Translating Time

Generating Regression Equations for New Species

Since the Translating Time model only makes direct predictions for 18 mammalian species (Workman et al., 2013), many people have asked if there is a way to employ the model for other species. In fact, there is. One would only need to know the gestational length and adult brain weight for the species of interest to be able to predict embryonic and early postnatal developmental events. However, the model may not be accurate in predicting any event beyond the range of the model (e.g., 3 years in humans). 

We have found that gestational length and adult brain weight predict with reasonable accuracy the timing of events in species that are not currently in the model. We don’t guarantee the accuracy of these predictions in the same way we do for the model data here. We understand that some prediction is better than none. Big-brained and big-bodied species (e.g., horse, elephant) are under-represented in our model and may not fit the model as well as those species similar in size to those in the model. Additionally, marsupials may not fit the model as well as eutherian species do.

Event timings were generated by deriving a slope and intercept regressed against an event scale for each modeled species (see Workman et al., 2013 for further information). For a species that is not currently in the model, you would need to know the adult brain weight and gestational length. Using the following equations, you can estimate intercept and slope of the selected species:

Species Intercept = 1.241 + 0.368*ln(gestational length in days)

Species Slope = 1.474 + 0.257*ln(adult brain weight in grams)

With these equations, you can find the equivalent times across mammals or find equivalent timing of specific events across species. For example, let’s say a user wanted to know when a particular developmental event occurs in the capuchin monkey (a species not yet in the model). One would first obtain the gestational length and the adult brain weight for the capuchin monkey: 155 days, and 65 grams. To obtain the species constant (i.e., intercept), we plug in gestational length into the first regression equation shown above:

1.241+ 0.368*ln(155) = 3.097

To obtain a species slope, we plug in the value for adult brain weight into the second equation shown above:

1.474 + 0.257*ln(65) = 2.547

Using the slope and constant we just computed, we can now predict when a given neural event will occur in the capuchin monkey.

Let’s say we want to know when an event such as onset of myelination of the optic tract occurs in the capuchin. The event score for this event is 0.597. (A full table of event scores for other events can be found in Workman et al., 2013). With the event score, as well as the slope and constant we just computed, we simply plug these values into the model equation and solve for Y:

Y = onset + slope*eventscale  + (interaction term)

Note that this event does not require an interaction term.

Y = 3.097 + 2.547*0.597

Y = 4.617

This is the natural-logged value for the time of this event’s occurrence in terms of post-conception days. If we un-log this value, we estimate that onset of myelination of the optic tract in the capuchin should occur around 101 days post-conception

Here is a second example, this time one that that involves an interaction term. The model features two interaction terms: (non-glire *cortex *neurogenesis) and (cat *retina *neurogenesis). The former denotes isocortical neurogenesis for all species except glires (i.e., primates, carnivores, ungulates, and marsupials, but not rodents and rabbits) and the latter denotes retinal neurogenesis for the cat. By neurogenesis we refer to a group of cells exiting the cell cycle, and by cortex we refer to structures within the isocortex.

To generate a prediction for a given event, the user needs to confirm the presence of an interaction term by determining the following: Is the event neurogenesis in a non-glires cortex? Is it neurogenesis in a cat retina? Or is it neither of these? The values for the two interaction terms are as follows:

non-glire*cortex*neurogenesis: 0.263

cat*retina*neurogenesis: 0.321

Let’s say we wanted to know when peak neurogenesis in cortical layer IV occurs in the capuchin monkey. This event 1) is occurring in a non-glire species, 2) is occurring in the cortex, and 3) is a neurogenesis event. Therefore, we include the interaction term when solving for Y in the equation. The event score for peak neurogenesis of cortical layer IV is 0.320. We can now solve the equation for Y:

Y = onset + slope*eventscale + (interaction term)

Y = 2.547 + 3.097*0.32 + 0.263

Y = 3.80104

This is the natural-logged value for the post-conception day at which peak neurogenesis in cortical layer IV will occur in the capuchin monkey. Un-logging this value yields a post-conception date of 44.7 days

We caution that the model is meant to make predictions for events exclusively within a specific maturational range, which extends from conception to ~3 years postnatal in humans. The model lacks empirical data for events beyond this range. Possible shifts and deviations from the developmental trajectories generated by the model may arise at later points in the developmental schedule, in which case the current model will yield inaccurate extrapolations.