图1 表型的适合度景观图。实线表示真实的适合度景观, 当生物体在这样有高峰有山谷的适合度景观上进化时, 很容易被困在某一更低的局部峰值上。虚线是在Frank提出的反应规范作用下的表型适合度景观, 即由某基因控制的表型的适合度景观, 该景观只有一个单峰, 使得表型更容易进化到适合度更高的表型。

Fig. 1 Fitness landscape of phenotypes. The solid line shows the fitness landscape observed. When an organism evolves on such a multipeak fitness landscape, it’s easy to be trapped at a lower local peak. The dashed line displays the phenotypic fitness landscape smoothed by reaction norm, i.e., the expect fitness for a genotype with a certain average phenotype. This fitness landscape just has one single peak, which makes it easier for any phenotype to evolve to another one with higher fitness.

图2 群体内表型从x0进化到xn过程的示意图。个体在每一时刻都会根据瞬时适合度以一定概率去选择自己下一时刻期望进化到的表型, 因此群体内的表型从t0到tn的进化过程中可能产生多条路径, a, b即为其中的两条。假设路径a上的表型为${{x}_{0}},{{x}_{1}},{{x}_{2}},...,{{x}_{n}}$, 该路径出现的概率为$P[({{t}_{0}}),{{x}_{1}}({{t}_{1}}),{{x}_{2}}({{t}_{2}}),\ldots,{{x}_{n}}({{t}_{n}})]$。

Fig. 2 An evolutionary process for phenotype in a population from x0 to xn. An individual selects the next phenotype to evolve with a certain probability according to its instantaneous fitness at each time step, thus many possible paths of phenotype in a population occur including paths a and b. Suppose that trajectory a consists of phenotype ${{x}_{0}},{{x}_{1}},{{x}_{2}},...,{{x}_{n}}$, then the possibility is $P[{{x}_{0}}({{t}_{0}}),{{x}_{1}}({{t}_{1}}),{{x}_{2}}({{t}_{2}}),\ldots,{{x}_{n}}({{t}_{n}})]$。

图3 进化路径的分布。不同颜色表示路径的频率。随着时间的演化, 表型从最初的状态分化出其他表型, 在此过程中, 表型只能向相邻的表型进化, 因此进化是连续的。若在t = 1,000这一时刻观察演化结果, 则可以看到明显不连续的物种分化(两个蓝色区域)。

Fig. 3 The distribution of evolutionary paths. Different colors represent different distribution probability of paths. As time goes by, one phenotype differentiates to other phenotypes with different probabilities. The evolutionary path is continuous in this process because that phenotypes can only evolve to adjacent phenotypes. If the evolutionary results are observed at the moment of t = 1,000, significant discontinuous phenotype differentiation (blue regions) can be seen.

图4 路径依赖下的状态进化。(a)状态量随时间演化的频率分布。状态量可以指基因型、性状特征、生态过程。(b) t = 10时的表型频率分布。(c) t = 600时的表型频率分布。若以表型作为状态量, 分化初期显示为单峰的频率分布, 在时间t = 600处时出现明显的分化且显示为双峰的频率分布。这意味着群体内个体从初始的单一表型(50)逐渐分化成两种表型(25和28), 可以进一步判断对应的个体是否为不同物种。

Fig. 4 Path-dependent evolutionary process of states. (a) The frequency distribution curve of states over time. The states represent genotype, phenotype or ecological process. (b) The frequency distribution curve of phenotypes at t = 10, (c) The frequency distribution curve of phenotypes at t = 600. From the perspective of phenotype, the distribution curve changes from unimodal in the early phase to bimodal at t = 600, which means the phenotype differentiates into two phenotypes (25 and 28) at t = 600 from one phenotype (50) in the initial stage. Then we can judge if the species with phenotype 25 and 28 are different species.

图5 不同时刻下表型和基因型的频率分布。(a)表示状态量x1(x2)未分化初期某时刻的频率分布; (b)表示群体内的表型x1在分化之后某时刻的频率分布; (c)表示群体内的基因型x2在分化之后相同时刻的频率分布。假设对于原始物种A, 其任意在两个状态x1和x2随着时间的演化受到基因突变和随机漂变的影响, 在相同或不同时刻出现不同程度的分化。当我们处于物种进化的一个“切面”去观察时, 表型x1分化成x11和x12, 并且进化依赖于特定的路径。若此时分化出的表型和基因型在数量统计上满足一定的条件, 同时在表型和基因型两个状态下同时具有特征x11, x21(x11, x22或x12, x21或x12, x22)的个体为新物种。

Fig. 5 Frequency distribution of phenotypes and genotypes at different time. (a) showing the frequency distribution curve of the state x1(x2) in the early differentiation. (b) demonstrating the frequency distribution curve of the phenotype x1 at a certain moment after differentiation. (c) indicating the frequency distribution curve of the genotype x2 at the same moment after differentiation. Suppose that any two states x1 and x2 of the original species A evolved influenced by random mutation and drift, then different degree of differentiation occurs in the same or different time. When observing in a “cutting plane” of a species evolution, we notice that x1(x2) differentiates into x11(x21) and x12(x22), and the evolution are path-dependent. Meanwhile, if the differentiated phenotypes and the genotypes in a quantity statistics satisfy certain conditions, the individuals with ${{x}_{11}},{{x}_{21}}({{x}_{11}},{{x}_{22}},or{{x}_{12}},{{x}_{21}},or{{x}_{12}},{{x}_{22}})$ are new species, respectively.

图6 随时间演替的物种界定示意图。状态量x1 (x2)在t1(t2)时刻出现分化, 在不同的时间点上根据分化情况判定物种是否属于新物种。

Fig. 6 schematic diagram of the species delimitation over time. The state x1 (x2) differentiates at t1(t2). It can be determined whether a specie at different moments is a new species.

图7 一表型在某一时刻分化出三个独立表型的示意图。该图作为判定表型分化成功的一个特例, 此时种内均值为?1的表型存在连续且程度较低的差异(差异范围是± 0.15), 均值为0的亦然。而这两个种间表型的不连续性达到了1, 其不连续差异程度远高于种内连续差异程度, 因此可以认为该表型达到了形态学物种概念中对于形态的要求。同时考虑原始物种的其他状态上的分化, 若满足同样条件的差异, 即可将相应个体确定为新物种。

Fig. 7 Differentiation of three independent phenotypes from one phenotype of a species at a moment. The figure is a special case of judging whether the phenotypic differentiates completely. There is a continuous and a little difference for the phenotype ?1 within the species (the difference range is ± 0.15), and the phenotype 0 versa. The discontinuity of these two interspecies phenotypes is 1, and the discontinuity is much higher than the intraspecies continuous difference. Therefore, it can be considered that the phenotype meets the requirements for phenotype in the concept of morphological species. Taking into account the differentiation of another state of this species, if the difference satisfies the same conditions, the corresponding individuals can be determined as a new species.

图8 不同的表型分化情形。如果已有一个生物学特征满足定义中的差异性关系, 再考虑性状这一特征。图(a)中, $d=|{{x}_{1}}-{{x}_{2}}|=|(-6)-6|=12,{{\sigma }_{1}}=3,{{\sigma }_{2}}=3.5,d>{{\sigma }_{1}}$且$d>{{\sigma }_{\mathbf{2}}}$, 若有表型分化满足此条件, 则对应个体属于不同物种; 图(b)中, $d=|{{x}_{1}}-{{x}_{2}}|=|(-2)-2|=4,{{\sigma }_{1}}=4,{{\sigma }_{2}}=3.5,d={{\sigma }_{1}}$且$d>{{\sigma }_{\mathbf{2}}}$, 若有表型分化满足此条件, 则对应个体属于同一物种; 图(c)中,$d=|{{x}_{1}}-{{x}_{2}}|=|(-2)-2|=4,{{\sigma }_{1}}=8.1,\ {{\sigma }_{2}}=8.2,$ $d<{{\sigma }_{1}}$且$d<{{\sigma }_{2}}$, 若有表型分化满足此条件, 则对应个体属于同一物种。

Fig. 8 Different case of phenotype differentiation. Imagine the relation of difference has been satisfied for one biological character. Then we consider phenotypes. In figure 8(a), $d=|{{x}_{1}}-{{x}_{2}}|=|(-6)-6|=12,{{\sigma }_{1}}=3,{{\sigma }_{2}}=3.5,d>{{\sigma }_{1}}$ and $d>{{\sigma }_{2}}$. If individuals in two populations satisfy these conditions, they are different species. In figure 8(b), $d=|{{x}_{1}}-{{x}_{2}}|=|(-2)-2|=4,{{\sigma }_{1}}=4,{{\sigma }_{2}}=3.5,d={{\sigma }_{1}}$ and $d>{{\sigma }_{2}}$. If those individuals satisfy these conditions, they are the same species. In figure 8(c), $d=|{{x}_{1}}-{{x}_{2}}|=|(-2)-2|=4,{{\sigma }_{1}}=8.1,{{\sigma }_{2}}=8.2,d<{{\sigma }_{1}}$ and $d<{{\sigma }_{2}}$. If those individuals satisfy these conditions, they are the same species.