Adaption,
neutrality, and life course diversity
Ulrich Karl Steiner1* & Shripad
Tuljapurkar2
1Institute of Biology, Freie Universität Berlin
2Department of Biology, Stanford University
*Corresponding author:
ulrich.steiner@fu-berlin.de
tulja@stanford.edu
Authorship statement: UKS and ST developed the concept and theory. UKS
analyzed the data. UKS wrote the first and final draft with substantial
contributions from ST.
Data Accessibility statement: No new data was generated. The data in
this study comes from the COMPADRE and COMADRE Data base and is open
access data under the terms of the Creative Commons CC BY-SA 4.0
license.
Running title: Life course diversity
Keywords: Life history evolution, phenotypic variance, matrix population
models, sensitivity, COMADRE, COMPADRE, individual heterogeneity,
demographic stochasticity
Words in abstract: 142
Words in text: 3308
Number of references: 45
Number of Fig.:3
Number of Tables: 2
Correspondence:
Ulrich Steiner
Institute of Biology, Freie Universität Berlin
Königin-Luise Str. 1-3
14195 Berlin
Phone: +49 30 83872559
Abstract
Heterogeneity among individuals in fitness components is what selection
acts upon. Evolutionary theories predict that selection in constant
environments acts against such heterogeneity. But observations reveal
substantial non-genetic and also non-environmental variability in
phenotypes. Here we examine whether there is a relationship between
selection pressure and phenotypic variability by analysing structured
population models based on data from a large and diverse set of species.
Our findings suggest that non-genetic, non-environmental variation is in
general neither truly neutral, selected for, or selected against. We
find much variation among species and populations within species, with
mean patterns suggesting nearly neutral evolution of life course
variability. Populations that show greater diversity of life courses do
not show, in general, increased or decreased population growth rates.
Our analysis suggests we are only at the beginning in understanding the
evolution and maintenance of non-genetic non environmental variation.
Introduction
Individuals in any population vary in their life courses, exemplified by
differences in lifespan, reproduction, phenotypes, and functional traits
(Endler 1986; Hartl & Clark 2007; Tuljapurkar et al. 2009;
Steiner & Tuljapurkar 2012). Classical evolutionary theories, founded
in seminal work by Fisher ( 1930), Wright ( 1931), and Haldane ( 1927,
1932), explain such variation by genotypic variation, environmental
variation, or their interaction. According to these theories, if
environments are constant over many generations, selection should erode
genotypic variation by selecting for adaptive phenotypes and their
associated genotypes; in population genetic terms, additive genetic
variation should erode. However neutral molecular variation maintains
some genetic diversity without substantial phenotypic variation, if the
phenotypes are selected upon (Kimura 1968; Crow & Kimura 1970). In
consequence, in a constant environment, among individual variation in
phenotypes and life courses should decline if phenotypes are linked to
fitness. These predictions are challenged by the observation that even
isogenic individuals, originating from parental populations that have
lived for many generations in highly controlled lab conditions, exhibit
high levels of variation among individual life courses and phenotypes,
even for phenotypes that directly link to fitness and that are under
selection (Jouvet et al. 2018; Steiner et al. 2019; Flatt
2020). Similarly, in less controlled genetic and environmental
conditions, environmental variation, genotypic variation, and their
interaction only account for a small fraction of the total observed
phenotypic variation of fitness components (Snyder & Ellner 2018; van
Daalen & Caswell 2020; Snyder et al. 2021; Steiner et al.2021). For systems where such a decomposition of genotypic,
environmental and other stochastic variation is challenging due to lack
of accurate data, similar amounts of total phenotypic variation are
observed as in more controlled systems (Finch & Kirkwood 2000; Snyder
& Ellner 2016; van Daalen & Caswell 2020). The question arises how
such high levels of phenotypic variation can be maintained as basic
evolutionary theories do not readily predict the persistence of such
levels of variability (Melbourne & Hastings 2008; Bell 2010; Bartonet al. 2017; Flatt 2020). From an empirical point of view,
estimates of heritability of functional traits and resulting
expectations of trait shifts frequently do not match observed
fluctuations in phenotypic traits of natural populations (Coulsonet al. 2008, 2010; Flatt 2020). These challenges in explaining
observed variability only by genotypes, environments and their
interaction, lead us to the view that non-genetic and non-environmental
processes generate and contribute to the high levels of variation in
phenotypes and life courses among individuals (Jouvet et al.2018; Snyder & Ellner 2018; Steiner et al. 2019, 2021; van
Daalen & Caswell 2020; Snyder et al. 2021).
The fundamental question we address here is whether such non-genetic,
non-environmental driven variation is truly neutral, selected for, or
against. In the case of neutral variation, the follow up question would
be, how is such neutral variation maintained (Demetrius 1974)? Here we
do not decompose variance in genetic, environmental, phenotypic plastic
(gene-by-environment), and neutral contributions to life course
variability, as previously done for datasets that have the needed depth
of information or by making assumptions about partitioning (Snyder &
Ellner 2018; Snyder et al. 2021; Steiner et al. 2021).
Instead, we aim at quantifying the selective forces on the processes
that generate variation among life courses by relying on the analysis of
structured population models (Steiner & Tuljapurkar 2020). We describe
this approach in the following section starting with structured
populations and associated life courses.
In any structured population, a life course of an individual can be
described by a sequence of stages that ends with death (Caswell 2001).
These stage sequences, or life course trajectories, differ among
individuals in length, i.e. age at death, and in the sequence and
frequency of stages experienced. In many situations every individual
starts in the same newborn stage. Thereafter life diversifies with
increasing age, and the rate at which these sequences diversify with
increasing length can be quantified by population entropy (Tuljapurkaret al. 2009; Hernández-Pacheco & Steiner 2017; Steiner &
Tuljapurkar 2020). High entropy leads to highly diverse life courses in
short times, and low entropy leads to few distinct life courses groups
of individuals follow (Hernández-Pacheco & Steiner 2017). The life
courses, i.e. the stage sequences, but also their diversification are
determined by the stage transition rates (Caswell 2001). To quantify the
contributions of each stage transition to the process of diversification
of life courses (Steiner & Tuljapurkar 2020), we can perturb each stage
transition rate, i.e. elements of the population matrix, and then
compute the contributions of these perturbations to population entropy.
Of course such estimation of the sensitivity of each transition rate to
the population entropy does not reveal anything about fitness—λ, the
rate at which a population grows (Caswell 2001; Steiner & Tuljapurkar
2020).
However, the desired linkage to fitness is revealed by the sensitivities
of the population growth rate, λ to the same perturbations of the
transition rates. If one then examines the correlation between the
sensitivities of entropy and of fitness, we can link life course
diversification and selective forces (Fig. 1) (Steiner & Tuljapurkar
2020). To expand on this argument, if a perturbation (of a stage
transition parameter) leads to both an increase in entropy and in
population growth rate (fitness λ), selection for diversification of
life courses is favoured, whereas, if a negative correlation between
these sensitivities occurs, selection against diversification is
suggested, and if there is no correlation between the two sensitivities,
the observed variability among life courses may be neutral. We base our
interpretation on the idea that selection should act more strongly on
stage-transitions that have higher sensitivities with respect to
population growth, λ, and hence fitness (Pfister 1998). To illustrate
the concept, imagine a mutation that changes a vital rate (any fertility
rate or stage transition rate), if this change in transition
probabilities influences fitness, λ, more than changes in other vital
rates, it should be under stronger selection than those vital rates that
only have little influence on fitness.
To evaluate how the diversity in life courses is selected
upon—positively, negatively, or neutral—, we explore the correlation
of the sensitivity with respect to entropy and the sensitivity with
respect to population growth for a large variety of species and taxa for
which population projection models have been collected within the
COMADRE and COMPADRE data base (Salguero‐Gómez et al. 2016; Joneset al. 2022) (COMPADRE & COMADRE Plant Matrix Database (2022).
Available
from: https://www.compadre-db.org;
accessed 7.3.2022). We estimate for each transition rate of each
population projection model the sensitivity with respect to entropy and
population growth, then correlate these two sensitivities for each
projection model, and compare these correlations across species, taxa,
phyla, ontology, age, organism type and matrix dimension, for plants and
animals. We find that both in plants and animals, substantial variation
in the correlation between the two sensitivities among species exists,
and we find a very weak or no overall correlation between sensitivities,
suggesting close to neutral evolution of life course variability.
We also address a different question, whether populations or species
with high rates of life course diversification, i.e. more diverse life
courses, exhibit high fitness compared to those that are less diverse in
their life courses. Such investigation might be understood in terms of
adaptive niche differentiation or specialization(Hernández-Pacheco &
Steiner 2017). Here, our findings suggest that matrices with high rates
of diversification (higher entropy) do not show increased or reduced
fitness. Note, only a single entropy and a single population growth rate
is calculated per matrix, while for each of the many non-zero matrix
element sensitivities can be calculated. Overall, we find that
populations that show greater diversity of life courses do not show
increased or decreased population growth rates and selective forces seem
not to increase or decrease life course variability.
MATERIAL & METHODS
Out of the 3317 population matrices in the COMADRE animal database and
the 8708 matrices in the COMPADRE plant database, we selected matrix
models that were ergodic and irreducible (1350 and 5823 respectively).
Of these, we selected only matrices that had for each stage (each matrix
column, Fig. 1) at least two non-zero elements; resulting in 37 matrices
on 11 animal species, and 2144 matrices on 262 plant species. The
extreme reduction in the animal matrix number reflects that many of
these animal matrices are sparse matrices, for instance age-structured
only (Leslie) population matrices.
We limited the analysis to matrices with at least two non-zero elements
as to evaluate perturbations (sensitivities) that do not trade-off
against survival, but against other stage transition or reproductive
rates (Fig. 1). We call these sensitivities, that do not trade-off
against survival, integrated sensitivities(Steiner & Tuljapurkar 2020).
Each integrated sensitivity evaluates by how much a perturbation of
amount b , in one focal matrix element k , influences
population entropy, H , and population growth, λ, when
simultaneously all other non-zero elements in the given stage (column)
are reduced by b/n , with n equals the number of non-zero
elements in a column minus the focal element. Note, integrated
sensitivities can have negative and positive effects on entropy or λ.
Before we estimated the integrated sensitivities we transformed the
absorbing population projection matrices into Markov chains (Tuljapurkar
1982). We then computed for each of the 41812 non-zero matrix elements
their integrated sensitivities with respect to population entropy and
population growth rate λ on the plant matrices, and 602 non-zero
elements of the animal matrices. As the integrated sensitivities had
very heavy tail distributions on both tails, we excluded extreme values
that likely arose from biologically unrealistic matrix parameter entries
or transition rates that were close to 1 or 0. We excluded extreme
values of integrated sensitivities that exceeded three times the
standard deviation for integrated sensitivities of entropy (13 animal
matrix elements; 811 plant matrix elements) and values on integrated
sensitivities of lambda that exceeded three times the standard deviation
for the animal data (16), or 0.02 for the plant data (559), leaving 577
integrated sensitivities and 40640 integrated sensitivities respectively
for the animal and plant data analysis (4 and 198 were outliers for both
integrated sensitivities of respectively animal or plant data).
Resulting distributions, after the outlier removal, remained heavy
tailed.
For statistical testing, we fitted linear models (despite symmetrically
long tails on both sides of the residual distribution) and used model
comparison based on Akaike’s information criterion (AIC). We defined a
difference in AIC>2 as substantial better support(Burnham
& Anderson 2004). We evaluated the model fit and the assumptions using
diagnostic plots.
For each matrix we also computed population matrix level entropy and
population growth rate, λ, note there is one value of entropy and
population growth for each matrix. We also correlated sensitivities with
respect to entropy and those with respect to lambda for the 37 animal
matrices and 2144 plant matrices against each other. Model comparisons
were done using AIC’s(Burnham & Anderson 2004).
RESULTS
We show the integrated sensitivities of entropy and those of lambda
across all animal species in our data in Fig 2A. The figure shows no
evident correlation between these sensitivities (supported by
statistical analysis, Table 1: Model 1 [null model], vs Model2
[simple regression, slope -0.084], both models receive equal
support). Hence, neither selection for nor against the diversity of life
courses is observed in animals. For plants we find a weak positive
correlation (Table 1: Model 1 vs Model2, Fig. 2B), though its effect
size (slope 0.056) is small (compare with effect size of non-significant
animal data). Hence, for plants selection tends to favour diverse life
courses. This said, there is substantial variation in the correlation
between the integrated sensitivities among the species (Fig. 2; Table 1:
Model 8 vs. Model 1,2,6,7), significant variation among matrices (Fig.
2, Table 1: Model 4 vs Model 2, 3, 5), and significant variation among
matrices within species (Table 1: Model 4 vs. model 8). These findings
suggest that selection differs among species, i.e. favouring diversity
in life courses in some species while selecting against such diversity
in others. On addition, comparisons among matrices for one species show
differences among populations, or the same population in different
years. The results reveal that variation within a single species and
among populations and years is also substantial. These patterns of
variance within and among species hold for both animal and plant data.
We investigated the effect on the correlation between sensitivities by
using several possible grouping variables, including age, matrix
dimension, phylum, organism types, or ontogeny. We found (Table 1, Fig.
S1) that in animals these variables do not play an important role, while
in plants they do account for a small amount of variability. Still,
compared to the variance among species and within species, these
grouping variables are of little importance. The number of stages per
matrix (dimension) could potentially affect our findings, because we
found an interaction among matrices of different dimensions and
integrated sensitivity with respect to lambda for plant species, but
there was no general trend with increasing matrix dimension, towards or
against selection for variance in life courses, suggesting no systematic
bias regarding matrix dimension (Fig. S1).
We further asked whether high or low diversity in life courses
(population entropy) is associated with high or low fitness (population
growth rates). Note here, we evaluate population entropy and lambda for
the total population, i.e. one value for each matrix, not as above, a
measure at the matrix element level (integrated sensitivities measures).
Fig. 3 shows this relationship between entropy and lambda (see Table 2
for model comparison). We did not find any simple relationship between
population entropy and fitness for animals (Table 2 Model 1 vs. 2, Fig.
3A), though for plants there was some tendency that matrices with higher
rates of diversification had lower fitness (Table 2 Model 1 vs. 2, Fig.
3B, slope -0.42). One necessary caution is that these results are
largely driven by biologically questionable and extremely high values of
population growth rates (see also Fig. S2). Overall, there is
significant variation in both population entropy and population growth
rate but no clear correlation among the two variables. Matrix dimension
explains some additional variance in the relationship between entropy
and lambda, though species differences are much more important in
explaining variance than matrix dimension.
DISCUSSION
We show that across a large collection of animal populations there is no
clear selective force that acts towards or against increased or
decreased diversification in life courses, whereas for a large
collection of plants there is weak selection favouring diversification
in life courses. In apparent contrast, we find that plant populations
(or species) with high rates of life course diversification tend to have
lower fitness than populations (or species) that show high rates of
diversification. However, the two measures, the selective forces acting
on the generating process of diversification in life courses, and the
level of diversification, reveal two distinct aspects. The integrated
sensitivity analyses investigates selection on diversification processes
within a population (Steiner & Tuljapurkar 2020), whereas the
population entropy quantifies the current rate of diversification
(Tuljapurkar et al. 2009). The sensitivity analyses therefore
focus on within population selective processes, whereas entropy and
population growth are best used for among population comparison.
Our finding of substantial variation in selective forces on the
generating processes, as well as substantial variation in the rate of
diversification, might be of greater interest than the small positive
selective trend favouring diversification for plant species. These
substantial levels of variability might have three different biological
origins or meanings: first, they might indicate substantial
(developmental) noise that leads to the observed variability in life
courses and selection for or against diversification in life
courses(Balázsi et al. 2011), second, it might indicate
fluctuating selection or high levels of phenotypic plasticity driven by
variable environmental conditions(Philadelphia 1973; Gillespie 1975), or
third, it might indicate large numbers of distinct adaptive life courses
that show similar fitness but might for instance fill different
niches(Hernández-Pacheco & Steiner 2017). In quantitative genetic terms
these options would relate to respectively, undetermined residual
variation, gene by environmental variation, or additive variation.
If one assumes that noise explains the variability, it is suggested that
selection might not act very strongly on this noise, as otherwise the
variability should be selected against and variability should
collapse(Haldane 1927, 1932; Fisher 1930; Wright 1931). Such neutral, or
close to neutral, arguments have been used in the past to explain life
course variability but are often met with scepticism(Steiner &
Tuljapurkar 2012). Our results might indicate that selective forces on
rates of diversification in life courses are not generally weak, but
partly go in opposing directions, i.e. selecting for diversification in
some populations or species and against in others, such conflicting
findings are not uncommon in quantitative genetic studies(Johnson &
Barton 2005; Charlesworth 2015; Flatt 2020).
If one assumes that fluctuating environments, or similar extrinsic
variation, causes vital rates to differ among matrices and leads to the
highly diverse life courses(Philadelphia 1973; Gillespie 1985), we might
assume that a large fraction of variability would be explained by among
matrix models within species, and less so among species.
Model selection indicates that among species variation is substantially
greater compared to variability among matrices within species. Hence,
variability among populations or time (years), or conditions
(environments) within species contribute less to variability in life
courses than variability among species. These arguments align with
findings that phenotypic plasticity might not be in general adaptive
(Acasuso-Rivero et al. 2019). The meta-analysis we did might not
be ideal for such within species evaluation, as the average number of
matrices per species (3.4 for animals, and 8.2 for plants) are not very
large, but our analysis still provides more general insights compared to
studies focusing on single model species for which rich data exist(Flatt
2020).
If one assumes that diversity in life courses is produced because many
life courses are equally fit (Hernández-Pacheco & Steiner 2017; Nevadoet al. 2019), we would be challenged to explain the strong
selective patterns against diversification that is observed for some
populations and species. Under such an assumption, the optimal number of
distinct life courses would need to differ substantially among species
or populations. Also, from more detailed analyses of systems, certain
life courses, or genotypes, that are commonly observed seem to have low
fitness (Flatt 2020; Steiner et al. 2021), suggesting that not
all life course variability might be adaptive.
The potential explanations that help to understand the selective forces
on diversification of life courses are not mutually exclusive and we do
not have means to quantify each contribution to the diversification
using the data in this study. More detailed studies that focus and
explore selection on diversification could help to better understand the
influence of these three factors (Flatt 2020). Studies might include how
genes (or gene knockouts) influence the rate of diversification, how
experimental evolution studies in stochastic environments differing in
amplitude and autocorrelation (noise color, wavelength) would lead to
the evolution of different rates of diversification, or how
“heritability” of distinct life course strategies potentially
determine life course diversification under different environmental
conditions. Quantitative genetics studies have identified a similar lack
of understanding of the maintenance and the evolution of variability
(Johnson & Barton 2005; Charlesworth 2015), though with a focus on
genetic explanations emphasizing mutation-selection balance being driven
by few strongly deleterious mutations (Muller 1950; Charlesworth 2015),
or alternatively many polymorphic loci that maintain variability
(Dobzhansky 1955; Johnson & Barton 2005). Such genetic variation
interacts with neutral and non-genetically determined processes that
influence evolutionary processes and the pace of evolution(Steiner &
Tuljapurkar 2012). For that a purely quantitative genetic vision might
be too short sighted. Generally, we believe we are only beginning to
understand selection on processes that lead to the observed variability
in life courses(Flatt 2020). Increased interest in stochastic gene
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