BioSystems 110 (2012) 156–161 Contents lists available at SciVerse ScienceDirect BioSystems jo urnal homepage: www.elsevier.com/locate/biosystems The significance of sex a,b,c,∗ d Arto Annila , Erkki Annila a Institute of Biotechnology, Viikinkaari 1, FI-00014 University of Helsinki, Finland b Department of Physics, Gustaf Hällströmin katu 2, FI-00014 University of Helsinki, Finland c Department of Biosciences, Viikinkaari 1, FI-00014 University of Helsinki, Finland d Finnish Forest Research Institute, Jokiniemenkuja 1, FI-01301 Vantaa, Finland a r t i c l e i n f o a b s t r a c t Article history: Sexual and asexual modes of proliferation are associated with advantages and disadvantages, yet a pro- Received 25 July 2012 found percept that would account for both ways of reproduction is missing. On the basis of the 2nd law Received in revised form of thermodynamics we find that both sexual and asexual reproduction can be regarded as a means to 14 September 2012 consume free energy in least time. Parthenogenesis is a fast way to consume a rich repository of free Accepted 17 September 2012 energy, e.g., an ample stock of food with a large number of individuals, whereas sexual reproduction is a fast way to consume diverse and dispersed resources with a large variety of individuals. Most organisms Keywords: have adapted to their surroundings accordingly and some organisms switch from one mode of repro- Entropy duction to the other depending on the amount and dispersion of free-energy sources. We conclude that Free energy the least-time free energy consumption in respective surroundings, as the general criterion of natural Natural process Reproduction selection, determines also sexual and asexual modes of reproduction. The principle of least action © 2012 Elsevier Ireland Ltd. All rights reserved. The two-fold cost of sex 1. Introduction of bearing young. Thus, the other sexual partner appears obsolete after mating and even disadvantageous when depleting resources For a long time it has been puzzling why some animals and from its own offspring. Indeed in some spider species females can plants reproduce sexually while others rely on asexual prolifera- kill and eat males after mating. Furthermore, males and females tion. On one hand a genetic recombination event will bring about must find each other to mate, which will invariably slow down more variation among a small population of individuals than a mere reproduction. In contrast individuals of an asexual species are capa- mutation within a clone (Fisher, 1930; Muller, 1932; Weismann, ble of giving birth on their own and are thereby able to generate 1889). Already Darwin reasoned that siblings will be able to acquire a large population rapidly. Moreover, it is conceivable that sex- more food from their environment than clones, because each dis- ual selection may also favor some traits, such as glorious feathers, tinct offspring may find and occupy a distinctive ecological niche which will reduce rather than increase survival of individuals when (Darwin, 1889; Doncaster et al., 2000). Variation by sexual repro- threatened by predators (Maynard Smith, 1978). If fitness were duction may also allow species to keep adapting to unrelenting merely equated with proliferation, sexual reproduction is disad- environmental changes, e.g., to keep ahead in an arms race against vantageous because it will pass only half of an antecedent’s genes parasites (Hamilton et al., 1990; Van Valen, 1973). Moreover, sexual to offspring (Ridley, 1995). Thus, sexual reproduction would seem reproduction seems to cause rivalries among individuals which can to conflict with the selfish-DNA hypothesis (Dawkins, 1976). More- be seen as events of natural selection for the fittest (Darwin, 1859). over, in some organisms sexual reproduction will enhance the Sex also promotes viable phenotypes by suppressing defunct geno- spread of parasitic genetic elements (Hickey, 1982). types (Kondrashov, 1988) and facilitating DNA repair (Bernstein The origin of sexual reproduction is also uncertain. It may stem et al., 1985). from an exchange of genetic material, i.e., horizontal gene transfer On the other hand sex is also associated with costs, in particu- to which, e.g., also bacteria resort (Judson, 2002). Alternatively, it lar with the two-fold cost of sex (Maynard Smith, 1978). Usually has been suggested that sexual reproduction came from selfish par- only one of the sexes, when excluding hermaphrodites, is capable asitic genetic elements as these elements spread with sex (Hickey, 1982). The common, although not ubiquitous two-sex convention may be linked to the double helical DNA structure of mutually complementary strands (Halvorson and Monroy, 1985). Specifi- ∗ Corresponding author at: Department of Physics, Gustaf Hällströmin katu 2, FI- cally, genetic recombination seems to be a mechanism to suppress 00014 University of Helsinki, Finland. Tel.: +358 9 191 50629; fax: +358 9 191-50639. expression of de-functional genes. E-mail address: arto.annila@helsinki.fi (A. Annila). 0303-2647/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biosystems.2012.09.006 A. Annila, E. Annila / BioSystems 110 (2012) 156–161 157 All in all the significance of sex has attracted many to propose systems (Annila and Salthe, 2010a; Kaila and Annila, 2008; Sharma meaningful mechanistic explanations, though not necessarily uni- and Annila, 2007). The logarithmic probability P measure is entropy versal rationalizations of sex. In this study we will neither advocate for some specific scenarios from which sex could have originated A S jk = k P = k P ≈ k N + nor propose some specialized mechanisms that could maintain sex, B ln B ln j B j 1 (1) kBT but we will seek for a more general selective principle of both sexual j j k and asexual proliferation from the fundamental law of nature. − where the free energy Ajk = k j + i Qjk contains energy dif- ferences of chemical potentials j = kBT ln[Njexp(Gj/kBT)] (Gibbs, 2. Aphids as an example organism 1993–1994) and energy in radiation Qjk that couple to the jk-reaction and kB is Boltzmann’s constant. The chemical potential Remarkably, some species are able to adapt to their environment denotes the energy that is bound in the population Nj, where by choosing between sexual reproduction and parthenogenesis. each individual is associated with Gj/kBT. It is a familiar concept The switch from one mode of proliferation to the other implies of chemistry yet valid for all entities, when using the self-similar that there is, in given circumstances, a subtle balance between the formalism that spans across levels of natural hierarchy (Annila and two modes. In the following we will exemplify and analyze the Kuismanen, 2009; Salthe, 1985). In other words, thermodynamics ubiquitous motif that underlies a taken mode of reproduction. makes no demarcation between animate and inanimate mecha- Aphids, also known as plant lice or greenflies (blackflies or nisms of free energy consumption (Annila and Annila, 2008). For whiteflies in Britain and the Commonwealth) are the small green example, the aphid population Nj is one among many populations insects commonly found on plant leaves and stems. Aphids are of mechanisms that constitute the energy transduction system, among those species capable of both sexual and asexual repro- commonly referred to as the food web. Likewise, the supplies duction (Grzimek, 1975; Wrensch and Ebbert, 1993). The simple of energy for the aphids, essentially sugar molecules in sap are annual lifecycle of Aphididae at temperate zones displays a clear numbered by Nk and valued by Gk/kBT. Sugar, in turn, is produced and distinct switch between the two modes of proliferation. In the by plants when consuming the energy difference denoted by spring a larva will hatch from an over-wintered egg and develop i Qjk in insolation relative to the cold space. The notation using into a wingless large female parent fundatrix. Its offspring are also the imaginary part for dissipation just makes it explicit that the wingless females, i.e., virgins exsulans that proliferate by partheno- vector potential of radiation is orthogonal to the scalar chemical genesis. During the summer these will produce several sequential potentials that are bound in the diverse populations (Tuisku et al., virgin-generations, i.e., estivals that are clones. Usually virgins are 2009). In the ecosystem there are obviously many more species vivipara, i.e., they give birth to live larvae. As the autumn arrives than the aforementioned, and the formalism in Eq. (1) will index the last generation of summer females known as sexupara will have them alike so that the conservation of quanta is satisfied. airborne progenies with both males and females, i.e., sexuals that When ln P in Eq. (1) is multiplied with the average energy of cannot reproduce asexually. After mating the female sexual will lay the system kBT, the bound kBT Nj and free NjAjk forms of energy only one or at most a few hard-shell eggs. Those eggs that winter become explicit. The approximation in Eq. (1), due to Stirling for will develop the next spring into new fundatrix, which will carry indistinguishable combinations ln Nj! ≈ Nj(ln Nj − 1), implies that on the cycle of reproduction. kBT is a sufficient statistics for the distribution of energy, i.e., Conversely, the life cycle of aphids that have adapted to constant Ajk/kBT 1. In other words, the energy content (heat capacity) of conditions and steady climates such as those prevailing in green- the system is big enough so that birth or death of a few individuals houses, cellars and other protected places, just as in the tropics, will not cause a marked change in the average energy of the system. display no bisexual phase. Obviously under steady-state conditions So, changes in the ecosystem appear mostly continuous.