Common-factor models assume that positively correlated variables emerge from a single latent trait. The mutualism model proposes that instead of a common factor, the positive correlations arise from beneficial, reciprocal causal interactions between the variables itself. This view can explain the same phenomena, but without the necessity of introducing a latent, unobserved trait. Namely, the mutualism model explains the positive manifold of intelligence through the mutualistic interactions of memory systems, cognitive processes and physical actions, which all influence one another in a positive feedback loop. In addition, the mutualism model can also explain the hierarchical factor structure of intelligence, the low predictability of intelligence from early childhood performance, the integration/differentiation effect, the Flynn effect, and more. The mutualism model is therefore an alternative to the latent g-factor model for intelligence. For an update on the mutualism model, see: van der Maas, H. L. J., Savi, A. O., Hofman, A., Kan, K.-J., & Marsman, M. (2019). The network approach to general intelligence. In D. J. McFarland (Ed.), General and specific mental abilities (pp. 108–131). Cambridge Scholars Publishing.
Assuming that all cognitive processes can be quantified by a psychological test score, we model the development of cognitive processes with a logistic growth function. We define the relationships between cognitive processes to be mostly positive, which makes our application a mutualism model. The basic logistic function incorporates self-reinforcing growth based on the notion that the development of cognitive processes is largely an autonomous, self-regulating process.
The logistic model includes three types of parameters: initial values, growth parameters, and carrying capacities (or limited resources).
The initial values x0 are not important in our application of the model.
The a-growth parameters determine the steepness of the logistic growth function associated with each x.
The K-parameters determine the asymptotes of the logistic growth processes. They are often interpreted as limiting resources for growth, which in our model translates to biological constraints, such as neuronal speed and size of neural systems.
In simulations, we found two independent mechanisms for the creation of a positive manifold in the correlations between a set of observed variables:(a) by simulating a g factor (correlated parameters) and (b) by mutualism (correlated cognitive processes). We therefore showed that the positive manifold can emerge without correlated growth parameters or K-parameters, while small, random variations in the K-parameter could still explain why we observe individual differences in intelligence in real life.
$$ \begin{equation} \ \frac{dx_i}{dt} = a_i x_i \left(1 - \frac{x_i}{K_i}\right) + a_i \sum_{\substack{j=1 \ j \ne i}}^{W} M_{ij} \frac{x_j x_i}{K_i}, \qquad \text{for } i, j = 1,\ldots,W. \ \end{equation} $$
We use the term cognitive processes in a general sense, including perceptual, memory and decision processes - or more broadly, all such capacities, abilities, or components of the (neuro)cognitive systems that are measured by intelligence tests. xi denotes individual cognitive processes.
Matrix M contains weights to specify the generally possible, possibly assymmetric, relations between pairs of processes in development. These relations hold for the entre population. Large values of M imply that the xi grow without bound, which is of course unrealistic and should be avoided in simulations Label: M
steepness of the logistic growth function associated with each x_i Label: a
limited resrouces of the logistic growth process Label: K
These parameters differ over subjects. Stable states of the model are independent of both x_0 and a, implying that individual differences in the initial phase of development do not predict later differences
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