Leaf nitrogen resorption is more important than litter nitrogen mineralization in mediating the diversity–productivity relationship along a nitrogen-limited temperate forest succession chronosequence

The resorption of nutrients by plants before litter fall and the mineralization of nutrients from plant litter by soil processes are both important pathways supporting primary productivity. While the positive relationship between plant biodiversity and primary productivity is widely accepted for natural ecosystems, the roles of nutrient resorption and mineralization in mediating that relationship remains largely unknown. Here, we quantified the relative importance of nitrogen(N) resorption and N mineralization in driving plant community N investment and the correlation between species diversity and community productivity along an N-limited successional chronosequence of the mixed broadleaved–Korean pine(Pinus koraiensis) forest in northeastern China. Leaf N resorption efficiency(NRE) at the community level increased significantly along the successional chronosequence,whereas litter N mineralization rate decreased significantly. Leaf NRE was more important than litter N mineralization rate in driving the diversity–productivity relationship. However, higher leaf NRE led to less N mineralization as succession progressed along the chronosequence. Our results highlight the importance of the N resorption pathway rather than the N mineralization pathway for forest N acquisition with community succession,and they provide mechanistic insights into the positive effects of biodiversity on ecosystem functioning. In future forest management practices, we recommend appropriate application of N fertilizer to mitigate the adverse effects of N-poor soil on seedling regeneration during late succession and thus maintain the sustainable development of temperate forest ecosystems.

THEOREM OF EXISTENCE OF EXACT n LIMIT CYCLES FOR LINARD'S EQUATION

Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler conjectured that the equation +μsin+x=0 has infinite number of limit cycles. Then H. S. Hochstadt and B. Stephan, R. N. D’Heedene and others proved that this equation has at least n limit cycles in the interval |x|<(n+1)π for specified parameter μ. In 1980, Professor Zhang Zhifen proved that this equation has exact n limit cycles in the interval |x|<(n+1)π for any nonzero parameter μ, and thus pushed the related work forward greatly. In this paper, we shall prove that the Liénard’s equation has exact n limit cycles in a finite interval under a class of very general condition.