The incessant wars of independence in the late 19th century slowed Cuba's growth somewhat. After Cuba became independent, the 1899 census recorded a total population of 1.57 million people, 89% of whom were born in Cuba. This Cuba was still at a very early
Abel F. Losada Alvarez' 2000 paper "Demographic change and economic growth in Cuba (1898-1958)" (PDF format) provides an excellent outline of the first six decades of independent Cuba's demographic history.
Let us bear in mind that most works on economic growth in developing countries locate the development threshold, demographically speaking, at a life expectancy between 50 and 55 years of age and a net reproduction rate between 2.0 and 1.75. In 1953, Cuba was already on its way to the so-called "modern population growth", with a life expectancy slightly over 60 for both sexes and a NRR of around 1.75.
In the 1950-1955 period, Cuba was clearly outside the "Strategic Growth Territory" of Latin America at that point, in an intermediate position between the Western European "territory" of the thirties and that of the whole of Latin America around 1985-90. These stages of demographic development have been conformed by the confluence of modernization factors and elements which have conditioned the rhythm and variety of this modernization.
Alvarez suggests that Cuba's population was helped along in its "demographic modernization" by the immigration of more than a million people in the three decades after independence, including 735 thousand immigrants from Spain. These Spanish immigrants, mostly from the regions of Galicia and Asturias in the northwest of Spain and from the insular Canary Islands, had already adopted for themselves many of the contraceptive and other behaviours typical of populations advanced on the demographic transition and communicated them to Cubans. Other factors--the growth of a culture of mass media and mass consumption aided by the nearness of the United States, Cuba's increasing urbanization, and a rapidly rising standard of living--played their standard role. By the time of the Cuban Revolution, despite continued high rates of net immigration from Spain and the Caribbean as well as a high birth rate, Cuba's population was starting to stabilize.
Cuba's Communization changed these trends substantially. After a brief post-revolutionary baby boom, Cuba went through an accelerated transition, TFRs dropping below replacement levels in 1978. At the same time, Cuba abruptly became a country of mass emigration; to date, more than a million Cubans have emigrated in successive waves, most to the United States where these have formed a famously coherent Cuban-American community in exile. Cuba's population growth has continued throughout the forty-seven years of Castro's rule and is still relatively young by the standards of First World countries, but with sustained sub-replacement fertility rates and continued high rates of emigration it is fast tapering off.
How is the Cuban population likely to evolve in the coming years? Sergio Díaz-Briquets' "Cuba's future Economic Crisis: The Ageing Population and the Social Safety Net" paints an alarming picture. As a result of Cuba's particular demographic trends, Cuba's "median age has risen from 23.4 years in 1960 to 32.9 in 2000; it is projected to increase to 43.1 by 2025, rising even further by 2050, the end of the projection period." This rapid aging will have serious effects on the Cuban work force.
In 2002, when the country had 1.6 million elderly, the [Potential Support Ratio] in Cuba was 7, a relatively favorable ratio. By 2050, as the number of elderly is projected to reach 3.7 million, with a relatively unchanged overall population size, the PSR is expected to decline to 2 potential workers per retiree.
By comparison, in 2050 the Dominican Republic is expected to have a PSR of 4 and Chile and the United States PSRs of 3. The problem of underfunded retirement and pension systems that bedevils First World countries will be catastrophic for Cuba, in Díaz-Briquets' words possibly "imperil[ling] the country’s economic development since financing pension and health care programs will consume a disproportionate share of national resources. Paying for elderly services will be a major drag on the economy, placing a heavy tax burden on individuals and businesses. The tax burden may even be so onerous as to make Cuba less than attractive as an international investment destination."
Cuba's substantial economic underperformance, taking Cuba from a position alongside the richest countries of Latin America and southern Europe to one closer to the poorer countries of the Caribbean and Central America, thus might never be remedied. Indeed, it almost certainly will worsen Cuba's population prospects. Leaving aside the obvious economic incentives for potential emigrants from Cuba, Luis Locay argues in his papers "Schooling vs. Human Capital: How Prepared is Cuba's Labor Force to Function in a Market Economy?" (PDF format) and "The Future of Cuba's Labor Market: Prospects and Recommendations" (PDF format) that Cuba's well-educated labor force is inefficiently deployed, with the professional sectors of the Cuban economy having far too many workers for their own good. Locay concludes in his second paper that "[t]he current occupational and skill distributions of Cuba’s labor force are probably quite different from what they will be in a future market-oriented economy. Considerable retooling will be necessary. This not only will be costly, but also means that Cuba’s relatively high levels of education and large stock of professional talent overstate the earning capacity of the island’s labor force." A population with basic expectations that aren't likely to be met in its country is certain to produce a good number of emigrants.
Students of Cuba's likely post-Castro transition have looked around the world for likely models. People interested in Cuba's population prospects might be best served by looking at the example of Bulgaria, where the country's population has fallen through the emigration of something like one million Bulgarians--a ninth of the 1990 population--between 1990 and 2005. Presently standing at 7.7 million, Bulgaria's population is commonly projected to fall by another third to 4.8 million by 2050, thanks to lowest-low fertility and massive emigration. Bulgaria is by some measures three times as wealthy as Cuba, though; disparities between the living standards of Bulgaria and Greece are much smaller than those prevailing between Cuba on the one hand and the United States or Spain on the other. Moldova's experience might be worth keeping in mind.
Most of the estimates made of Cuba's future population expect the island nation's population to remain more or less stable until 2050 at around 11 million people. It's safe to say that these estimates are almost certainly overcounts. For the time being, I feel comfortable in predicting that after Castro, the Cuban diaspora will grow very strongly indeed.