical scheme to measure the probability of colonization history dependence. Finally, we show, via numerical simulations, that for gLV dynamics with a single interior equilibrium, the probability that community composition is dominated by colonization history increases monotonically with community size, network connectivity, and the variation of intrinsic growth rates across species. These results reveal that in the absence of multiple interior equilibria and recurrent invasions, community composition is a probabilistic process mediated by ecological dynamics via the interspecific variation and the size of regional pools.

Opto‐regulation for the 2D to 3D transformation of a liquid crystal network membrane

“…In the calculation, we have P 0// =0.001, η 0 = 2.2 Â 10 À4 s À1 , T 0 = 0.4 s, E // /E = 1, G/E // = 0.2, ν // = ν = 0.25, d 0 /h = 1, and the benchmark light intensity I 0 = 5kw/m 2 . 25,26 The non-dimensional parameter x ¼ x=l, y ¼ y=l, and w ¼ w=h are used for better describing the effect of membrane dimension on the photoinduced deformation. Here the effect of non-uniformed illumination is focused so that the director n of the LCN membrane is along z direction, that is, ϕ = 90 and θ = 0 are fixed in the following discussion.…”

“…T 0 represents the thermal characteristic time from the cis state to the trans state, and d 0 is the light decay distance. [24][25][26] I 0 (x, y) denotes the light intensity at arbitrary point (x, y) in the membrane. Through tuning I 0 (x, y) at different points, the nonuniform light mode could be set.…”

“…As to the uniform illumination, I 0 (x, y) equals to a constant, and independent to x and y. For a three-dimensional director alignment n = (cos ϕ cosθ, cos ϕ sinθ, sin ϕ) T , the components of the light induced spontaneous strain ε L is given as 25,26 :…”

“…The total strain ε in the membrane can be decomposed into the elastic strain ε e and the spontaneous strain ε L , that is, and the light induced spontaneous strain ε L is with the form 25 where I represents the unit tensor and is the dyadic product of two vectors.…”

“…Obviously, the surface pattern of the membrane could be tuned by the intrinsic properties of the LCN material, such as elastic modulus 22 and director orientation. 23,24 In addition, the size effect 25,26 and the boundary constraint [26][27][28][29] of the membrane are other important regulative factors. While for a LCN membrane with determined geometric and material parameters, the surface pattern could also be regulated by the external illumination conditions.…”