The global impact of climate change on food security is generally assessed to be negative—but there are large variations across continents and regions. In a minority of cases (most of them in the higher latitudes), the net effect may even be positive, but for countries in the tropics (where all the SIDS lie), the impacts of climate change on food security are almost certain to be negative.
For the major crops (wheat, rice and maize) in both tropical and temperate regions, climate change will negatively impact production for local temperature increases of 2°C or more, although individual locations may benefit. After 2050, the risk of more severe impacts increases with projections consistently showing that production is negatively affected in tropical latitudes. Climate change will also progressively increase the inter-annual variability of crop yields in many regions.
Undernourishment in the SIDS
The primary indication of food insecurity is obviously hunger–defined as a chronic condition of undernourishment caused by the inability to acquire food intake that is sufficient to meet dietary requirements.
The FAO estimates published in 2014 showed that globally there has been continued progress in the reduction of hunger. About 805 million people were estimated to be chronically undernourished in 2012-2014, a reduction of more than 100 million over the preceding decade, and more than 200 million less than 1990-1992.
The decline in the share of undernourished and hungry people has been sharper than the decline in absolute numbers, because population gains have sometimes been greater than the reduction in hunger. Between 1992 and 2014, the level of undernourishment fell from 18.7 % to 11.3 % globally, and from 23.4 % to 13.5 % in developing countries.
Despite the progress in developing regions as a whole, there are large differences across regions. Africa has made slow progress–especially south of the Sahara, where one in four people remain undernourished.
The FAO does not report on undernourishment for all the small island states. The countries for which data were recorded are shown in the table below. 
Apart from Haiti, all the SIDS in this table show progress in reducing undernourishment. But more than half the population of Haiti and more than a quarter of population of Timor Leste remain chronically undernourished.
Poverty and climate change
Reducing poverty has been a key objective of the major international development agencies for decades. Progress has been slow but significant. But the changing climate is a major challenge to the eradication of poverty.
Most of the shocks that keep households into poverty (or bring them to that level) are related to climate: natural disasters such as floods that destroy assets and disable families; health shocks such as malaria and diarrhea (triggered or worsened by flooding) that result in increased expenditures on medicines and hospital charges, and lost labor income. Crop losses and food price shocks due to drought, disease, or reduced yield due to temperature stress, are often catastrophic for poorer families.
Poor families are disproportionately affected because they are generally more exposed and more vulnerable to climate-related shocks, because they have fewer resources and receive less support from family, community, the financial system, and even social safety nets. Climate change will worsen these shocks and stresses, eventually decoupling economic growth and poverty reduction because of the constant shocks and setbacks caused by extreme weather, the increased frequency of natural disasters, and the inherent vulnerability of poorer communities. 
Natural hazards, to which poor people are often more exposed and more vulnerable, are expected to become more intense and frequent in many regions. For instance, heat waves that are considered exceptional today will become more common. In Europe, the 2003 heat wave, which led to more than 70,000 deaths, will be an average summer at the end of the century under a high-emission scenario.
The number of drought days could increase by more than 20 percent in most of the world by 2080, and the number of people exposed to droughts could increase by 9-17 percent in 2030 and 50-90 percent in 2080.
The number of people exposed to river floods could increase by 4-15 percent in 2030 and 12-20 percent in 2080, and coastal flooding risks can increase rapidly with sea level rise. 
When disaster strikes
Catastrophic events and natural disasters have huge and lasting impact:
Loss of revenue by the poorest
The repercussions of natural catastrophes are extremely grave for island economies because in addition to causing losses and deaths, they provoke a considerable deterioration in revenue, in employment, and in resources when these events hit economic activities essential for the poor. These activities are agriculture, livestock raising, fishing, and other subsistence livelihoods. Moreover, the infrastructure and resources lost are not covered by any insurance. The poor are the hardest hit by these types of disasters because they tend to live and work in the zones where the risk is highest. The poor are the first to be decapitalized without any opportunity to recover or rebuild their assets.
The necessity of urgency
In the short term, the needs in terms of human and financial resources are enormous as government agencies try to respond to the urgency of rebuilding dwellings and damaged infrastructure. The cost of rebuilding and rehabilitating impose substantial costs on the State and households, and above all on those that are not insured or where no government funds are allocated for these events. Funding originally allocated for investments are diverted to disaster relief. In calling for foreign assistance, countries increase their dependence which in turn may undermine the local economy.
A consequence of natural disasters is often the degradation of sanitation systems. The proliferation of bacteria and disease together with the lack of clean water and the problem of evacuating wastewater and rainwater bring major health problems linked to contaminated water– especially cholera. The poor have to take care of these problems themselves because they are rarely covered by insurance.
The impact of the changing climate on small islands is almost certain to worsen food insecurity and to drive many families down into deepening poverty. Haiti was lucky in 2017. Harvey, Irma, and Maria just missed the island.
For more information check out these sources:
 See the FAO report: The state of food insecurity in the world 2015. Available at : http://www.fao.org/3/a-i4646e.pdf
 See the World Bank report: Shock waves: managing the impacts of climate change on poverty. Available at : https://openknowledge.worldbank.org/handle/10986/22787
 See the World Bank report cited above