what are some assumptions that have to be made when predicting population?

You have to assume that the present rate of population growth (or decline), since the last census, will continue. You also have to assume that the previous census was accurate.

Are you talking about human population or modelling population growth in general?

In general population growth modelling you will need to look at factors affecting fitness, such as food supply, predation, disease etc. The same factors are also used for modelling human population growth. Some of these can be estimated with some confidence, some cannot.

Two factors that can be estimated are:
the age structure of the population and
the total fertility rate (TFR).

Total Fertility Rate (TFR)
The total fertility rate is the average number of children that each woman will have during her lifetime. The TFR is an average because, of course, some women will have more, some fewer, and some no children at all.

Theoretically, when the TFR = 2, each pair of parents just replaces itself.

As an example there has been a decline in total fertility rates (TFRs) in undeveloped countries, presumably as the various factors involved in the demographic transition take hold, e.g.,
improved standard of living
increased confidence that your children will survive to maturity
improved status of women
increased use of birth control measures

When predicting population, several assumptions need to be made. Here are some of the key assumptions:

1. Constant fertility rate: One common assumption is that the fertility rate will remain constant. This means assuming that the average number of children born per woman will not change over time.

2. Constant mortality rate: Another assumption is that the mortality rate will remain constant. This means assuming that the average number of deaths per population will not change over time.

3. Stable immigration/emigration: Population predictions often assume that migration rates will remain relatively stable. This means assuming that the number of people entering (immigration) or leaving (emigration) a country will not change significantly over time.

4. No major demographic changes: Assumptions are often made that there will be no major shifts or changes in population demographics. This means assuming that factors like age distribution, ethnic composition, and socio-economic characteristics will remain relatively stable.

5. Linear growth: Population projections commonly assume that growth will be linear, meaning that the population will increase at a constant rate over time. This assumption does not account for possible variations in birth rates, mortality rates, or other factors that might influence population growth.

It's important to note that assumptions made in population predictions may not always hold true in reality. Demographic trends can change due to factors such as social, economic, and environmental conditions. Adjustments and updates in predictions are often required to account for these changes.