Ecological opportunity and food resource use in the three models

Building on existing theory on ecological diversification [17,27–29], our models consider n food resources with density F_i (i = 1, …, n), and m emerging consumer ecomorphs (j = 1,…, m), each with life history trait ℓ_j and feeding niche trait η_j determining their resource use. In the absence of consumers, resource density dynamics follow , where ρ and are the renewal rate and the carrying capacity of the ith resource, respectively. Because the product of the carrying capacity and the supply rate corresponds to the maximum possible production rate of each resource, we measure the total productivity of food resources as .

Assuming that there exists an optimal trait value θ_i to consume each resource, these optimal traits are ordered along a one-dimensional niche trait space (i.e., ), separated by a distance D > 0. The attack rate, , of an ecomorph with feeding niche trait η_j on the ith resource equals the maximum attack rate α when its feeding niche trait η_j equals θ_i, and decreases in a Gaussian manner as η_j moves away from θ_i, that is (Fig 1A). In this expression, τ determines the width of the Gaussian function and thus the breadth of the feeding niche. Hence, when τ is small, an ecomorph must be highly specialized to successfully attack resource i. Consequently, a tradeoff between feeding on alternative food resources emerges, in which the specialization on one food resource is at the expense of specialization on the others [30]. Such tradeoffs have been generally observed in heterotrophic organisms, including bacteria [31], insects [32], and vertebrates [33].

Model 1: Diversification and evolution of offspring size

Model 1 considers an ecomorph population j that is composed of juvenile and adult individuals. Individuals are born at size ℓ_j and mature (i.e., enter the adult stage) when they reach size w. The feeding rate of juveniles of the jth ecomorph is and of adults is , with . The general rule across animal taxa is that larger organisms have higher foraging capacity than smaller conspecifics [34–36]. To meet this rule in the model, the factor γ < 1 scales the juvenile feeding rate, such that it is lower than that of the adults. The flux of energy that juveniles allocate to somatic growth is , where ε is the assimilation efficiency and ν is the metabolic cost. Hence, juveniles grow when the assimilated food exceeds the metabolic cost ν and do not shrink in size. De Roos and Persson showed that the maturation rate depends on the somatic growth, the mortality rate, and the size range over which an individual grows in the juvenile stage (see Box 3.1 in ref [37]), as given by:

where δ_J is the juvenile mortality rate. The maturation rate thus decreases as the range over which an individual growsin the juvenile stage increases; that is, as the ratio decreases. Conversely, the maturation rate increases as the rate at which individuals grow increases. Adults only reproduce when assimilated food exceeds the metabolic cost incurred by adults, ν, such that their birth rate is Birth rate is divided by the offspring size, reflecting the well-known tradeoff between offspring number and size that has been ubiquitously observed across diverse plant and animal taxa [22,38–40]. Additionally, juvenile survival was documented to increase with offspring size in wild populations of diverse animal species [41]. Because larger organisms often have greater survival than smaller conspecifics [42–53] and this relationship scales exponentially with respect to body size [54], we assume that juvenile mortality decreases with offspring size, following , where δ_max is a boundary of maximum possible mortality. Adults die at a rate δ_A. Starvation mortality is not considered because, at the ecological equilibrium, a population is viable (i.e., its density is positive) only if starvation conditions do not occur, i.e., if and .

Based on the assumptions described above, the dynamics of juveniles J_j and adults A_j of the jth ecomorph, as well as of food resources, follow

(1)

The total population density, , varies following

(2)

where C_j is the fraction of adults (for the ecological dynamics rewritten in terms of N_j and C_j, see eq. S1.1 in S1 Text). The per capita growth rate, and thus the fitness of the jth ecomorph, is . Using this fitness expression and following adaptive dynamics techniques [25,26], we obtained analytical expressions for the selection gradient and the curvature of the fitness landscape when both the feeding niche trait and the offspring size evolve (see S1 Text: eq. S1.4–S1.6). For a population encountering an environment with two different food resources with carrying capacities , we obtained analytical expressions for the food and population densities as well as the fraction of adults at the ecological equilibrium (see S2 Text). Using these quantities and the expressions for the selection gradient and the curvature of the fitness landscape, we analytically derived the conditions that enable diversification (see S3 Text) and determined their relationship with the life history trait (see S4 Text).

Additionally, we numerically computed the evolutionary trajectories of a diversifying lineage that encounters an environment with ecological opportunity represented by two or more different food resources. To do so, we used eq. S1.1–S1.3 (S1 Text) and parameter values in Table A in S5 Text. Moreover, we evaluated whether a diversification event occurs by calculating the curvature of the fitness landscape (using eq. S1.6 in S1 Text) when directional selection in the feeding niche trait ceases (i.e., when the change in this trait was smaller than 1E−8 per evolutionary time step). If the curvature of the fitness landscape indicated that the population experiences disruptive selection in the feeding niche trait (selection in the life history trait is always directional or stabilizing), population j was split into two distinct ecomorph populations with trait values 0.1% larger and smaller than η_j, and abundance equal to N_j/2. Subsequently, the evolutionary trajectories were computed simultaneously for the two ecomorph populations until directional selection in the feeding niche trait ceased, and the curvature of the local fitness landscape was evaluated for each ecomorph. Each computation finished when all ecomorph populations experienced stabilizing selection. Throughout each computation, we followed the number of ecomorphs, their traits, and their densities, as well as the densities of resources, which we used to calculate the fitness gradient and the curvature of the fitness landscape (using eq. S1.4–S1.6 in S1 Text).

By altering the stability of evolutionary equilibria, life history influences the conditions for diversification

For diversification to occur, theory proposes that a population must experience disruptive selection for a significant amount of time [12]. This is possible when natural selection drives a population towards a local minimum of the fitness landscape, where intermediate phenotypes have a fitness disadvantage relative to more extreme phenotypes [13,55]. Although our model describes the evolution of two phenotypic traits, ecological opportunity is provided only along the axis of the feeding niche trait. As a result, the possibility of a local fitness minimum exists only along this trait axis. Consequently, our model behaves similarly to previous diversification models with a single evolving trait (i.e., one-dimensional trait space diversification models, e.g., ref [55,56]). In such models, two conditions need to be satisfied for diversification to occur in a population colonizing an environment with two different food resources:

Condition 1 (condition for mutual invasibility according to Geritz and colleagues [55]): The mean phenotype of the population at an evolutionary equilibrium must be a local fitness minimum. A population satisfies this condition when:

(3)

(see analytical derivation in S3 Text: eq. S3.19). Because the ratio D/τ determines the strength of the tradeoff between feeding on the alternative food resources, eq. 3 implies that this tradeoff needs to be sufficiently strong to induce disruptive selection [27,57]. In other words, the broader the niche of a population, i.e., the larger τ, the greater must be the distance between the optimal trait values for feeding on alternative food resources for disruptive selection to occur. Otherwise, the generalist strategy, corresponding to the evolutionary equilibrium in between the optima to feed on the resources, is a fitness maximum and thus selection is stabilizing.

Condition 2 (condition for convergence stability according to Geritz and colleagues [55]): The evolutionary equilibrium at which the population experiences disruptive selection must be an attractor of the evolutionary dynamics, or in other words, natural selection must be able to drive a population toward this evolutionary equilibrium. This condition is satisfied when productivity exceeds the threshold

(4)

where is a scaling factor of the population birth rate and is the rate of biomass loss through various processes (e.g., metabolic maintenance, mortality). These two compound variables regulate population growth, as shown by rewriting eq. 2 as Population growth increases as E increases due to greater efficiency to assimilate food (high ε) or a higher fraction of adults in the population (high C), or due to smaller offspring size (small ℓ) that increases the adult birth rate. Conversely, population growth decreases as G increases due to increased metabolic cost (high ν), higher adult mortality (high δ_A), or higher juvenile mortality (high δ_J).

Eq. 4 implies that there exists a minimum productivity of the environment that enables the evolutionary equilibrium at which the population experiences disruptive selection to be an attractor of the evolutionary dynamics (see analytical derivation in S3 Text: eq. S3.21). Below this threshold of minimum productivity, the population density is low and intraspecific competition is weak, hindering diversification. This threshold depends on parameters underlying the provision of ecological opportunity, such as the distance between the optimal values to feed on alternative resources D and the resource supply rate ρ, as well as organismal properties, such as the maximum attack rate α, and the breadth of the feeding niche τ. Additionally, this threshold also depends on the compound variables, E and G. Large values of E or small values of G reduce this threshold, enabling diversification over a larger range of productivities. This is because by increasing E, the population birth rate increases. Analogously, by reducing G, the rate of biomass loss decreases. Consequently, in both cases, the population density increases, leading to stronger intraspecific competition that, in turn, facilitates diversification.

Life-history evolution through changes in offspring size in Model 1 does not affect Condition 1, but it affects Condition 2. Indeed, eq. 3 shows that the breadth of the feeding niche, τ, is the only organismal property influencing Condition 1. In contrast, multiple organismal properties, including offspring size, influence Condition 2. As a result, changes in this life history trait driven by natural selection alter the stability condition that determines when selection drives the feeding niche trait to the value where it becomes disruptive. This is due to the effect of offspring size evolution on the population birth rate through E and the biomass losses through G. These effects are direct; for instance, the offspring size negatively affects the birth rate, i.e., E decreases as ℓ increases. Similarly, because decreases with increasing ℓ, the offspring size negatively affects the mortality experienced by the offspring, and thus the biomass losses G. In addition, these effects are indirect, mediated by changes in population composition, C. Hence, by influencing the population composition, its birth rate, and its losses, the offspring size determines whether the feeding niche trait value at which selection is disruptive is an attractor or repeller of the evolutionary dynamics and thus dictates whether diversification occurs or not.

The evolution of life history traits enables diversification

To understand how life history evolution influences ecological diversification, we numerically computed evolutionary trajectories in two scenarios: (1) a null model in which only the niche trait can evolve (i.e., the mutation rate for offspring size is set to zero), and (2) an alternative model in which both traits, niche and offspring size, can evolve. In the first scenario, in which offspring size remains constant (Fig 2A), the niche trait of the ancestral population evolves towards one of the resource feeding optima (Fig 2B). At this point, diversification cannot occur because selection is stabilizing. In the second scenario, the niche trait is initially driven toward one of the resource feeding optima (between time 0 and 5,000 in the examples given here); however, later, when the offspring size approaches an intermediate trait value (offspring size of 1.5 in Fig 2C), the direction of selection on the niche trait changes. As a result, the niche trait evolves to the value between the two optima. At this point, selection becomes disruptive; therefore, the population undergoes a diversification event in the niche trait. After diversification, the niche traits of the two resulting ecomorph populations diverge. Each population then evolves towards its nearest optimal feeding trait value (Fig 2D).

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Fig 2. The evolution of offspring size enables diversification.

Evolutionary dynamics of a population that colonizes an environment with two food resources (optimal niche traits to feed on resources are θ₁ = 1, θ₂ = 2) A, B) when the offspring size cannot evolve, and C, D) when it can evolve. E) Selection gradient with respect to the offspring size of the colonizing population. F) Sum of the food densities at the ecological equilibrium as a function of the offspring size. G) Fitness landscape of the niche trait as a function of the offspring size. Diversification occurs only when the offspring size of the population is near the optimal trait (indicated with purple vertical dashed line) because the niche trait evolves towards a fitness minimum, where the trait equals 1.5 (arrows indicate the direction of selection). Evolutionary equilibria (black lines; solid when stable and dotted when unstable) in the striped regions are fitness maxima, whereas outside these regions they are fitness minima. In the gray region in the left, the population is extinct. In A–D, the initial offspring size and niche trait are 1 and 1.3, respectively. In F, the niche trait value is fixed and equal to 1.4. However, regardless of the niche trait value, the food density is always depleted to the lowest level at the value of the offspring size that is selected for (analytical proof in S4 Text). Parameter values as in table A in S5 Text. The code needed to generate this Figure can be found in https://zenodo.org/records/17049771.

https://doi.org/10.1371/journal.pbio.3003492.g002

To better understand the mechanism by which life history evolution enables diversification, we analyzed the fitness landscape of the niche trait experienced by the colonizing population. Our analysis revealed that ecological diversification can only occur when the offspring size is near its optimal value (purple vertical line in Fig 2E). In the neighborhood of the optimal offspring size, food resources are strongly depleted, causing strong intraspecific competition (Fig 2F). Under this regime of strong competition, the gain from becoming more specialized on the underused resource outweighs the loss from a decreased intake of the most used resource. As a consequence, the niche trait evolves in the direction that enables increasing use of the underused resource. This process ceases when both resources are equally exploited, that is when the niche trait value is equal to the intermediate value between the two optima to feed on the resources (niche trait 0.5 in Fig 2). Therefore, this niche trait value is an attractor of the evolutionary dynamics that may be either (1) a global attractor, and thus, evolution drives the niche trait towards it regardless of the initial trait value of the colonizing population (e.g., when offspring size is larger than 2.2. and smaller than 4.2 in Fig 2G), or (2) a local attractor, and thus, evolution can only drive the niche trait towards it if the trait value of the colonizing population is in its neighborhood (e.g., when offspring size is between 1.2 and 2.2 or between 4.2 and 5.9 in Fig 2G). In the first case, diversification always occurs, whereas in the second case, it is contingent on the initial niche trait of the colonizing population. Conversely, when the offspring size is far from its optimal value, the niche trait value between the two optima to feed on the resources is a repeller of the evolutionary dynamics, and consequently, evolution drives the niche trait away from this value (offspring size elow 1.2 and above 5.9 in Fig 2G).

The evolutionary rate of life history traits influences diversification and the ensuing diversity

The effect of life history traits on the fitness landscape of the feeding niche trait suggests that the speed at which life history traits evolve affects diversification. To test this, we computed the evolutionary trajectories of two lineages colonizing an environment with 10 different unexploited niches. These lineages differ in the mutation rate of the life history trait (i.e., the offspring size), thereby representing different levels of evolvability for this trait, but share the same mutation rate for the feeding niche trait. At time 0, both lineages are seeded at opposite ends of the trait space, ensuring equal access to the available niches. The computation shows that the diversification process initiates earlier in the lineage with the highest mutation rate (Fig 3). This is because, in this lineage, the rate of change of the offspring size is higher, enabling natural selection to drive this trait towards the optimal value faster. Then, in the neighborhood of the optimal offspring size, natural selection drives the feeding niche trait towards the value in between two optima (e.g., between θ₁ and θ₂ at time 2,500), where selection becomes disruptive, enabling diversification. Conversely, in the lineage with the lower mutation rate, the evolutionary process driving changes in the offspring size is slower. Consequently, it takes roughly twice as long for the feeding niche trait to reach the value in between two optima (e.g., between θ₉ and θ₁₀ at time 5,000). As a result of the earlier diversification process, the lineage with the higher evolutionary rate in the life history trait occupies more niches, resulting in higher diversity.

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Fig 3. The speed of offspring size evolution influences lineage diversity.

Evolutionary trajectories of two lineages colonizing an environment with 10 different unexploited food resources. The lineage with a higher mutation rate in offspring size results in 1.5-fold higher diversity than the lineage with lower mutation rate (the former diversifies into six different ecomorph populations, whereas the latter diversifies into four). The total productivity is 2 gL⁻¹ unit time⁻¹. The lineages are seeded at the beginning of the simulation in the extremes of the niche trait space (trait values of the ancestral populations are 0.8 and 10.2). The offspring size of both ancestral populations is 1. Parameter values as in table A in S5 Text. The code needed to generate this Figure can be found in https://zenodo.org/records/17049771.

https://doi.org/10.1371/journal.pbio.3003492.g003

Local adaptation facilitates diversification

We next explored how variation in environmental conditions across habitats affects life history evolution and diversification. To this end, we computed evolutionary trajectories for environments that differed in the mortality risk experienced by juveniles. In more risky environments, natural selection favors a larger offspring size because juvenile mortality decreases as offspring size increases. The optimal offspring size is therefore shifted towards a larger trait value when the mortality risk of juveniles is higher (top row in Fig 4A). Interestingly, we observed that the range of productivity levels over which diversification can occur is larger when the offspring size is near its optimum than when it is far from the optimum (bottom row Fig 4A). Hence, by driving offspring size towards the optimal trait value, natural selection reduces the threshold of minimum productivity required for diversification to occur, facilitating diversification. We proved this effect analytically in S4 Text by showing that eq. 4 always assumes its minimum value when the offspring size is at its optimum.

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Fig 4. Local adaptation in life history traits facilitates diversification.

The range of productivities over which diversification is enabled increases in the neighborhood of the optimal life history trait (i.e., where the selection gradient of the offspring size in A, maturation size in B, and timing at diet shift in C equals zero). For each model, three scenarios that differ in the mortality risk experienced by juveniles in A, all individuals in B, or the small individuals in C were computed. The fitness landscape along the transect of the blue dotted line in A is shown in Fig 2G. Other parameter values of Model 1 as in Table A in S5 Text, of Model 2 as in Table B in S6 Text and of Model 3 as in Table C in S6 Text. The code needed to generate this Figure can be found in https://zenodo.org/records/17049771.

https://doi.org/10.1371/journal.pbio.3003492.g004

Model 2 and 3: Diversification and evolution of maturation size and timing of diet shift

To test the generality of our results, we examined how natural selection influences ecological diversification by driving changes in other life history traits (Fig 1B). In model 2, we studied the effect of the evolution of body size at maturation, which determines the transition of energy allocation from growth to reproduction (Fig A in S6 Text). Here, the optimal energy allocation strategy, and thus the optimal size at maturation, depends on the tradeoff between early reproductive investment and individual growth that increases size-dependent survival [24]. In this model, we studied evolutionary trajectories in alternative environments that differ in the magnitude of size-dependent survival to examine how environmental variation in survival affects the evolution of body size at maturation and diversification. In Model 3, we studied the consequences of the evolution of the timing of a diet shift, a key life history trait that determines when organisms with ontogenetic diet shifts begin exploiting a secondary food source. Such shifts are widespread across the animal kingdom, occurring in taxa ranging from amphibians and fishes to many invertebrates [58,59]. The timing of a diet shift involves a tradeoff between individual growth potential and survival [60,61], and is thus fundamental in determining individual fitness [ 61–64]. In this model, we studied evolutionary trajectories in alternative environments that differ in the mortality experienced by small individuals (i.e., individuals feeding on the early food resource) to examine how environmental variation in mortality in early life influences the evolution of the timing of a diet shift and diversification. For both models, we leveraged existing ecological models [65–67] that we extended to include evolution of the life history and feeding niche trait. See S6 Text for a detailed description of the two models. All analyses were performed using the PSPManalysis software package [68], which allows for the evolutionary analysis of population models structured by body size [69,70].

General patterns: Optimal life histories maximize the potential for diversification

Across all studied models, we found that the productivity necessary for diversification decreases as the distance of the life history trait from its optimum becomes smaller (Fig 4). Extending our previous results from Model 1, the analysis of two additional model systems shows that life-history adaptation makes the environmental conditions for diversification, in this case, productivity, less restrictive. Notably, the three models differ substantially in their formulation of the population dynamics, the evolving life history traits, and the assumptions underlying life history processes (Fig 1B). Yet, despite these differences, they consistently demonstrate that natural selection, by driving life history adaptation, facilitates trophic diversification.