Clarification on the question
The question is a little unclear and I will try to interpret it and answer it. I hope I won't fail to see your goal.
Quantitative vs predictive
There is a big difference between
predictive. To understand the difference you might want to ask the question on Philosophy.SE.
Quantified vs quantifiable
As @chelonian said in the comments, if you are asking
Is evolution quantitative, then you would need to say whether you meant
quantifiable. Almost everything in evolutionary biology (just like in other sciences) is quantifiable but most of it is not quantified as it takes a lot of money and time to do so.
What I think you are trying to ask
Paying attention to the question in your post
Can we tell if a species will develop a specific character [..] and assuming that by
develop, you meant
evolve, then what you meant is
Is evolution predictive rather than
What I am answering
I will try to answer to the question
How good are we to predict future evolution? and just say a few words about how quantitative a science is evolutionary biology.
Evolutionary Biology is a quantitative science
Evolutionary Biology is definitely a quantitative science. It relies a lot on mathematical modelling (incl. statistics and probability theory) and numerical modelling. You might for example want to have a look at Population Genetics and Quantitative Genetics which are at the core of evolutionary Biology.
What are we good at predicting?
Here are a few examples of things we can predict. We can predict how many pairwise differences (or other measures of molecular differentiation) do we expect between two lineages that recently split in a given number of years. We can predict how many mutations of a given fitness effects (whether beneficial or deleterious) do we expect to accumulate over a given period of time in a population. We can make also some predictions about the evolution of multicellularity, sociality, etc. in lineages that are limit-cases (relating again to our ability at a short time only). We can make predictions about the speed of evolution measured in Haldanes or in Darwins (these are units) if we know the genes involved and the heritability of the trait of interest. We can predict the heterozygosity of a structured population. I could cite many other examples. Generally speaking, we have good predictive abilities at short time scale OR for neutral sequences OR for conserved (DNA) regions (strong purifying selection).
In short, we can predict a lot of things but by far not everything yet.
What are we bad at predicting?
I would suggest to decompose the reasons for why predictions can be hard into the following categories. However, I might well forget something and one could argue that my semantic is less helpful some other semantic.
- One issue related to make predictions at long time scale is that the environment changes through time in a way that we are not able to predict accurately enough yet.
- I am not here talking about measurement error or sampling error (these are concept of statistics you may want to check if you don't know them), I am talking about the stochastic process that are inherent to biological systems such as the randomness of mutation processes and genetic drift.
- Genotype-phenotype map
- We have too little understanding of molecular genetics in order to be able to predict how different specific mutation would affect the phenotype. As a consequence, we today still have very little predictive power about the evolution of a phenotypic trait that is currently totally inexistent.
- Complex systems
- For example: demography affects evolution which affects the social environments, which affects demography which affects pattern of species competitions which affects the evolution of another species which affects its demography which affects the evolution of a third species which affects the demography of our first species, etc... These kind of complex systems are often mathematically not tractable.
- We often don't know the exact parameters of the lineage we are interested in. There is a lot of measures to take to be able to make predictions and we often don't have the money (or the time) to make all these measurements (assuming we are able to accurately measure them). For this reason, we are often relatively good to make predictions for a few model organisms but pretty bad for the vast majority of species.
I apologize for my total lack of reference but it would take hours to search references for every claim
Applications of evolutionary biology
There are not a lot of applications of evolutionary biology for the moment but still there are some proving its predictive power. These applications include
- medicine and epidemiology (incl. evolution of resistance)
- artificial selection and other technics mainly to improve crops nut not only
- Various search algorithm such as genetic algorithm
The best way to learn about evolution and to answer your own questions (or help you to ask more accurate questions) is to actually take a short course. Understanding Evolution by UC Berkeley is probably a good place to start.