Orthology and paralogy relations are often inferred by methods based on gene similarity, which usually yield a graph depicting the relationships between gene pairs. Such relation graphs are known to frequently contain errors, as they cannot be explained via a gene tree that both contains the depicted orthologs/paralogs, and that is consistent with a species tree $S$. This idea of detecting errors through inconsistency with a species tree has mostly been studied in the presence of speciation and duplication events only. In this work, we ask: could the given set of relations be consistent if we allow lateral gene transfers in the evolutionary model? We formalize this question and provide a variety of algorithmic results regarding the underlying problems. Namely, we show that deciding if a relation graph $R$ is consistent with a given species network $N$ is NP-hard, and that it is W[1]-hard under the parameter "minimum number of transfers". However, we present an FPT algorithm based on the degree of the $DS$-tree associated with $R$. We also study analogous problems in the case that the transfer highways on a species tree are unknown.
翻译:以基因相似性为基础的方法往往可以推断出正方形关系,通常会产生描述基因配对之间关系的图象。这种关系图经常含有错误,因为不能通过既含有所描述的正方形/paralogs的基因树解释,也不符合树种的树种。通过与树种不符来发现错误的想法大多只在有分辨和重复事件的情况下研究过。在这项工作中,我们问:如果我们允许在进化模型中横向基因转移,那么特定的一系列关系能否保持一致?我们正式确定这一问题,并就根本问题提供各种算法结果。也就是说,我们表明,根据参数“最小转移次数”确定,关系图是否与特定物种网络一致,$-R$是硬的,而且W[1]-硬值是硬值。然而,我们根据与美元有关的美元-树种的转移程度,我们提出了一种FPT算法。我们还研究了类似问题,即树种的转移高速公路是未知的。