Period-3 dominant phase synchronisation of Zelkova serrata: border-collision bifurcation observed in a plant population

Abstract

The population synchrony of tree seed production has attracted widespread attention in agriculture, forestry and ecosystem management. Oaks usually show synchronisation of irregular or intermittent sequences of acorn production, which is termed ‘masting’. Tree crops such as citrus and pistachio show a clear two-year cycle (period-2) termed ‘alternate bearing’. We identified period-3 dominant phase synchronisation in a population of Zelkova serrata. As ‘period-3’ is known to provide evidence to imply chaos in nonlinear science, the observed period-3 phase synchronisation of Zelkova serrata is an attractive real-world phenomenon that warrants investigation in terms of nonlinear dynamics. Using the Hilbert transform, we proposed a procedure to determine the fractions of periods underlying the survey data and distinguished the on-year (high yield year) and the off-year (low yield year) of the masting. We quantified the effects of pollen coupling, common environmental noise and individual variability on the phase synchronisation and demonstrated how the period-3 synchronisation emerges through a border-collision bifurcation process. In this paper, we propose a model that can describe diverse behaviours of seed production observed in many different tree species by changing its parameters.

EcoQBNs: First Application of Ecological Modeling with Quantum Bayesian Networks

“…The intransitive structure of roshambo has been likened to persistent cycles of species competition in ecological communities, as competitive advantages get traded off among species with no clear winner [ 41 , 42 ]; to the development and stability of species diversity [ 43 , 44 ]; and to the development of high social efficiency in human decision-making [ 45 ]. In ecological contexts, Sakai et al [ 46 ] specifically used the Hilbert transform (a mathematical technique for deriving phase amplitudes) to represent an intransitive three-period stable cycle of ‘masting’ in tree crops, and they further [ 47 ] described how a coffee agroecosystem can constitute a stable dynamic, intransitive situation with the interactions of three elements of an insect pest, parasitoid, and predator. Further, a prime example of an intransitive ecological system was described by Yule and Burns [ 48 ] in New Zealand, who revealed an unexpected additive adverse impact on a native tree species from the reintroducing an insectivore parrot thought to control an herbivorous moth which damages that tree species.…”

Spatial Phase Synchronisation of Pistachio Alternate Bearing

“…Several researchers have reported that alternate bearing of pistachios do not always exhibit a clear two-year cycle but may feature various types of synchronisations both spatially and annually 20,[36][37][38] . Sakai et al (2019) proposed a practical approach to determine the composition of periodic components of alternate bearing and masting of plant populations 16 . For instance, period-two and period-three sequences are defined as 'ON ⇒ OFF ⇒ ON' and 'ON ⇒ OFF ⇒ OFF ⇒ ON', respectively (see METHODS-Fraction of period section).…”

“…A resource budget model (RBM), which is a tent map 18 , has been previously used to model the dynamics of seed production of perennial plant species [7][8][9][12][13][14][15][16][17] . For cross-pollinating species, the global coupled map (GCM) and local coupled map (LCM)…”

“…As the conventional index of synchronisation 𝑆𝑌𝑁𝐶 = 𝑆 𝑏𝑦 𝑆 𝑤𝑦 𝑆 𝑏𝑦 (Sby : standard deviation of between years, Swy :within years standard deviation) is based on "amplitude" synchronisation, the index determines the degree of synchrony only for a given population [12][13][14] . Instead, by focusing on "phase" synchronisation, Prasad et al (2017) and Sakai et al (2019) developed an in-phase/out-of-phase analysis technique 15 that enables us to determine the strength of the phase synchrony both in individual and population levels for Citrus and Zerkova seratta 16 . The yield data that were analysed here are remarkable since they included measurements pertaining to 9,562 trees obtained over five years 17 .…”

“…A resource budget model (RBM), which is a tent map 18 , has been previously used to model the dynamics of seed production of perennial plant species [7][8][9][12][13][14][15][16][17] . For cross-pollinating species, the global coupled map (GCM) and local coupled map (LCM) of RBMs have been used with mean-field pollen coupling to establish the pollen limitation theory as an endogenous mechanism [12][13][14][18][19][20] .…”