Mathematical modeling and mechanisms of pattern formation in ecological systems: a review

Sun, Gui‐Quan; Zhang, Hong-Tao; Wang, Jinshan; Li, Jing; Wang, Yi; Li, Li; Wu, Yongping; Feng, Guolin; Zhou, Jin

doi:10.1007/s11071-021-06314-5

Cited by 42 publications

(21 citation statements)

References 118 publications

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“…This function provides a modeler with the simplest possibility to implicitly include the various effects of the environmental heterogeneity and the spatial behavior of consumers into a non-spatial model. Recent studies emphasize the importance of spatial effects in predator-prey systems, in particular, the mechanisms of pattern formation and dynamic properties emerging at a large spatiotemporal scale Frank et al, 2021;Sun et al, 2021;Xue et al, 2021;Wang et al, 2022). Modeling gives a mechanistic explanation for the emergence of mutual interference.…”

Section: Underlying Mechanisms and Minimal Model Of Predator Interferencementioning

confidence: 99%

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Tyutyunov

Titova

2021

Front. Ecol. Evol.

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The functional response (trophic function or individual ration) quantifies the average amount of prey consumed per unit of time by a single predator. Since the seminal Lotka-Volterra model, it is a key element of the predation theory. Holling has enhanced the theory by classifying prey-dependent functional responses into three types that long remained a generally accepted basis of modeling predator-prey interactions. However, contradictions between the observed dynamics of natural ecosystems and the properties of predator-prey models with Holling-type trophic functions, such as the paradox of enrichment, the paradox of biological control, and the paradoxical enrichment response mediated by trophic cascades, required further improvement of the theory. This led to the idea of the inclusion of predator interference into the trophic function. Various functional responses depending on both prey and predator densities have been suggested and compared in their performance to fit observed data. At the end of the 1980s, Arditi and Ginzburg stimulated a lively debate having a strong impact on predation theory. They proposed the concept of a spectrum of predator-dependent trophic functions, with two opposite edges being the prey-dependent and the ratio-dependent cases, and they suggested revising the theory by using the ratio-dependent edge of the spectrum as a null model of predator interference. Ratio-dependence offers the simplest way of accounting for mutual interference in predator-prey models, resolving the abovementioned contradictions between theory and natural observations. Depending on the practical needs and the availability of observations, the more detailed models can be built on this theoretical basis.

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Section: Underlying Mechanisms and Minimal Model Of Predator Interferencementioning

confidence: 99%

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Tyutyunov

Titova

2021

Front. Ecol. Evol.

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“…Extracting the typical modes of daily variation of wind speed is helpful to study the appearance time of strong wind. The classification method has been verified to be useful to extract the typical modes, which can obtain more information from the system [8,9]. In the classification, the typical spatial modes can be extracted by taking the spatial field as the sample (Makra et al [10]).…”

Section: Introductionmentioning

confidence: 99%

Typical Modes of the Wind Speed Diurnal Variation in Beijing Based on the Clustering Method

et al. 2021

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Wind speed is an important meteorological condition affecting the urban environment. Thus, analyzing the typical characteristics of the wind speed diurnal variation is helpful for forecasting pollutant diffusion. Based on the K-means clustering method, the diurnal variation characteristics of the wind speed in Beijing during 2008–2017 are studied, and the spatiotemporal characteristics of the wind speed diurnal variations are analyzed. The results show that there are mainly five to seven clusters of typical characteristics of the wind speed diurnal variation at different stations in Beijing, and the number of clusters near the city is smaller than that in the suburbs. The typical number of the wind speed diurnal variation during 2013–2015 is smaller than that in other periods, which means the anomalous clusters of the diurnal variation are reduced. Besides, the numbers of different clusters in different years are often switched. Especially, the switch between clusters five and six and the switch between clusters six and seven are frequent. Based on the second cluster analysis of the clustering results at the Beijing station, we find 12 clusters of the diurnal variation, including nine clusters of “large in the daytime, while small at night,” two clusters of “monotonous,” and one cluster of “strong wind.” Furthermore, the low-speed clusters of wind mainly locate in the city with a significant increasing trend, while the high-speed clusters and the monotonous clusters of wind locate in the suburbs with a decreasing trend.

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“…In 1999, Klausmeier firstly proposed the classical vegetated-water model, explaining the regular stripes on the slopes and irregular mosaics on the ground, and pointed out that nonlinear mechanisms play a major role in determining the spatial structure of plant communities [19]. In 2013, Sun et al revealed the relationship between precipitation and pattern formation: when rainfall is small, the vegetation will form spot pattern; when precipitation increases, the density of the spot pattern will increase, and vegetation appears as spot-stripes mixed pattern with low density [20]. In 2018, Liu et al proposed a cross-diffusion vegetation system, in which the phenomenon of spot pattern transition was found [17].…”

Section: Introductionmentioning

confidence: 99%

Pattern Dynamics of Vegetation Growth With Saturated Water Absorption

Cao

Bao³

2021

Front. Phys.

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Regular pattern is a typical feature of vegetation distribution and thus it is important to study the law of vegetation evolution in the fields of desertification and environment conservation. The saturated water absorption effect between the soil water and vegetation plays an crucial role in the vegetation patterns in semi-arid regions, yet its influence on vegetation dynamics is largely ignored. In this paper, we pose a vegetation-water model with saturated water absorption effect of vegetation. Our results show that the parameter 1/P, which is conversion coefficient of water absorption, has a great impact on pattern formation of vegetation: with the increase of P, the density of vegetation decrease, and meanwhile it can induce the transition of different patterns structures. In addition, we find that the increase of appropriate precipitation can postpone the time on the phase transition of the vegetation pattern. The obtained results systematically reveal the effect of saturated water absorption on vegetation systems which well enrich the findings in vegetation dynamics and thus may provide some new insights for vegetation protection.

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Mathematical modeling and mechanisms of pattern formation in ecological systems: a review

Cited by 42 publications

References 118 publications

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

Typical Modes of the Wind Speed Diurnal Variation in Beijing Based on the Clustering Method

Pattern Dynamics of Vegetation Growth With Saturated Water Absorption

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