Punctuated Evolution of Influenza Virus Neuraminidase (A/H1N1) under Opposing Migration and Vaccination Pressures

Table 2

Superstrain roughness ℛ_MZ(17) plateaus and vaccination/migration transitions.

		MZ	KD	Superstrains
18–49	Aver.	163.8	211.3	A
	𝜎	3.8	9.8
50–57	Aver.	147.6	192.2	B
	𝜎	1.7	4.5
76 (FD)	Aver.	169.7	236.0	AR
86	Aver.	164.7	214.0	A′
	𝜎	3.1	4.3
88	Hokkaido	148.7	201.4	T
89–03	Aver.	141.5	198.5	C
	𝜎	1.9	4.4
05–07	Aver.	145.5	197.0	Swine flu
	𝜎	2.5	7.4
09-10	Aver.	124.8	174.7	D
	𝜎	0.4	0.6

The time periods are abbreviated (1918–1945 is written as 18–45, and 2009 as 09). The average values and standard deviations σ are estimated from small samples but are thought to be accurate enough to exhibit the main features of both vaccination and migration, as described in the text. Four superstrain plateaus (A–D) are evident. Also the Fort Dix reversion AR, the transition T from A′ to C, and the incipient swine flu pandemic are indicated. The overall trend towards reducing roughness (MZ drops from ~164 to ~120 {D∗, just emerging in Wash DC 2010-2011}) by large-scale vaccinations, which has overriden migration pressures, is clear, as is the convergence after 2009 (very small 𝜎). A more detailed comparison of ℛ(17) for 20 strains (1918–2010) using the MZ and KD scales showed a 90% correlation. However, the even more detailed Hawaii 2007 analysis in the text shows that the MZ scale is about 3x more accurate than the KD scale for NA. Finally, a search on more recent data (2011–2013) confirms the stability of superstrain D. The value of 123.0 (AHA56775 Czech Republic/196/2013(H1N1)) is the lowest in this period. This is still significantly larger than the value of our engineered strain 114.4.