Path probability selection in nature and path integral.

Understanding of any biological evolutions, such as speciation, adaptation behavior and biodiversity pattern, is based on a fundamental concept of fitness, in which natural selection implies the improvement and progress of fitness in either direct/indirect benefit or genetic transmission to the next generation. However, this basic idea of biological evolution, which is mathematically described by Price equation or its relations, has not fully considered feedback effects from the environment or other generations. They lost the global dynamics of the evolutions consequently. Drawing on the idea of modern physics, we introduce the path integral by iterating the Price equation step by step to characterize the evolutionary path in which the stationary fitness is replaced by the path probability. The evolutionary selection therefore will depend on path probability instead of fitness advantage. In such a framework of the evolutionary path, the intermediate process of evolution is not always pointing to the fitness-maximizing equilibrium and multiple evolutionary paths could thus coexist without fitness advantage discrimination. This mechanism could potentially explain fitness evolutionary strategies with the diversified fitness (e.g., coexistence of altruism and selfishness) and thus species diversity.

Super-rational aspiration induced strategy updating helps resolve the tragedy of the commons in a cooperation system with exit rights.

Avoiding the tragedy of the commons requires altruists to incur some losses to benefit the group. Although specific rules and self-enforcing agreements could help maintain the cooperation system stable, the costly recognition and free-rider problem are still questioned these two cooperation maintenance mechanisms. We here considered the situation of both exit costs and exit benefits in the asymmetric prisoner's dilemma game and introduced a super-rational aspiration induced strategy updating, where players adjust strategies in line with their payoffs and aspirations. If their payoffs reach or exceed the aspiration levels, which may be rational or super-rational, they keep their strategies. Otherwise, they imitate a local neighbor's strategy. We explored this rule in the structured and well-mixed population. The results show that super-rationality and asymmetry could together promote cooperation when exit costs exist. With exit benefit, super-rationality promotes cooperation in both structures and asymmetry only works in the well-mixed population. This suggests that the introduced strategy updating rule could sustain cooperation among egoists with exit rights.

[Comparison on moisture dynamics of two different soil types in desert steppe]. / è’æ¼ è‰åŽŸä¸¤ç§ç±»åž‹åœŸå£¤çš„æ°´åˆ†åŠ¨æ€å¯¹æ¯”.

Based on the positioning monitoring data from 2017 to 2018, we analyzed the spatial-temporal dynamic characteristics of moisture in two different soil types (sierozem and aeolian sandy soil) in the Yanchi desert steppe in the eastern Ningxia. The results showed that the rainfall in the study area was 208.2 and 274.8 mm in the growing season of 2017 and 2018 (May-October), respectively. The distribution of rainfall varied across different months. Except for the extreme rainfall event (129.6 mm) in May in 2018, rainfall in other months was lower than that in 2017. The seasonal dynamics of soil water content was roughly divided into two phases: compensation period (early May to early June) and fluctuation period (mid June to late September). The soil moisture of 0-20 cm layer had a pulse characteristic of rapid increase and decrease after rainfall, while that of the deep soil was relatively stable. The soil water content of sierozem showed a "rise-fall-liter" change with increasing soil depth. The saeolian sandy soil increased sharply from 0 to 60 cm then increased slowly, whereas soil water content gradually increased with increasing soil depth. In 2017, soil moisture in the soil profile (0-100 cm) of the sierozem was accumulated, and the aeo-lian sand soil was in the consumption type. In 2018, both soil water across the full profile in both soil types were the consumption type. The temporal stability of soil moisture of two soil types increased with increasing soil depth. The average soil water content of the whole sections of sierozem and aeolian sandy soil were 80-100 and 40-60 cm, respectively. The two soil types had different spatial and temporal distributions of soil moisture. Aeolian sandy soil was more affected by precipitation than sierozem. Precipitation would reduce the variability of soil moisture and change its temporal stability.