photo: what-when-how.com

標題：The effect of dominance on polymorphism in Müllerian mimicry

摘要

Dominance controls the phenotype of heterozygous individuals, and plays an important role in the maintenance of polymorphism. Here we focus on the dominance acting on warning-pattern polymorphism in species engaged in Müllerian mimicry. Müllerian mimics are toxic species which display bright colour patterns used as a warning signal to predators and are subject to local positive density-dependent selection. Some Müllerian mimics are polymorphic due to a selection/migration balance in spatially heterogeneous communities of prey. Since heterozygotes at a locus controlling warning pattern might exhibit intermediate, non-mimetic heterozygous morphs, dominance is likely to influence the polymorphism at this locus. Using a deterministic model describing migration, density-dependent predation and reproduction, we investigated the influence of dominance on the dynamics of alleles at locus determining mimetic phenotype. Our results suggest dominance may interact with migration and selection and plays an important role in shaping the conditions of polymorphism persistence and the frequency of alleles at this locus. Our results thus highlight the important role of dominance in the dynamics of polymorphism at loci under balancing selection due to environmental heterogeneity.

有些穆氏擬態物種多態性的產生與維持，一直是個吸引科學家的問題，雖然已經從很多個方面討論，但總很難有個結論，主要是因為要解釋斑紋的有效性與不同斑紋的族群間的平衡來自多重複雜的因素，並且因素間可能有交互作用，很不容易從一而論，解釋所有的情況。

這個研究的目的是想從遺傳學的角度著手，解釋顯性遺傳在穆氏擬態多態性的維持上的重要性。如果穆氏擬態的多態性來自不同斑紋族群遷徙時的雜交，那麼控制這個斑紋的基因座(locus)的顯隱性必然影響斑紋性狀的表現，當兩個族群雜交時就會出現中間型 (intermediate forms)，又因為只有顯性的斑紋可以表現在斑紋上，演化的歷程中就可能根據這些顯性表型逐漸的影響讓基因頻率轉移，進而產生新的斑紋。

本篇所使用的數學模型的一部分

作者用數學模型討論顯性基因的演化模式，其中考慮物種的遷徙、密度為基礎的被捕食率與生殖等因素探索顯性性狀對於多態性演化產生的影響。經過一堆公式的推導與模擬後，結果顯示遷徙與擇汰對多態型的維持與斑紋基因的頻率扮演重要的角色，這個結果也同時揭示顯性遺傳在多態性的平衡上的重要性。

Fig. 2 假設一個對偶基因ab在不同的狀況下的模擬結果。 灰：多態型維持 白：a被固定 黑：b被固定 A：全隱性 B：部分隱性 C：共顯性 D：全顯性

說實在的，這真是篇讓人看完頭很痛的文章......

photo from The magic of life butterfly house

標題：Molecular mechanisms of dominance evolution in Müllerian mimicry.

摘要

Natural selection acting on dominance between adaptive alleles at polymorphic loci can be sufficiently strong for dominance to evolve. However, the molecular mechanisms underlying such evolution are generally unknown. Here, using Müllerian mimicry as a case-study for adaptive morphological variation, we present a theoretical analysis of the invasion of dominance modifiers altering gene expression through different molecular mechanisms. Toxic species involved in Müllerian mimicry exhibit warning coloration, and converge morphologically with other toxic species of the local community, due to positive frequency-dependent selection acting on these colorations. Polymorphism in warning coloration may be maintained by migration–selection balance with fine scale spatial heterogeneity. We modeled a dominance modifier locus altering the expression of the warning coloration locus, targeting one or several alleles, acting in cis or trans, and either enhancing or repressing expression. We confirmed that dominance could evolve when balanced polymorphism was maintained at the color locus. Dominance evolution could result from modifiers enhancing one allele specifically, irrespective of their linkage with the targeted locus. Nonspecific enhancers could also persist in populations, at frequencies tightly depending on their linkage with the targeted locus. Altogether, our results identify which mechanisms of expression alteration could lead to dominance evolution in polymorphic mimicry.

根據很多對於擬態的觀測與研究結果，無庸置疑的這是一個天擇的結果，但科學家無論如何觀測，從野外的族群到細胞裡的基因體，都只能觀測到這些結果，與推測可能的原因，對於天擇實際上透過什麼樣的「工具」來留下有優勢的斑紋，至今仍然是個很大的謎團。

文章中基礎的方程式(1)與(2)式

這個研究透過數學模型，模擬分子生物學中的調節子 (modifier) 如何作用在控制顏色斑紋的基因上。方程式中假設不同族群的多態型能夠透過族群某種比例的遷徙交換基因，在不同的族群就會產生不同的斑紋，進而模擬天擇是如何透過調節子來留下具有優勢的基因。方程式的展開與建構很複雜就姑且不提，總之是透過考量了優勢參數、突變、毒性程度、族群遷徙、基因重組率與捕食者的認知等等參數建構出的數學模型。結果發現具有優勢的斑紋能夠透過顏色基因的多態型平衡來達成。這個優勢的演化能夠從調節子來增強某個特殊的基因，無論這個基因是否與某個特殊的基因在同一條染色體上。

總之，這篇實在太抽象了，有興趣或有需要的朋友請自行詳細研讀吧。

photo from what-when-how

標題：Costs of Learning and the Evolution of Mimetic Signals.

摘要

Predators must use the appearance of their prey to decide whether it is likely to be defended. Most theory assumes that predators have completed learning about prey appearance, yet we do not understand how predators learn which aspects of appearance to use for classifying prey. If sampling prey can be risky, predators might forgo opportunities to learn about the relationship between prey appearance and defense. Using Bayesian inference and dynamic programming, we modeled how the immediate risks and future rewards of learning about prey appearance influence how predators learn. In addition, we explored how variation in predator learning affects the evolution of mimicry, which occurs when two prey evolve to share a common signal to predators. We found that when learning about prey with distinct appearances was expensive, optimal predators tended to lump them into the same category or exhibit an unwillingness to sample at all (neophobia). This resulted in a reduction in selection for defensive mimicry. However, the same predator behavior favored the evolution of aggressive mimicry, because in that case, mimics benefited from being sampled. When prey were very rare and costs of sampling them were high, predators exhibited neophobia, refusing to attack. This behavior could forestall the evolution of mimicry and instead select for polymorphism.

捕食者的學習對於警戒性/擬態的演化實在很重要，因為這是最主要的天擇來源，但科學家實在對捕食者的學習模式太不瞭解，主要的癥結點在於不知道捕食者什麼時候吃，什麼時候不吃，要幾次才學的起來，學的多快才能推動這些斑紋的演化，有多少心理學的因子牽涉在裡面，其中一種研究方法就是透過數學模型的模擬，來推估哪些因子可能牽涉其中。

擷取自文中的方程式

捕食者在面對具有警戒性/擬態訊號的獵物時，吃了，可能會拉肚子甚至喪命，不吃，浪費了難得可以得到能量的機會，在這中間捕食者時如何評估獲得(reward)與學習的消耗(cost)，這會如何對獵物產生影響，就是這篇文章所要探討的。作者評估了一些因子，建立了一些模型，跑了一些模擬（過程很複雜也很難，容我跳過），得到的結論是捕食者對於分辨兩個長的很像的東西的代價是非常昂貴的，可以想像一下，捕食者首先要先學到兩種獵物，如果是貝氏擬態，牠要分辨這個物種是不是能吃的那個，如果是穆氏擬態，要學到兩邊都不能吃，更別提如果環境中同時存在兩個系統，光在那邊學半天餓都餓死了。因此模擬出來的結果顯示，捕食者傾向把這類的獵物通通歸類於不能吃的那邊（也就是恐新症，neophobia），這就讓擬態的斑紋有演化的空間了。此外，作者發現侵略性擬態（aggressive mimicry）也有類似的趨勢。

photo from Ecuatoria: Dendrobatids

標題：Number of genes controlling a quantitative trait in a hybrid zone of the aposematic frog Ranitomeya imitator

摘要

The number of genes controlling mimetic traits has been a topic of much research and discussion. In this paper, we examine a mimetic, dendrobatid frog Ranitomeya imitator, which harbours extensive phenotypic variation with multiple mimetic morphs, not unlike the celebrated Heliconius system. However, the genetic basis for this polymorphism is unknown, and not easy to determine using standard experimental approaches, for this hard-to-breed species. To circumvent this problem,we first develop a newprotocol for automatic quantification of complex colour pattern phenotypes from images. Using this method, which has the potential to be applied in many other systems, we define a phenotype associated with differences in colour pattern between different mimetic morphs. We then proceed to develop a maxi- mum-likelihood method for estimating the number of genes affecting a quantitative trait segregating in a hybrid zone. This method takes advantage of estimates of admixture proportions obtained using genetic data, such as microsatellite markers, and is applicable to any other system where a phenotype has been quantified in an admixture/introgression zone. We evaluate the method using extensive simulations and apply it to the R. imitator system. We show that probably one or two, or at most three genes, control the mimetic phenotype segregating in a R. imitator hybrid zone identified using image analyses.

photo from content

photo from content

模擬的結果顯示看起來是兩個，至多三個基因控制這些擬態的斑紋。這個方式有很多好處：

標題：Diversity in Müllerian mimicry: The optimal predator sampling strategy explains both local and regional polymorphism in prey

摘要

The convergent evolution of warning signals in unpalatable species, known as Müllerian mimicry, has been observed in a wide variety of taxonomic groups. This form of mimicry is generally thought to have arisen as a consequence of local frequency-dependent selection imposed by sampling predators. However, despite clear evidence for local selection against rare warning signals, there appears an almost embarrassing amount of polymorphism in natural warning colors, both within and among populations. Because the model of predator cognition widely invoked to explain Mullerian mimicry (Muller’s “fixed nk” model) is highly simplified and has not been empirically supported; here, we explore the dynamical consequences of the optimal strategy for sampling unfamiliar prey. This strategy, based on a classical exploration–exploitation trade-off, not only allows for a variable number of prey sampled, but also accounts for predator neophobia under some conditions. In contrast to Müller’s “fixed nk” sampling rule, the optimal sampling strategy is capable of generating a variety of dynamical outcomes, including mimicry but also regional and local polymorphism. Moreover, the heterogeneity of predator behavior across space and time that a more nuanced foraging strategy allows, can even further facilitate the emergence of both local and regional polymorphism in prey warning color.

在開始前，我們先思考一件事：如果擬態是十分有用的禦敵策略，那麼物種在演化的初期發展出一個紋路後，是否應該其他的物種都加入擴大這個擬態群，讓這個紋路變的廣泛的有用結果大家都長的一樣，更增強這個紋路的作用才對？

但現實中明顯不是這樣，各種不同區域的擬態群各自林立，物種內出現各種不同的多態型，這代表上面那個假設必然出了什麼狀況，才會讓這個假設與實際上差異這麼大。

這篇所使用的方法是大家都頭痛的數理模型，考慮不同的參數後進行模擬，通常這類型的文章考慮的不外乎有幾個因子：防禦/非防禦獵物的比例，捕食者攻擊的頻率，記憶力，一些學習參數等等，而這個研究考量的是「捕食者的最佳取食策略」，也就是透過計算攻擊防禦/非防禦獵物的比率，來達到利益的最大化，然後跟傳統的穆氏擬態的數學模型（捕食者一定要透過攻擊固定數量的獵物才能讓利益最大化）比較。結果顯示這個新的模型比較能夠解釋現實上的狀況，也就是解釋為何擬態中的多態型能夠穩定的存在。捕食者透過挑選防禦/非防禦能讓捕食效益產身變化外，其本身的恐新症（neophobia）在某種情況下也會成為影響挑選獵物的因子之一。

結論上來說，就是用數理的方式告訴大家捕食者如何維持多態型的穩定，不過這個穩定在之前的研究中也有些討論，可能是來自微棲地的分隔所造成。

老話一句，電腦上看起來是這樣，那在自然環境中看起來又是怎樣呢？

原文標題：Disentangling taste and toxicity in aposematic prey

[摘要][原文網址]
Many predators quickly learn to avoid attacking aposematic prey. If the prey vary in toxicity, the predators may alternatively learn to capture and taste-sample prey carefully before ingesting or rejecting them (go-slow behaviour). An increase in prey toxicity is generally thought to decrease predation on prey populations. However, while prey with a higher toxin load are more harmful to ingest, they may also be easier to recognize and reject owing to greater distastefulness, which can facilitate a taste-sampling foraging strategy. Here, the classic diet model is used to study the separate effects of taste and toxicity on predator preferences. The taste-sampling process is modelled using signal detection theory. The model is applicable to automimicry and Batesian mimicry. It shows that when the defensive toxin is sufficiently distasteful, a mimicry complex may be less profitable to the predator and better protected against predation if the models are moderately toxic than if they are highly toxic. Moreover, taste mimicry can reduce the profitability of the mimicry complex and increase protection against predation. The results are discussed in relation to the selection pressures acting on prey defences and the evolution of mimicry.