Population where most of the newborns die soon?
Yes, we talk about r/K selection theory:


  In ecology, r/K selection theory relates to the selection of combinations of traits in an organism that trade off between quantity and quality of offspring. The focus upon either increased quantity of offspring at the expense of individual parental investment of r-strategists, or reduced quantity of offspring with a corresponding increased parental investment of K-strategists, varies widely, seemingly to promote success in particular environments.


The type of species you describe are the r type.

Please note the following potential confusions:

A species can vary its strategy through time and space

Species can change from K to r (and vice-versa) depending on the environment and number of individuals. Consider humans as an example.

The expression r/K selection theory can be misleading

The term "selection" in "r/K selection theory" can be a bit misleading as it refers more to a demographic reality (which has come to be due to selection pressures) but not to the selection process behind it.

Alternative meaning of 'r/K selection theory'

The terms r and K are sometimes used to mean whether a species has reached carrying capacity (K) or whether they are growing in number (r) which is not exactly the same as the interpretation of whether there is much parental investment in the species presented in the wikipedia article.

This second interpretation is actually closer to the origin of the terms r and K. The most common (and one of the simplest) equation of population growth through time is the logistic equation (see here for an easy explanation and also wiki > Population ecology )

$$\frac{dN}{dt} = rN \left( 1 - \frac{K}{N}\right) $$



, where $N$ is the population size, $t$ is time in generation, $r$ is the maximal growth rate and $K$ is the carrying capacity. On the graph above, $r$ represent the maximal slope (that is the maximal growth rate).

r selected species are those that have a growth rate as indicated at the center of the graph. K selected species are those that have a growth rate of 1 (no increase in $N$) as the ones that are at carrying capacity $K$.