(Appendix) Bathyal benthic foraminifera in ODP Hole 166-1006A sediments

The percent carrying capacity Kp is the equilibrium population in percentage terms of a species that an area can support while adequately meeting the needs of every individual. It is readily determined from a time series of percentage abundances for a species, in which pit is the percentage abundance of the ith species at time t. The percentage point change in abundance of a species Dpi between two samples is given by Dpi = pit + 1 ? pit, where pit + 1 is the percentage abundance at a subsequent time t + 1. The rate of population change in percentage points for each percent at a given time or point t, here termed rt, is given by rt = Dpi/pit. Linear regression of rt against pit gives rt = rm-s · pit, in which the constant rm is the rate of increase in rt where pit approaches zero, and the negative slope s represents the combined strength of intraspecific, interspecific and abiotic interactions for the species investigated. Setting rt = 0, so that pit = Kp and rm-s · Kp = 0, gives Kp = rm/s. The Upper Quaternary of ODP 1006A contains two subsections with rich bathyal benthic foraminiferal assemblages separated by samples yielding few specimens. Values of rm, s and Kp were calculated for five species (Globocassidulina subglobosa, Planulina ariminensis, Cibicidoides pachyderma, Cassidulina laevigata, Uvigerina laevis) within these subsections and 95% confidence intervals were computed for rm and s. The rate of change of the percentage abundance for each percent rt, as indicated by the slope s, differs between species (P. ariminensis and C. pachyderma vs. C. laevigata) and can also vary within a single species over time (G. subglobosa). Likewise, values of rm differ between species (P. ariminensis vs. C. pachyderma) and can also change within a single species over time (G. subglobosa). Points of change from one value of Kp to another in a stratigraphic section mark regime shifts and have potential for ecostratigraphic correlation. Within the Upper Quaternary of ODP Hole 1006A they apparently reflect an increase in the organic matter flux in the uppermost part of the section. The method described here can be applied to any species in any taxon for which percentage data are available. For those in the hydrocarbon industry it should prove especially useful for detailed studies of intervals of economic interest.百分承载量（percent carrying capacity, Kp）指某一区域可支撑某物种且能充分满足每个个体生存需求的种群百分比平衡规模。该参数可依托某物种的百分比丰度时间序列便捷求得，其中$p_{it}$代表第$i$个物种在时刻$t$的百分比丰度。某物种在两个采样点间的丰度百分点变化量$Dp_i$满足公式：$Dp_i = p_{i,t+1} - p_{it}$，其中$p_{i,t+1}$为后续时刻$t+1$时的百分比丰度。给定时刻$t$下，各百分比丰度对应的种群变化率（以百分点计）记为$r_t$，其计算公式为$r_t = Dp_i / p_{it}$。对$r_t$与$p_{it}$进行线性回归可得$r_t = r_m - scdot p_{it}$，其中常数项$r_m$为$p_{it}$趋近于0时的$r_t$增长率，负斜率$s$则代表所研究物种的种内、种间及非生物相互作用的综合强度。令$r_t=0$，此时$p_{it}=Kp$，代入回归公式可得$r_m - scdot Kp=0$，进而解得$Kp = r_m / s$。 大洋钻探计划（Ocean Drilling Program, ODP）1006A孔的晚第四纪地层包含两个亚段，二者均发育丰富的半深海底栖有孔虫组合，中间被仅产出少量标本的采样层段隔开。研究人员针对这两个亚段中的5个物种（Globocassidulina subglobosa、Planulina ariminensis、Cibicidoides pachyderma、Cassidulina laevigata、Uvigerina laevis）计算了$r_m$、$s$与$Kp$的数值，并为$r_m$和$s$计算了95%置信区间。由斜率$s$表征的各百分比丰度对应的丰度变化率$r_t$，在不同物种间存在差异（如Planulina ariminensis与Cibicidoides pachyderma和Cassidulina laevigata之间），且同一物种的该变化率也可随时间发生变化（如Globocassidulina subglobosa）。同理，$r_m$的数值在不同物种间也存在差异（如Planulina ariminensis与Cibicidoides pachyderma之间），且同一物种的$r_m$数值同样可随时间发生变化（如Globocassidulina subglobosa）。地层剖面中$Kp$数值发生跃迁的点位代表生态系统状态转换，具备生态地层对比的应用潜力。在ODP 1006A孔的晚第四纪地层中，这类状态转换点位显然反映了地层最上部的有机物质通量升高。本文所述方法可应用于所有可获取百分比丰度数据的分类单元中的任一物种。对于油气行业从业者而言，该方法在具经济价值的地层段的精细化研究中尤为实用。