You really only appear to have two data points since all begin with zero. If the population counts were 7,15,123 then it might make some sense, though very limited sense.
Part of the issue is that a regression should, generally, be replicating your data generation process. Is your data generation process linear? If it is not, then it is dubious.
There are ways where you could begin with zero and eventually have many. For example, you could have an object with no defects or no deaths and then have many defects or deaths. It doesn't appear meaningful here though. The initial value doesn't really appear to be data, but rather the value before the start of a process. The regression should measure the impact of a process.
I could imagine a process where people could choose which group to opt into where all groups begin with zero, except something isn't a group without people in it. This begs another question. Is zero here a real number? Can zero actually happen and does it mean "nothing." Zero degrees Fahrenheit does not mean that there is no temperature, but zero degrees Kelvin does. Is zero, in this case, really "before we started" and not "no people."
Finally, there may be population dynamics that matter here. For example, if at time 5 there are a total of 75 people who must allocate among 8 choices and these 75 are not a sample from 10,000,000 people then there are other constraints that should be considered in your modeling. After all, if you know 7 groups, then you automatically know the composition of the eighth group. That can change how things are modeled.
If this is a fixed colony with eight subcolonies and you are working with the entire population at each point in time, then no you cannot use a linear model with sampling statistics because you are not working with samples, you are working with the population. Subcolonies are not samples in the same sense that Pittsburgh, Pennsylvania is not a random sample of the United States.
I think you need to work out how people end up in a subcolony and/or the broader population. Changes only make sense with respect to a theory about how changes would happen. So, no, you cannot use a linear model unless you believe there is a theoretical reason that the process should be strictly linear with each subcolony totally independent of the others and even then only if zero doesn't mean before the experiment starts.