Origins of evolution: Non-acquired characters dominates over acquired characters in changing environment

Journal of Theoretical Biology 304 (2012) 111–120

Contents lists available at SciVerse ScienceDirect

Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/yjtbi

Origins of evolution: Non-acquired characters dominates over acquired characters in changing environment Ce´dric Gaucherel a,b,n, Henrik Jeldtoft Jensen c a

UMR AMAP - INRA, Montpellier F-34000, France French Institute of Pondicherry, IFP - CNRS, 605001 Pondicherry, India c Department of Mathematics and Complexity & Networks Group, Imperial College London, London SW7 2AZ, UK b

a r t i c l e i n f o

abstract

Article history: Received 31 August 2011 Received in revised form 6 February 2012 Accepted 29 February 2012 Available online 21 March 2012

Natural Selection is so ubiquitous that we never wonder how it appeared as the evolution rule driving Life. We usually wonder how Life appeared, and seldom do we make an explicit distinction between Life and natural selection. Here, we apply the evolution concept commonly used for studying Life to evolution itself. More precisely, we developed two models aiming at selecting among different evolution rules competing for their supremacy. We explored competition between acquired (AQ) versus non-acquired (NAQ) character inheritance. The first model is parsimonious and non-spatial, in order to understand relationships between environmental forcings and rule selection. The second model is spatially explicit and studies the adaptation differences between AQ and NAQ populations. We established that NAQ evolution rule is dominating in case of changing environment. Furthermore, we observed that a more adapted population better fits its environmental constraints, but fails in rapidly changing environments. NAQ principle and less adapted populations indeed act as a reservoir of traits that helps populations to survive in rapidly changing environments, such as the ones that probably Life experienced at its origins. Although perfectible, our modeling approaches will certainly help us to improve our understanding of origins of Life and Evolution, on Earth or elsewhere. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Evolution Lamarckism Gaia hypothesis Disturbances Pre-biotic Life

1. Introduction Natural Selection (NS) is usually understood in the sense that the competition according to some measure of viability will lead to some species, or some procedure, to be selected instead of some others. Surprisingly, NS seems so powerful that it could be applied to evolution itself, i.e. the selection of evolution rules possibly driving Life. Here, we intentionally reduce Life to a system able to reproduce itself. By NS we mean a simplified principle consisting of a competition mechanism acting on a pool of variation, which in turn is brought about through some kind of mutations. Such a competition is involved when different varieties co-evolve subject to some shared constraints. In this theoretical study, we investigate why the specific characteristics of Darwinian evolution are so ubiquitous, and why Life, at its early beginning for example, did not build its foundations on the basis of ‘‘another’’ evolution rule. Here, we do not intend to explore the link between genetic information and NS, instead we focus on their common foundations (i.e. selection of variants).

n Correspondence to: French Institute of Pondicherry (IFP), 11 St Louis Street, 605001 Pondicherry, India. Tel.: þ91 413 233 4168; fax: þ 91 413 233 9534. E-mail address: [email protected] (C. Gaucherel).

0022-5193/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtbi.2012.02.028

At least four different modes of evolutionary dynamics seem to be relevant, at different levels, to the history of Life on Earth (Jablonka and Lamb, 2006a). For Life as we know it, we can identify genetic, epigenetic, behavioral and symbolic types of inheritance systems, as responsible for the transmission of characters (or traits, or information, in a wide sense) across generations (Jablonka and Lamb, 2006b). The competition between hereditary adaptation and purely mutational adaptation has been studied before (Ackley and Littman, 1993; Paenke et al., 2007; Sasaki and Tokoro, 2000). Here, we address the question of the ubiquitous presence of NS by modeling two simple and contrasting modes of evolutionary dynamics (hereafter called evolution rules). The first one, denoted Non-Acquired (NAQ) inheritance, consists in pure undirected mutations plus some selective pressure. Our representation of this mode of inheritance is highly simple to discriminate between relevant processes, and is somewhat remote from biological systems. The second evolution rule consists in exactly the same undirected mutations as for NAQ, but supplemented by acquired changes of the phenotype, (called acquired features, AQ). The NAQ rule is consistent with the standard formulation of Darwinian evolution by NS (Darwin, 1859). The AQ rule contains characteristics usually associated with Lamarckian evolutionary dynamics (Por, 2006). This more complicated model improves on the biological relevance of our study and includes for the first time in a spatially explicit scheme.

112

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

Evolution according to both rules will only occur in our models when a selective pressure is applied to a heterogeneous population. By construction, this population is composed of individuals belonging to species evolving according to NAQ or AQ rules, with possible exchanges of rules between them after each generation. We developed two models in which populations of AQ individuals and NAQ individuals compete for the same resources, in the same physical environment, and study which mode is the most successful under various conditions. The first simple model is used to understand basic mechanisms leading to the domination of either one or the other rule. We will in particular focus on the effect of abrupt changes in the physical environment forcing the population. The second model, although still theoretic and parsimonious, is a more realistic model inspired by Daisyworld (Gaia) dynamics (Lovelock and Margulis, 1974). This model is spatially explicit, with possible population ‘‘specialization’’ (i.e. with differential adaptation abilities among evolution rules), and allows feedback of the heterogeneous population on environment conditions. Such a process was called homeostasis by Lovelock and Watson, because they were considering Gaı¨a as an extended organism regulating its internal environment; whereas some people would have interpreted it as a niche construction (i.e. the regulation of an external environment). At least, we should admit that such regulations would increase the chance for survival of the biota. Indeed, regulations are observed across a wide range of living organization levels, spanning from individual organisms to the entire biosphere (Lenton and van Oijen, 2002). We will therefore assume that the ability to establish homeostasis is essential for Life, and these entities which can most efficiently maintain homeostasis across generations, will be the most successful. This, in turn, will lead to the corresponding evolution rule to become the most successful. When competition occurs, our aim is to understand which type of environmental pressure will favor which type of rule, NAQ or AQ. To study the mechanisms responsible for the modeled evolution rules is beyond the scope of this work, although it is obviously a highly relevant question. We refer the reader to the book by Jablonka and Lamb (2006a) in which a number of mechanisms are discussed, ranging from methylation at the level of microbiology through epigenetic transfer via the cytoplasm, to a cultural inheritance at the level of community communication. This study may also be of relevance to Ecosystems, which sometimes are seen as evolving entities (Bouchard, 2009). The ability of individuals to adjust their traits towards a better (or an optimal) response to the physical environment will lead to a reduction in the trait variations (specialization). We therefore expect an AQ population to possess a much smaller diversity in those traits that relate to the external pressure. This explains why the AQ rule, having more optimized distribution of traits, is expected to dominate over NAQ rule, in case of relatively constant environmental conditions. In contrast, external conditions undergoing rapid and sharp changes should favor NAQ over AQ. In this case indeed, we expect that the AQ rule may match too perfectly the previous environmental conditions and may be disfavored after the environment has undergone a rapid change. Our first hypothesis can be stated as: NAQ dominates over AQ when the environment changes rapidly. Furthermore, we want to study the ability to survive in such a competitive environment, in relation to the adaptation capacity of each evolution rule. Our second hypothesis states that the more specialized AQ is, the stronger the effect assumed in the first hypothesis. Indeed, we expect the domination of the rule NAQ in rapidly changing environments to increase over the AQ rule, for a higher specialization of AQ over NAQ populations. These hypotheses are partly inspired from the r/K strategy stating that there often exists a trade off between quantity and quality of offspring in the species demography (Pianka, 1970). Although this paradigm lost importance in last decades, it has been argued that a reduced quantity

of offspring, with a corresponding increased parental investment (K-selection), is less successful (than r-selection) in stable or predictable environments (Roff, 1992) and vice versa. Our two models enable us to discuss these hypotheses by use of twodimensional maps showing the results of the competition between AQ and NAQ individuals, for different levels of perturbation intensities and degrees of specialization.

2. Methods 2.1. First model: non-spatial dynamics 2.1.1. Model description Our first model is a schematic framework that allows us to study the dynamics of a population of two types of reproducing individuals. The reproduction of both types of individuals is prone to mutations (with a certain probability) and both types are able to evolve their phenotype (one trait) in response to the environment. The essential difference between the two types is that members of the first group will pass the phenotype they have acquired onto their offspring. We denote individuals of this type: AQ. The other type of individuals also acquires changes to their phenotype during their life, but they do not pass the acquired phenotype onto their offspring. Instead they pass their inherited ‘‘genotype’’ on (i.e. the trait they inherited at birth). We denote individuals of this type NAQ. There are NAQ(t) individuals of type AQ and NNAQ(t) individuals of type NAQ (see Table 1 for a parameter list). Each individual k

Table 1 Parameter list and interpretation of both models. Model 1 parameters

Model 2 parameters

Ni ¼ AQ,NAQ

Number of individuals of Ai ¼ b,w,g AQ and NAQ populations

xk

Phenotype of each k individual

ai ¼ b,w,g

m

System ability to support a certain population size Amplitude of the reproduction curve Width of the reproduction curve Central trait value

bi ¼ b,w

A W xfix

Ti ¼ b,w S T0

Tgrowth

Number of iterations for s growth

Tgeo

Number of iterations for div generation (i.e. sweeps of annihilation, reproduction and growth) des

Damax

pkill

Albedos of dark daisies (b), pale daisies (w), and bare soils (g) Normalized areas covered by dark and pale daisies, and by bare soils Growth rates of dark and pale daisies per unit of time Local temperatures of dark and pale daisies Planet (Daisyworld) received insolation Central trait value (mean temperature of the planet) Width of the trait (temperature) distribution Factor quantifying the differential adapting behavior between NAQ and AQ evolution rules Intensity of the Daisyworld perturbation Maximal width (variation) of the parent albedo mutation Death rate per dimensionless unit of time

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

possesses a trait parameter at time t denoted xk(t) called the phenotype. The dynamics of the model consist in successive stages of annihilation, reproduction, and growth. We now describe this in detail. Firstly, annihilation: each individual is visited and removed from the population with probability: pkill ¼ 1emðNAQ þ NNAQ Þ

ð1Þ

Here m is a parameter that controls the system ability to support a certain population of total size NAQ þNNAQ, the parameter can be thought of as determining the system carrying capacity. We have used m ¼0.001, to obtain a population size convenient to manage in simulations. Secondly, reproduction: each individual in the population is visited and reproduction of the individual k takes place with probability: 2

pof f ðxk Þ ¼ Aeððxk xf ix Þ=wÞ

ð2Þ

where xf ix is the central trait value, and A and w are the amplitude and the width of the Gaussian curve, equal in this work to A¼0.9, w¼0.05. Reproduction is prone to mutations. To emphasize the effect of mutations we let them occur with probability pmut ¼1; and its effect is to change the inherited trait by a certain amount. In the simulations reported here, the mutations correspond to adding a number uniformly distributed on a variable domain of width dmut around the trait value xk. Type AQ passes on the phenotype xk(trep) they have acquired during their lifetime up to the moment trep of

113

reproduction. During the reproduction step mutations can occur, so the offspring will then obtain the phenotype xk(trep) slightly modified by mutations. The NAQ can only pass on the genetic trait value xk(0) they inherited at birth. So the offspring of an NAQ organism will obtain the genetic trait value xk(0), possibly modified by mutations. Thirdly, the reproduction is followed by a stage during which the phenotype of each individual is allowed to develop. This consists in iterating the value of each individual trait in the population, for both AQ and NAQ individuals, according to the logistic map for Tgrowth iterations. In each iteration step, the trait xk is replaced by a new one: ¼ f ðxk Þ ¼ rxk ð1xk Þ xnew k

ð3Þ

The logistic map is a convenient representation of dynamical change towards the fixed point xf ix ¼ ðr1Þ=r, for appropriate choices of the parameter r. Changes in the environment are modeled by letting xfix vary with time. Either xfix varies smoothly (and in a stationary regime, i.e. with stable statistical moments along time) according to   p t ð4Þ xf ix ¼ 1:1þ sin T geo Or xfix remains constant for Tgeo sweeps of annihilation, reproduction and growth. We denote this as Tgeo generations. After a round of Tgeo generations we then abruptly change xfix. We do this by changing the value of the constant r (successively equal

Fig. 1. The temporal variation of the average of trait values for the AQ and NAQ populations. The blue (solid line) curve corresponds to the trait optimum, the black (short dash) curve to the AQ population, the red (long dash) curve to the phenotypic value of the NAQ population and the green (long þ short dash) curve to the genotypic value of the NAQ population. Initially both populations have 20 members. The mutations are in the range dmut ¼0.1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

114

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

to r¼ 1.11 or 2.10), and thereby inducing a move of the optimal trait value xfix. So, after Tgeo generations, we change the value of r and thereby the value of xfix. In the case of this piecewise constant xfix, we think of Tgeo as the duration of ‘‘geologically stable epochs’’ during which the environmental conditions remain constant. We used the smooth variation given by Eq. (4) in Fig. 1 and we use the abrupt variation (described after Eq. (4)) in Fig. 2. In other words for the abruptly varying xfix the population undergoes Tgeo rounds of annihilation attempts, reproduction attempts and growth cycles (each growth cycle consists of Tgrowth iterations of the map in Eq. (3)), under constant environmental conditions given by a constant value of xfix. After Tgeo rounds of updates, xfix is changed to the other value, and another round of generations are carried out Tgeo times. The process continues up to a total of Tmax annihilation, reproduction and growth sweeps of the entire population.

2.1.2. Methodology To understand the competition between the NAQ and AQ evolution rules under various environmental pressures with this simple model, we proceeded in two successive stages. Firstly, we studied single realizations of the time dependence populations, for different choices of Tgrowth and Tgeo. We registered the average trait



geno xk for the AQ population

pheno xk AQ and both the genotypic, xk NAQ , and the phenotypic, xk NAQ , averages for the NAQ population. In a first set of runs, we let the optimal value xfix of the trait vary smoothly with time, according to Eq. (4). We studied what happens when no adaptation (i.e. changing phenotypes) is possible, corresponding to Tgrowth ¼0 (with Tgeo ¼200). Then, we investigated the effect of adaptation by choosing different positive values for Tgrowth and compare the relative effect on acquired and non-acquired traits. We successively simulated parameter couples (Tgrowth, Tgeo)¼ (1, 200); (100, 200); (1, 20); (100, 20). Secondly, we generalized

Fig. 2. The survival probability of NAQ and AQ individuals for different values of Tgrowth and Tgeo. The mutations are uniformly distributed on [  1/8,1/8] with appropriate cut-offs to ensure the resulting trait value to belong to xk A ½0; 1.

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

these single examples by computing the survival probability of the AQ and NAQ populations respectively, for a wide range of Tgrowth and Tgeo parameter values. By monitoring the survival probabilities, we have investigated our hypotheses about possible dominance of NAQ or AQ evolution rules, depending on the environment changes, and the duration of the adaptation period. Note that the sum of the survival probability for each of the two populations AQ and NAQ can add up to more than 1 due to the fact that the populations may coexists for times longer than the 220 simulation time. The survival probabilities are measured in the simulation by simulating the evolutionary dynamics for time spans typically equal to 10–100 times Tgeo. We then monitor the number of simulated realizations for which population AQ survives and NAQ goes extinct, or NAQ survives and AQ goes extinct or both AQ and NAQ populations survive. We do occasionally for some parameter choices encounter situations where both AQ and NAQ survive, say, during 75% of the simulated runs. Finally, it is worth mentioning that accidental extinctions due to small population sizes in our simulations may occur, but they have no effect on this comparative study as they are equally probable for AQ and NAQ populations. 2.2. A Daisyworld model: complex dynamics The original planet of Daisyworld was invented by Watson and Lovelock to illustrate the Gaia hypothesis. Their hypothesis consists in the assumption that the biosphere regulates the physical environment, keeping the Earth’s abiotic components (climate, chemical ratios, etc.) stable and favorable for life (Lovelock and Margulis, 1974; Watson and Lovelock, 1983). This imaginary planet is seeded with individuals (daisies) of different ‘‘colors’’ that modify the albedo (reflectivity of insolation) of the whole system and, as a consequence, the temperature of the planet (see Appendix 1 for a detailed presentation of earlier versions of the Daisyworld model). The feedback between the climate and the biota made of these individuals leads to a regulating system. This system has been the subject of many studies, sometimes with mutating daisies and/or spatial influences (Lenton, 1998; Lovelock, 2003; Von Bloh et al., 1997). While Daisyworld studies the feedbacks between the living and nonliving, the mutating Daisyworld suggests that environmental regulation can emerge by the way of natural selection acting at levels from the individual to the global. The spatially explicit twodimensional version of Daisyworld in particular exhibits the property that under enforced habitat fragmentation, the system is able to regulate temperature unimpaired up to a ‘critical’ threshold on the fragmentation (Von Bloh et al., 1997). The spatial and evolutionary versions of Daisyworlds are appropriate for our purpose (Downing and Zvirinsky, 1999; Saunders, 1994; Sugimoto, 2002). 2.2.1. The competing Daisyworld We defined two different evolution rules. Lenton’s Daisyworld scheme suits our purpose nicely (Lenton, 1998). Random mutations of daisy albedos have been introduced and are combined with a selection principle embedded into mutation probabilities that depends on differential growth rates and neighborhoods (Lenton and van Oijen, 2002). We used exactly the same definition as in the original Daisyworld model (described in Appendix 1), to model a realistic yet simplified NAQ evolution rule. Local temperature and reproduction probabilities are unchanged compared to the initial mutating Daisyworld found in the literature. In order to simulate the growth of each individual we allow for a period during which they may acquire (or not) new characters. We do this through cycles of population dynamics. Between each

115

generation Tgeo, i.e. at each time step for which environmental conditions (insolation) change, the model allows the Daisyworld to grow during Tgrowth iterations (see Table 1 for a parameter list). Hence, each generation stage is a combination of seedling, reproduction, growth and killing. We implement a second evolution rule to compete with the NAQ rule. This second rule allows inheritance of Acquired Characters (AQ) from parent to child daisies, and is modeled with an algorithm intending to mimic Lamarckian evolution rule (Gould, 2002; Por, 2006). Two differences with the NAQ rule have been implemented for this purpose. While NAQ individuals are keeping their initial trait value before the growth, AQ ones are keeping the value obtained during the growth cycle (subject to mutations). In addition, AQ individuals are assumed to become more specialized than NAQ. We model this by assuming a more narrow peaked growth rate distribution. The standard deviation of the growth rate of the AQ population taken to be equal to the standard deviation of the NAQ divided by a factor div. So if we make div o1 we have the opposite situation, namely that the NAQ population is the most specialized. Individual daisies reproduce and grow in a way depending on their specific growth rate and neighborhood. At a given instant in time (growth and reproduction) either the AQ or the NAQ rules is ascribed to each individual on the planet. The choice between AQ and NAQ is done by choosing a random neighbor and copy the trait of that site. Daisies reach a stationary state after the growth cycle (Tgrowth ¼15 is enough in this study). This procedure allows us to study competition between the AQ and NAQ populations. Environmental pressure of the Daisyworld planet is simulated with a periodic insolation S, rather than the gradually increasing insolation used in the original Daisyworld. This environmental forcing is intending to mimic variable (and possibly intense) perturbations described as    2pt S ¼ 0:8 þdesUsign cos , with t A ½1; 50 ð5Þ 20 where sign function returns a 1 when cosð2pt=20Þ is positive and  1 when cosð2pt=20Þ is negative. The factor des sets the intensity of the perturbation. Before Eq. (5) is applied, insolation first increased from value 0.6 to 0.8, to gently settle the planet into a usual life-like period (Lovelock and Margulis, 1974). We estimated the outcome of the competition by systematically computing the normalized ratio R between AQ and NAQ populations:





 1 1 NAQ

 if N AQ 4 N NAQ R¼ þ ð6Þ 2 2N N NAQ or R¼





 1 1 N NAQ

 if N NAQ 4 N AQ  2 2N N AQ

where N is the total number of individuals of the planet. Bare earth albedos (Ag) have been systematically removed from this computation (see Appendix 1), as they were not considered as ‘‘alive’’ daisies, such as pale (Aw 4Ag) and dark albedos (Ab oAg). Finally, the R ratio will assume values between 0 and 1, with a value greater than 0.5 in case of AQ rule dominating, or less than 0.5 in case of NAQ rule dominating. As a reference simulation, we will briefly describe results of the original and modified Daisyworld dynamics. We analyzed independently (non-competing) NAQ and AQ evolution rules, with the global temperature stabilization during a gradual and linear insolation increase, from values 0.6 to 1.4, with 0.004 steps. Next, we simulated the competition between the two evolution rules using the dynamics described above. Results were robust regarding for a broad range of parameters, such as the size of the torique planet, the duration of growth, the perturbation shape

116

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

(different from a periodic switching between  1 and 1). The size of the planet has been here assigned to 15  15 daisies, but we checked that this choice has no qualitative influence on our results. Similarly to the simpler non-spatial model, we computed in the spatial case R for a range of specialization values (div A ½0; 2:5 here) and a range of perturbation intensities (desA ½0; 0:4 here), thus leading to a twodimensional map describing the outcome of the competition. The competition map has been averaged over 30 runs for each couple of (des; div) parameters, and the corresponding standard deviations for each couple have been computed too.

3. Results 3.1. Non-spatial model 3.1.1. Model description Single realizations of dynamics of AQ population genotypic traits and NAQ population genotypic and phenotypic traits for different choices of Tgrowth and Tgeo help to interpret mechanisms responsible for the relative success of the evolution rules. First we consider the non-spatial model and let the optimal value (xfix) of the trait vary smoothly with time (Fig. 1a, in blue), with no adaptation (Tgrowth ¼0). Because the external environment changes so slowly, AQ and NAQ manage equally well to adapt to the changes. Hence, all curves in Fig. 1a fall on top of each other and one cannot distinguish any difference between the optimal value, AQ and NAQ populations. The time variation in all three curves is caused by the mutations during reproduction. Pure Darwinian adaptation through NS is able to ensure that the average genotypic value of the trait closely follows the optimal value, though with a slight delay. When the adaptation mechanism (Tgrowth 40) is allowed to act, the AQ population follows the optimal trait value with a high accuracy. The phenotype of the NAQ population is attracted towards this optimum during the growth period, but not sufficiently to make up for the diffusive wandering off of the genotypic value of the NAQ population’s trait value. The NAQ population is outcompeted by the AQ population, and the NAQ population finally goes extinct at about time t ¼90. This is indicated in Fig. 1b by the curves for the phenotype and the genotype of NAQ population ending at t ¼90. When significantly increasing the growth period (Tgrowth ¼Tgeo/2¼100, Fig. 1c), the NAQ acquired phenotype is able to compensate for the deviation between the genotypic trait value and its optimum (red zigzagging curve). During each reproduction event, the NAQ phenotypic value will be drawn towards the NAQ genotypic curve, while during the adaptation round, the NAQ phenotypic value will move towards the optimum. This makes the AQ and the NAQ populations fair equally well when the environment changes slowly. The phenotype is allowed to undergo substantial adaptation. The situation shifts when the environment changes rapidly (Tgeo ¼20, Fig. 1d and e). In this case, the narrow distribution of AQ trait values becomes a disadvantage. The diffusive wandering of the distribution of the NAQ genotypic values acts as a reservoir of genotypes, which enables this population to respond to the rapid variations in environment. Hence, the NAQ population has a tendency to perform better than the AQ population when the trait optimum rapidly changes with time. 3.1.2. Simple competition The survival probability of AQ and NAQ populations against generation time and adaptation time respectively (Fig. 2), shows that the NAQ population is most successful when the environment is changing rapidly with time (i.e. for small values of Tgeo) for similar intensities. In these cases, the AQ population will be narrowly distributed around the optimum trait; this is caused by

the focusing effect of the adaptation, represented by the iteration of the logistic map during the growth period (Fig. 2a). Although the NAQ population also experiences the adaptation round, the acquired specialization towards the current optimal trait value is not passed on to the offspring. Accordingly, the variation in the NAQ genotype remains sufficiently broad to allow some members of the NAQ population to possess values of trait sufficiently close to the new optimum to be able to reproduce (Fig. 2b). However, it is not only the size of the variation across the population that determines the outcome of the competition between AQ and NAQ populations. The variation in the NAQ population is always bigger than the variation in the AQ population, but the AQ population can compensate for this if the acquired adaptation is sufficient (not too small Tgrowth) and the environment changes slowly (not too small Tgeo). 3.2. Spatial model 3.2.1. Daisyworld dynamics The NAQ evolution we simulated corresponds to the population dynamics already described in the original Lenton’s model (Fig. 3). The dark types (close to albedo Ab) flourished initially, when alone, and still had a significant population size later (Fig. 3b). Then, paler mutants of these dark albedos (still less than Ag) arose and dominated at low insolation. Progressively paler albedo mutants (up to Aw) were favoured in sequence when insolation increased background temperatures above the beginning of the life-like period. The combination of different albedo types stabilized the planetary temperature evolution at 39 1C between 1 and  1.3 insolation, which is confirmed by the cited literature. Contrary to the Lenton’s model, the spatial albedo mutation did not extend the range of temperature regulation beyond that in the original model, this is because we explicitly chose that no paler types than the original ‘‘white’’ ones, nor darker types than the original ‘‘black’’ ones, could arise. We observed the emergence of two distinct behaviors of dark (oAg) and pale ( 4Ag) daisy populations, both arising quickly (after S 0.6). This was caused by the spatial cohesion favouring the presence of pale daisies even when dark daisies should dominate in a non-spatial case, because they are geographically separated. Hence, both groups of albedo competed up to S 1, with the main consequence that the dark daisies did not succeed to stabilize the global temperature (the pale daisies cooled simultaneously). Temperature stabilization was only possible for S41, when pale daisies dominated leading to a cooling of the global temperature at these high insolation levels. This has also been observed in the literature (Lenton, 1998), although it is not easy to detect this effect with several mutant curves. NAQ rule runs lead to a more efficient temperature stabilization (Fig. 3a), i.e. with a lower temperature standard deviation during life-like periods (37.6370.611 for NAQ instead of 39.1170.871 for AQ populations). For AQ rule, dark daisies radically dominated for low insolation levels as they appeared first. Every new albedo is constrained by the mean neighbor temperature and thus by the mean of dark daisies only. When insolation was high enough to reduce the number of AQ dark daisies, paler daisies could stochastically appear and then rapidly propagated by neighboring influences (S  0.95). Yet, they could not survive for an extended time because they are not able to propagate rapidly enough. Finally, conversely to NAQ life-like period, AQ life-like period is corresponding to a warming of the global temperature at low insolation levels. 3.2.2. Daisyworld competition The relative success between AQ and NAQ on the Daisyworld planet depends on parameter choice as illustrated (Fig. 4). NAQ

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

117

Temperature (°C)

a

NAQ AQ

Solar luminosity

b Daisies Grid covers (%)

NAQ

AQ

Pale daisies Dark daisies

Solar luminosity Fig. 3. Global average temperature evolutions (a, in 1C) and daisy proportions (b) for the three evolution rules (NAQ: Non-Acquired Characters, and AQ: Acquired Character evolution rules, from top to bottom) as a function of the solar insolation increase. The solid and dotted population curves (b) concern pale (A4 Ag) and dark daisies (A o Ag) of successive rules respectively. Life-like periods corresponding to stabilized planet temperatures are plotted as dashed lines for each evolution rule.

dominates for higher perturbation intensities (high des) and for higher specialization (high div) of the AQ rule (Fig. 4, blue zones). Similarly to the non-spatial model, we observe that the distribution of genotypic values of the NAQ population acts as a reservoir of types, because it is more slowly evolving. This enables this population to respond to rapid variations in trait. This effect is particularly pronounced when the AQ population consists of highly adaptive individuals (higher div values). The AQ population then becomes much focused and therefore unable to survive when the conditions undergo abrupt changes. This effect, still present, becomes less significant for higher degree of specialization (Fig. 4, zone 1), which is due to higher standard deviations of the R ratio (equal to 70.2 in average). Yet, the AQ evolution rule appeared to dominate in case of less specialized AQ rule (Fig. 4, zone 2, low div). Moreover, the AQ rule with a weak degree of specialization is able to dominate whatever the environmental changes are. This is due to the fact that less specialized AQ populations increase their trait reservoirs in the same way than NAQ populations. In addition, it is noticeable that the shift between AQ and NAQ dominance is not occurring, in our model, at an equal degree of specialization between the two rules (i.e. for div ¼1, Fig. 4, zone 3). In brief, low perturbations and/or low AQ specialization usually leaded to a dominance of the AQ evolution

rule, while high perturbations and high AQ specialization is associated to the dominance of the NAQ evolution rule.

4. Discussion 4.1. When NAQ dominates over AQ populations We have focused on the behaviors of two modes of evolutionary dynamics. Each model makes use of simplified representations of inheritance of traits. To bring out the involved mechanisms as clearly as possible, we first studied a non-spatial schematic model. The lesson of this preliminary work allowed us to formulate a version of the Daisyworld model in which two types of inheritance mechanisms are competing in a spatially explicit scheme. The external selective pressure is assumed to vary with time, and we studied the co-evolution of two types of populations, each associated with different types of evolution rules. During their lifetime, individuals from both populations will develop their traits towards the one which is optimal, given the environmental pressure at the time. Their reproduction ability is determined by the value of their trait. The first population is able to pass on the improvements of the trait acquired during the individual life

118

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

Perturbation more intense

AQ daisies dominates

Zone 2 Evolution rule Ratio R

Zone 1

Zone 3 Des

Perturbation intensity

NAQ

AQ

Less intense

NAQ more specialized

NAQ daisies dominates

Div Degree of specialisation

AQ more specialized

Fig. 4. The NAQ and AQ evolution rule ratio R, as a function of the Degree of specialization (div) and the perturbation intensity (des). This ratio belongs to RA ½0; 1, and uses a color scale to visualize its distribution in the 2D parameter space. R values greater than 0.5 (in red) corresponds to the dominance of the AQ evolution rule, while those lesser than 0.5 (in blue) corresponds to the dominance of the NAQ evolution rule. Zones 1, 2 and 3 highlight zones to be discussed in Section 3.2.2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

history (the AQ type). The second population (NAQ type) can only pass on the ‘‘genotypic’’ trait value it inherited at birth. To concentrate on the relation between the various processes and timescales involved, we first studied a simplified non-spatial model. We found that individuals following the AQ evolutionary dynamics will out compete NAQ individuals when external conditions vary slowly in time. The inheritance of optimized traits leads to a population with a narrow distribution of traits, centered on the optimal value. The AQ population consists of highly reproductive individuals. The less specialized NAQ population exhibits a broader distribution of trait values. Yet, the lesser degree of specialization becomes a relative advantage when the external conditions undergo abrupt changes, separated by more quiescent periods during which the AQ population becomes finely tuned to the existing life conditions. When the environment changes, the AQ population is specialized to the wrong conditions, whereas the broader distribution of traits in the NAQ population enables this population to more efficiently cope with the new environmental requirements. The bigger variation in the NAQ population, with its lack of inheritance of optimized traits, becomes an advantage whenever rapid changes occur in the physical environment (Figs. 1 and 2), and is a disadvantage otherwise. This result confirms our first hypothesis. At the moment we are unable to validate our model against real data. Yet, this principle seems relatively realistic as it has been inspired by the r and K reproduction strategy today discussed in evolutionary biology (Roff, 1992). On the basis of these findings we developed a generalization of the Daisyworld model, which allows us to address questions concerning spatial relationships of populations. In this model, we study the effect of various degrees of specialization of the AQ as compared to NAQ populations. In agreement with the findings of our first model, we interpreted specialization as related to the

width of the trait distribution, whatever is the mode of inheritance. We found that the relative strength of the two evolutionary strategies depends on the relation between the degree of specialization and the strength of perturbation of the environment (Fig. 4). Furthermore, the degree of specialization is partly a consequence of the growth duration Tgrowth and of the high mutation ratio linked to Tgeo. If there is no time for adaptation, AQ and NAQ populations would behave similarly. For high intensity of the perturbation of the environment and for high degree of specialization of the AQ population the NAQ population is the most successful (Fig. 4, zone 2). The shift between AQ and NAQ rule dominances is occurring, in our Daisyworld model, at a slightly weaker degree of specialization (div  0.4 instead of unity) for AQ populations (Fig. 4, zone 3). Indeed, it has no reason to precisely shift at an equal degree of specialization, due to the nonsymmetrical behavior of both rules. This result confirms our second hypothesis. 4.2. On origins of Life Finally, we observe a sharp dichotomy between a dominant NAQ rule for changing environments, and a dominant AQ rule for relatively persistent environments (Fig. 4). Yet, this is depending on a set of parameters. Firstly, spatial properties of such idealistic ecosystems are important and could shift the dichotomy location (frontier between zones 1 and 2 in Fig. 4). For example, it would be relevant to model different mutation rates between AQ and NAQ populations and to analyze simulations obtained. Secondly, other factors may play a role, in particular the evolution rule adaptation, here modeled as a degree of specialization (a capability to more rapidly adjust its trait towards the environmental pressure, Eqs. (4) and (5)). For example, it is plausible that a weak degree of AQ specialization would lead the AQ evolution rule to

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

dominate, whatever is the perturbation intensity (Fig. 4, zone 2). This is easily understandable if we consider that a weaker specialization is able to mimic the reservoir of traits associated to the NAQ rule. This observation of interrelation between selection and adaptation processes is interesting in the context of origins of Life (Maynard-Smith and Szathma´ry, 1995). Life certainly experienced high intensity perturbations in the past (e.g. meteoric and volcanic catastrophes). Our findings above suggest that the AQ evolution rule necessarily leads to a high degree of specialization, which becomes a liability in a rapidly changing environment. Otherwise, we could have expected the AQ rule to become the dominated evolutionary mode on Earth. Furthermore, it is relevant to consider how the picture we have developed above might change if the effect of the environment is multidimensional (i.e. more than one trait). In general, it might not be possible to reduce the effect of the environment to influence only one well-defined and unidirectional strain (trait) of the population. There may be many mutually incompatible demands from the environment leading to a frustrated situation, in which the individuals are unable to develop one optimal strategy as a response to the pressure of the environment. In such situations, and in particular, if this high-dimensional strain on the population is also changing in time, the NAQ dynamics with its broader distributed genotypic possibilities may be preferable. It will be interesting in future studies to address this question by use of mechanistic models, which explicitly deals with populations characterized by multiple traits, exposed to a set of competing environmental pressures. It is to be expected that a number of factors play a role in determining which kind of evolutionary dynamics is most effective. We have compared populations that are similar in all respects, except whether they can inherit an acquired trait or not. We have also neglected the ability to pass on acquired traits that might be costly and, in some cases that can be detrimental to the evolutionary competition. Also, we proposed here one of the most parsimonious model to confirm the central result already shown in the literature (Ackley and Littman, 1993; Paenke et al., 2007; Sasaki and Tokoro, 2000): NAQ populations are likely to dominate AQ populations for highly changing environments. Yet, our model also demonstrates that non-stationary environments are not necessary for this conclusion. Oscillating environments lead to the same conclusion, a clue that might be confirmed in future studies to improve our understanding of the influence of either catastrophic or stationary perturbations experienced by Life. Finally, as a more general perspective, we would recommend now to develop more realistic models, to progressively shift from theoretical and qualitative studies (such as ours or colleagues (Paenke et al., 2007)) towards more quantitative and more realistic studies. Our study highlights several important points for the understanding of the origins of Life, for which we have so little information (Jablonka and Lamb, 2006b; Maynard-Smith and Szathma´ry, 1995). First, we see no objection why other evolution rules might have appeared in the past, hence our focus on the origins of Evolution rather than origins of Life. Obviously, other rules should be associated to another information storage and reading. No doubt that NS has partly emerged due to the adequate genetic information storage. Yet, since other evolutionary rules can be imagined, we do need to understand why and how NS finally came to dominate Life on Earth as we know it. The kind of modeling approach we used here is a fruitful way to explore possible scenarios for the formation of Life forms and its evolution, (on planet Earth or elsewhere). Secondly, in terms of Lamarckian mechanisms, it has been often mentioned that it is difficult, if not impossible, to code the information inherited in case of AQ individuals. If Lamarckism is to be found in epigenetic,

119

it might partly be because molecular structures offer relevant places and scales at which it becomes possible to write back to the genotype from the phenotype. At another scale, it has been discussed that ecosystems too are exhibiting acquired character inheritance (Bouchard, 2009). But do these entities (genes, molecules, organisms and ecosystems) experience the same ‘‘environments’’? After this study, we might consider whether environments of molecules and ecosystems are not relatively more stable to that of genes and organisms. Finally, our models studied the competition between different cohabiting modes of evolution. Is this hypothetical scenario realistic? Is only cohabitation possible or will one mode out compete all other modes of evolutionary dynamics? Cohabitation is certainly seen, if we already accept that different types of evolutionary dynamics take place at different levels, as argued by Jablonka and Lamb (2006a, b). But if we insist only to consider evolution at the lowest genetic or epigenetic level observations suggest that only one mode of evolutionary inheritance is able to exist and that this is the NS.

Acknowledgments We would like to thank N. Mouquet for interesting discussions about this paper. This research has been funded in 2009 by a specific funding of the EFPA Department of the Institut National de la Recherche en Agronomie (INRA, a French Research Institute).

Appendix 1 1.1. The original Daisyworld modified Daisyworld is a flat cloudless planet with negligible atmospheric greenhouse effect. Its entire biota consists of two species of daisies (or individuals) that differ only in color, i.e. their characteristic traits. The original equations are retained where possible (Watson and Lovelock, 1983). Those governing the growth of biota are daw ¼ aw ðag bpkill Þ, dt

dab ¼ ab ðag bpkill Þ, dt

ag ¼ 1aw ab

ð7Þ

where t is the dimensionless time, aw and ab are the normalized areas covered by light (called ‘‘white’’) and dark (‘‘black’’) daisies, respectively, ag the normalized area of fertile ground not covered by daisies. The entire planet is potentially fertile, i.e. there is no habitat restriction (Von Bloh et al., 1997). pkill is the death rate per dimensionless unit time, here equal to 0.3 for numerical calculations. bw and bb are the growth rates of daisies per unit time, allowing daisies to spread over the planet. In our study, individuals are then belonging to either dark or light daisy colors, and simultaneously to either NAQ or AQ rules. In the original model, growth rates follow a parabolic function of the local temperature Ti ¼ w,b. We modified the original model into a similar Gaussian function for a more realistic shape and an easier control of its dependence to the environment (the local temperature): 2

bNAQ ¼ eððT 0 T i Þ

=2sÞ

2

and bAQ ¼ eððT 0 T i Þ

=ð2s=divÞÞ

ð8Þ

With T0 ¼22.5 1C playing the role of the central trait value xfix of the previous model, s ¼17.5 1C. Finally, div is a correcting factor modeling the differential adapting behavior between NAQ and AQ evolution rules (i.e. for NAQ rule). The highest div, the more specialized or adapted AQ are relatively to NAQ individuals. Notice that, if div¼ 1, i.e. when evolution rules adapt in a similar way, bw,b can be neglected for temperatures below 4.85 1C (278 K) and above 39.85 1C (313 K) as in the original Daisyworld.

120

C. Gaucherel, H.J. Jensen / Journal of Theoretical Biology 304 (2012) 111–120

In steady-state conditions, (daw/dt) ¼(dab/dt)¼0 and the temperature of daisies ranges between 7.75 1C and 36.95 1C, since the growth rates must be at least equal to the death rate. It is finally possible to define the mean albedo and the effective planetary temperature linked to the insolation or solar luminosity S: A ¼ aw Aw þab Ab þ ag Ag ,

sT 4e ¼ Sð1AÞ

ð9Þ

Insolation is playing the role of the environmental pressure, which drives the evolution of the whole planet (see Eq. (5)). We will vary the insolation S in a way that helps us to understand the response of the heterogeneous population made of NAQ and AQ daisies. 1.2. The spatial mutating Daisyworld Early version of the model neglected local interactions between daisies as well as mutations. This allows focusing on the effect of local interactions on the ability for adaptive system behavior. We have here followed the lead of others to construct a spatial Daisyworld, using the same numerical values when possible (Lenton and van Oijen, 2002). We consider a square grid with eight neighbors to each cell. The probability of seeding an empty cell (poff ¼0.001) is used to enable populations to establish, but once they are established it has little impact. For an empty cell with nb black neighbors each with growth rate bb and nw white neighbors each with growth rate bw, the following reproduction (called colonization principle, in the initial model) principles apply. The probability that black will colonize when only they are present is Pðb9nw ¼ 0Þ ¼ 1ð1bb Þnb

ð10Þ

The probability that white will colonize when only they are present is Pðw9nb ¼ 0Þ ¼ 1ð1bw Þnw The probability that the cell remains empty is PðrÞ ¼ 1Pðw9nb ¼ 0ÞPðb9nw ¼ 0Þ The probability that black will colonize when both daisies are present is PðbÞ ¼

ð1PðeÞÞPðb9nw ¼ 0Þ Pðb9nw ¼ 0Þ þ Pðw9nb ¼ 0Þ

The probability that white will colonize when both daisies are present is PðwÞ ¼

ð1PðeÞÞPðw9nb ¼ 0Þ Pðb9nw ¼ 0Þ þ Pðw9nb ¼ 0Þ

The spatial Daisyworld model has less smooth dynamics than the original zero-dimensional model, in that it can exhibit bifurcations and limit cycling as shown in details by Lenton (Lenton and van Oijen, 2002). Note that the system is stabilized by at least three effects: if one daisy type reaches an uninhabitable temperature, the other may still be able to spread because of their different local temperature; in the mid-range of forcing, a combination of both daisy types generates a global temperature closer to optimal; and the presence of one daisy type reduces the area available for the other to expand. We concentrated here on the spatial effects. Life may develop the ability to drive an environmental variable into an uninhabitable or barely habitable

state, if the environmental effect is strong and local interactions that encourage growth outweigh negative feedback on growth from the environment. In the initial growth phase, clusters form and cells at the edge of clusters are better able to spread than those within clusters. This first version of the model does not include natural selection, in that all the daisies are identical and are always equally fit in terms of growth rate. Following Lenton, we used a Daisyworld version with random mutation of albedo to the model, generalizing the previous reproduction equations to deal with any albedo type (Lenton and van Oijen, 2002). Mutations are assumed to always occur in the process of reproduction of an empty cell. Albedo can mutate within a parameterized width of the parent albedo a (here, Damax ¼ 7 0:05, by 10  5 steps). Limits to mutations are set between Ab (0.15) and Aw (0.65). As mentioned in the literature, with mutation and natural selection within the model system, its behavior could be said to be ‘adaptive’ in that it evolves to counteract forcing. Increasing Damax drives the average planetary temperature more rapidly towards the optimum for daisy growth. We developed on this basis a Daisyworld model with two competing evolution rules.

References Ackley, D.H., Littman, M.L., 1993. A case for Lamarckian evolution. In: Langton, C.G. (Ed.), Articial Life III: SFI Studies in the Sciences of Complexity, vol. XVII. Addison-Wesley, Reading, MA, pp. 3–10. Bouchard, F., 2009. Understanding colonial traits using symbiosis research and ecosystem ecology. Biol. Theory 4, 240–246. Darwin, C., 1859. On the Origin of Species by Means of Natural Selection or the Preservation of Favoured Races in the Struggle for Life. John Murray, London. Downing, K., Zvirinsky, P., 1999. The simulated evolution of biochemical guilds: reconciling Gaia theory and natural selection. Artif. Life 5, 291–318. Gould, S.J., 2002. The Structure of Evolutionary Theory. The Belknap Press of Harvard University Press. Jablonka, E., Lamb, M.J., 2006a. Evolution in Four Dimensions. Genetic, Epigenetic, Behavioral, and Symbolic Variation in the History of Life. The MIT Press, Cambridge, MA, England. Jablonka, E., Lamb, M.J., 2006b. The evolution of information in the major transitions. J. Theor. Biol. 239, 236–246. Lenton, T.M., 1998. Gaia and natural selection. Nature 394, 439–447. Lenton, T.M., van Oijen, M., 2002. Gaia as a complex adaptive system. Philos. Trans. R. Soc. London Ser. B-Biol. Sci. 357, 683–695. Lovelock, J., 2003. The living Earth. Nature 426, 769–770. Lovelock, J., Margulis, L., 1974. Atmospheric homeostasis by and for the biosphere: the gaia hypothesis. Tellus, 36. Maynard-Smith, J., Szathma´ry, E., 1995. The Major Transitions in Evolution. W.H. Freeman, Oxford. Paenke, I., Sendhoff, B., Rowe, J., Fernando, C., 2007. On the Adaptive Disadvantage of Lamarckianism in Rapidly Changing Environments, vol. 4648/2007. Springer-Verlag, Berlin, Heidelberg, pp. 355–364. Pianka, E.R., 1970. On r and K selection. Am. Nat. 104, 592–597. Por, F.D., 2006. The actuality of Lamarck: towards the bicentenary of his Philosophie Zoologique. Integr. Zool. 1 (48), 52. Roff, D., 1992. The Evolution of Life Histories: Theory and Analysis. London, Routledge, Chapman and Hall. Sasaki, T., Tokoro, M., 2000. Comparison between Lamarckian and Darwinian evolution on a model using neural networks and genetic algorithms. Knowl. Inform. Syst. 2, 201–222. Saunders, P.T., 1994. Evolution without Natural-Selection—further implications of the Daisyworld Parable. J. Theor. Biol. 166, 365–373. Sugimoto, T., 2002. Darwinian evolution does not rule out the gaia hypothesis. J. Theor. Biol. 218, 447–455. Von Bloh, W., Block, A., Schellnhuber, H.J., 1997. Self-stabilization of the biosphere under global change: a tutorial geophysiological approach. Tellus Ser. B-Chem. Phys. Meteorol. 49, 249–262. Watson, A.J., Lovelock, J., 1983. Biological homeostasis of the global environment: the parable of Daisyworld. Tellus B 35B, 284–289.