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Laurent Loison
email: laurentloison@yahoo.fr

Disentangling Genetic Assimilation from the Baldwin Effect: A Philosophical Perspective

Keywords: genetic assimilation, Baldwin effect, dispositional property, systemic property, Ivan Schmalhausen, Conrad Waddington

Since the early 1950s, there has been lingering terminological and conceptual confusion in evolutionary biology regarding the definition and mechanism of the Baldwin effect (BE) and genetic assimilation (GA). This paper aims at clearing it up by proposing a distinction of the conceptions of the phenotypic effects of genetic mutations in BE and GA, relying on a classical distinction in metaphysics between two main kinds of properties: "extrinsic" and "intrinsic". I argue that in its traditional understanding, BE implies that mutations' effects on the phenotype are dispositional (i.e. intrinsic) properties, whereas GA needs them to be systemic (i.e. extrinsic) properties.

Introduction

Since its earliest days, i.e. since 1896-1897 and the publication of Baldwin's, Lloyd Morgan's and Osborn's foundational papers, the history of the Baldwin effect has mainly been a history of controversies about its definition. Many names and almost as many ways to depict this evolutionary mechanism have been proposed: "organic selection" [START_REF] Baldwin | A new factor in evolution[END_REF][START_REF] Baldwin | Development and Evolution[END_REF], "coincident selection" (Russian school), "post-adaptation" [START_REF] Hovasse | Adaptation et changement de milieu : préadaptation ou postadaptation ?[END_REF], "stabilizing selection" [START_REF] Schmalhausen | Stabilizing selection and its place among the factors of evolution[END_REF], "genetic assimilation" (Waddington, 1953a), "Baldwin effect" [START_REF] Simpson | The Baldwin effect[END_REF], etc. The debate is still going on today, as the important book by Mary-Jane West-Eberhard has recently shown [START_REF] West-Eberhard | Developmental Plasticity and Evolution[END_REF]. This terminological and conceptual uncertainty has at least a twofold origin. (1) All these evolutionary mechanisms are designed to explain the same phenomenology: the progressive genetic reinforcement of a phenotype that was first elicited by specific and unusual environmental conditions. (2) Major ambiguities between the description of the stages of the phenomenon and the explanation of its causality have always existed. This is exactly why Waddington and Schmalhausen opposed the view that their own conceptualization might be understood in the terms of the Baldwin effect (Schmalhausen, 1949, p. 204;[START_REF] Waddington | The 'Baldwin effect,' 'genetic assimilation,' and 'homeostasis[END_REF]Levit et al., 2006, pp. 101-102). For Waddington especially, genetic assimilation (thereafter GA) was supposed to involve a completely different mode of causality than the Baldwin effect (thereafter BE), which he saw as an almost ineffective process in adaptive evolution (Waddington, 1961, pp. 287-288;[START_REF] Loison | Canalization and genetic assimilation: Reassessing the radicality of the Waddingtonian concept of inheritance of acquired characters[END_REF].

Were Waddington and Schmalhausen right? Are there good reasons to draw a substantial distinction between BE on the one side and GA (or "stabilizing selection" as defined by Schmalhausen) on the other? This question is difficult, in particular because some arguments developed during the 1950s and 1960s might no longer seem valid. For instance, one of the main reasons Waddington opposed the identification of BE and GA was that plasticity should be itself conceived as an evolved and hereditary property that is the target of selection, an aspect that was, according to him, ignored in BE [START_REF] Waddington | The 'Baldwin effect,' 'genetic assimilation,' and 'homeostasis[END_REF][START_REF] Waddington | Genetic assimilation[END_REF]). Yet, it happens that this issue was already discussed at the very beginning [START_REF] Baldwin | A new factor in evolution[END_REF](Baldwin, , p. 551, 1902, p. 157), p. 157), and, even it is true that this aspect was absent in some definitions proposed in the mid-1950s (Emerson, 1958, p. 318;Mayr, 1958, p. 354), the genetic basis of plasticity was quickly reintroduced in the standard definition of BE around 1960. For example, one of the most influential definitions of BE was formulated by Ernst Mayr in his seminal book Animal Species and Evolution (Mayr, 1963, p. 610, my emphasis):

" Simpson (1953b), who gives an excellent critical discussion of the Baldwin effect, points out that it involves three steps (rephrased by me):

(1) The genetically determined reaction norms of individual organisms permit the development of behavioral, physiological, or structural modifications of the phenotype which are not hereditary as such, but which are advantageous for survival and permit the descendants of the organisms that have them to continue in the given environment; (2) Mutations (and gene combinations) occur in this population that produce the favored phenotype obligatory and rigidly rather than as a facultative modification;

(3) The genetic factors under (2) are favored by natural selection and therefore spread in the population over the course of generations until the facultative character becomes obligatory and fixed."

Thus, it could perfectly be the case that Waddington and Schmalhausen were wrong in their effort to distance their views from BE. The aim of the present paper is to show that they were not. Based on a careful study of the literature published since 1896 until now, I will characterize and emphasize what might be a key difference between these two evolutionary mechanisms. My specific claim is that BE and GA can be distinguished on the basis of their different understandings of the phenotypic effects of genetic mutations. My argument will rely on a classical distinction in metaphysics between two main kinds of properties: "extrinsic" and "intrinsic". I will put forth that, in its traditional (i.e. "Simpsonian") understanding, BE implies mutations' effects on the phenotype to be dispositional (intrinsic) properties of the mutations, whereas GA needs them to be systemic (extrinsic) properties. In the first case, the phenotypic effect is a property of the mutation itself (this is why a selective coefficient could be ascribed to a specific allele). In the second case, the phenotypic effect is the outcome of an interacting process that encompasses the whole genome and the developmental system. This philosophical distinction has direct implications on both experimental and theoretical levels, some of which will be addressed in the last section of the present article.

Why most existing attempts at distinction are unsatisfactory

Most of the time, BE and GA are understood as more or less synonymous phrases that refer to equivalent concepts [START_REF] Loison | Canalization and genetic assimilation: Reassessing the radicality of the Waddingtonian concept of inheritance of acquired characters[END_REF]. Nowadays, it seems that the term "genetic assimilation" is by far the most commonly used, without any necessary reference to the original Waddingtonian conception. Yet, a few biologists are unsatisfied with this terminological vagueness and have recently proposed ways to distinguish between these two mechanisms. In this section, I argue that these existing attempts at demarcation are not conclusive, either because they are misleading (1.a.) or because they remain incomplete (1.b.).

a. The issue of the decrease of plasticity: an unwarranted and inoperative criterion

West-Eberhard and Crispo have been especially eager to disentangle BE and GA. A part of West-Eberhard's argument in her 800-page book is indeed that BE is a much more interesting mechanism than GA because it does not necessarily imply a decrease of plasticity in the course of adaptive evolution. At the same time, she explicitly opposes the view that GA could be of any interest, because, in her understanding, the concept of canalization deprives the developmental process of any creative significance in evolution (West-Eberhard, 2003, p. 7, p. 8, p. 25). In such a theoretical framework, the distinction between GA and BE is simple and straightforward: "The Baldwin effect [START_REF] Baldwin | A new factor in evolution[END_REF][START_REF] Baldwin | Development and Evolution[END_REF]) is a broader concept (see chapter 6). It includes the possibility of selection for increased condition sensitivity rather than just increased genotypic influence on trait expression" (West-Eberhard, 2003, p. 24; see also p. 151). The exact same distinction is supported in Crispo's 2007 review [START_REF] Crispo | The Baldwin Effect and Genetic Assimilation: Revisiting Two Mechanisms of Evolutionary Change Mediated by Phenotypic Plasticity[END_REF](Crispo , p. 2474)). This distinction is historically difficult to support, and introduces further confusion in the literature. Additionally and may be more importantly, it remains unsatisfactory because it focuses only on BE and GA's possible outcomes and not on their causal mechanism.

First, the Baldwin effect, for most scientists from Lloyd [START_REF] Morgan | On modification and variation[END_REF] and Osborn (1896) to [START_REF] Simpson | The Baldwin effect[END_REF], has been about a loss in plasticity, about hereditary fixation. For Baldwin himself, the issue is more problematic and open. On some occasions, when he reflected on human evolution and intelligence, he did consider that "organic selection", in the end, could preserve or even enhance plasticity (Baldwin, 1902, p. 35; see also p. 117 and p. 207; West-Eberhard refers to those paragraphs precisely (West-Eberhard, 2003, p. 151)). Still in 1909, in Darwin and The Humanities, he argued that "in cases where the intelligent or other adjustive factor is on the whole of greater utility, variations toward the disintegration of the instinctive congenital part would be selected" (Baldwin, 1909, p. 21). Yet, such an understanding is missing from the various definitions of organic selection he proposed (see section 2.b.), conceiving it as a more general evolutionary mechanism not restricted to mental evolution in higher vertebrates. For instance, in Development and Evolution, he summarized his theory of "orthoplasy", i.e. the causal process of both organic selection and social heredity, into a diagrammatic representation where the "congenital" variations gradually tend to replace "accommodations" (Baldwin 1902, p. 188):

Half a century later, in Simpson's classical account, the decrease of plasticity is unambiguously pictured as the necessary outcome of BE (Simpson, 1953, p. 112, my emphasis):

"(1) Individual organisms interact with the environment in such a way as systematically to produce in them behavioral, physiological, or structural modifications that are not hereditary as such but that are advantageous for survival, i.e., are adaptive for the individuals having them.

(2) There occur in the population genetic factors producing hereditary characteristics similar to the individual modification referred to in (1), or having the same sorts of adaptive advantages.

(3) The genetic factors of (2) are favored by natural selection and tend to spread in the population over the course of generations. The net result is that adaptation originally individual and non-hereditary becomes hereditary."

Moreover, when Mayr entered the debate in the late 1950s and early 1960s, he explicitly opposed BE on the ground that if plasticity is an advantageous character, then natural selection will maintain or even enhance it whereas in BE the new phenotype will in the end be produced "obligatorily and rigidly rather than as a facultative modification" (Mayr, 1963, p. 610, my emphasis). In other words, a process of selective maintenance or improvement of phenotypic plasticity, is, according to Mayr, a completely legitimate hypothesis in the framework of the standard Modern Synthesis (Mayr, 1963, pp. 611-612):

"The Baldwin effect makes the tacit assumption that phenotypic rigidity is selectively superior to phenotypic flexibility. This is certainly often not true. […] It would seem to me that either an epigenetic system such as is found in many plants, in which the phenotype is highly modifiable, or one like that described by Thoday (1953) and Lerner (1954), which achieves great phenotypical stability in spite of great genetic variability, through developmental flexibility, would be selectively superior to the system postulated in the Baldwin effect."

Given what history tells us, it seems difficult to support the view that a definition of the Baldwin effect should be primarily based on the idea of an increase in plasticity.

Second, and more importantly, to depict GA as a mechanism that will reduce a trait's plasticity is a superficial and incorrect interpretation of Waddington's and Schmalhausen's work. What GA is about cannot be reduced to only the over-simplistic idea of genetic fixation of a plastic trait. The misunderstanding comes from (1) the intrinsic difficulty (and sometimes obscurity) of Waddington's and Schmalhausen's writings; (2) a focus on discrete traits instead of reaction norms; (3) the fact that, usually, canalization and plasticity are understood as strictly opposite properties. As Pigliucci has recently emphasized, this last assumption is inaccurate, given that plasticity could itself be a canalized property (Pigliucci, 2010, pp. 357-358). Such an asymmetric conception of these two properties was already pivotalyet rarely explicitly -in Waddington's and Schmalhausen's original work. To them, GA was about the transformation of the developmental phase space (the so-called "epigenetic landscape" for Waddington) where some favored pathways will become more canalized, i.e. more resistant to genetic and environmental perturbations, and others less, then significantly altering the reaction norm.

Thus, a much more faithful and enriched characterization of GA should underline the fact that it is a populational transformation of the reaction norm that will result in the canalization of a new one -what Waddington termed the "tuning" of canalization. This more specific definition of GA has an immediate and important consequence: the same canalized reaction norm could be builtprecisely because it is canalizedon a wide range of different sets of genetic factors. This aspect will be given special attention in section 3.a.

The fact that GA is about the transformation of a reaction norm and not about a loss of plasticity is especially clear in Schmalhausen's 1949 book Factors of Evolution, The Theory of Stabilizing Selection. As he emphasized repeatedly, "modern genetic analysis does not operate with traits but only with the norms of reactions of organisms and their hereditary variations" (Schmalhausen, 1949, p. 139). He distinguished between two types of phenotypic variations causally produced by a change in the environment: "modifications" and "morphoses". Modifications are plastic and adaptive responses encoded in the genome, the environmental change being only a signal inducing a developmental mechanism that will automatically lead to them. On the other hand, morphoses are the consequences of more drastic environmental changes, pushing embryogenesis beyond the standard canalized reaction norm. GA, as Schmalhausen conceived it,1 consists in the evolutionary transformation of morphoses into modifications, i.e. in the progressive rebuilding of a new reaction norm (Schamlhausen, 1949, pp. 8-10). Stabilizing selection will reconstruct the developmental basis of the new reaction norm (called "adaptive norm" in the quotation below), one of the most creative aspects of evolution (Schmalhausen, 1949, p. 204, my emphasis):

"The specific results of such reactions are said to be stabilized when a given modification has been acquired by an entire population over a number of generations. It is known that the action of stabilizing selection is based upon a selective advantage possessed by the adaptive norm (including also new adaptations) over all deviations from it. It operates by the accumulation of all mutations which do not bring the phenotype beyond the limits of the established norm."

From cover to cover, Factors of Evolution is a theoretical dissertation devoted to a single topic: how a norm of reaction defined at a populational level could be transformed and stabilized into a new one. At the end of his book, Schmalhausen made sure to emphasize the fact that this ongoing process, driven by stabilizing selection, will not at all lead to a decrease in plasticity, but exactly to the opposite (Schmalhausen, 1949, pp. 242-243):

"In stressing the importance of the stabilization of morphogenesis and the role of stabilizing selection in this process, in order to avoid misunderstanding it must be pointed out that, in the opinion of the author, this stabilization of form does exclude the converse process of labilization. Moreover, there is no implication here of the existence of a tendency towards a decline in individual lability, especially in the adaptivity of forms (nor is there any implication of a diminution of evolutionary plasticity or a "congelation of form" in the sense of Beurlen). On the contrary, attention is called to the increasing plasticity of organic forms, to the growing importance of individual adaptability, and to the organic bond existing between the processes that make for instability and stability of forms. Instability in the general reactions (the acquisition of new norms of general value) is accompanied by stability in particular reactions; namely, by the autonomization of development and the incorporation of new differentiations into the normal organization. Simultaneously with the continuous stabilization of special types of reaction, in particular, of functional differentiations which have attained permanent value in the given conditions of existence, there are also acquired entirely new reactions forms. And the capacity for individual adaptability, including the capacity for adaptive modifications, is based upon these new reaction forms. The capacity for more extensive adaptation is an important acquisition which leads the organism into new paths of progressive evolution."

It follows, again, if we consider history of science seriously, that GA cannot be defined as a mechanism that will lead to a loss of plasticity. The distinction supported by Crispo and by West-Eberhard is not historically grounded. Moreover, focusing only on BE and GA's possible end-results means ignoring the causal mechanisms at stake, i.e. the issue's most central aspect. A conceptually fecund distinction should primarily say something about evolutionary causality.

b. Existing hidden mutations versus new mutations

Possibly the most frequently used criterion for the few who have tried to distinguish between GA and BE is the origin of the mutations leading to the genetic reinforcement of the initially plastic and individual response, this time an aspect that is directly related to the causality involved. It is argued that, at least in its original Waddingtonian understanding, GA is an adaptive process that, contrary to BE, does not need new spontaneous mutations to occur. GA builds adaptations only with existing genetic variability (i.e. "hidden" or "cryptic" mutations), an intrinsic polymorphism that previously remained phenotypically unexpressed because of the canalization of development.

For example, Brian K. Hall bases his demarcation between BE and GA mostly on this criterion (from Hall, 2001, p. 220):

This specificity of the Waddingtonian concept of GA has also been recently emphasized by Laura Fanti and her colleagues in their experiments of selection of de novo induced mutations in Drosophila. In their proposed model, the induced stress increases mutability, which favors the probability of occurrence of adaptive mutations that will eventually be selected and fixed. They are perfectly aware that on this aspect, their own evolutionary model "recalls the concept of 'organic selection', also defined as 'the Baldwin effect'" [START_REF] Fanti | Canalization by Selection of de Novo Induced Mutations[END_REF](Fanti et al. , p. 2005)).

This distinction is without a doubt a historically grounded one: it is true that throughout its history, BE had been conceptualized as requiring the occurrence of adaptive mutations (see section 2.b. for more details) and that GA, as defined by Waddington and Schmalhausen, had been on the contrary based only on existing cryptic mutations (Schmalhausen, 1949, p. 127;[START_REF] Waddington | The Strategy of the Genes[END_REF][START_REF] Waddington | Genetic assimilation[END_REF]). Yet, even if this distinction is historically founded, it remains unsatisfactory unless further developed, because we do not understand why it would matter: what are the reasons why Waddington and Schmalhausen always emphasize this aspect? Could GA involve new mutations instead of existing ones without significant conceptual alterations? Moreover, many theoretical models in population genetics are based on populations of infinite size, which implies that all the genetic variants are present. In such cases, what is left from such a demarcation? As far as I know, these questions are never asked, which makes this distinction only of descriptive and limited value.

The rest of the present article is indeed specifically devoted to the explanation of the theoretical meaning of the distinction between hidden mutations and new mutations. My aim is to show why this distinction was so central to Waddington and Schmalhausen, and why their argument might still be relevant today.

Mutations' effects: Extrinsic or intrinsic properties? a. What metaphysics tells us

In order to develop the clearest argument possible regarding this pivotal theoretical aspect, I will rely on a series of conceptual distinctions that have a long history in metaphysics. The most fundamental is between two main kinds of properties that can be ascribed to entities, extrinsic versus intrinsic. This distinction is usually introduced as follows: intrinsic properties are those that characterize an entity only because of what it is (mass is the textbook example of this) whereas extrinsic properties result from the interactions between this entity and the world (such as weight).

David Lewis's work in the 1980s was the starting point of several attempts at clarification, which philosophers are currently still working on. Some excerpts from his 1983 article "Extrinsic properties" are of particular interest for my argument. The most helpful might be the following: "The intrinsic properties of something depend only on that thing; whereas the extrinsic properties of something may depend, wholly or partly, on something else. If something has an intrinsic property, then so does any duplicate of that thing; whereas duplicates situated in different surroundings will differ in their extrinsic properties" (Lewis, 1983, p. 197).

This quotation emphasizes two aspects specifically: (1) an entity's extrinsic property cannot be described without referring to something else than the entity (2) it will differ depending on the environment ("surroundings"). My aim is to show, in the next section, that these two aspects are especially well suited to accounting for the phenotypic effects (the properties) of mutations (the entity or the "thing") when one compares BE and GA. In BE, phenotypic effects are close to intrinsic properties of genetic mutations, whereas in GA, they are extrinsic properties that "depend, wholly or partly, on something else", in this case the developmental system.

This classical distinction between extrinsic and intrinsic properties has recently been a core concern in the reappraisal of the stem cell concept. In a series of publications, Lucie Laplane elaborated a more precise typology, distinguishing four forms of properties: categorical, dispositional, relational and systemic [START_REF] Laplane | Cancer Stem Cells, Philosophy and Therapies[END_REF][START_REF] Laplane | Towards a classification of stem cells[END_REF]. A categorical property is an intrinsic property that is independent of any interaction with surrounding entities (e.g., the atomic mass of an element). A dispositional property is also an intrinsic feature, but one that only manifests upon interaction with external stimuli (e.g., fragility, which is apparent only on impact). A relational property is an extrinsic property that relies on the interaction between entities (e.g., body weight, which depends on gravity). Lastly, a systemic property is a characteristic that is provided and maintained by the system, i.e. one where the intrinsic properties of the entity considered are almost irrelevant.

These new distinctions prove to be fruitful in the reconsideration of different kinds, ontologically speaking, of stem cells [START_REF] Laplane | Cancer Stem Cells, Philosophy and Therapies[END_REF]. In sections 2.b. and 2.c., I will support the view that two of these four categories are tailor-made to account for how the effects of genetic mutations have been considered in GE on the one hand and by Schmalhausen and Waddington on the other. Throughout the history of BE, mutations' effects have been thought as dispositional properties, which could be expressed or not depending on various conditions, but remain nevertheless intrinsic features of the mutations themselves. This understanding is far broader than the one at work in BE, and is also at the basis of the Modern Synthesis (MS). This is why selective coefficients, in standard population genetic models, could be directly ascribed to alleles. On the contrary, for Waddington and Schmalhausen, as I will argue, mutations' effects are best defined as systemic properties, because their consequences on the phenotype are in the main provided by the developmental system as a whole.

b. BE: phenotypic effects as dispositional properties of mutations

At the root of the MS is the idea that mutations are random variations regarding adaptation: there is a causal independence between the probability that a mutation will occur and its fitness in a given environment. This axiomatic proposition implies that the effect of a mutation is an intrinsic property in the sense defined in the previous section: the causal relationship between a genotype and a phenotype is robust enough that it means something to say that mutations are random. It would be complete nonsense to base an explanatory framework on the randomness of genetic mutations if their phenotypic effects were not the consequences of what they are essentially.

The effect of a single mutation could of course be altered by various features such as the presence of other alleles (genetic background) or the "environment". Yet, it remains that genes have phenotypic effects that are specific enoughi.e., the genotype-phenotype map is close to linearthat it is reasonable to ascribe selective coefficients to genotypes if not to single alleles, even if the competitive interactions arise in the main at the organism's level. This is the very basis of the mechanistic models of standard population genetics.

From the start, i.e. from the late 1890s, and until nowadays, this view has also been universally expressed in the numerous definitions proposed for BE. In BE, the plastic response is important first because it allows time for adaptive mutations to occur. Adaptive mutations are the ones that parallel plastic accommodations. The property of being adaptiveor maladaptiveis an intrinsic feature of the mutation. The table below presents a representative sample of BE definitions elaborated over more than a century (note that before 1900 and the rediscovery of Mendel's laws, "variations" or "congenital variations" was the term used for what is now called mutations).

J.M. Baldwin

1902 "The imitative function, by using muscular coordinations, supplements them, secures accommodations, keeps the creature alive, prevents the incidence of natural selection, and so gives the species all the time necessary to get the variations required for the full instinctive performance of the function." S. Kirpichnikov 1947 "If individual adaptive modifications happen to be present, those among the numerous divers congenital variations will be favoured that are coincident with a given useful modification. Such variations will gradually accumulate. If the conditions that called forth the given plastic modification are continued for a considerable period, the accumulation of coincident variations will progress slowly, but inevitably." G.F. [START_REF] Gause | Problems of evolution[END_REF][START_REF] Baldwin | A new factor in evolution[END_REF][START_REF] Baldwin | Development and Evolution[END_REF], [START_REF] Osborn | The limits of organic selection[END_REF] and Lloyd Morgan (1900) suggested about half a century ago that modifications repeated for a number of generations may serve as the first step in evolutionary change, not by becoming impressed upon the germ-plasm, but by holding the strain in an environment where mutations tending in the same direction will be selected and incorporated into the constitution." R. Hovasse (my translation from French)

1950 "Thanks to these non-inherited phenotypes [accommodats], however, the organism finds itself in harmony with its environment: it is temporarily adjusted, and, in a sense, able to wait… For the arrival, one day or the other, among the germinal variations found in each organism, of mutations corresponding to adaptive noninherited phenotypes, and that are vis-à-vis the latter "coincident"; they will find themselves automatically retained by the selective sieve, already oriented "as appropriate". Thus the ontogenetic modification will be able to become congenital; in other words, the summation, the non-inherited phenotype, will become mutations, or more accurately, will be replaced by corresponding mutations." J. [START_REF] Huxley | Evolution, The Modern Synthesis[END_REF]We have here a beautiful case of the principle of organic selection (p. 523), as enunciated by [START_REF] Baldwin | A new factor in evolution[END_REF][START_REF] Baldwin | Development and Evolution[END_REF] and Lloyd Morgan (1900), according to which modifications repeated for a number of generations may serve as the first step in evolutionary change, not by becoming impressed upon the germ-plasm, but by holding the strain in an environment where mutations tending in the same direction will be selected and incorporated into the constitution. The process simulates Lamarckism but actually consists in the replacement of modifications by mutations (see also [START_REF] Osborn | The limits of organic selection[END_REF]." B.K. [START_REF] Hall | Baldwin and Beyond: Organic Selection and Genetic Assimilation[END_REF]The essential elements of organic selection therefore are:

-animals choose a new habitat or life style and adapt to it; -mutations occur that favor the changes; and -selection favors those individuals best adapted to that new habitat or life style, and the adaptation spreads through the population" P. Godfrey-Smith 2003 "Here is my understanding of the original 'effect.' Suppose a population encounters a new environmental condition, in which its old behavioral strategies are inappropriate. If some members of the population are plastic with respect to their behavioral program, and can acquire in the course of their lifetime new behavioral skills that fit their new surroundings, these plastic individuals will survive and reproduce at the expense of less flexible individuals. The population will then have the chance to produce mutations that cause organisms to exhibit the new optimal behavioral profile without the need for learning. Selection will favor these mutants, and in time the behaviors which once had to be learned will be innate." Sznajder et al. 2012 "The prediction from theory on the Baldwin effect is that if genetic variation in the direction of the learned traits exists (or it subsequently occurs through mutation) then there is potential for learning to guide the evolution of the genetic basis for these traits (provided that they are indeed positively associated with fitness)."

I hope these instances unambiguously demonstrate that from the start and throughout this complex history phenotypic effects have been conceived as something close to intrinsic properties of mutations. Essentially, BE is about allowing time for "good mutations" to spontaneously occur and be selected. This aspect is especially apparent in the term "coincident" variations/mutations, initially coined by Lloyd Morgan in the late 1890s and then very quickly used by other biologists, including Baldwin himself (Baldwin, 1902, p. 142). To label a mutation "coincident" clearly underlines that its phenotypic effect is a consequence that can be traced back to the mutation itself: some have the property to mimic the plastic response, others have not.

In BE, the issue of the preexistence of these "good" mutations is indeed irrelevant. Whether they were there before or not does not change the fact that they are coincident because of what they are essentially, i.e. intrinsically. Statistically speaking, the most probable is that most of them are not already present in a population, but this remains an empirical question for existing populations.

All being considered, such an understanding is nothing more than what is already at stake within the standard MS. This is why, for instance, Mayr always claimed that BE was not a threat. It is only chance mutations and natural selection.

c. GA: phenotypic effects as systemic properties of the developmental system

Things are completely different when one carefully looks at Schamlhausen's and Waddington's writings.

In Factors of Evolution's second part, Schmalhausen gradually develops a conception of mutations' effects as systemic properties of the developmental system. He starts by criticizing standard population genetics on several grounds. One of them, the most interesting for my argument, is that "even an individual mutation does not necessarily have a constant effect" (Schmalhausen, 1949, pp. 141-142). According to him, this is an over-simplistic view because mutations' effects "are influenced by individual characteristics of each genotype, so that their phenotypic expressions and their physiologic effects may vary considerably" (Schmalhausen, 1949, p. 144). The more an organism is complex, the more epistasis and pleiotropy are the rule, until a point where it becomes almost impossible to individualize a specific gene effect on the phenotype. What drives embryogenesis and the phenotype production is no longer a sum of discrete genes, but a much more complicated system that cannot be described in terms of additive gene action. Schmalhausen repeatedly emphasizes this crucial theoretical stance in the final third of his book, and especially on pages 218 and 219 (Schmalhausen, 1949, p. 219):

"As the systems of correlations become more complex, they lose their genetic character; in other words, the effects on individual genes can no longer be distinguished (more precisely their disruption by mutations has lethal consequences). Morphophysiologic interrelationships and their systems may be regarded as entities that are not capable of analysis in genetic terms. These correlation systems consist fundamentally of the mutually related vital functions of the organism, which are responsible for the harmonious course of the general physiologic processes." Thus, for Schmalhausen, there is no sense, at least for complex organisms that produce their phenotype through an elaborated developmental process, in ascribing discrete phenotypic effects to specific mutations. Phenotypic effect is a systemic property.

The same exact position can be found in Waddington's later writings, from the early 1950s until his death. As emphasized by Paul Griffiths, "in Waddington's vision, phenotypes are global expressions of genomes, but it does not follow that particular parts of the phenotype express particular parts of that genome" (Griffiths, 2006, p. 97). Already in 1953, as Waddington tried to avoid any conflation between GA and BE, he emphasized that "by speaking of mutations as 'random', which is true enough at the level of the gene as a protein-DNA complex, we obscure the fact that the effect of a mutation, as far as natural selection is concerned, is conditioned by the way it modifies the reaction with the environment of a genotype which has already been selected on the basis of its response to that environment" (Waddington, 1953b, p. 386, my emphasis). He makes this point much explicit and clearer in his 1957 magnum opus, The Strategy of the Genes (Waddington, 1957, p. 188, my emphasis):

"We have been led to conclude that natural selection for the ability to develop adaptively in relation to the environment will build up an epigenetic landscape which in its turn guides the phenotypic effects of the mutations available. In the light of this, the conventional statement that the raw materials of evolution are provided by random mutation appears hollow. The changes which occur in the nucleoproteins of the may well be indeterminate, but the phenotypic effects of the alleles which have not yet been utilized in evolution cannot adequately be characterized as 'random': they are conditioned by the modelling of the epigenetic landscape into a form which favours those paths of development which lead to end-states adapted to the environment." Such a conception, at odds with the standard view of the MS, can be found in many articles and books after 1957 and should not be seen as a speculative and secondary proposition. It was at the core of Waddington's thinking (see for example Waddington, 1959, p. 56;1961, p. 288;1968, pp. 184-185).

This explains why it matters, for both Schmalhausen and Waddington, that GA works on existing mutations (and does not need to wait for "coincident" ones). GA needs hidden genetic diversity in order to rebuild developmental pathways, but GA, in opposition to BE, does not need specific mutations precisely because phenotypic effects are close to systemic properties. Thus, this philosophical distinction between GA and BE explains why the criterion to distinguish between existing mutations and new mutations is relevant, i.e. why it makes sense in Schmalhausen's and Waddington's theoretical framework.

Theoretical and experimental implications: a quick overview

If this distinction between GA and BE is well-founded, it implies a series of consequences on both experimental and theoretical levels for the mechanism of GA. As I cannot address them all in detail in this section, I will only offer a brief survey.

a. GA: multiple realizability of the same reaction norm by different sets of genes

What might be the most immediate implication of such a systemic understanding of mutations' effects concerns the final genetic reinforcement of the new reaction norm. It is not a single "coincident" mutation or even a few genes that accommodate and hereditarily stabilize phenotypic change, but "a new system of genic connections" (Schmalhausen, 1949, p. 155). In 1953, Waddington already emphasized this aspect too when he wrote that "the same phenotypic effect might be produced with quite a different genetic basis" (Waddington, 1953a, p. 124).

In the late 1950s and 1960s, he tirelessly restated its centrality for GA, especially in comparison to BE. In his detailed 1961review, he concluded that GA involves the genome as a whole (Waddington, 1961, p. 264 and p. 267), exactly as Schmalhausen did in 1949 (Schmalhausen, 1949, p. 219 and p. 229).

A contextual difference between Waddington and Schmalhausen is that Schmalhausen was greatly affected by Lysenkoism in USSR, to such an extent that he was unable to conduct any experimental researches on evolution in the early 1950s [START_REF] Levit | From the 'Modern Synthesis' to Cybernetics: Ivan Ivanovich Schmalhausen (1884-1963) and his Research Program for a Synthesis of Evolutionary and Developmental Biology[END_REF]. During those crucial years, Waddington, in the much more peaceful and conducive environment of the University of Edinburgh, was able to devise several key experiments for testing some aspects of GA. In the late 1950s, in close collaboration with his student K.G. Bateman, he designed experiments to test the possibility that a single phenotype could be stabilized upon different genetic bases (1956)(1957)(1958)(1959). Using several stocks of Drosophila, the goal was to observe weather or not different strains might evolve, through GA, towards the same adaptive phenotype despite their initial genetic differences. Bateman repeated and extended the original experiments on the selection of the four venation phenocopies (namely pcvl, acvl, fpcv and smcv). Waddington and Bateman eventually came to disagree about the results and their interpretation. For Bateman, if these series of experiments unambiguously shows the reality of GA, it remains that "assimilated characters are not controlled merely by an indefinite number of genes of individually small effect, i.e. are not 'polygenic'" (Bateman, 1959, p. 461). On the contrary, for Waddington, GA "have involved changes at many loci throughout the whole genotype" (Waddington, 1961, p. 267).

This direct implication for GA of the fact that mutations effects are systemic properties is also explicit in Waddington's numerous diagrammatic representations, and especially in one of the more meaningful figures published in The Strategy of the Genes. In Figure 5 (p. 36), he aimed at picturing "the complex system of interactions underlying the epigenetic landscape". Each peg represents a gene and each string its contribution to the network that causally produces the epigenetic landscape.

The more present-day genetics learns about genes' products and their causal roles in development, the more these are viewed as included in a complex system of interactions, namely an interactor, where it becomes difficult to individualize the effect of a specific gene. To put it briefly, thinking of the genome in terms of Genetic Regulatory Networks (GRNs) where the topology of the network is more relevant than the genes involved gives scientific substance to some of Schmalhausen's and Waddington's core speculations (A. Wagner, 2005, Chapter 13;[START_REF] Wilkins | Between "design" and "bricolage": Genetic networks, levels of selection, and adaptive evolution[END_REF].

b. Two types of mutations, two forms of selection

If mutations' effects are close to systemic properties of the developmental system, then it also implies that natural selection is, at least in some cases, not so much about the cumulative addition of alleles with specific phenotypic expressions but rather about the stabilization/canalization of developmental paths.

This was explicitly addressed by Schmalhausen in section 2.D. of Factors of Evolution, where he contrasts two forms of selection, dynamic selection and stabilizing selection. What he calls the "dynamic role" of natural selection is the standard understanding of it: when selective pressures are changing, natural selection alters the reaction norm in order to adapt the phenotype to the new environmental conditions. "Stabilizing selection" is a different form of selection, and a creative one in its own way (Schmalhausen, 1949, pp. 92-94), because it transforms the developmental path that leads to the new phenotype. For Schmalhausen, "stabilizing selection" is close to what Waddington later termed "canalizing selection" (Waddington, 1957, p. 73), and it eventually leads to the reorganization of the interactions between the genome and the developmental system in order to optimize the reliability of the new reaction norm, which becomes resistant to genetic and environmental perturbations.

Canalizing selection produces developmental canalization and canalization, in return, guides the phenotypic effects of genetic mutations.

Therefore, as soon as the genome works as an integrated system, the process is self-reinforcing: canalization diminishes the impact of mutations, which favors the efficiency of stabilizing/canalizing selection and thus enhances canalization. In the course of evolution, as more complex organizations are produced, stabilizing selection tends to become more important and more creative than standard "dynamic" selection (Schmalhausen, 1949, pp. 238-245).

For both Waddington and Schmalhausen, canalizing/stabilizing selection was a much more powerful and complex mode of natural selection than in our modern understanding. In the standard framework of present-day evolutionary theory, stabilizing selection is often reduced to normalizing selection, i.e. cases where an intermediate phenotype for a variable trait (such as size) is the fittest (see for example Futuyma, 1998, p. 366 or Barton et al., 2007, p. 476). Normalizing selection, understood as selection against phenotypes that deviate in either direction from an optimal value of a character, has no necessary impact on canalization. Whether this was well-founded or not, Schmalhausen and Waddington attributed major consequences to stabilizing/canalizing selection, described as capable of generating canalization because of its complete restructuring of the developmental pathway leading to the adapted phenotype. Ascertaining the extent to which canalizing selection is able to produce a significant degree of canalization remains tricky to this day. This issue has been tackled anew by Günter Wagner and his colleagues since the late 1990s: on what conditions could canalization evolve [START_REF] Wagner | A population genetic theory of canalization[END_REF]? It must be emphasized that Wagner, exactly like Waddington, makes a clear-cut distinction between what he calls "stabilizing selection" (normalizing selection) and the much more interesting process of canalizing selection, which "refers to the different process by means of which the genetic architecture of the trait evolves so that it is less likely to produce extreme individuals (Gibson and Wagner, 2000, p. 374, my emphasis).

c. Genome as follower

In the wake of West-Eberhard, Pigliucci and others, the "genes-as-followers" label has gained momentum over the past twenty years or so. The positive reappraisal of the possible evolutionary role of plasticity is usually connected to the idea that the first step in a micro-evolutionary process is not the spontaneous occurrence of chance mutations but the plastic and adaptive accommodation of phenotypes to new environmental challenges [START_REF] West-Eberhard | Developmental Plasticity and Evolution[END_REF]. This primary phase of the physiological response is "buying time" [START_REF] Pennisi | Buying Time[END_REF] for genetic evolution to catch up: the phenotype takes the lead, genes are only followers. This is consistent with the logic of BE, where phenotypic effects are intrinsic properties of mutations. It is quite easy, indeed, to find instances in the history of BE of phrases very close in their formulation to our contemporary "genes-as-followers". For example, Baldwin himself put it as follows: "The line of acquired modification takes the lead, variations [i.e. mutations] follow." (Baldwin, 1902, p. 180). Yet, this BE concept of genes-as-followers is a weak one as long as phenotypic effects are intrinsic properties of mutations. If the genetic basis of an adaptation is too specific, selection of adaptive mutations remains the decisive step in the evolutionary building of adaptations, which is of course fully compatible within the internal logic of the MS. Ultimately, what is selected are the adaptive alleles, and the plastic response is reduced to only a transient phase that will necessarily lead to their fixation. This is also the main reason why BE is difficult to experimentally ascertain: in the end, establishing whether the good set of alleles has been directly or only indirectly selected remains difficult.

Whereas if (3.a.) the genome as a whole accommodated the building of the new reaction norms and if (3.b.) stabilizing/canalizing selection is a creative process, things would be significantly different. Selecting for an appropriate developmental system, in such a framework, is not tantamount to indirectly selecting for a specific set of alleles. The genome, as a system, follows developmental reorganizations. This distinct understanding, not focused on specific point mutations, might give the phenotype-as-aleader a much more creative role in the causal process of evolutionary adaptation.

Conclusion

The philosophical distinction between GA and BE proposed in the present article is founded on two opposite conceptions of the phenotypic effects of genetic mutations. Based on an almost comprehensive survey of the literature published since 1896, I put forth that BE requires phenotypic effects to be dispositional properties of mutations whereas GA, in its original and still neglected understanding, conceives them as systemic properties of the whole developmental system. The proposed distinction is purely theoretical in the sense that it does not need to be confronted to empirical knowledge to be well-founded. It could perfectly be the case that, in experimental and natural populations, there is a continuous line between cases where phenotypic variants are mostly the consequences of specific mutations and cases where such a bijective relationship is impossible to establish. As always in biology, this is an issue of relative frequencies between different theoretical possibilities and the clear-cut metaphysical distinction between "extrinsic" and "intrinsic" is unlikely to be directly applicable in our complex empirical world.

Yet, unlike in the twentieth century, nowadays, genomics and systems biology are giving more and more momentum to the idea that the genome is a highly integrated system and that new entities, the interactome and the GRNs, has to be considered between the genotype and the phenotype. This new holistic perspective is much more congruent with Schmalhausen's and Waddington's unorthodox conceptions than with the mechanistic models of standard population genetics [START_REF] Wilkins | Waddington's Unfinished Critique of Neo-Darwinian Genetics: Then and Now[END_REF].

In Factors (1946[START_REF] Schmalhausen | Factors of Evolution, The Theory of Stabilizing Selection[END_REF], Schmalhausen never used the term GA, which was coined only in 1953 byWaddington.

Acknowledgements

I would like to thank David Ceccarelli and Barbara Continenza for their invitation to contribute to this special issue. Remarks and criticisms of "reviewer 1" were especially stimulating, unfortunately, because of the very short time available for submitting the revised version, I was unable to take all of them into account. I will discuss some of them in greater detail in forthcoming works. During the first stages, the present paper greatly benefited from discussions with Lucie Laplane and Arnaud Le Rouzic, to whom I am indebted to. Last and not least, Jean-Yves Bart edited the final version of the article.


C Parmar

R Verma

S S Modak

Frédéric Mazaleyrat

Tetiana Tatarchuk
email: tatarchuk.tetyana@gmail.com

S N Kane
email: kane_sn@yahoo.com

Effect of 16 O 6+ ion-irradiation on structural, magnetic properties and antistructural modeling of Zn-nanoferrites

Keywords: Spinel ferrite, Sol-gel auto-combustion, Ion irradiation, Magnetic nanoparticles, Cationic distribution

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Ferrimagnetic spinel ferrites with general formula M 2+ Fe 3+ 2O4, display face-centered cubic fcc structure, Fd3m space group, and have two inter-penetrating sub lattices tetrahedral (A), octahedral (B) [START_REF] Smit | Ferrite[END_REF]. Structural modification of spinel ferrites brings assorted properties suitable for a wide range of applications including those in the microwave; spintronic devices, drug delivery, computer memories, bio-sensing, space application, in a radioactive environment, and Magnetic Resonance Imaging, etc. [START_REF] Willard | [END_REF]3,4,5].

Swift heavy ion (SHI) irradiation is a novel technique, used for structural modification [6], and can be employed to study the variation of structural and magnetic properties of materials [7,[START_REF] Avasthi | Swift Heavy Ions for Materials Engineering and Nanostructuring[END_REF][START_REF] Jain | Ion beam induced surface and interface engineering[END_REF]10].

When ions pass through a material, they pass on their momentum, energy to the material, and depending on the energy of ions two regimes can be defined: via nuclear energy regime (few keV), and electronic energy regime (> few MeV). Tailoring structural, magnetic properties of spinel ferrites by SHI is a work of quite a significance, as it not only increases the applicability of spinel ferrites e.

g. in photocatalytic materials for renewable energy [11], but also elucidates the interaction of swift heavy ions with magnetic nanomaterials. Studies [12] also describe the SHI irradiation-induced generation of defects in metal oxides resulting in the modifications on the surface of the nanoparticles which leads to noticeable changes in the structural and physical properties. It is well recognized that changes in the properties of materials are immensely affected by the type of ion beam; its energy, and the material composition [13]. Although literature reports SHI irradiation-induced modification of structural and magnetic properties Co-Zn, Mn-Zn, Ni-Zn, ZnFe2O4, NiFe2O4 ferrites [14,15,16,[START_REF] Sharma | AIP Conf. Proc[END_REF][START_REF] Dolia | [END_REF]19,20], it infrequently reports the effect of irradiation on the antistructural modeling to describe surface active centers, the correlation between structural, cationic distribution, and magnetic properties of Zn ferrite [20].

Thus, the current work aims to study the effect of 80 MeV the dominant process, which produces the structural modification in the material. To avoid ion implantation, sample thickness was selected such that it is less than RP, thus ions will pass through the sample.

Room temperature X-ray diffraction (XRD) measurements (θ  2θ configuration) were done by using Bruker D8 advance diffractometer utilizing Cu-Kα radiation (= 0.154056 nm). Room temperature hysteresis loops were obtained using a vibrating sample magnetometer 'VSM', (Model: Lakeshore Model 7410) by applying a maximum applied field: Hmax. = ± 1.9 ´ 10 4 Oe.

Rietveld refinement software MAUD (Material Analysis Using Diffraction) [22] was employed to obtain a Full profile analysis of XRD patterns that confirmed the formation of a single cubic spinel phase, no other phases were detected.

XRD data were analyzed to compute structural parameters: experimental lattice parameter (aexp.), cell volume (V), and X-ray density (ρxrd) as described in [16,23]. By using Williamson-Hall (W-H) method, grain diameter (DW-H) was obtained by incorporating both instrumental and strain broadening [16,24]. The XRD data of the standard LaB6 sample was used to obtain instrumental broadening. By using this method, x-ray diffraction peak broadening is given by the following expression: bhkl = bsize + bstrain. The actual peak broadening (b) is obtained by correcting the experimental peak broadening 'bex' and the instrumental broadening 'bin' as:

b 2 = bex 2 bin 2 .
Consequently, the modified form of XRD peak broadening bhkl = bsize + bstrain equation [16,24] can be given as: bhkl= (0.94 / DW-Hcosθ) + 4tanθ and bhklcosθ= (0.94 / DW-H) + 4sinθ [START_REF] Smit | Ferrite[END_REF] where  is the wavelength of the X-ray used, b is full width at half maximum (FWHM), DW-H is Williamson-Hall grain diameter, and  is a strain.

Dislocation density (rD) was calculated by using the following expression [START_REF] Parmar | AIP Conference Proceedings[END_REF]:

= 15 / . × (2)
where aexp is the lattice parameter, DW-H is Williamson-Hall grain diameter, and  is a strain.

Cationic distribution was estimated by XRD peak intensities employing Bertaut method [START_REF] Bertaut | [END_REF].

It gives cationic distribution by matching the computed, experimental ratios of intensity for: (422), (400), and (220) planes as described in [27]. For dissimilar cation distribution on A and B sites, intensity ratio: I(400)/I(422), I(220)/I(400) varies. The best cation distribution amongst the A and B sites for which theoretical, experimental ratios (Ihkl Obs. and Ihkl Cal. ) of the observed, and calculated intensities agree noticeably, is taken to be the right one. Obtained cationic distribution was used to calculate theoretical magnetization at 0 K: 'Ms(th)' (also known as Néel magnetic moment 'nN'). By utilizing the cationic distribution, oxygen position parameter (u), Inversion parameter (d), and bond angles (q1, q2, q3, q4, q5), canting angle αY-K were calculated as described in [16,23]. The bulk saturation magnetization (MB), and magnetic dead layer thickness (t) were computed as described in [16,20,28]. As magnetization curves are not saturated, but are in approach to saturation region, the saturation magnetization 'Ms' values were obtained by plotting magnetization 'M' versus 1/H (magnetic field), and linear fit was obtained with extrapolation to zero, where curve intersects the yaxis, is taken as saturation magnetization 'Ms', as was also reported in [16]. The coercivity (Hc), and remanence (Mr) are obtained from hysteresis loops. Anisotropy constant (K1) was calculated by using the equation described in [23]:

K1 = [Hc´Ms] / 0.96 (3)
where Ms is a saturation magnetization, and Hc is a coercivity. with observed changes in aexp, shown in Table 1 along with other XRD parameters. Table 1.

Table 2 depicts experimental, theoretical lattice parameter (aexp., ath.), WillimsonHall (W-H) grain diameter (DW-H), x-ray density, specific surface area (S), strain, and dislocation density. A perusal of Table 1 shows that the observed variation of S is consistent with obtained DW-H and ρXRD values, and higher S values are useful in heterogeneous catalysis as is also reported earlier [20].

Table 2.

Table 3 depicts the cationic distribution, oxygen parameter u, inversion parameter δ, canting angle 'αY-K' and intensity ratios of I400/I422, I220/I440 . A perusal of Table 3 shows that ion irradiation results in cationic redistribution, as was also reported earlier [15,16,[START_REF] Sharma | AIP Conf. Proc[END_REF]. Ion irradiation leads to the reduction of Fe 3+ ions on B-site with simultaneous increase on the A-site, while Zn 2+ ions remain more populated on the A-site than on the B-site, obtained from cationic distribution. Rather close agreement of aexp., ath. (see Table 1), and intensity ratios of I400/I422, I220/I440 (see Table 3) reveal that the cation distribution on A and B-site (see Table 3) is close to reality [START_REF] Sharma | AIP Conf. Proc[END_REF]. Ion irradiation induced strain reduction is also reflected in decrease of oxygen positional parameter 'u' (see table 3). Ion irradiation mediated changes in cationic distribution also results in increase of inversion degree from 0.15 to 0.30. The perusal of Table 3 also depicts canting angle values, and finite αY-K values show the applicability of the Yafet-Kittel three sub-lattice model [29] to describe magnetic properties. Table 3 shows ion irradiation prompted changes in u (range between: 0.3836 0.3846) for all the investigated samples, which is greater than its ideal value of u = 0.375 [START_REF] Smit | Ferrite[END_REF], indicates the presence of some deviation from the ideal spinel structure, gives information about oxygen distortion in the structure, and its enhancement suggests higher structural disorder.

Table 3.

Variation of u with δ (Figure 4a) depicts a linear decrease of Oxygen positional parameter u, with inversion parameter, expressed by following experimental equation: u = 0.36 -0.007 δ. Figure The observed modification will have an effect on magnetic properties, as was also observed earlier in [6,16,[START_REF] Satalkar | AIP Conf. Proc[END_REF].

Figure 4.

Table 4 depicts the irradiation-dose dependence of magnetic parameters: experimental (Ms(exp.)) ; theoretical saturation magnetization Ms(th.)), coercivity (Hc), magnetocrystalline anisotropy (K1), remanence (Mr) squareness ratio (Mr/Ms), and dead layer thickness (t). A perusal of Table 4 depicts the reduction of Ms(exp.) with increasing ion irradiation, which is consistent with the increase of dead layer thickness (t) [START_REF] Coey | [END_REF], leading to a reduction of Ms(exp.), attributed to irradiation-induced spin disorder at the surface of the particle, as described earlier [16,20]. Obtained Mr/Ms is ~ 0.07, indicates dissimilarity of inter-grain interaction, and isotropic behavior of multi-domain grains, as described in [32,33,34], with no preferential magnetization direction is consistent with the literature [16,35].

Table 4 The effect of ion irradiation on hysteresis loops of the studied samples is shown in Figure 5 (a), while the inset of Figure 5(a) shows expanded view of M-H curves, showing coercivity, and its variation with ion irradiation. Figure 5 (b) depicts a variation of Ms(exp.) and Ms(th.) with irradiation dose, non-similar trend governed by three sub-lattice mode [36,37], shown by non-zero canting angles given in Table 4. Figure 5 (b) (inset) shows dependence of Ms(exp.), Ms(th.) on oxygen positional parameter (u), and the increase of the magnetization (Ms(exp.), Ms(th.)), which is attributable to increase of disorder [16,20]. strong dipolar interaction [39,40]. Broader peaks indicate nanocrystalline samples containing dislocations and defects in the crystal [41]. Peak broadness is also linked with the stability of the material: broader the peak of first derivative, the more stable is the structure of the nanoparticle [42].

Table 5 depicts the irradiation dose dependence of full width at half maxima (FWHM) of 1st derivative peak, switching field distribution (SFD), and peak height of 1st derivative. Perusal of Table 5 shows that for the peak height varies between 3.27 -136.47, as was also observed in [41]. An increase of dM / dH peak height indicates that the studied samples have a good magnetic state of crystalline cubic spinel structure [33].

Table 5 A perusal of Table 5, the full width at half maxima (FWHM) of 1 st derivative (ranges between 7.75 and 513.32). Lower FWHM values suggest uniform particle size [43] and irradiation-induced variation of FWHM indicates modification of particle size, as can also be seen in Table 2. Switching field distribution 'SFD' is an important magnetic parameter and it measures the energy barrier distribution in a nanoparticle system, and is accompanied by a distribution of particle coercivity [33,42,[START_REF] Jiles | Introduction to Magnetism and Magnetic Materials[END_REF]. Systems with small SFD and high Hc are appropriate for high-density recording [START_REF] Lodder | Handbook of Magnetic Materials , chapter 2, Magnetic recording hard disk thin film media[END_REF], and the smaller the distribution of the switching field, the better is the performance of magnetic recording materials. For the studied samples the SFD range is between 0.17 and 11.72. Thus, among the studied samples: i) the samples irradiated with 1 × 10 12 (ions/cm 2 ), lowest SFD (0.17), and highest Hc (44.72 Oe) show potential application in magnetic recording, and ii) 1 × 10 13 (ions/cm 2 ) irradiated sample with lowest Hc (42.63 Oe), highest SFD (11.72), would be of use for targeted drug delivery applications [43]. Switching field distribution 'SFD' values have a strong relation with the particle size distribution because particles with different sizes and shapes will tend to reverse at different magnetic field strengths. Consequently, in studied samples, the observed variation of SFD values is ascribable to the variation of the particle size distribution [42].

The irradiation causes the formation of donor and acceptor active centers on the ferrites' surface.

Antistructural modeling is used to describe the active centers formed on the zinc ferrite surface.

Combining the crystal-chemical composition with spinel antistructure

V A '' V 2 ''' B (V 4 •• ) O allows seeing
the ions with excessive charge in the spinel lattice:

Zn 1-x 2+ Fe x 3+ A Zn x 2+ Fe 2-x 3+ B O 4 2- O +V A '' V 2 ''' B (V 4 •• ) O → (Zn 1-x ⨯ Fe x • ) A Zn x ' Fe 2-x ⨯ B (O 4 ⨯ ) O
where • is an excess of the positive charge, ' is an excess of the negative charge, ´ is an effective zero charge; the x value changes from 0.20 (for pristine sample) to 0.15, 0.21, 0.30 (for samples irradiated at 1×10 11 , 1×10 12 and 1×10 13 ions/cm 2 respectively). It can be seen that the concentration of positively charged ferric ions Fe A • in A-sites and negatively charged zinc ions Zn ' in octahedral (B) sites increases with an increase in irradiation dose. Therefore, the irradiated samples will be more active in the catalytic or other processes in comparison with the pristine sample due to the presence of a higher amount of surface-active centers.

Conclusions

To summarize, XRD analysis confirmed the formation of a single-phase nanocrystalline cubic spinel phase. Irradiation results in the alteration of lattice parameters, cationic distribution, disorder, and dislocation density, which in turn affects A-O-B, A-O-A, and B-O-B super-exchange interaction.

Irradiation-induced structural changes noticeably affect the dead-layer thickness, thus affecting saturation magnetization. Magnetization derivative with field (dM/dH) suggests the presence of large number of dislocations and proposes applications in high-density recording, and in targeted drug delivery. Antistructural modelling for Zn ferrites describes the surface-active centres. Present studies demonstrate the effectiveness of ion irradiation-assisted tuning of magnetic properties of spinel ferrites.

3 .

 3 The errors shown in Tables and Figures are the Standard Deviation obtained from the data. Results and Discussions XRD patterns of pristine and irradiated ZnFe2O4 samples are shown in Figure 1(a), confirming the formation of a single-phase cubic spinel structure. Inset of Figure 1 (a) shows the expanded view of (311) peak. Figure 1(b) depicts the reduction of aexp. with irradiation dose, indicates irradiationinduced shrinkage of spinel unit cell, described by experimental relation: aexp. = 0.8401+0.0025[Irr. dose]-0.0007 [Irr. dose] 2 , showing strong correlation between irradiation dose and aexp., while the inset of Figure 2 (b) depicts irradiation dose dependence of ρXRD (right), and ρD (left) are consistent

Fig. 1 .

 1 Fig. 1.

Figure 2

 2 Figure2depicts the Rietveld refined XRD patterns, and Table1gives the refined R; shape parameters

Fig. 2 .Fig. 3 .

 23 Fig. 2.

  4 (b) illustrates ion irradiation dependence of bond angles (θ1, θ2, θ3, θ4, θ5), provides information onA-O-A, A-O-B, B-O-B super-exchange interaction[START_REF] Smit | Ferrite[END_REF]. A perusal of Figure4(a) depicts that with increasing irradiation dose, a gradual increase of θ1, θ2, θ5 with the concurrent decrease of θ3, θ4 suggests, the strengthening of A-O-B, A-O-A super-exchange interaction weakening of B-O-B interaction.

Figure 5 Figure 6

 56 Figure 5

Figure 6 Figure 7

 67 Figure 6

Figure 1 .

 1 Figure 1. (a) XRD patterns of Pristine, and ion-irradiated (dose: 1´10 11 ions/cm 2 , 1´10 12 ions/cm 2 ,

Figure 2 .

 2 Figure 2. Rietveld refined XRD patterns of pristine and irradiated samples.

Figure 3 .

 3 Figure 3. Representative WH plot for (a) pristine and (b) irradiated sample (dose: 1 ´ 10 11 Ions/cm 2 ).

Figure 4 .

 4 Figure 4. (a) Bond angle variation with ion flounce, (b) Variation of oxygen parameter (u) with

Figure 5 .

 5 Figure 5. (a) M-H curves for pristine and irradiated samples. Upper inset: expanded view of M-H

24

 24

Figure 6 . 25 -Figure 7 .

 6257 Figure 6. Irradiation dose dependence of (a) anisotropy and (b) coercivity (Hc). Inset: variation of

  16

  O 6+ ion-irradiation on structural, magnetic properties, anti-structural modeling of as-burnt ZnFe2O4 synthesized by sol-gel autocombustion technique, monitored by XRD, and magnetic measurements.

	2. Material synthesis, material characterization, and data analysis
	ZnFe2O4 was synthesized utilizing AR grade citrate-nitrate precursors: [Zinc Nitrate -
	[(Zn(NO3)2.6H2O, Ferric Nitrate -Fe(NO3)3•9H2O and Citric acid -C6H8O7] by sol-gel auto
	combustion method. All the precursors were taken in stoichiometric ratio and were mixed in 10 ml

de-ionized water, and pH 7 was maintained by adding ammonia (NH4OH) solution. The obtained clear solution was then heated at ~115 ºC in the air to obtain the fluffy powder, called 'dry gel'. Prepared ZnFe2O4 sample was irradiated with 80 MeV

16

O 6+ ion at a flounce of 1×10

  11

Table 1 .

 1 Reitveld refined R-parameters (Rwp, Rp, Rexp.), Shape parameters (u, v, w), the goodness of fit (GOF) for pristine, irradiated samples

	Irradiation dose	Rwp	Rp	Rexp	GOF u	v	w
	(ions/cm 2 )
	0	20.9	18.21	10.25	2.03	0.001	-0.004	0.015
	1´ 10 11	1.29	1.27	3.94	0.4	-0.025	-0.012	0.013
	1´ 10 12	30.43	26.64	14.07	2.16	0.003	-0.041	0.002
	1´ 10 13	1.65	1.31	3.82	0.43	0.002	0.003	-0.002

Table 2 .

 2 Irradiation dose dependence of theoretical and experimental lattice parameter (ath., aexp.),

	Williamson Hall (W-H) grain diameter (DW-H), x-ray density (rxrd), cell volume (V), strain (), and
	dislocation density (ρD) for the ZnFe2O4 samples
	Irradiation	aexp	ath	DW-H	rxrd	V	S	Strain	ρD ´ 10 15
	dose	(nm)	(nm)	(nm)	(kg/m 3 )	(nm 3 )	(m 2 /g)		(Lines/m 2 )
	(ions/cm 2 )	(±0.0011)	(±0.0003)	(±3.96)	(±20.09)	(±0.0022)	(±26.75)	(±0.0009)	(±1.22 ´ 10 15 )
	0	0.8400	0.8440	16.69	5402.44	0.5927	66.54	0.0017	1.82
	1´ 10 11	0.8423	0.8442	17.92	5358.31	0.5976	62.49	0.0035	3.48
	1´ 10 12	0.8421	0.8439	9.25	5362.13	0.5972	120.9	0.0021	4.04
	1´ 10 13	0.8417	0.8435	12.63	5369.78	0.5963	88.47	0.0033	4.65

Table 3 .

 3 Irradiation dose dependence of the cationic distribution (for A and B-site), oxygen positional parameter (u), inversion parameter (δ), and canting angle (αY-K), and intensity ratios of I400/I422, I220/I440 for ZnFe2O4 samples.

	Irr. dose	Cation Distribution	u	δ	αY-K (º)	I400/I422	I220/I440
	(Ions/cm 2 )	A site	B site	(±0.0005)	(±0.06)	(±1.74)	Calc.	Obs.	Calc.	Obs.
	0	(Zn 2+ 0.80Fe 3+ 0.20)	[Zn 2+ 0.20Fe 3+ 1.80]	0.3846	0.20	80.86	1.4962 1.5213	0.9337 1.0684
	1´ 10 11	(Zn 2+ 0.85Fe 3+ 0.15)	[Zn 2+ 0.15Fe 3+ 1.85]	0.3846	0.15	83.19	1.1012 1.0876	0.8942 0.9211
	1´ 10 12	(Zn 2+ 0.79Fe 3+ 0.21)	[Zn 2+ 0.21Fe 3+ 1.79]	0.3842	0.21	83.14	1.3857 1.3667	0.8717 0.9191
	1´ 10 13	(Zn 2+ 0.70Fe 3+ 0.30)	[Zn 2+ 0.30Fe 3+ 1.70]	0.3836	0.30	79.67	1.2153 1.1585	0.8602 0.9165

Table 4 .

 4 Variation of magnetic parameters (at 300 K): saturation magnetization (Ms(exp.)), coercivity (Hc), anisotropy (K1), retentivity (Mr), squareness ratio (Mr/Ms), and deadlayer thickness with irradiation doses of O 6+ on ZnFe2O4 .

	Irradiation	Ms(exp.)	Ms(th.)	Hc	K1 ´10 3	Mr	Mr/Ms	t (nm)
	dose	(Am 2 /kg)	(Am 2 /kg)	(Oe)	(erg/cc)	( Am 2 /kg)
	(Ions/cm 2 )	(±4.78)	(±14.51)	(±0.87)	(±1.13)	(±0.3116)	(±0.0153)	(±0.41)
	0	9.96	185.34	42.63	2.34	0.6890	0.0692	2.21
	1´ 10 11	8.05	196.27	44.02	1.94	0.3163	0.0392	2.49
	1´ 10 12	1.10	183.57	44.72	0.27	0.0427	0.0399	1.51
	1´ 10 13	0.57	161.63	43.90	0.14	0.0211	0.0370	2.08

Table 5 .

 5 Irradiation dose dependence of coercivity (Hc), full width at half maxima (FWHM) of 1 st derivative peak, switching field distribution (SFD), and a peak height of 1 st derivative.

	Irradiation dose	Hc	FWHM or ΔH of	SFD	Peak Height of
	(ions/cm 2 )	(Oe)	1 st derivative peak (Oe)	(ΔH /HC)	1 st derivative
	0	42.63	325.37	7.63	136.47
	1´ 10 11	44.02	504.60	11.46	50.31
	1´ 10 12	44.72	7.75	0.17	18.94
	1´ 10 13	43.79	513.32	11.72	3.27

  ).

						72.72
						72.00
						71.28
						126.336
	0.3846			(a)		126.240
						126.144
	0.3843					94.95
						94.50
	u					94.05	B-O-B
	0.3840					141.9	A-O-B
						140.8
						139.7	q 2
	0.3837					122.50	A-O-B
	0.15	0.20	d	0.25	0.30	122.00 122.25	q 1 1´10 13 Irraditaion dose (Ions/cm 2 ) 1´10 11 0

Acknowledgments: Authors thank Dr. M. Gupta UGC-DAE CSR, Indore, for XRD measurements.

SNK acknowledges gratefully for one month of "Invited Professor" stay at ENS Paris-Saclay, Cachan (France). This work is supported by Seed money grant: No. Dev/Seedmoney2.0/2020-21/649, 20 Jan. 2022 of Devi Ahilya University, Indore (India). TT thanks the Ministry of Education and Science of Ukraine (project number 0121U109476) for financial support.