Okasha, Cancer and the Levels of Selection

British Journal for the Philosophy of Science
LETTERS TO THE EDITORS

Target Article

SAMIR OKASHA
Cancer and the Levels of Selection

British Journal for the Philosophy of Science, 75, pp. 537–60.

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Author

Andy Gardner

University of St Andrews
andy.gardner@st-andrews.ac.uk

Cite As

Gardner, A. [2024]: ‘Multilevel Selection and Cancer: Okasha, On Cancer and the Levels of Selection’, BJPS Letters to the Editors, 2024.

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28 August 2024

Multilevel Selection and Cancer

The idea of multilevel selection has long caused conceptual difficulty. Wynne-Edwards acknowledged that what is favoured at a within-group level may be different from what is favoured at a between-group level, but felt that the action of between-group selection must completely negate the action of within-group selection.¹ Williams used similar reasoning to argue for the exact opposite view.² Accordingly, a huge contribution was made by Price in showing that the overall action of selection may be decomposed into simple between-group and within-group components that straightforwardly add together—neither one negating, or having conceptual primacy, over the other.³

Yet difficulties have persisted, particularly concerning the precise meaning of the concepts of group trait and group fitness. In an effort to resolve this ambiguity, I developed a genetical theory of multilevel selection and, in passing, made a remark about the relationship between multilevel selection and cancer.⁴ Although cancer has often been described in terms of it representing a tension between different levels of selection—that is, favoured at a within-organism level and disfavoured at a between-organism level—I pointed out that it is not possible to conceive of cancer in this way within the framework of the genetical theory insofar as cancerous cell lineages perish upon the death of the organism. In the words of Norm Macdonald, ‘If you die, the cancer also dies at exactly the same time. So that, to me, is not a loss. That’s a draw’.

More formally, the impact that each segment of an evolving population has on the overall action of natural selection is in proportion to its reproductive value—that is, its asymptotic contribution to future generations⁵—and the reproductive value of somatic cells, including cancerous ones, is zero. All the reproductive value of the population lies in the germline and, accordingly, the overall action of natural selection within a population is driven by the differential fitness of germline cells. Although the differential proliferation of somatic cell lineages may modulate the action of selection in relation to the germline cells, it does not in and of itself make any contribution to the overall action of natural selection.⁶ So there is no tension between different levels of selection in respect to cancer.

In a recent BJPS article, Okasha has criticized my remark about cancer and multilevel selection, in three different ways.⁷ First, he points out that some multilevel selection phenomena do not involve genes, and hence resist application of the genetical framework. He acknowledges that this criticism is ‘not directly related to the issue of cancer and reproductive value’, but nevertheless suggests that it casts doubt upon what I said about cancer. However, I had specified that it is only ‘in the strict sense of the genetical theory’ that cancer fails to admit a multilevel selection interpretation. Indeed, as a prelude to introducing the genetical theory, I presented Price’s covariance formulation as a ‘general theory of selection’ and made clear that the genetical theory represents a very special case.

Second, Okasha suggests that, were my remark about cancer and multilevel selection correct, then the standard ‘clonal evolution’ model of cancer—which concerns selection between different cell lineages within a genetically heterogeneous cancerous tissue—would be invalid. I disagree. Competition between cancerous cell lineages within a single organism’s somatic tissues can be described in terms of a selection covariance, including in the strict genetical sense, even if the zero reproductive value of the somatic tissue means that this bout of selection does not contribute to a multilevel decomposition of natural selection into its between-organism and within-organism components.

Third, Okasha suggests that, were my reasoning to be applied to a higher level of biological organization—in particular, to a species that suffers eventual extinction without giving rise to any new species—then it would yield a clearly nonsensical conclusion that selection cannot occur within species that have no long-term future. Again, I disagree. Just as competition between cancerous cell lineages within a single organism’s somatic tissues can be rendered in the form of a selection covariance even if this has no impact on the overall action of natural selection within the evolving population, so too can competition between individuals within a dying species be rendered in the form of a selection covariance, even if this ultimately has no impact on the overall evolutionary trend across a multispecies clade.

In making my remark about cancer and multilevel selection, I explicitly limited my attention to non-transmissible cancer, and on that basis treated cancer cells as having zero reproductive value. More generally, recognizing as Okasha does that all cancerous cell lineages may have a vanishingly small but non-zero probability of spontaneously giving rise to a new transmissible cancer—or perhaps even being harvested and maintained indefinitely in laboratory culture—one might say that the reproductive value of cancer cells is negligible rather than zero. In a formal sense, this could yield a non-zero within-organism selection term pertaining to the proliferative success of cancerous cell lineages, to be set against the action of natural selection at the between-organismal level. But from a scientific perspective, this within-organism selection term would be negligible. In no empirically relevant way would cancer present a tension between the cell and the organism—in the strict sense of the genetical theory of multilevel selection.⁸

Andy Gardner

Notes

¹ Wynne-Edwards, V. C. [1962]: Animal Dispersion in Relation to Social Behaviour, Edinburgh: Oliver and Boyd.

² Williams, G. C. [1966]: Adaptation and Natural Selection, Princeton, NJ: Princeton University Press.

³ Price, G. R. [1972]: ‘Extension of Covariance Selection Mathematics’, Annals of Human Genetics, 35, pp. 485–90.

⁴ Gardner, A. [2015]: ‘The Genetical Theory of Multilevel Selection’, Journal of Evolutionary Biology, 28, pp. 305–19.

⁵ Fisher, R. A. [1930]: The Genetical Theory of Natural Selection, Oxford: Clarendon Press.

⁶ These issues may be rendered mathematically, as follows. In the absence of class structure, the action of natural selection may be expressed as:
$$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \text{cov}_{i \, \in \, I}(v_i, g_i), \qquad (1)$$ where $I$ is the set of all individuals in the population, $v_i$ is the $i$th individual’s relative fitness, $g_i$ is the $i$th individual’s genetical ‘breeding’ value for a trait of interest, $E$ is an expectation taken over the indicated set, and cov is a covariance taken over the indicated set. That is, the action of natural selection is defined in terms of the covariance of relative fitness and genetical trait value across all the individuals in the population. This is equation 2 of (Gardner [2015]).

In the context of class structure, a separate selection covariance may be expressed for each class, and the total action of natural selection is given as a weighted sum of the class-specific selection covariances, with the reproductive values of each class providing the weights, that is: $$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \sum_{k \, \in K} c_k \text{cov}_{i \, \in \, I_k}(v_i, g_i), \qquad (2)$$ where $K$ is the set of all classes, $I_k$ is the set of all individuals belonging to class $k$ and $c_k$ is the reproductive value of class $k$. This is equation 4 of (Gardner [2015]).

In the context of a group-structured population, equation 1 may be decomposed into its between-group and within-group components, yielding the multilevel selection form:
$$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_j} (v_i) E_{i \, \in \, I_j} (g_i) \big)$$ $$ \hspace{3cm} + \, E_{j \, \in \, J} \big(\text{cov}_{i \, \in \, I_j}(v_i, g_i) \big), \qquad (3)$$ where $J$ is the set of all groups and $I_j$ is the set of all individuals belonging to group $j$. The first term on the right-hand side of equation 3 is the covariance of group fitness (that is, the average fitness of the individuals within the group) and group trait value (that is, the average trait value of the individuals within the group) across all the groups in the population, and defines ‘between-group selection’. The second term on the right-hand side of equation 3 is the average, across all groups, of the covariance of individual fitness and individual trait value across all the individuals within a group, and defines ‘within-group selection’. This is equation 5 of (Gardner [2015]).

In the context of a population that is both class-structured and group-structured, the multilevel selection decomposition of equation 3 may be applied separately for each class described in equation 2, yielding: $$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \sum_{k \, \in \, K} c_k \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{kj}} (v_i) E_{i \, \in \, I_{kj}} (g_i) \big)$$ $$ \hspace{3cm} + \, \sum_{k \, \in \, K} c_k E_{j \, \in \, J} \big(\text{cov}_{i \, \in \, I_{kj}}(v_i, g_i) \big), \qquad (4)$$ where $I_{kj}$ is the set of individuals belonging to class $k$ and group $j$. This is equation 7 of (Gardner [2015]).

An illustration of the points given in the main text in relation to cancer may be made by assuming that the ‘individuals’, $i$, represent cells, the ‘groups’, $j$, represent multicellular organisms, and there are two cell classes, with $k = 1$ denoting germline cells and $k = 2$ denoting somatic (including cancerous) cells. I also denote the reproductive value of the germline by $c_1 = 1 – \varepsilon$ and that of the soma by $c_2 = \varepsilon$. Making these substitutions into equation 4: $$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = (1 – \varepsilon) \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{1j}} (v_i) E_{i \, \in \, I_{1j}} (g_i) \big)$$ $$ \hspace{3cm} + \, \varepsilon \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{2j}} (v_i) E_{i \, \in \, I_{2j}} (g_i) \big)$$ $$ \hspace{3cm} + \, (1 – \varepsilon) E_{j \, \in \, J} \big( \text{cov}_{i \, \in \, I_{1j}}(v_i, g_i)\big)$$ $$ \hspace{3cm} + \, \varepsilon E_{j \, \in \, J}\big(\text{cov}_{i \, \in \, I_{2j}}(v_i, g_i) \big). \qquad (5)$$ That is, the overall action of natural selection is given by the sum of between-organism selection among the germline cells (first term on right-hand side of equation 5), between-organism selection among the somatic cells (second term), within-organism selection among the germline cells (third term), and within-organism selection among the somatic cells (fourth term).

In the limit of all the reproductive value of the population being held by the germline $(\varepsilon \rightarrow 0)$, the action of natural selection is given by:
$$\Delta_{\text{NS}} E_{i \, \in \, I} (g_i) \rightarrow \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{1j}} (v_i) E_{i \, \in \, I_{1j}} (g_i) \big)$$ $$ \hspace{3cm} + \, E_{j \, \in \, J} \big( \text{cov}_{i \, \in \, I_{1f}} (v_i, g_i) \big). \qquad (6)$$ That is, although proliferation of cancerous cell lineages may result in a non-zero within-organism selection covariance $(\text{cov}_{i \, \in \, I_{2j}} (v_i, g_i) \neq 0)$, if the somatic tissue has negligible reproductive value $(\varepsilon \rightarrow 0)$ then this selection covariance has no substantive impact on the multilevel decomposition of natural selection into its between-organism versus within-organism components.

⁷ Okasha, S. [2024]: ‘Cancer and the Levels of Selection’, British Journal for the Philosophy of Science, 75, pp. 537–60.

⁸ I thank K. Twyman for helpful discussion. This work was supported by a European Research Council Consolidator Grant (no. 771387).

Author

Samir Okasha

University of Bristol
Samir.Okasha@bristol.ac.uk

Cite As

Okasha, S. [2024]: ‘Cancer and Multilevel Selection: Reply to Gardner’, BJPS Letters to the Editors, 2024.

8 September 2024

Cancer and Multilevel Selection: Reply to Gardner

Cancer is often regarded as an example of multilevel selection. On this view, there is selection for cancer at the cellular level, since cancer cells proliferate faster than ordinary somatic cells within an organism, but selection against cancer at the organismic level, leading organisms to evolve adaptations to prevent cancer from arising and spreading. This leads naturally to the idea that cancer cells are ‘cheats’ that undermine group welfare by their selfish actions and has inspired many authors to conceptualize cancer as an evolutionary conflict between cell and organism.¹

Despite its popularity, this view of cancer has its critics. Gardner, and Shpak and Liu, argue that cancer is not a bona fide case of multilevel selection and should not be thought of in terms of conflict between cell and organism.² Their main point is that cancer is an evolutionary dead end, since however fast a cancerous cell lineage replicates within an organism’s soma, the lineage dies with the organism and so leaves no descendants over organismic generations (apart from in very rare cases of transmissible cancers). This contrasts with standard cases of multilevel selection, in which selection at the lower level can potentially affect the future composition of the gene pool.

My recent BJPS article offered a detailed assessment of this evolutionary dead end argument. I described the evolutionary dead end argument as ‘powerful but not decisive’, and I wrote that Gardner and Shpak and Liu had posed ‘a serious challenge’ to those biologists who view cancer in multilevel selection terms. My reason for the ‘not decisive’ verdict was that multilevel selection is a disputed concept, so a proponent of the evolutionary dead end argument could conceivably respond to Gardner and Shpak and Liu by rejecting their conception of what constitutes ‘real’ or ‘strict sense’ multilevel selection. My article’s main contribution, however, was to suggest a novel response to the evolutionary dead end argument based on the (presumed) link between cancer and the origin of multicellularity. I argued that if Leo Buss’s theory of how multicellularity evolved is true,³ or if the atavistic interpretation of cancer is true, then there would be a solid rationale for conceiving cancer in multilevel selection terms despite the non-transmission of cancer cells across organismic generations.

In his reply, Gardner does not address, nor indeed mention, my main argument. Rather, he takes issue with my three reasons for describing his version of the evolutionary dead end argument as not decisive. My first reason was that Gardner’s own ‘genetical theory of multilevel selection’ arguably covers only a subset of the phenomena traditionally included under the multilevel selection rubric, so is a questionable basis on which to adjudicate the case of cancer. In reply, Gardner stresses that it is only in the sense of his ‘genetical theory’ that cancer is disqualified from counting as multilevel selection; thus implying, presumably, that in other (legitimate?) senses of the phrase ‘multilevel selection’ cancer would not be so disqualified. This looks suspiciously like the sort of verbal disagreement that I was at pains to avoid.⁴

My second reason was that if Gardner’s argument were accepted, it would seemingly tell against the clonal evolution model of cancer widely endorsed by cancer researchers, on which tumorigenesis is hypothesized to result from Darwinian competition between variant cancer cell lineages within a single organism. In reply, Gardner says that ‘competition between cancerous cell lineages within a single organism’s somatic tissues’ does indeed count as selection, ‘including in the strict genetical sense’. I find this claim hard, indeed impossible, to square with what Gardner wrote in 2015, namely, that the ‘proliferation [of cancerous tissues] within the organism cannot correspond to selection in the strict sense of the genetical theory’.⁵ Gardner seems not to have made up his mind here.

My third reason was that if Gardner’s argument were frameshifted up the biological hierarchy, to a setting where species are the smaller units and clades the larger ones, it would have an unwelcome consequence. For over geological time, the vast majority of species leave no daughter species, hence the organismal lineages within them are also evolutionary dead ends; yet selection clearly does take place on these lineages within the species’ lifetimes. In reply, Gardner grants that such selection clearly does take place, but does not see it as a threat to what he says about cancer since he now says he is happy to regard differential proliferation of cancer cells within a single organism as natural selection in the strict sense. However, I was critiquing Gardner’s 2015 position, which was that such proliferation is not natural selection in the strict sense.

The crux of the matter, and likely the source of Gardner’s equivocation, is this: Given a hierarchically organized system, comprising smaller biological units nested within larger ones, there is a crucial distinction between, on the one hand, a single process of multilevel selection and, on the other, multiple processes of single-level selection (that possibly interact with each other). The former means that the two levels of selection contribute to a single overall evolutionary change (for example, allele frequency change over organismic generations); the latter means that the two levels of selection contribute to two distinct evolutionary changes, at different levels and usually over different timescales, though with the potential for causal interaction between them. Cancer is of the second type, not the first. Whether this invalidates the idea that cancer involves conflict between levels of selection, or the related idea that cancer is usefully viewed through the lens of social evolution theory, is precisely the topic of my original article.⁶

Samir Okasha

Notes

¹ For references, see the target article.

²   Gardner A. [2015a]: ‘The Genetical Theory of Multilevel Selection’, Journal of Evolutionary Biology, 28, pp. 305–19.
  Gardner, A. [2015b]: ‘More on the Genetical Theory of Multilevel Selection’, Journal of Evolutionary Biology, 28, pp. 1747–51.
  Shpak, M. and Lu, J. [2016]: ‘An Evolutionary Genetic Perspective on Cancer Biology’, Annual Review of Ecology, Evolution, and Systematics, 47, pp. 25–49.

³ Buss, L. [1987]: The Evolution of Individuality, Princeton, NJ: Princeton University Press.

⁵ Gardner [2015a], p. 310.

Notes

1
Wynne-Edwards, V. C. [1962]: Animal Dispersion in Relation to Social Behaviour, Edinburgh: Oliver and Boyd.
2
Williams, G. C. [1966]: Adaptation and Natural Selection, Princeton, NJ: Princeton University Press.
3
Price, G. R. [1972]: ‘Extension of Covariance Selection Mathematics’, Annals of Human Genetics, 35, pp. 485–90.
4
Gardner, A. [2015]: ‘The Genetical Theory of Multilevel Selection’, Journal of Evolutionary Biology, 28, pp. 305–19.
5
Fisher, R. A. [1930]: The Genetical Theory of Natural Selection, Oxford: Clarendon Press.
6
These issues may be rendered mathematically, as follows. In the absence of class structure, the action of natural selection may be expressed as:
$$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \text{cov}_{i \, \in \, I}(v_i, g_i), \qquad (1)$$ where $I$ is the set of all individuals in the population, $v_i$ is the $i$th individual’s relative fitness, $g_i$ is the $i$th individual’s genetical ‘breeding’ value for a trait of interest, $E$ is an expectation taken over the indicated set, and cov is a covariance taken over the indicated set. That is, the action of natural selection is defined in terms of the covariance of relative fitness and genetical trait value across all the individuals in the population. This is equation 2 of (Gardner [2015]).

In the context of class structure, a separate selection covariance may be expressed for each class, and the total action of natural selection is given as a weighted sum of the class-specific selection covariances, with the reproductive values of each class providing the weights, that is: $$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \sum_{k \, \in K} c_k \text{cov}_{i \, \in \, I_k}(v_i, g_i), \qquad (2)$$ where $K$ is the set of all classes, $I_k$ is the set of all individuals belonging to class $k$ and $c_k$ is the reproductive value of class $k$. This is equation 4 of (Gardner [2015]).

In the context of a group-structured population, equation 1 may be decomposed into its between-group and within-group components, yielding the multilevel selection form:
$$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_j} (v_i) E_{i \, \in \, I_j} (g_i) \big)$$ $$ \hspace{3cm} + \, E_{j \, \in \, J} \big(\text{cov}_{i \, \in \, I_j}(v_i, g_i) \big), \qquad (3)$$ where $J$ is the set of all groups and $I_j$ is the set of all individuals belonging to group $j$. The first term on the right-hand side of equation 3 is the covariance of group fitness (that is, the average fitness of the individuals within the group) and group trait value (that is, the average trait value of the individuals within the group) across all the groups in the population, and defines ‘between-group selection’. The second term on the right-hand side of equation 3 is the average, across all groups, of the covariance of individual fitness and individual trait value across all the individuals within a group, and defines ‘within-group selection’. This is equation 5 of (Gardner [2015]).

In the context of a population that is both class-structured and group-structured, the multilevel selection decomposition of equation 3 may be applied separately for each class described in equation 2, yielding: $$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = \sum_{k \, \in \, K} c_k \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{kj}} (v_i) E_{i \, \in \, I_{kj}} (g_i) \big)$$ $$ \hspace{3cm} + \, \sum_{k \, \in \, K} c_k E_{j \, \in \, J} \big(\text{cov}_{i \, \in \, I_{kj}}(v_i, g_i) \big), \qquad (4)$$ where $I_{kj}$ is the set of individuals belonging to class $k$ and group $j$. This is equation 7 of (Gardner [2015]).

An illustration of the points given in the main text in relation to cancer may be made by assuming that the ‘individuals’, $i$, represent cells, the ‘groups’, $j$, represent multicellular organisms, and there are two cell classes, with $k = 1$ denoting germline cells and $k = 2$ denoting somatic (including cancerous) cells. I also denote the reproductive value of the germline by $c_1 = 1 – \varepsilon$ and that of the soma by $c_2 = \varepsilon$. Making these substitutions into equation 4: $$\Delta_\text{NS}E_{i \, \in \, I}(g_i) = (1 – \varepsilon) \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{1j}} (v_i) E_{i \, \in \, I_{1j}} (g_i) \big)$$ $$ \hspace{3cm} + \, \varepsilon \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{2j}} (v_i) E_{i \, \in \, I_{2j}} (g_i) \big)$$ $$ \hspace{3cm} + \, (1 – \varepsilon) E_{j \, \in \, J} \big( \text{cov}_{i \, \in \, I_{1j}}(v_i, g_i)\big)$$ $$ \hspace{3cm} + \, \varepsilon E_{j \, \in \, J}\big(\text{cov}_{i \, \in \, I_{2j}}(v_i, g_i) \big). \qquad (5)$$ That is, the overall action of natural selection is given by the sum of between-organism selection among the germline cells (first term on right-hand side of equation 5), between-organism selection among the somatic cells (second term), within-organism selection among the germline cells (third term), and within-organism selection among the somatic cells (fourth term).

In the limit of all the reproductive value of the population being held by the germline $(\varepsilon \rightarrow 0)$, the action of natural selection is given by:
$$\Delta_{\text{NS}} E_{i \, \in \, I} (g_i) \rightarrow \text{cov}_{j \, \in \, J} \big( E_{i \, \in \, I_{1j}} (v_i) E_{i \, \in \, I_{1j}} (g_i) \big)$$ $$ \hspace{3cm} + \, E_{j \, \in \, J} \big( \text{cov}_{i \, \in \, I_{1f}} (v_i, g_i) \big). \qquad (6)$$ That is, although proliferation of cancerous cell lineages may result in a non-zero within-organism selection covariance $(\text{cov}_{i \, \in \, I_{2j}} (v_i, g_i) \neq 0)$, if the somatic tissue has negligible reproductive value $(\varepsilon \rightarrow 0)$ then this selection covariance has no substantive impact on the multilevel decomposition of natural selection into its between-organism versus within-organism components.
7
Okasha, S. [2024]: ‘Cancer and the Levels of Selection’, British Journal for the Philosophy of Science, 75, pp. 537–60.
8
I thank K. Twyman for helpful discussion. This work was supported by a European Research Council Consolidator Grant (no. 771387).
1
For references, see the target article
2

Gardner A. [2015a]: ‘The Genetical Theory of Multilevel Selection’, Journal of Evolutionary Biology, 28, pp. 305–19.

Gardner, A. [2015b]: ‘More on the Genetical Theory of Multilevel Selection’, Journal of Evolutionary Biology, 28, pp. 1747–51.

Shpak, M. and Lu, J. [2016]: ‘An Evolutionary Genetic Perspective on Cancer Biology’, Annual Review of Ecology, Evolution, and Systematics, 47, pp. 25–49.
3
Buss, L. [1987]: The Evolution of Individuality, Princeton, NJ: Princeton University Press.
4
Okasha [2024], p. 547.
5
Gardner [2015a], p. 310.
6
This work is part of a project that has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant 101018533).