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The climax intestinal flora is attained in successive stages.
The foetal intestine is sterile and bathed in swallowed amniotic fluid. Following delivery, multiple different antigens challenge the intestine of the newborn. The maternal intestinal flora is a source of bacteria for the neonatal gut.
The bacterial flora is usually heterogeneous during the first few days of life, independently of feeding habits. After the first week of life, a stable bacterial flora is usually established. In full-term infants a diet of breast milk induces the development of a flora rich in Bifidobacterium spp. Other obligate anaerobes, such as Clostridium spp. and Bacteroides spp., are more rarely isolated and also enterobacteria and enterococci are relatively few. During the corresponding period, formula-fed babies are often colonized by other anaerobes in addition to bifidobacteria and by facultatively anaerobic bacteria; the development of a "bifidus flora" is unusual. In other studies the presence of a consistent number of bifidobacteria in infants delivered in large urban hospitals has not been demonstrated, whether the babies were bottle fed or exclusively breastfed. The predominant faecal bacteria were coliforms and bacteroides. According to these studies, environmental factors may be more important than breastfeeding in gut colonization after delivery.[1]
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The most important determinants of the gut microbiotic composition in infants were the mode of delivery, type of infant feeding, gestational age, infant hospitalization, and antibiotic use by the infant. Term infants who were born vaginally at home and were breastfed exclusively seemed to have the most "beneficial" gut microbiota (highest numbers of bifidobacteria and lowest numbers of C difficile and E coli).[2]
[1]S Fanaro; R Chierici; P Guerrini; V Vigi Intestinal microflora in early infancy: composition and development Acta Paediatrica, Volume 92, Supplement 441, Supplement 441/September 2003, pp. 48-55(8)
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The FF baby who is not cared for properly, given inappropriate things to eat, not kept clean, and left where there is animal faeces or spoilt food is OBVIOUSLY more at risk of contracting e.coli and similar than an excellently cared-for FF baby.
You're thinking of e-coli infection, not contracting e.coli. We already have e.coli, and that bacteria exists everywhere in our environment. People to people transmission occurs, its not just a matter of 'clean' environments or avoiding animal faeces. E-coli is also not the only gram negative bacteria that is capable of shedding toxins during reproduction or dying, there are other gram neg bacteria that exist in babies not breastfed, not born at home, given ab's etc.