Quantifying the impact of ecological memory on the dynamics of interacting communities

Linking microbiome temporal dynamics to host ecology in the wild

Ignoring the dynamic nature of microbial communities risks underestimating the power of microbes to impact the health of their hosts. Microbiomes are thought to be important for host fitness, yet the coarse temporal scale and population-level focus of many studies precludes the ability to investigate the importance of among-individual variation in stability and identify the ecological contexts in which this variation matters. Here we briefly summarise current knowledge of temporal dynamics in wild host-associated microbial communities. We then discuss the implications of among-individual variation in microbiota stability and suggest analytical approaches for understanding these patterns. One major requirement is for future studies to conduct individual-level longitudinal analyses, with some systems already well set up for answering these questions.

Time delays modulate the stability of complex ecosystems

What drives the stability, or instability, of complex ecosystems? This question sits at the heart of community ecology and has motivated a large body of theoretical work exploring how community properties shape ecosystem dynamics. However, the overwhelming majority of current theory assumes that species interactions are instantaneous, meaning that changes in the abundance of one species will lead to immediate changes in the abundances of its partners. In practice, time delays in how species respond to one another are widespread across ecological contexts, yet the impact of these delays on ecosystems remains unclear. Here we derive a new body of theory to comprehensively study the impact of time delays on ecological stability. We find that time delays are important for ecosystem stability. Large delays are typically destabilizing but, surprisingly, short delays can substantially increase community stability. Moreover, in stark contrast to delay-free systems, delays dictate that communities with more abundant species can be less stable than ones with less abundant species. Finally, we show that delays fundamentally shift how species interactions impact ecosystem stability, with communities of mixed interaction types becoming the most stable class of ecosystem. Our work demonstrates that time delays can be critical for the stability of complex ecosystems.

Fractional modeling of urban growth with memory effects

The previous urban growth model by L. M. A. Bettencourt was developed under the framework of a constant β scaling law in an ordinary differential equation based model assuming instantaneous dynamic growth. In this paper, we improve the model by considering the memory effects based on fractional calculus. By testing this new fractional model to different urban attributes related to sustainable growth, such as congestion delay, water supply, and electricity consumption for selected countries (the USA, China, Singapore, Canada, Switzerland, New Zealand), this new model may provide better agreement to the annual population growth by numerically finding the optimal fractional parameter for different attributes. Based on the theoretical time-independent scaling of β = 5 / 6 (sub-linear) and β = 7 / 6 (super-linear), we also analyze the population growth of 42 countries from 1960 to 2018. Furthermore, time-dependent scaling law extracted from empirical data is shown to provide further improvements. With better agreement between this proposed fractional model and the collected empirical population growth data, useful parameters can be estimated. For example, the maintenance cost and additional cost related to the sustainable growth (for a given city's attribute) can be quantitatively determined for the informed decision and urban planning for the sustainable growth of cities.