The improbability of detecting trade-offs and some practical solutions

Trade-offs are a fundamental concept in evolutionary biology because they are thought to explain much of nature’s biological diversity, from variation in life-histories to differences in metabolism. Despite the predicted importance of trade-offs, they are notoriously difficult to detect. Here we contribute to the existing rich theoretical literature on trade-offs by examining how the shape of the distribution of resources or metabolites acquired in an allocation pathway influences the strength of trade-offs between traits. We further explore how variation in resource distribution interacts with two aspects of pathway complexity (i.e., the number of branches and hierarchical structure) affects tradeoffs. We simulate variation in the shape of the distribution of a resource by sampling 106 individuals from a beta distribution with varying parameters to alter the resource shape. In a simple “Y-model” allocation of resources to two traits, any variation in a resource leads to slopes less tha..., Overview of Flux Simulations
To study the strength and direction of trade-offs within a population, we developed a simulation of flux in a simple metabolic pathway, where a precursor metabolite emerging from node A may either be converted to metabolic products B1 or B2 (Fig. 1). This conception of a pathway is similar to De Jong and Van Noordwijk’s Y-model (Van Noordwijk & De Jong, 1986; De Jong & Van Noordwijk, 1992), but we used simulation instead of analytical statistical models to allow us to consider greater complexity in the distribution of variables and pathways. For a simple pathway (Fig. 1), the total flux Jtotal (i.e., the flux at node A, denoted as JA) for each individual (N = 106) was first sampled from a predetermined beta distribution as described below. The flux at node B1 (JB1) was then randomly sampled from this distribution with max = Jtotal = JA and min = 0. The flux at the remaining node, B2, was then simply the remaining flux (JB2 = JA - JB1). Simulations of..., , # The improbability of detecting trade-offs and some practical solutions

[https://doi.org/10.5061/dryad.xpnvx0kq5](https://doi.org/10.5061/dryad.xpnvx0kq5)

We performed simulations of resource trade-off pathways with various initial resource allocation distributions and pathway shapes. Using Python, we simulated initial resource distributions according to either a uniform distribution or a beta distribution with various values for parameters alpha and beta. We then randomly sampled resource allocation for each individual according to the various models, as described in the main manuscript.

## Description of the data and file structure

The source code used to generate the data is organized by the resource model distribution type:

* \"y_model\": Simple y-model where resources are allocated to one of two branches
* \"multiple_branchpoints_model\": Modified y-model where additional branches are added.
* \"hierarchical_model\": Complex model where resources from the second branch of a y-model...