Spatial Phase Synchronisation of Pistachio Alternate Bearing

Nonlinear physics and agroecosystems can be of great relevance in the synchronisations of chaotic oscillators. The endogenous dynamics of the seed production of perennial plant species which include alternate bearing and masting, portray typical synchronisation patterns in nature and can be modelled using a tent map known as a resource budget model (RBM). This study investigates the collective rhythm in 9,562 pistachio trees caused by their endogenous network dynamics and exogenous forces (common noise). Common noise and a local coupling of RBMs are the two primary factors emerging from the bearing phase synchronisation in this orchard. The in-phase/out-of-phase analysis technique quantifying the strength of the phase synchronisation in trees (population /individual) allows us to study the observed spatial synchrony in detail. We demonstrate how three essential factors, i.e. (a) common noise, (b) local direct coupling, and (c) the gradient of the cropping coefficient, explain the spatial synchrony of the orchard. Here, we also show that the methodology employing nonlinear physics to study agroecological systems can be useful for resolving practical problems in agriculture including yield variability and spatial synchrony which often compromise efficient resource management.

Density Dependent Resource Budget Model for Alternate Bearing

ABSTRACTAlternate bearing, seen in many types of plants, is the variable yield with a strongly biennial pattern. In this paper, we introduce a new model for alternate bearing behavior. Similar to the well-known Resource Budget Model, our model is based on the balance between photosynthesis (carbon accumulation) and reproduction processes. We consider two novel features with our model, 1) the existence of a finite capacity in the tree’s resource reservoir and 2) the possibility of having low (but non-zero) yield when the tree’s energy level is low. We achieve the former using a density dependent resource accumulation function, and the latter by removing the concept of the well-defined threshold used in the Resource Budget Model. At the level of an individual tree, our model has a stable two-cycle solution, which is suitable to model plants in which the alternate bearing behavior is pronounced. We incorporate environmental stochasticity by adding two uncorrelated noise terms to the parameters of the model associated with the carbon accumulation and reproduction processes. Furthermore, we examine the model’s behavior on a system of two coupled trees with direct coupling. Unlike the coupled Resource Budget Model, for which the only stable solution is the out-of-phase solution, our model with diffusive coupling has stable in-phase period-2 solutions. This suggests that our model might serve to explain spatial synchrony on a larger scale.

Correlated seed failure as an environmental veto to synchronize reproduction of masting plants

Highly variable, synchronized seed production, called masting, is a widespread reproductive strategy in plants. Resource dynamics, pollination success, and, as described here, environmental veto, are possible proximate mechanisms of masting. We extended the resource budget model of masting with correlated and uncorrelated reproductive failure, and ran this model across its parameters space. Next, we parametrized the model based on a 16-year seed production data for red (Quercus rubra) and white (Q. alba) oaks. Simulations showed that resource dynamics and reproduction failure produce masting even in the absence of pollen coupling. In concordance, in both species, among-year variation in resource gain and correlated reproductive failure were necessary and sufficient to produce masting. Environmental variation is a form of reproduction failure caused by environmental veto that may drive large-scale synchronization without density-dependent pollen limitation. Reproductive-inhibiting weather events are prevalent in ecosystems, suggesting that these described mechanisms likely operate in many masting systems.

Direct coupling: a possible strategy to control fruit production in alternate bearing

We investigated the theoretical possibility of applying phenomenon of synchronization of coupled nonlinear oscillators to control alternate bearing in citrus. The alternate bearing of fruit crops is a phenomenon in which a year of heavy yield is followed by an extremely light one. This phenomenon has been modeled previously by the resource budget model, which describes a typical nonlinear oscillator of the tent map type. We have demonstrated how direct coupling, which could be practically realized through grafting, contributes to the nonlinear dynamics of alternate bearing, especially phase synchronization. Our results show enhancement of out-of-phase synchronization in production, which depends on initial conditions obtained under the given system parameters. Based on these numerical experiments, we propose a new method to control alternate bearing, say in citrus, thereby enabling stable fruit production. The feasibility of validating the current results through field experimentation is also discussed.