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Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group selection methods. In this article, we give a selective review of group selection concerning methodological developments, theoretical properties and computational algorithms. We pay particular attention to group selection methods involving concave penalties. We address both group selection and bi-level selection methods. We describe several applications of these methods in nonparametric additive models, semiparametric regression, seemingly unrelated regressions, genomic data analysis and genome wide association studies. We also highlight some issues that require further study.

Humans often behave altruistically towards strangers with no chance of reciprocation. From an evolutionary perspective, this is puzzling. The evolution of altruistic cooperative behavior—in which an organism’s action reduces its fitness and increases the fitness of another organism (e.g. by sharing food)—only makes sense when it is directed at genetically related organisms (kin selection) or when one can expect the favor to be returned (reciprocal altruism). Therefore, evolutionary theorists such as Sober and Wilson have argued that we should revise Neo-Darwininian evolutionary theory. They argue that human altruism evolved through group selection in which groups of altruists were naturally selected because they had a comparative advantage over other groups. Wilson and Sober’s hypothesis attracted followers but is rejected by most of their peers. The heated debate between advocates and critics of group selection often suffers from a lack of conceptual clarity. In response, I set out to clearly distinguish ‘genetic’ from ‘cultural’ group selection (developed by Boyd, Richerson & Henrich) and argue that the latter does not face the potentially debilitating problems plaguing the former. I defend the claim that human altruistic dispositions evolved through cultural group selection and gene-culture coevolution and offer empirical evidence in support. I also argue that actual altruistic behavior often goes beyond the kind of behavior humans have evolved to display. Conscious and voluntary reasoning processes, I show, have an important role in altruistic behavior. This is often overlooked in the scientific literature on human altruism.

The emergence of multicellularity is one of the major transitions in evolution that happened multiple times independently. During aggregative multicellularity, genetically potentially unrelated lineages cooperate to form transient multicellular groups. Unlike clonal multicellularity, aggregative multicellular organisms do not rely on kin selection instead other mechanisms maintain cooperation against cheater phenotypes that benefit from cooperators but do not contribute to groups. Spatiality with limited diffusion can facilitate group selection, as interactions among individuals are restricted to local neighbourhoods only. Selection for larger size (e.g. avoiding predation) may facilitate the emergence of aggregation, though it is unknown, whether and how much role such selection played during the evolution of aggregative multicellularity. We have investigated the effect of spatiality and the necessity of predation on the stability of aggregative multicellularity via individual-based modelling on the ecological timescale. We have examined whether aggregation facilitates the survival of cooperators in a temporally heterogeneous environment against cheaters, where only a subset of the population is allowed to periodically colonize a new, resource-rich habitat. Cooperators constitutively produce adhesive molecules to promote aggregation and propagule-formation while cheaters spare this expense to grow faster but cannot aggregate on their own, hence depending on cooperators for long-term survival. We have compared different population-level reproduction modes with and without individual selection (predation) to evaluate the different hypotheses. In a temporally homogeneous environment without propagule-based colonization, cheaters always win. Predation can benefit cooperators, but it is not enough to maintain the necessary cooperator amount in successive dispersals, either randomly or by fragmentation. Aggregation-based propagation however can ensure the adequate ratio of cooperators-to-cheaters in the propagule and is sufficient to do so even without predation. Spatiality combined with temporal heterogeneity helps cooperators via group selection, thus facilitating aggregative multicellularity. External stress selecting for larger size (e.g. predation) may facilitate aggregation, however, according to our results, it is neither necessary nor sufficient for aggregative multicellularity to be maintained when there is effective group-selection.

When Hamilton defined the concept of inclusive fitness, he specifically was looking to define the fitness of an individual in terms of that individual's behavior, and the effects of its' behavior on other related individuals. Although an intuitively attractive concept, issues of accounting for fitness, and correctly assigning it to the appropriate individual make this approach difficult to implement. The direct fitness approach has been suggested as a means of modeling kin selection while avoiding these issues. Whereas Hamilton's inclusive fitness approach assigns to the focal individual the fitness effects of its behavior on other related individuals, the direct fitness approach assigns the fitness effects of other actors to the focal individual. Contextual analysis was independently developed as a quantitative genetic approach for measuring multilevel selection in natural populations. Although the direct fitness approach and contextual analysis come from very different traditions, both methods rely on the same underlying equation, with the primary difference between the two approaches being that the direct fitness approach uses fitness optimization modeling, whereas with contextual analysis, the same equation is used to solve for the change in fitness associated with a change in phenotype when the population is away from the optimal phenotype.

An experiment was conducted comparing multilevel selection in Japanese quail for 43 days weight and survival with birds housed in either kin (K) or random (R) groups. Multilevel selection significantly reduced mortality (6.6% K vs. 8.5% R) and increased weight (1.30 g/MG K vs. 0.13 g/MG R) resulting in response an order of magnitude greater with Kin than Random. Thus, multilevel selection was effective in reducing detrimental social interactions, which contributed to improved weight gain. The observed rates of response did not differ significantly from expected, demonstrating that current theory is adequate to explain multilevel selection response. Based on estimated genetic parameters, group selection would always be superior to any other combination of multilevel selection. Further, near optimal results could be attained using multilevel selection if 20% of the weight was on the group component regardless of group composition. Thus, in nature the conditions for multilevel selection to be effective in bringing about social change maybe common. In terms of a sustainability of breeding programs, multilevel selection is easy to implement and is expected to give near optimal responses with reduced rates of inbreeding as compared to group selection, the only requirement is that animals be housed in kin groups.

Declines in populations of birds that breed in disturbance-dependent early-successional forest have largely been ascribed to habitat loss. Clearcutting is an efficient and effective means for creating early-successional vegetation; however, negative public perceptions of clearcutting and the small parcel size typical of private forested land in much of the eastern United States make this practice impractical in many situations. Group selection harvests, where groups of adjacent trees are removed from a mature forest matrix, may be more acceptable to the public and could provide habitat for shrubland birds. Although some shrubland bird species that occupy clearcuts are scarce or absent from smaller patches created by group selection, some of these smaller patches support shrubland species of conservation concern. The specific factors affecting shrubland bird occupancy of these smaller patches, such as habitat structure, patch area, and landscape context, are poorly understood. We sampled birds in forest openings ranging 0.02–1.29 ha to identify species-specific minimum-area habitat requirements and other factors affecting shrubland birds. We modeled bird occurrence in relation to microhabitat-, patch-, and landscape-level variables using occupancy models. The minimum-area requirements for black-and-white warblers (Mniotilta varia), common yellowthroats (Geothlypis trichas), chestnut-sided warblers (Setophaga pensylvanica), eastern towhees (Pipilo erythrophthalmus), and gray catbirds (Dumetella carolinensis) were ≤0.23 ha, whereas indigo buntings (Passerina cyanea) and prairie warblers (S. discolor) required openings of 0.56 ha and 1.11 ha, respectively. Notably, prairie warblers were more likely to occur in openings closer to large patches of habitat such as powerline corridors, even if those openings were small in size. We concluded that, despite their inability to support the entire suite of shrubland species, small forest openings can provide habitat for several species of conservation concern if proper attention is given to promoting suitable microhabitat, patch, and landscape characteristics.

Organisms from prokaryotes to plants and animals make costly investments in diffusible beneficial external products. While the costs of producing such products are born only by the producer, the benefits may be distributed more widely. How are external goods-producing populations stabilized against invasion by nonproducing variants that receive the benefits without paying the cost? This question parallels the classic question of altruism, but because external goods production need not be altruistic per se, a broader range of conditions may lead to the maintenance of these traits. We start from the physics of diffusion to develop an expression for the conditions that favor the production of diffusible external goods. Important variables in determining the evolutionary outcome include the diffusion coefficient of the good, the distance between individuals, and the uptake rate of the external good. These variables join the coefficient of relatedness and the cost/benefit ratio in an expanded form of Hamilton's rule that includes both selfish and altruistic paths to the evolution of external goods strategies. This expanded framework can be applied to any external goods trait, and is a useful heuristic even when it is difficult to quantify the fitness consequences of producing the good.

Morality can be adaptive or maladaptive. From this fact come polarizing disputes on the meta-ethical status of moral adaptation. The realist tracking account of morality claims that it is possible to track objective moral truths and that these truths correspond to moral rules that are adaptive. In contrast, evolutionary anti-realism rejects the existence of moral objectivity and thus asserts that adaptive moral rules cannot represent objective moral truths, since those truths do not exist. This article develops a novel evolutionary view of natural law to defend the realist tracking account. It argues that we can identify objective moral truths through cultural group selection and that adaptive moral rules are likely to reflect such truths.

Humans regularly help strangers, even when interactions are apparently unobserved and unlikely to be repeated. Such situations have been simulated in the laboratory using anonymous one-shot games (e.g., prisoner's dilemma) where the payoff matrices used make helping biologically altruistic. As in real-life, participants often cooperate in the lab in these one-shot games with non-relatives, despite that fact that helping is under negative selection under these circumstances. Two broad explanations for such behavior prevail. The \"big mistake\" or \"mismatch\" theorists argue that behavior is constrained by psychological mechanisms that evolved predominantly in the context of repeated interactions with known individuals. In contrast, the cultural group selection theorists posit that humans have been selected to cooperate in anonymous one-shot interactions due to strong between-group competition, which creates interdependence among in-group members. We present these two hypotheses before discussing alternative routes by which humans could increase their direct fitness by cooperating with strangers under natural conditions. In doing so, we explain why the standard lab games do not capture real-life in various important aspects. First, asymmetries in the cost of perceptual errors regarding the context of the interaction (one-shot vs. repeated; anonymous vs. public) might have selected for strategies that minimize the chance of making costly behavioral errors. Second, helping strangers might be a successful strategy for identifying other cooperative individuals in the population, where partner choice can turn strangers into interaction partners. Third, in contrast to the assumptions of the prisoner's dilemma model, it is possible that benefits of cooperation follow a non-linear function of investment. Non-linear benefits result in negative frequency dependence even in one-shot games. Finally, in many real-world situations individuals are able to parcel investments such that a one-shot interaction is turned into a repeated game of many decisions.