A new synthesis of plant population ecology.

建立了一个能够理解植物种群生态学中三个著名规律的综合理论：产量与密度的关系(1953年由Kira等人发现，后来由Shinozaki和Kira(1956)提出)，自疏的-3/2次方规则(1963)，以及Hozumi等(1968)提出的大小频率分布或MNY方法。Kobayashi和Kikuzawa(提交给《理论生物学杂志》)提出了一个新的基本生长方程，其中植物的生长可以用植物本身的重量、比焦点植物大的周围植物的影响和周围所有植物的影响来描述。积分这个方程可以得到屈服密度关系，积分这个方程在不同的临界条件下可以得到Y-N关系。在完全单边竞争条件下，产量密度关系和Y-N关系完全一致，Kikuzawa(1999)已经直观地推导出这一关系。通过引入最大树高、树重和林分干物质密度之间的异速生长，导出了Y-N曲线中的参数关系。由Y-N关系推导出生长方程。通过对生长方程进行时间微分，得到生长为零的权值，得到了自稀疏方程。这个自疏方程是包含3/2次方程式的更全面的方程。

A synthetic theory was constructed which can comprehend the three well known laws and rules in plant population ecology; yield and density relationship first found by Kira et al (1953) and later formulated by Shinozaki and Kira (1956), -3/2 power rule of self thinning (1963) and size frequency distribution or MNY method proposed by Hozumi et al (1968). Kobayashi and Kikuzawa (submitting to Journal of theoretical Biology) proposed a new fundamental growth equation in which growth of a plant can be described by weight of itself, effect of surrounding plants larger than the focal plant and the effect of all surrounding plants. Integration of this equation can derive yield density relationship and integration of this equation under different critical conditions can derive Y-N relationship. Under complete one-sided competition, yield density relationship and Y-N relationship conincide completely which was already derived intuitively by Kikuzawa (1999). By incorporating an allometry between maximum tree height and tree weight and dry matter density of a stand, parametric relationship in a Y-N curve was derived. A growth equation was derived from the Y-N relation. By differentiating with time the growth equation and obtaining the weight in which growth becomes zero, the self-thinning equation was derived. This self thinning equation is more comprehensive equation involving 3/2 power law.