The Aftermath: South America
Brazil:
Brazil is the biggest winner from the war as they establish a hegemony over much of South America, and have broken Argentine hopes for a reunited Viceroyalty of the Rio de la Plata. Brazil, in being able to successfully invade and effectively blockade Argentina, has done what no European power could successfully do. A renewed if uneasy alliance and respect from the British Empire helps solidify Brazil's place in the world, and earns it the respect of European powers. The war and helping the British has earned them a powerful ally and the status of regional power, and Brazil would be relatively stable and prosperous compared to many of its neighbours. The Empire of Brazil entered into a period of great economic, scientific, and cultural prosperity, lasting from 1850 onward.
Venezuela and Guyana:
Venezuela, home to just over 1.25 million people, saw two somewhat unforeseen events occur over the course of the war: a rebellion led by former leader Jose Antonio Páez against the actions and rule of his own chosen successor, Jose Tadeo Monagas, and Brazilian military aid to Britain. This was unexpected and poorly handled by Monagas. The costly war to reinstate Páez as president would ultimately make Venezuela a de facto British puppet state. Venezuela was forced to relinquish all claims on disputed territory in British Guyana, and the British themselves helped steer Venezuelan politics by helping Páez hold on to power in exchange for more trade and British preference for goods and services. [1]
Guayaquil and Ecuador:
Guayaquil saw relatively little fighting or destruction once Peru got involved in the war against Ecuador. The war had had the effect of justifying the militaristic mindset present at the time in Guayaquil; "Everyone wants to annex us, so we need to constantly be ready." Thanks to its protectorate status however, Guayaquil was an island of relative stability, growth, and progress, and began to come into its own as the "Pearl of the Pacific." Unlike the more conservative Ecuador, liberalism began to flourish in Guayaquil whereas conservatism became entrenched in Ecuador. [2]
Ecuador, annoyed and surprised by Peru's involvement, begins to foster even more intimate relations with the United States and Colombia. They now know that Peru may intervene and they would not have the capability to fight the Guayaquileños, Peruvians, and British should they ally again in the future. Though these ideas and fears persist into the future, the failure of the war forces a rebellion that sees Flores flee into exile.
Peru and Chile:
In aiding the British, Peru helped secure some respect and favours from the British which were seen as necessary given Peru's relations and territorial disputes with neighbours. Peru's involvement in the Pan American War was as much about pragmatism as it was about settling territorial disputes with Ecuador.
Chile on the other hand, while not exactly militarily involved, did allow the British to use their ports and coaling stations. The Chileans helped supply British forces, especially those in Guayaquil. Chile had found that their interests often overlapped with British interests and so sought to associate themselves with the eminent world power. This would come to be Chile's advantage in the future. Unfortunately for Chile at that moment, there was an attempted revolution in 1851 that came about as a Liberal challenge to suspect election results. Santiago was seized, causing the conservative government to focus on restoring order. [3]
José María de la Cruz
Opposition presidential candidate and leader of the 1851 revolution
Argentina:
Following Argentine defeat in the Platine/Pan American War, the San Nicolas Agreement was signed. It was meant to comply with the constitutional mandate of the Federal pact that presided over the Argentine Confederation, convening a Constitutional Assembly to meet in Santa Fe. This agreement was not accepted by the province of Buenos Aires, since it reduced its influence and power over the other provinces. Buenos Aires thereupon seceded from the confederation. Thus was Argentina divided into two rival, independent states which fought to establish dominance. On the one side were the Federalists of the Argentine Confederation, led by Justo José de Urquiza. On the other, the Autonomists of Buenos Aires led by Bartolome Mitre.
Uruguay:
With its long and costly civil war that captured the world's imagination at an end, Uruguay came firmly under the sphere of Brazil and Great Britain. Britain would endeavour to have a stabilizing influence, as well as having a base of operations in the strategically important area. As such, the British continued to help supply their preferred Uruguayan faction in order to prevent further conflicts such as the Pan American War from happening again. [4]
Venancio Flores, post-war President of Uruguay
Paraguay:
Paraguay, having gotten involved when Brazil mobilized to invade Argentina, came out of the war with Argentine territory north of the Bermejo River. With the opening of the Platine rivers, Paraguay now found it possible to contract with European technicians and Brazilian specialists to aid in its development. Unhindered access to the outside world also enabled it to import more advanced military technology.
During the greater part of the 1850s however, the dictator Carlos López harassed Brazilian vessels attempting to freely navigate the Paraguay River. López feared that the province of Mato Grosso might become a base from which an invasion from Brazil could be launched. This dispute was also leverage with the Imperial government of Brazil for acceptance of his territorial demands in the region. Strangely enough, Paraguay became one of the biggest winners of the Pan American War.
Map of South America after the Pan American War:
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[1] In OTL, Monagas won out and would remain president of an unstable Venezuela. Though Paez has returned ITTL, he has somewhat traded stability and power for being a puppet state of Britain. This will however be to Venezuela's benefit in the future. This also butterflies away (or severely reduces the impacts of) the Federalist War. This also means a more conservative Venezuela for some time.
[2] Guayaquil's independence is ensured for now, causing massive butterflies in this area of South America.
[3] In OTL's aborted revolution, the coup in Santiago fails and a major opposition general died in the process, throwing the rest of the attempt into chaos. ITTL, he survives and the attempt goes better for them, resulting in at least an occupied capital. The revolution will still largely be a failure, though.
[4] Relatively massive POD. This additional British involvement would butterfly away the Uruguayan War, as well as the associated Paraguayan War.