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第1行： − 此词条暂由彩云小译翻译，翻译字数共1046，未经人工整理和审校，带来阅读不便，请见谅。+ 第23行：
第23行： − + − 双相进化是复杂适应系统中驱动自我组织的一个过程。+ 第31行：
第31行： − Social networks provide a familiar example. In a social network the nodes of the network are people and the network connections (edges) are relationships or interactions between people. For any individual, social activity alternates between a local phase, in which they interact only with people they already know, and a global phase in which they can interact with a wide pool of people not previously known to them. Historically, these phases have been forced on people by constraints of time and space. People spend most of their time in a local phase and interact only with those immediately around them (family, neighbors, colleagues). However, intermittent activities such as parties, holidays, and conferences involve a shift into a global phase where they can interact with different people they do not know. Different processes dominate each phase. Essentially, people make new social links when in the global phase, and refine or break them (by ceasing contact) while in the local phase.+ − 社交网络提供了一个熟悉的例子。在社会网络中，网络的节点是人，网络连接(边缘)是人与人之间的关系或互动。对于任何个人来说，社会活动在一个局部阶段和一个全球阶段之间交替进行，前者只与他们已经认识的人进行互动，后者则是他们可以与他们以前不认识的大量人进行互动。从历史上看，这些阶段是由于时间和空间的限制而强加给人们的。人们把大部分时间花在一个局部的阶段，只与周围的人(家人、邻居、同事)互动。然而，间歇性的活动，如聚会、假期和会议，涉及到一个转变到全球阶段，在那里他们可以与不同的人互动，他们不知道。不同的过程控制着每个阶段。本质上，人们在全球阶段建立新的社会联系，在局部阶段(通过停止联系)优化或破坏这些联系。+ − | author2 = Liu, J. + − | author3-link = Hussein Abbass + + + + + − The following features are necessary for DPE to occur.+ − 发生 DPE 需要以下特性。+ + + + + − − DPE occurs where a system has an underlying network. That is, the system's components form a set of nodes and there are connections (edges) that join them. For example, a family tree is a network in which the nodes are people (with names) and the edges are relationships such as "mother of" or "married to". The nodes in the network can take physical form, such as atoms held together by atomic forces, or they may be dynamic states or conditions, such as positions on a chess board with moves by the players defining the edges. − − DPE 发生在系统具有底层网络的地方。也就是说，系统的组件形成一组节点，并且有连接它们的连接(边)。例如，家谱是一个网络，其中的节点是人(有名字) ，边是关系，如“母亲”或“已婚”。网络中的节点可以采取物理形式，比如由原子力连接在一起的原子，或者它们可以是动态状态或条件，比如棋盘上的位置，由定义边缘的棋手走棋。 第63行：
第67行： − + − 在数学术语(图论)中，图形 < math > 文本样式 g = langle n，e rangle </math > 是一组节点 < math > 文本样式 n </math > 和一组边 < math > 文本样式 e {(x，y) mid x，y In n } </math > 。每个边 < math > textstyle (x，y) </math > 提供了一对节点 < math > textstyle x </math > 和 < math > textstyle y </math > 之间的链接。网络是一个图，其中的值分配给节点和/或边。+ 第75行：
第79行： − Graphs and networks have two phases: disconnected (fragmented) and connected. In the connected phase every node is connected by an edge to at least one other node and for any pair of nodes, there is at least one path (sequence of edges) joining them.+ − 图和网络有两个阶段: 不连接(支离破碎)和连接。在连接阶段，每个节点通过边连接到至少一个其他节点，对于任意一对节点，至少有一条路径(边序列)连接它们。+ 第83行：
第87行： − The Erdős–Rényi model shows that random graphs undergo a connectivity avalanche as the density of edges in a graph increases. In a local phase, the nodes behave as individuals; in the global phase, nodes are affected by interactions with other nodes. Most commonly the two processes at work can be interpreted as variation and selection. Variation refers to new features, which typically appear in one of the two phases. These features may be new nodes, new edges, or new properties of the nodes or edges. Selection here refers to ways in which the features are modified, refined, selected or removed. A simple example would be new edges being added at random in the global phase and edges being selectively removed in the local phase. − Erd s-Rényi 模型表明，随机图的边密度增加，图的连通度发生雪崩。在局部阶段，节点表现为个体; 在全局阶段，节点受到与其他节点交互的影响。最常见的两个过程在工作中可以解释为变异和选择。变异指的是新的特征，通常出现在两个阶段之一。这些特征可能是新的节点，新的边，或新的性质的节点或边。这里的选择指的是修改、细化、选择或删除特性的方法。一个简单的例子是在全局相位中随机添加新边，在局部相位中有选择地去除边。 + + − Social networks provide a familiar example. In a [[social network]] the nodes of the network are people and the network connections (edges) are relationships or interactions between people. For any individual, social activity alternates between a ''local phase'', in which they interact only with people they already know, and a ''global phase'' in which they can interact with a wide pool of people not previously known to them. Historically, these phases have been forced on people by constraints of time and space. People spend most of their time in a local phase and interact only with those immediately around them (family, neighbors, colleagues). However, intermittent activities such as parties, holidays, and conferences involve a shift into a global phase where they can interact with different people they do not know. Different processes dominate each phase. Essentially, people make new social links when in the global phase, and refine or break them (by ceasing contact) while in the local phase.+ 第95行：
第99行： − The effects of changes in one phase carry over into the other phase. This means that the processes acting in each phase can modify or refine patterns formed in the other phase. For instance, in a social network, if a person makes new acquaintances during a global phase, then some of these new social connections might survive into the local phase to become long-term friends. In this way, DPE can create effects that may be impossible if both processes act at the same time.+ − 一个阶段的变化的影响会传递到另一个阶段。这意味着在每个阶段中作用的过程可以修改或细化在另一个阶段中形成的模式。例如，在一个社交网络中，如果一个人在一个全球阶段结识了新朋友，那么这些新的社交关系中的一部分可能会在当地阶段存活下来，成为长期的朋友。通过这种方式，DPE 可以创建如果两个进程同时工作可能不可能的效果。+ 第107行：
第111行： − DPE has been found to occur in many natural and artificial systems.+ − DPE 已被发现存在于许多自然和人工系统中。+ − − Small world networks, which are common in traditional societies, are a natural consequence of alternating local and global phases: new, long-distance links are formed during the global phase and existing links are reinforced (or removed) during the local phase. The advent of social media has decreased the constraining influence that space used to impose on social communication, so time has become the chief constraint for many people. − − 在传统社会中常见的小世界网络是地方和全球阶段交替的自然结果: 在全球阶段形成新的长途联系，在地方阶段加强(或删除)现有联系。社会媒体的出现减少了空间对社会交流的限制，因此时间成为许多人的主要限制。 + + − The alternation between local and global phases in social networks occurs in many different guises. Some transitions between phases occur regularly, such as the daily cycle of people moving between home and work. This alternation can influence shifts in public opinion. Major fires (or other disturbances) clear away large tracts of land, so the network of free sites becomes connected and the landscape enters a global phase. In the global phase, competition for free sites is reduced, so the main competitive advantage is adaptation to the environment. − 社会网络中局部和全局阶段之间的交替以许多不同的形式出现。有些阶段之间的转换是有规律的，例如人们每天在家和工作之间来回移动。这种变化会影响公众舆论的转变。大型火灾(或其他干扰)清除了大片土地，因此自由场地网络连接起来，景观进入全球阶段。在全球化阶段，免费网站的竞争减少，因此主要的竞争优势是适应环境。 第129行：
第129行： − Most of the time a forest is in the local phase, as described above. The net effect is that established tree populations largely exclude invading species. A simple example is the Great Deluge algorithm in which the searcher can move at random across the landscape, but cannot enter low-lying areas that are flooded. At first the searcher can wander freely, but rising water levels eventually confine the search to a local area. Many other nature-inspired algorithms adopt similar approaches. Simulated annealing achieves a transition between phases via its cooling schedule. The cellular genetic algorithm places solutions in a pseudo landscape in which they breed only with local neighbours. Intermittent disasters clear patches, flipping the system into a global phase until gaps are filled again.+ − 大多数时候，森林都处于局部阶段，如上所述。净效应是，已建立的树种群基本上排除了入侵物种。一个简单的例子是大洪水算法，在这种算法中，搜索者可以在地形上随机移动，但不能进入被淹没的低洼地区。起初，搜寻者可以自由漫步，但不断上升的水位最终将搜寻限制在局部地区。许多其他受自然启发的算法也采用了类似的方法。模拟退火通过其冷却时间表实现了两阶段之间的转换。细胞遗传算法将解决方案放置在一个只与当地邻居交配的伪景观中。断断续续的灾难清除了一小块一小块，将整个系统翻转到一个全球阶段，直到空隙再次被填满。+ − === Phase shifts ===+ − Some variations on the memetic algorithm involve alternating between selection at different levels. These are related to the Baldwin effect, which arises when processes acting on phenotypes (e.g. learning) influence selection at the level of genotypes. In this sense, the Baldwin effect alternates between global search (genotypes) and local search (phenotypes).+ − 模因算法的一些变化涉及不同层次的选择之间的交替。这些都与鲍德温效应有关，鲍德温效应是在表型作用过程中产生的。学习)影响基因型水平的选择。在这个意义上，Baldwin 效应在全局搜索(基因型)和局部搜索(表型)之间交替。+ − Graphs and networks have two phases: disconnected (fragmented) and connected. In the connected phase every node is connected by an edge to at least one other node and for any pair of nodes, there is at least one path (sequence of edges) joining them.+ + + + + − Dual phase evolution is related to the well-known phenomenon of self-organized criticality (SOC). Both concern processes in which critical phase changes promote adaptation and organization within a system. However, SOC differs from DPE in several fundamental ways. Under SOC, a system's natural condition is to be in a critical state; in DPE a system's natural condition is a non-critical state. In SOC the size of disturbances follows a power law; in DPE disturbances are not necessarily distributed the same way. In SOC a system is not necessarily subject to other processes; in DPE different processes (e.g. selection and variation) operate in the two phases.+ − 双相进化与众所周知的自组织临界性现象有关。两者都涉及关键阶段变化促进系统内部适应和组织的过程。然而，SOC 与 DPE 在几个基本方面有所不同。在 SOC 中，系统的自然状态是临界状态，在 DPE 中，系统的自然状态是非临界状态。在 SOC 中，扰动的大小遵循幂律，而在 DPE 中，扰动不一定按相同的方式分布。在 SOC 中，一个系统不一定受制于其他过程; 在 DPE 中，不同的过程(例如:。选择和变异)分两个阶段进行。+ − | author = Erdős, P.+ 第162行：
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Moved page from wikipedia:en:Dual-phase evolution (history)
此词条暂由彩云小译翻译，翻译字数共1029，未经人工整理和审校，带来阅读不便，请见谅。
{{short description|A process that drives self-organization within complex adaptive systems}}
{{short description|A process that drives self-organization within complex adaptive systems}}
'''Dual phase evolution''' ('''DPE''') is a process that drives [[self-organization]] within [[complex adaptive system]]s.<ref name="DPE2">
'''Dual phase evolution''' ('''DPE''') is a process that drives [[self-organization]] within [[complex adaptive system]]s.<ref name="DPE2">
Dual phase evolution (DPE) is a process that drives self-organization within complex adaptive systems.
Dual phase evolution (DPE) is a process that drives self-organization within complex adaptive systems. It arises in response to phase changes within the network of connections formed by a system's components. DPE occurs in a wide range of physical, biological and social systems. Its applications to technology include methods for manufacturing novel materials and algorithms to solve complex problems in computation.
在复杂适应系统中，双相进化是一个驱动自我组织进化的过程。它产生于对系统组件形成的连接网络中的相位变化的响应。DPE 广泛存在于物理、生物和社会系统中。它在技术上的应用包括制造新材料的方法和解决复杂计算问题的算法。
{{cite book
{{cite book
| author = Green, D.G.
| author = Green, D.G.
| author2 = Liu, J.
| author3-link = Hussein Abbass
Dual phase evolution (DPE) is a process that promotes the emergence of large-scale order in complex systems. It occurs when a system repeatedly switches between various kinds of phases, and in each phase different processes act on the components or connections in the system. DPE arises because of a property of graphs and networks: the connectivity avalanche that occurs in graphs as the number of edges increases. This avalanche amounts to a sudden phase change in the size of the largest connected subgraph. In effect, a graph has two phases: connected (most nodes are linked by pathways of interaction) and fragmented (nodes are either isolated or form small subgraphs). These are often referred to as global and local phases, respectively.
双相演化(DPE)是复杂系统中促进大规模有序出现的过程。当一个系统在不同的相位之间反复切换，并且在每个相位中不同的过程作用于系统中的组件或连接时，就会发生这种情况。DPE 的出现是因为图和网络的一个性质: 连通雪崩发生在图的边的数量增加。这种雪崩相当于最大连通子图大小的突然相变。实际上，一个图有两个阶段: 连接(大多数节点通过交互路径连接)和支离破碎(节点要么是孤立的，要么形成小的子图)。这些阶段通常分别称为全局和局部阶段。
| author3 = Abbass, H.
| author3 = Abbass, H.
Fragmented graph.
零碎的图表。
| name-list-style = amp
| name-list-style = amp
Connected graph.
连通图。
| year = 2014
| year = 2014
| title = Dual Phase Evolution: from Theory to Practice
| title = Dual Phase Evolution: from Theory to Practice
An essential feature of DPE is that the system undergoes repeated shifts between the two phases. In many cases, one phase is the system's normal state and it remains in that phase until shocked into the alternate phase by a disturbance, which may be external in origin.
DPE 的一个基本特征是系统在两个阶段之间进行重复的转换。在许多情况下，一个阶段是系统的正常状态，它保持在该阶段，直到受到一种可能来自外部的扰动而进入交替阶段。
| publisher = Springer
| publisher = Springer
| location = Berlin
| location = Berlin
| isbn = 978-1441984227
| isbn = 978-1441984227
| author2-link = Liu Jing (programmer)
| author2-link = Liu Jing (programmer)
In mathematical terms (graph theory), a graph <math>\textstyle G = \langle N,E\rangle</math> is a set of nodes <math>\textstyle N</math> and a set of edges <math>\textstyle E \subset \{ (x,y) \mid x,y \in N \}</math>. Each edge <math>\textstyle (x,y )</math> provides a link between a pair of nodes <math>\textstyle x</math> and <math>\textstyle y</math>. A network is a graph in which values are assigned to the nodes and/or edges.
In each of the two phases, the network is dominated by different processes.
在这两个阶段中的每一个阶段，网络都由不同的进程控制。
| author-link = David G. Green
| author-link = David G. Green
== Introduction ==
== Introduction ==
DPE is capable of producing social networks with known topologies, notably small-world networks and scale-free networks. In the absence of social interaction, the uptake of an opinion promoted by media is a Markov process. The effect of social interaction under DPE is to retard the initial uptake until the number converted reaches a critical point, after which uptake accelerates rapidly.
DPE 能够生成具有已知拓扑结构的社会网络，特别是小世界网络和无标度网络。在缺乏社会互动的情况下，媒体宣传的观点的理解是一个马尔可夫过程。DPE 下的社会相互作用的效果是延缓初始吸收，直到转化数量达到临界点，之后吸收迅速加速。
Dual phase evolution (DPE) is a process that promotes the emergence of large-scale order in [[complex systems]]. It occurs when a system repeatedly switches between various kinds of phases, and in each phase different processes act on the components or connections in the system. DPE arises because of a property of [[Graph theory|graphs]] and [[Network theory|networks]]: the connectivity avalanche that occurs in graphs as the number of edges increases.<ref name=Erdos1960 />
Dual phase evolution (DPE) is a process that promotes the emergence of large-scale order in [[complex systems]]. It occurs when a system repeatedly switches between various kinds of phases, and in each phase different processes act on the components or connections in the system. DPE arises because of a property of [[Graph theory|graphs]] and [[Network theory|networks]]: the connectivity avalanche that occurs in graphs as the number of edges increases.<ref name=Erdos1960 />
Social networks provide a familiar example. In a [[social network]] the nodes of the network are people and the network connections (edges) are relationships or interactions between people. For any individual, social activity alternates between a ''local phase'', in which they interact only with people they already know, and a ''global phase'' in which they can interact with a wide pool of people not previously known to them. Historically, these phases have been forced on people by constraints of time and space. People spend most of their time in a local phase and interact only with those immediately around them (family, neighbors, colleagues). However, intermittent activities such as parties, holidays, and conferences involve a shift into a global phase where they can interact with different people they do not know. Different processes dominate each phase. Essentially, people make new social links when in the global phase, and refine or break them (by ceasing contact) while in the local phase.
DPE models of socio-economics interpret the economy as networks of economic agents. Several studies have examined the way socioeconomics evolve when DPE acts on different parts of the network. One model interpreted society as a network of occupations with inhabitants matched to those occupations. In this model social dynamics become a process of DPE within the network, with regular transitions between a development phase, during which the network settles into an equilibrium state, and a mutating phase, during which the network is transformed in random ways by the creation of new occupations.
社会经济学的 DPE 模型将经济解释为经济主体的网络。一些研究已经检查了当 DPE 作用于网络的不同部分时，社会经济学的发展方式。一种模式将社会解释为一个有居民从事与这些职业相匹配的职业网络。在这个模型中，社会动力学成为网络内部的 DPE 过程，在发展阶段和变异阶段之间有规律地转换，在这个阶段中，网络进入一个平衡状态，在这个阶段中，网络通过创造新的职业以随机的方式进行转换。
== The DPE mechanism ==
== The DPE mechanism ==
Another model interpreted growth and decline in socioeconomic activity as a conflict between cooperators and defectors. The cooperators form networks that lead to prosperity. However, the network is unstable and invasions by defectors intermittently fragment the network, reducing prosperity, until invasions of new cooperators rebuild networks again. Thus prosperity is seen as a dual phase process of alternating highly prosperous, connected phases and unprosperous, fragmented phases.
另一个模型将社会经济活动的增长和减少解释为合作者和背叛者之间的冲突。合作者形成了通向繁荣的网络。然而，网络是不稳定的，叛逃者的入侵断断续续地破坏了网络，减少了繁荣，直到新的合作者再次入侵重建网络。因此，繁荣被视为一个高度繁荣、相互关联的阶段与不繁荣、分裂的阶段相互交替的双重阶段过程。
=== Underlying network ===
=== Underlying network ===
In a forest, the landscape can be regarded as a network of sites where trees might grow. Some sites are occupied by living trees; others sites are empty. In the local phase, sites free of trees are few and they are surrounded by forest, so the network of free sites is fragmented. In competition for these free sites, local seed sources have a massive advantage, and seeds from distant trees are virtually excluded. Even if a few isolated trees do find free ground, their population is prevented from expanding by established populations, even if the invaders are better adapted to the local environment. A fire in such conditions leads to an explosion of the invading population, and possibly to a sudden change in the character of the entire forest.
在森林中，景观可以被看作是树木可能生长的地点网络。有些地方被活树占据，有些地方则是空的。在局部阶段，没有树木的地点很少，而且被森林包围，所以免费地点的网络是支离破碎的。在争夺这些免费种植地的竞争中，当地的种子资源有着巨大的优势，而来自远方树木的种子几乎被排除在外。即使一些孤立的树木找到了自由的土地，它们的种群数量也会被已有的种群所阻止，即使这些入侵者更好地适应了当地的环境。在这种情况下，一场火灾会导致入侵种群的爆发，并可能导致整个森林特征的突然改变。
DPE occurs where a system has an underlying network. That is, the system's components form a set of nodes and there are connections (edges) that join them. For example, a family tree is a network in which the nodes are people (with names) and the edges are relationships such as "mother of" or "married to". The nodes in the network can take physical form, such as atoms held together by atomic forces, or they may be dynamic states or conditions, such as positions on a chess board with moves by the players defining the edges.
DPE occurs where a system has an underlying network. That is, the system's components form a set of nodes and there are connections (edges) that join them. For example, a family tree is a network in which the nodes are people (with names) and the edges are relationships such as "mother of" or "married to". The nodes in the network can take physical form, such as atoms held together by atomic forces, or they may be dynamic states or conditions, such as positions on a chess board with moves by the players defining the edges.
This dual phase process in the landscape explains the consist appearance of pollen zones in the postglacial forest history of North America, Europe, as well as the suppression of widespread taxa, such as beech and hemlock, followed by huge population explosions. Similar patterns, pollen zones truncated by fire-induced boundaries, have been recorded in most parts of the world
这种景观中的双重阶段过程解释了北美、欧洲冰后森林历史中花粉带的出现，以及广泛分布类群的抑制，如山毛榉和铁杉，随之而来的大规模种群爆发。世界上大部分地区都有类似的花粉带被火灾引起的边界所截断的记录
In mathematical terms ([[graph theory]]), a graph <math>\textstyle G = \langle N,E\rangle</math> is a set of nodes <math>\textstyle N</math> and a set of edges <math>\textstyle E \subset \{ (x,y) \mid x,y \in N \}</math>. Each edge <math>\textstyle (x,y )</math> provides a link between a pair of nodes <math>\textstyle x</math> and <math>\textstyle y</math>. A network is a graph in which values are assigned to the nodes and/or edges.
In mathematical terms ([[graph theory]]), a graph <math>\textstyle G = \langle N,E\rangle</math> is a set of nodes <math>\textstyle N</math> and a set of edges <math>\textstyle E \subset \{ (x,y) \mid x,y \in N \}</math>. Each edge <math>\textstyle (x,y )</math> provides a link between a pair of nodes <math>\textstyle x</math> and <math>\textstyle y</math>. A network is a graph in which values are assigned to the nodes and/or edges.
=== Phase shifts ===
Dual phase evolution is a family of search algorithms that exploit phase changes in the search space to mediate between local and global search. In this way they control the way algorithms explore a search space, so they can be regarded as a family of metaheuristic methods.
双相进化算法是利用搜索空间中的相位变化，在局部搜索和全局搜索之间进行调节的一类搜索算法。通过这种方式，它们控制算法探索搜索空间的方式，因此它们可以被看作是一族元启发式方法。
Graphs and networks have two phases: disconnected (fragmented) and connected. In the connected phase every node is connected by an edge to at least one other node and for any pair of nodes, there is at least one path (sequence of edges) joining them.
Problems such as optimization can typically be interpreted as finding the tallest peak (optimum) within a search space of possibilities. The task can be approached in two ways: local search (e.g. hill climbing) involves tracing a path from point to point, and always moving "uphill". Global search involves sampling at wide-ranging points in the search space to find high points.
诸如优化之类的问题通常可以解释为在可能的搜索空间中找到最高的峰(最优)。这个任务可以通过两种方式来完成: 本地搜索(例如:。爬山)包括沿着一条小路从一个点到另一个点，并且总是“上山”。全局搜索包括在搜索空间中的广泛点上进行抽样，以找到高点。
The [[Erdős–Rényi model]] shows that random graphs undergo a connectivity avalanche as the density of edges in a graph increases.<ref name="Erdos1960">
The [[Erdős–Rényi model]] shows that random graphs undergo a connectivity avalanche as the density of edges in a graph increases.<ref name="Erdos1960">
Many search algorithms involve a transition between phases of global search and local search. A simple example is the Great Deluge algorithm in which the searcher can move at random across the landscape, but cannot enter low-lying areas that are flooded. At first the searcher can wander freely, but rising water levels eventually confine the search to a local area. Many other nature-inspired algorithms adopt similar approaches. Simulated annealing achieves a transition between phases via its cooling schedule. The cellular genetic algorithm places solutions in a pseudo landscape in which they breed only with local neighbours. Intermittent disasters clear patches, flipping the system into a global phase until gaps are filled again.
许多搜索算法涉及到全局搜索和局部搜索阶段之间的过渡。一个简单的例子是大洪水算法，其中搜索者可以随机移动的景观，但不能进入低洼地区是洪水。起初，搜寻者可以自由漫步，但是不断上升的水位最终将搜寻限制在局部地区。许多其他受自然启发的算法也采用了类似的方法。模拟退火通过其冷却时间表实现了两阶段之间的转换。细胞遗传算法将解决方案置于一个伪景观中，在这个伪景观中，解决方案只与当地邻居交配繁殖。断断续续的灾难清除了一小块一小块，将整个系统翻转到一个全球阶段，直到空隙再次被填满。
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{{cite journal
| author = Erdős, P.
Some variations on the memetic algorithm involve alternating between selection at different levels. These are related to the Baldwin effect, which arises when processes acting on phenotypes (e.g. learning) influence selection at the level of genotypes. In this sense, the Baldwin effect alternates between global search (genotypes) and local search (phenotypes).
模因算法的一些变化涉及在不同层次的选择之间的交替。这些都与鲍德温效应有关，这种效应在表型作用过程中出现(例如:。学习)影响基因型水平的选择。在这个意义上，Baldwin 效应在全局搜索(基因型)和局部搜索(表型)之间交替。
| author2 = Rényi, A.
| author2 = Rényi, A.
| title = On the evolution of random graphs
| title = On the evolution of random graphs
Dual phase evolution is related to the well-known phenomenon of self-organized criticality (SOC). Both concern processes in which critical phase changes promote adaptation and organization within a system. However, SOC differs from DPE in several fundamental ways. Under SOC, a system's natural condition is to be in a critical state; in DPE a system's natural condition is a non-critical state. In SOC the size of disturbances follows a power law; in DPE disturbances are not necessarily distributed the same way. In SOC a system is not necessarily subject to other processes; in DPE different processes (e.g. selection and variation) operate in the two phases.
双相进化与众所周知的自组织临界性现象有关。两者都涉及关键阶段变化促进系统内部适应和组织的过程。然而，SOC 与 DPE 在几个基本方面有所不同。在 SOC 下，系统的自然状态是临界状态，在 DPE 中，系统的自然状态是非临界状态。在 SOC 中，扰动的大小遵循幂律，而在 DPE 中，扰动不一定按相同的方式分布。在 SOC 中，一个系统不一定受制于其他过程; 在 DPE 中，不同的过程(例如:。选择和变异)分两个阶段进行。
| journal = Publications of the Mathematical Institute of the Hungarian Academy of Sciences
| volume =5
| pages = 17–61
| url = http://www.renyi.hu/~p_erdos/1960-10.pdf
| author2-link = Alfréd Rényi
Category:Nature-inspired metaheuristics
Category:Nature-inspired metaheuristics