Plasmodium falciparum

White, Nicholas J.  “Antimalarial drug resistance.”  Journal of Clinical Investigation 113(8):1084–1092.  Apr 2004.  A review by the Mahidol and Oxford malaria clinician.  Free to read at the journal.  Read from the publisher PDF;  page numbers are the printed folios.  The PDF text flattens exponents, which were restored from context.

1. 1a.

   Page 1085:  “Resistance to chloroquine in P. falciparum has arisen spontaneously less than ten times in the past fifty years (14).  This suggests that the per-parasite probability of developing resistance de novo is on the order of 1 in 10²⁰ parasite multiplications.”  Reference 14 is Su, Kirkman, Fujioka and Wellems 1997, Cell 91:593–603.  The reference number is left out of the pull quote at the head of the article. ↩ ↩

2. 1b.

   Page 1091:  “This is particularly powerful in malaria, because there are only about 10¹⁷ malaria parasites in the entire world.”  “As there is a cumulative total of less than 10²⁰ malaria parasites in existence in one year, such a simultaneously resistant parasite would arise spontaneously roughly once every 10,000 years”.  Page 1087:  “these ill people would contain between 5 × 10¹⁶ and 5 × 10¹⁷ malaria parasites (8).”  “we have estimated that there must be less than 3 × 10¹⁶ malaria parasites in the world's asymptomatic carriers (Figure 5) (8).”  Reference 8 is White and Pongtavornpinyo 2003, Proceedings of the Royal Society B 270:545–554, which was not obtained. ↩ ↩ ↩ ↩

3. 1c.

   Page 1085:  “To put this in context, an adult with approximately 2% parasitemia has 10¹² parasites in his or her body.” ↩

4. 1d.

   Page 1084:  “In this review, the emergence of resistance to current antimalarial drugs is considered in two parts: first, the initial genetic event that produces the resistant mutant, and second, the subsequent selection process in which the survival advantage in the presence of the antimalarial drug leads to preferential transmission and the spread of resistance (8).” ↩

5. 1e.

   Page 1087:  “Thus approximately 100,000–300,000 merozoites are liberated into the bloodstream to begin the 48-hour asexual reproduction cycle.”  The tenfold growth per generation is this article's assumption. ↩ ↩

6. 1f.

   Page 1085:  “The single point mutations in the gene encoding cytochrome b (cytB), which confer atovaquone resistance, or in the gene encoding dihydrofolate reductase (dhfr), which confer pyrimethamine resistance, have a per-parasite probability of arising de novo of approximately 1 in 10¹² parasite multiplications (5).”  The sentence after the next says that much higher mutation rates than 1 in 10¹² are recorded in the laboratory, citing Rathod, McErlean and Lee 1997.  It is paraphrased here because the published sentence contains a misprint. ↩ ↩

7. 1g.

   Page 1084:  “P. falciparum is now highly resistant to chloroquine in most malaria-affected areas.  Resistance to SP is also widespread and has developed much more rapidly.”  SP is sulfadoxine with pyrimethamine. ↩

8. 1h.

   Page 1086:  “By examination of the sequence of the regions flanking the Pfdhfr gene, it has become apparent that, even for SP, multiple de novo emergence of resistance has not been a frequent event, and that, instead, a single parasite (with a mutation in Pfdhfr at positions 51, 59, and 108) has in recent years swept across each of these continents (24–26).” ↩

9. 1i.

   Page 1091:  “Stable, therapeutically significant resistance to the artemisinin derivatives has not yet been identified and cannot be induced yet in the laboratory, which suggests that it may be a very rare event.” ↩

Behe, Michael J.  The Edge of Evolution: The Search for the Limits of Darwinism.  Free Press.  2007.  Behe is a biochemist at Lehigh University and a senior fellow of the Discovery Institute.  The wording was read from the publisher's e-book.  Page numbers were pinned on the archive.org scan of the 2007 hardback, item isbn_9780743296205, read by search-inside because the item cannot be borrowed.  Printed page equals scan leaf minus 14.  That offset was anchored on the scan's own page map at leaf 65, page 51, and leaf 152, page 138, and agrees with the pages Luskin 2019 and Durrett and Schmidt 2009 cite.  The scan's text destroys exponents, so exponents are from the e-book.

1. 2a.

   Page 51:  “The development of drug resistance in malaria, like the development of the sickle cell gene and thalassemia in humans, is a crystal clear example of Darwinian evolution in action.” ↩

2. 2b.

   Figure 7.4, page 144:  “the value of 5 x 10²¹ is calculated from 10²⁰ malaria cells each year for the past fifty years, the approximate time since chloroquine was introduced.”  From the figure caption. ↩

3. 2c.

   Page 57:  “Nicholas White of Mahidol University in Thailand points out that if you multiply the number of parasites in a person who is very ill with malaria times the number of people who get malaria per year times the number of years since the introduction of chloroquine, then you can estimate that the odds of a parasite developing resistance to chloroquine is roughly one in a hundred billion billion.  In shorthand scientific notation, that’s one in 10²⁰.”  Behe's endnote 16 cites White 2004.  White's paper gives the estimate and its inputs and does not spell out the multiplication. ↩

4. 2d.

   Page 59:  “Let’s compare the two numbers for the odds of achieving resistance to atovaquone, where just one mutation is needed, versus chloroquine, where (presumably—since if a single mutation could help, chloroquine resistance would originate much more frequently) two are needed.” ↩

5. 2e.

   Page 60:  “Let’s dub mutation clusters of that degree of complexity—1 in 10²⁰—“chloroquine-complexity clusters,” or CCCs.” ↩

6. 2f.

   Page 63:  “What if a problem arose during the course of life on earth that required a cluster of mutations that was twice as complex as a CCC?  (Let’s call it a double CCC.)  For example, what if instead of the several amino acid changes needed for chloroquine resistance in malaria, twice that number were needed?  In that case the odds would be that for a CCC times itself.  Instead of 10²⁰ cells to solve the evolutionary problem, we would need 10⁴⁰ cells.”  “Put more pointedly, a double CCC is a reasonable first place to draw a tentative line marking the edge of evolution for all of life on earth.” ↩

7. 2g.

   Page 101:  “Very, very rarely, several amino acid mutations appear simultaneously to confer a beneficial effect, such as in chloroquine resistance with mutant PfCRT.” ↩

8. 2h.

   Page 138:  “(This means a chloroquine-type resistance mutation—where two particular amino acids had to appear before there was a net beneficial effect—would occur in each AIDS patient every day.” ↩

9. 2i.

   Page 59:  “there are an enormous number of parasitic cells (about a trillion) in an infected patient’s body, and about a billion infected people in the world in a year.”  Page 138:  “About a hundred billion billion, 10²⁰, malarial cells are born each year.” ↩

10. 2j.

    Page 75:  “Some of those extra mutations (but not the first one) seem to interfere with the normal work of the protein.  Perhaps, though, if other mutations in other genes could compensate for these harmful effects, greater resistance could be acquired without causing harm in the process.  In other words, to move to the next level of resistance after the first mutation, two further, simultaneous mutations seem to be necessary.”  Page 76:  “That double mutant is, it seems, roughly as rare as a CCC.”  Behe's source is a 2004 review by Hayton and Su, which was not obtained. ↩

11. 2k.

    Page 145:  “Nor has malaria developed new cellular protein-protein interactions.” ↩

12. 2l.

    Page 61:  “There are about five thousand species of modern mammals.  If each species had an average of a million members, and if a new generation appeared each year, and if this went on for two hundred million years, the likelihood of a single CCC appearing in the whole bunch over that entire time would be only about one in a hundred.”  Two endnote markers are left out.  5,000 × 10⁶ × 2 × 10⁸ = 10¹⁸. ↩

13. 2m.

    Page 62:  “So a CCC isn’t just the odds of a particular protein getting the right mutations; it’s the probability of an effective cluster of mutations arising in an entire organism.” ↩

Generations per year:  365.25 days ÷ 2 days = 182.6.  Parasites per year:  10¹⁷ × 182.6 = 1.8 × 10¹⁹ and 5 × 10¹⁷ × 182.6 = 9.1 × 10¹⁹, from White's standing totals;  White's own yearly figure is less than 10²⁰.¹  Drug era:  75 years from the early 1950s to 2025,¹⁴ and 75 × 182.6 = 13,700 generations.  Parasites in the drug era:  75 × 2 × 10¹⁹ = 1.5 × 10²¹ and 75 × 10²⁰ = 7.5 × 10²¹.  Substitutions per parasite:  2.45 × 10⁻¹⁰ × 2.33 × 10⁷ = 0.0057.^{17 17}  Substitutions per year:  2 × 10¹⁹ × 0.0057 = 1.1 × 10¹⁷ and 10²⁰ × 0.0057 = 5.7 × 10¹⁷.  Substitutions in the drug era:  1.5 × 10²¹ × 0.0057 = 8.6 × 10¹⁸ and 7.5 × 10²¹ × 0.0057 = 4.3 × 10¹⁹.  The totals assume the parasite population of the 1950s was as large as today's.  No census exists for the earlier decades. ↩ ↩ ↩ ↩ ↩

Possible single-base substitutions:  3 × 2.33 × 10⁷ = 7 × 10⁷.  Rate of one specific substitution:  2.45 × 10⁻¹⁰ ÷ 3 = 8.2 × 10⁻¹¹ per parasite per generation, or one in 1.2 × 10¹⁰.  This treats the three possible substitutions at a site as equally likely.  They are not:  changes from G or C to A or T are the most common.¹⁷  Per year:  2 × 10¹⁹ × 8.2 × 10⁻¹¹ = 1.6 × 10⁹ and 10²⁰ × 8.2 × 10⁻¹¹ = 8.2 × 10⁹.  In a patient with 10¹² parasites:  10¹² × 8.2 × 10⁻¹¹ = 82 per generation.  A specific pair in one generation:  (8.2 × 10⁻¹¹)² = 6.7 × 10⁻²¹, or one in 1.5 × 10²⁰.  A specific pair in two steps in one patient:  White gives 100,000 to 300,000 parasites leaving the liver to begin the 48-hour blood cycle,¹ and tenfold growth per generation from there reaches 10¹² in about 7 generations.  Assume 8, so that a neutral single mutant reaches a frequency of 8 × 8.2 × 10⁻¹¹ = 6.5 × 10⁻¹⁰, or 650 parasites at the peak.  Each of those gains the second mutation at 8.2 × 10⁻¹¹ per generation, which is 5.3 × 10⁻⁸ per patient per generation.  Over an assumed three generations at the peak that is 1.6 × 10⁻⁷ per patient, or one event per 6 × 10¹⁸ parasites.  Allowing either order and two alternative second sites multiplies the rate by four, giving one event per 1.6 × 10¹⁸.  A third specific mutation in the same lineage multiplies the cost by 1 ÷ (6.5 × 10⁻¹⁰), giving about 10²⁸.  The eight generations of growth and the three generations at the peak are assumptions. ↩ ↩ ↩ ↩ ↩

Wootton, John C. et al.  “Genetic diversity and chloroquine selective sweeps in Plasmodium falciparum.”  Nature 418:320–323.  Jul 18, 2002.  Read in abstract only, from the Europe PMC record.  The full text is behind a paywall and was not obtained.

1. 5a.

   Section Abstract:  “Using 342 highly polymorphic microsatellite markers from a genetic map, here we show that the level of genetic diversity varies substantially among different regions of the parasite genome, revealing extensive linkage disequilibrium surrounding the key CQR gene pfcrt and at least four CQR founder events.” ↩ ↩

2. 5b.

   Section Abstract:  “This disequilibrium and its decay rate in the pfcrt-flanking region are consistent with strong directional selective sweeps occurring over only approximately 20-80 sexual generations, especially a single resistant pfcrt haplotype spreading to very high frequencies throughout most of Asia and Africa.” ↩ ↩

Summers, Robert L. et al.  “Diverse mutational pathways converge on saturable chloroquine transport via the malaria parasite's chloroquine resistance transporter.”  Proceedings of the National Academy of Sciences 111(17):E1759–E1767.  Apr 29, 2014.  Read from the publisher PDF;  page numbers are the printed folios.  The PDF text flattens the superscript strain names, written here as PfCRT-HB3 and PfCRT-Dd2 in notes.  CQ is chloroquine, CQR chloroquine-resistant.  Mirror:  PMC

1. 6a.

   Page E1759:  “mediates saturable CQ transport, whereas the wild-type form of the protein from CQ-sensitive (CQS) strains does not”.  Said of the mutant protein from the resistant strain Dd2. ↩

2. 6b.

   Page E1759:  “These haplotypes all contain a mutation at position 76—the replacement of the positively-charged lysine (K) with an uncharged residue, usually threonine (T)—but are otherwise diverse, containing at least 4 and up to 10 mutations (13).” ↩ ↩

3. 6c.

   Page E1759:  “CQR parasites that have arisen independently in Columbia, Peru, Papua New Guinea, the Philippines, and Southeast Asia (Fig. 1A) have distinct PfCRT haplotypes.”  The spelling of Colombia is the paper's. ↩

4. 6d.

   Page E1759:  “We measured the ability of more than 100 variants of PfCRT to transport CQ when expressed at the surface of Xenopus laevis oocytes.”  “A minimum of two mutations sufficed for (low) CQ transport activity, and as few as four conferred full activity.”  “Moreover, the attainment of full activity followed a rigid process in which mutations had to be added in a specific order to avoid reductions in CQ transport activity.” ↩ ↩

5. 6e.

   Page E1760:  “Nevertheless, introduction of K76T or N75E into PfCRT HB3 (D38 and D39, respectively) did not result in significant uptake of CQ.  However, the addition of both mutations to PfCRT HB3 produced modest but significant CQ transport activity (D32; ∼19% of PfCRT Dd2).”  HB3 is the unmutated protein of a sensitive strain.  The strain names are superscripts in the original.  The second route, K76T with N326D, gave about 45% of the activity of the Ecuadorian protein. ↩ ↩

6. 6f.

   Page E1763:  “Moreover, the fact that PfCRT Dd2 (but not PfCRT D28 or PfCRT E2) increased the CQ IC50 in HB3 parasites indicates that the extent to which mutant PfCRT alters the parasite's sensitivity to CQ is dependent on its capacity for CQ transport.”  D28 carries N75E, K76T and N326S.  E2 carries K76T, N326D and I356L.  The test genes were added on a plasmid beside the parasite's own unmutated gene, so this is weaker evidence than a gene replacement. ↩

7. 6g.

   Page E1761:  “Given that all known PfCRT haplotypes contain either N75E/D or N326D (13), these results indicate that PfCRT acquires the ability to transport CQ via one of two main mutational routes, both of which entail the introduction of K76T plus the replacement of an asparagine (N75 or N326) with an acidic residue.” ↩

Gabryszewski, Stanislaw J. et al.  “Combinatorial Genetic Modeling of pfcrt-Mediated Drug Resistance Evolution in Plasmodium falciparum.”  Molecular Biology and Evolution 33(6):1554–1570.  2016.  Open access, CC BY-NC.  Read from the Europe PMC full text, which has no page numbers, so places are given by section.  CQR is chloroquine resistance and md-CQ is the drug's main breakdown product.  Mirror:  PMC

1. 7a.

   Section Results, Effect of pfcrt Combinatorial Alleles on In Vitro Parasite Growth:  “Notably, in this genetic background, PfCRT K76T was insufficient for CQR and had a deleterious impact on parasite growth that was exacerbated by CQ.” ↩ ↩

2. 7b.

   Section Results, Effect of pfcrt Combinatorial Alleles on In Vitro Parasite Growth:  “As compared with the 7G8 GC03 parasite line, our isogenic, pfcrt-modified parasites exhibited various degrees of in vitro fitness (range of mean s values: −0.26 to 0.11), with the majority of pfcrt alleles conferring comparable (s = 0) or inferior (s < 0) relative fitness”.  The selection coefficient s is per 48-hour generation, measured over ten generations of growth in competition.  The line name is printed with a superscript in the original. ↩ ↩

3. 7c.

   Section Discussion, paragraph 1:  “Our simulations revealed pronounced biological constraints associated with the evolution of Ecu1110 pfcrt, a prototypical CQ-resistant allele comprised of four mutations, the smallest number required for resistance”.  “Among the pathways based on the sequential accumulation of single mutations leading to the Ecu1110 allele, the maximum realization probabilities for CQ and md-CQ resistance were, respectively, ∼5 × 10⁻⁷ and ∼10⁻⁶”.  The same paragraph gives about 3 × 10⁻⁴ for the four-step path in the pyrimethamine gene, from Kumpornsin and colleagues 2014. ↩ ↩ ↩

4. 7d.

   Section Discussion, paragraph 2:  “As the fixation of pfcrt alleles bearing one to three mutations has not been documented in the field, we hypothesize that pfcrt-mediated CQR arose through mutational bursts with brief periods of intervening growth, whereby one or more mutations were acquired and expanded during a short time window prior to the acquisition of additional mutations.  Based on our combined IC50 and growth data, the most likely scenario would be the near-simultaneous emergence of three to four mutations.”  The source prints IC50 with a subscript. ↩ ↩ ↩

Lozovsky, Elena R. et al.  “Stepwise acquisition of pyrimethamine resistance in the malaria parasite.”  Proceedings of the National Academy of Sciences 106(29):12025–12030.  Jul 21, 2009.  Read from the publisher PDF as archived by the Wayback Machine;  page numbers are the printed folios.  The paper codes each form as four digits for positions 51, 59, 108 and 164, so 0010 is S108N alone.  Mirrors:  PMC | Archive.org

1. 8a.

   Page 12025:  “The coding sequence for dihydrofolate reductase (DHFR) from the malaria parasite Plasmodium falciparum was mutagenized, and tests were carried out in Escherichia coli under conditions in which the endogenous bacterial enzyme was selectively inhibited.”  “The most frequent pathway (S108N and then C59R, N51I, and I164L) accounts for more than half of the simulated realizations.” ↩ ↩

2. 8b.

   Page 12026:  “Fig. 1 shows that 2 of the 4 possible single mutants (1000 and 0001) are about equally sensitive to pyrimethamine as the nonmutant allele 0000.  Thus, the first step in the evolutionary pathway toward pyrimethamine resistance is likely either 0010 or 0100.” ↩

3. 8c.

   Page 12028:  “Just 3 pathways in Fig. 2 account for 87.5% of the pathways traversed at significant frequencies in the simulations.  All 3 of these pathways feature S108N as the first step, and the 2 most likely pathways include C59R as the second step.” ↩

4. 8d.

   Page 12028:  “a strongly deleterious interaction between N51I and I164L occurs, with the result that the fourth mutation decreases the growth rate in the absence of pyrimethamine by 30%–40% (Fig. S1), even though it increases the IC50 value by 25%–50% (Fig. 1).”  “According to table 3 in ref. (6), relative to the nonmutant DHFR, the quadruple mutant shows an approximate 500-fold increase in Ki/Km at the expense of about a 6-fold decrease in kcat/KM.”  The growth rates were measured in bacteria carrying the parasite enzyme. ↩

5. 8e.

   Page 12029:  “Elsewhere in the genome, a selective sweep associated with pyrimethamine resistance has been reported across a region of chromosome 13 (39).  It is an interesting, testable hypothesis that this region of chromosome 13 may include 1 or more mutations that also alleviate the deleterious fitness effects of DHFR resistance alleles.”  Reference 39 is Volkman and colleagues 2007. ↩

6. 8f.

   Page 12028:  “In the absence of pyrimethamine, the growth rates of the strains bearing 0010 (S108N), 0110 (S108N + C59R), or either of the triple mutants are not manifestly impaired relative to the previous step or even the nonmutant allele (Fig. 3; Table S2).”  Measured in bacteria carrying the parasite enzyme. ↩ ↩

Lents, Nathan H.  “'Darwin Devolves' -- who's the one really going backward here?”  AIPT.  Feb 12, 2019.  Retrieved Sep 27, 2026.  Lents is a biologist at John Jay College.  The page as read in 2026 no longer discusses chloroquine.  The withdrawn passage survives as quoted by Luskin 2019.

1. 9a.

   “Note: An earlier version of this article misrepresented Behe’s claims about the evolution of chloroquine resistance in malaria.  The author regrets the error.”  Printed at the foot of the article. ↩ ↩

Burgess, Robert W., and Martin D. Young.  “The development of pyrimethamine resistance by Plasmodium falciparum.”  Bulletin of the World Health Organization 20(1):37–46.  1959.  Read in abstract only, from the PubMed Central record.  The scanned article itself could not be downloaded.

1. 10a.

   Section Abstract:  “Of seven cases observed after 25-mg treatment, five relapsed.”  “It is concluded that under the experimental conditions of this study resistance to pyrimethamine by P. falciparum may occur rapidly after a single dose of 25 mg, being manifested during relapses on the second challenge with the drug.  Increasing the drug dosage does not overcome the resistance.  The resistant character is readily transmitted by mosquitos.” ↩ ↩

Living wild land mammals:  bats are two-thirds of individuals and less than one-tenth of 20 million tonnes.⁵⁰  One-tenth of 20 million tonnes is 2 × 10⁹ kilograms.  At an assumed 10 grams per bat that is at most 2 × 10¹¹ bats, and 2 × 10¹¹ ÷ (2/3) = 3 × 10¹¹ mammals.  At an assumed one generation a year for 2 × 10⁸ years the total is 6 × 10¹⁹.  Wild marine mammals are large and few, and livestock are recent, so neither changes the order.  New mutations:  6 × 10¹⁹ births × 63 = 3.8 × 10²¹.⁵¹  Each specific substitution:  1.2 × 10⁻⁸ ÷ 3 × 2 copies = 8 × 10⁻⁹ per birth, and 8 × 10⁻⁹ × 6 × 10¹⁹ = 4.8 × 10¹¹.  For the parasite:  8.2 × 10⁻¹¹ × 1.5 × 10²¹ = 1.2 × 10¹¹ and 8.2 × 10⁻¹¹ × 7.5 × 10²¹ = 6.2 × 10¹¹.⁴  Giving every mammal the human mutation rate and treating all mammals as one genome are both simplifications.  The published HIV article's statement that fewer than 10²⁰ mammals have lived cites an anonymous 2014 Stack Exchange answer, and its footnote quotes only that answer's count of bacteria.  The answer does give a mammal figure:  an upper bound of 2.88 × 10²⁵ mice over 200 million years, which it says is "probably about around 4-10 orders of magnitude less than this", so "probably something like 10²⁰ total mammals ever existed".  That is about 10²⁰, not fewer.  The figure here is derived independently. ↩ ↩ ↩

Dondorp, Arjen M. et al.  “Estimation of the total parasite biomass in acute falciparum malaria from plasma PfHRP2.”  PLoS Medicine 2(8):e204.  2005.  Open access, CC BY.  Read from the Europe PMC full text.  Mirror:  PMC

1. 12a.

   Section Abstract:  “The estimated geometric mean parasite burden was 7 × 10¹¹ (95% confidence interval [CI] 5.8 × 10¹¹ to 8.5 × 10¹¹) parasites per body, and was over six times higher in severe malaria (geometric mean 1.7 × 10¹², 95% CI 1.3 × 10¹² to 2.3 × 10¹²) than in patients hospitalised without signs of severity (geometric mean 2.8 × 10¹¹, 95% CI 2.3 × 10¹¹ to 3.5 × 10¹¹; p < 0.001).”  The patients were adults.  Most African cases are young children, who have less blood. ↩

World Health Organization.  Malaria.  Dec 4, 2025.  Retrieved Sep 27, 2026.  Fact sheet.  The counts are for all malaria species.

1. 13a.

   Section Key facts:  “Globally in 2024, there were an estimated 282 million malaria cases and 610 000 malaria deaths in 80 countries.”  “In 2024, the WHO African Region was home to 95% of malaria cases (265 million) and 95% (579 000) of malaria deaths.”  Section Overview:  “P. falciparum is the deadliest malaria parasite and the most prevalent on the African continent.” ↩

2. 13b.

   Section Genetic mutations:  “In 2024, these mutated parasites were reported in 42 malaria endemic countries”. ↩

Payne, D.  “Spread of chloroquine resistance in Plasmodium falciparum.”  Parasitology Today 3(8):241–246.  Aug 1987.  Read in abstract only, from the Europe PMC record.  The full text is behind a paywall and was not obtained.

1. 14a.

   Section Abstract:  “The drug was introduced in 1934, but was not in large-scale use until the early 1950s.  Anecdotal reports suggest that resistance emerged as early as 1957 both in Colombia and along the then Cambodia-Thailand border area.  But by 1960, resistance in these areas was confirmed - and may represent two separate events.” ↩ ↩ ↩

Bopp, Selina E. R. et al.  “Mitotic evolution of Plasmodium falciparum shows a stable core genome but recombination in antigen families.”  PLoS Genetics 9(2):e1003293.  2013.  Open access, CC BY.  Read from the Europe PMC full text.  Mirror:  PMC

1. 15a.

   Section Abstract:  “Using these derived mutation rates for P. falciparum (1.0–9.7×10⁻⁹ mutations per base pair per generation), we can now model the frequency at which drug or immune resistance alleles will emerge under a well-defined set of assumptions.” ↩

Claessens, Antoine et al.  “Generation of antigenic diversity in Plasmodium falciparum by structured rearrangement of var genes during mitosis.”  PLoS Genetics 10(12):e1004812.  2014.  Open access, CC BY.  Read from the Europe PMC full text.  Mirror:  PMC

1. 16a.

   Section Results:  “From these data we estimate mutation rates of 4.07×10⁻¹⁰, 3.63×10⁻¹⁰ and 3.78×10⁻¹⁰ SNPs per erythrocytic life cycle per nucleotide for 3D7, Dd2 and HB3 respectively (Table 1).” ↩

2. 16b.

   Section Results:  “This means that in the Dd2 strain, for every 48-hour intraerythrocytic generation approximately 0.2% of parasites will have undergone a var exon 1 recombination event producing a new chimeric var gene.”  Section Abstract:  “the crossovers were error-free and occurred in such a way that the resulting sequence was in frame and domain architecture was preserved.”  At 0.2% of 10¹² parasites, a heavily infected patient would produce 2 × 10⁹ new chimeric genes per generation.  That figure is this article's arithmetic. ↩

Hamilton, William L. et al.  “Extreme mutation bias and high AT content in Plasmodium falciparum.”  Nucleic Acids Research 45(4):1889–1901.  2017.  Open access, CC BY.  Read from the Europe PMC full text, which has no page numbers.  ELC in the quotations means one erythrocytic life cycle of 48 hours, and BPS means base-pair substitution.  Mirror:  PMC

1. 17a.

   Section Materials and Methods:  “the mean overall BPS rate per ELC per bp for all clone trees (2.45 × 10⁻¹⁰ BPS/ELC/bp)”.  Table 1:  Per-isolate means in units of 10⁻¹⁰:  3D7 2.10, HB3 2.95, Dd2 3.20, KH1-01 2.27, KH2-01 1.64.  A sixth isolate, W2, had too few clones for a rate.  In all, 279 clones were sequenced and 85 substitutions found. ↩ ↩

2. 17b.

   Section Materials and Methods:  “we divided μ1 by the total genome size of P. falciparum (G), 2.33 × 10⁷ bp”.  The source prints μ with a subscript 1. ↩ ↩

3. 17c.

   Section Results:  “The 3D7 indel rate was extremely high, around 10-fold greater than the BPS rate, at 21.1 × 10⁻¹⁰ (95% confidence interval, CI, 13.2 × 10⁻¹⁰–28.9 × 10⁻¹⁰) indels/ELC/bp; i.e. about one in every 20 parasites (95%CI 15–33) would be expected to harbor a de novo indel per 48-h ELC, compared with one de novo BPS in every 175 parasites (95%CI 134–253) per ELC.” ↩

4. 17d.

   Section Abstract:  “Genome sequence analysis of these samples revealed a significant excess of G:C to A:T transitions compared to other types of nucleotide substitution”. ↩ ↩

Gardner, Malcolm J. et al.  “Genome sequence of the human malaria parasite Plasmodium falciparum.”  Nature 419:498–511.  Oct 3, 2002.  Free to read at the journal.  Read from the publisher PDF;  page numbers are the printed folios.

1. 18a.

   Page 498:  “The 23-megabase nuclear genome consists of 14 chromosomes, encodes about 5,300 genes, and is the most (A + T)-rich genome sequenced to date.” ↩

2. 18b.

   Page 506:  “The 3D7 genome contains 59 var, 149 rif and 28 stevor genes, but for each family there are also a number of pseudogenes and gene truncations present.” ↩

Sidhu, Amar Bir Singh et al.  “Chloroquine resistance in Plasmodium falciparum malaria parasites conferred by pfcrt mutations.”  Science 298(5591):210–213.  Oct 4, 2002.  Read from the author manuscript at PubMed Central, which has no page numbers.  Mirror:  PMC

1. 19a.

   Paragraph 1:  “This safe and inexpensive 4-aminoquinoline compound accumulates inside the digestive vacuole of the infected red blood cell, where it is believed to form complexes with toxic heme moieties and interfere with detoxification mechanisms that include heme sequestration into an inert pigment called hemozoin (2–4).” ↩

2. 19b.

   Section Abstract:  “Here, we provide conclusive evidence that mutant haplotypes of the pfcrt gene product of Asian, African, or South American origin confer chloroquine resistance with characteristic verapamil reversibility and reduced chloroquine accumulation.” ↩

Shafik, Sarah H. et al.  “The natural function of the malaria parasite's chloroquine resistance transporter.”  Nature Communications 11:3922.  2020.  Open access, CC BY.  Read from the Europe PMC full text.  Mirror:  PMC

1. 20a.

   Section Abstract:  “We identify host-derived peptides of 4-11 residues, varying in both charge and composition, as the substrates of PfCRT in vitro and in situ, and show that PfCRT does not mediate the non-specific transport of other metabolites and/or ions.” ↩

Kublin, James G. et al.  “Reemergence of chloroquine-sensitive Plasmodium falciparum malaria after cessation of chloroquine use in Malawi.”  Journal of Infectious Diseases 187(12):1870–1875.  2003.  Read in abstract only, from the Europe PMC record.  The full text was not obtained.

1. 21a.

   Section Abstract:  “The prevalence of the chloroquine-resistant pfcrt genotype decreased from 85% in 1992 to 13% in 2000.  In 2001, chloroquine cleared 100% of 63 asymptomatic P. falciparum infections, no isolates were resistant to chloroquine in vitro, and no infections with the chloroquine-resistant pfcrt genotype were detected.” ↩

Batten, Don.  “Clarity and confusion.”  Journal of Creation 22(1):28–33.  Apr 2008.  Retrieved Sep 27, 2026.  A review of Behe's book by a scientist on the staff of Creation Ministries International.  Read from the publisher's web page, which does not mark the journal's page breaks.

1. 22a.

   Section Clarity:  “For example, chloroquine resistance in Plasmodium is due to a fault in a transport protein that moves the poison into the organism’s vacuole.” ↩

Behe, Michael J.  “A Key Inference of The Edge of Evolution Has Now Been Experimentally Confirmed.”  Evolution News.  Jul 14, 2014.  Retrieved Sep 27, 2026.  The site is published by the Discovery Institute and now carries the name Science and Culture Today.

1. 23a.

   Paragraph 7:  “The bottom line is that the need for an organism to acquire multiple mutations in some situations before a relevant selectable function appears is now an established experimental fact.” ↩

2. 23b.

   Paragraph 6:  “(Interestingly, one of the two mutations I discussed in The Edge of Evolution as possibly required, at position 76 of the protein chain, is in fact one of the two that Summers et al. proved to be needed.  But the other one I discussed, at position 220, isn’t.” ↩

Luskin, Casey.  “So, Michael Behe Was Right After All; What Will the Critics Say Now?”  Evolution News.  Jul 16, 2014.  Retrieved Sep 27, 2026.  Luskin was then a staff member of the Discovery Institute.

1. 24a.

   Paragraph 4:  “It can no longer be denied that the critics were dead wrong: chloroquine resistance does not arise at all until two mutations or more are present.”  Paragraph 6:  “His argument was based upon an empirically observed data point from public health studies which found that chloroquine resistance arose in about 1 in every 10²⁰ organisms.” ↩

Myers, PZ.  “Quote-mined by Casey Luskin!”  Pharyngula.  Jul 17, 2014.  Retrieved Sep 27, 2026.  Myers is a developmental biologist at the University of Minnesota Morris.

1. 25a.

   Paragraph 3:  “That the malaria parasite needs two mutations was never a point of contention, nor was it particularly worrisome.  What was wrong with Behe’s work is that he naively claimed that the two mutations had to occur simultanously in the same individual organism, so that the probability that could happen was the product of multiplying the two individual probabilities.  That’s ridiculous.”  The spelling is the original's. ↩

Behe, Michael J.  “An Open Letter to Kenneth Miller and PZ Myers.”  Evolution News.  Jul 21, 2014.  Retrieved Sep 27, 2026.  Exponents were read from the page's HTML.

1. 26a.

   Paragraph 5:  “From the sequence and laboratory evidence it’s utterly parsimonious and consistent with all the data — especially including the extreme rarity of the origin of chloroquine resistance — to think that a first, required mutation to PfCRT is strongly deleterious while the second may partially rescue the normal, required function of the protein, plus confer low chloroquine transport activity.”  Paragraph 6:  “It’s also entirely reasonable shorthand to characterize such a situation as needing “simultaneous” or “concurrent” mutations, as has been done by others in the malaria literature, even if the second mutation actually occurs separately in the recent progeny of some sickly, rare cell that had already suffered the first, harmful mutation.” ↩

Miller, Kenneth R.  Edging towards Irrelevance, part 3: Parasites and Drugs.  2014.  Retrieved Sep 27, 2026.  Miller is a cell biologist at Brown University.  The page is undated;  part 2 of the series refers to Behe's posts of 14 and 21 July 2014.

1. 27a.

   Section Parasites and Drugs:  “But Behe was dead wrong about it being “strongly deleterious.”  In fact, it seems to have no effect on transport activity at all.  A neutral mutation like this can easily propagate through a population, and field studies of the parasite confirm that is exactly what has happened.  In fact, a 2003 study recommended against using the K76T mutation to test for chloroquine resistance since that same mutation was also found in 96% of patients who responded well to chloroquine.”  Miller does not name the 2003 study and it was not identified.  In the field K76T is found only inside forms carrying four to ten mutations, so its presence in patients who recovered does not show that it spreads alone. ↩

2. 27b.

   Section Parasites and Drugs:  “To put it clearly, the problem with the logic of The Edge isn’t the specific figure of one chance in 10²⁰, but the way in such probabilities are multiplied.  In fact, it doesn’t really matter if chloroquine resistance emerges at a probability of one chance in 10²⁰, one in 10¹⁵, or even one chance in 10¹⁰.” ↩

Moran, Laurence A.  “Taking the Behe challenge!”  Sandwalk.  Aug 2014.  Retrieved Sep 27, 2026.  Moran is a biochemist, emeritus at the University of Toronto.  His post treats the blood-stage parasite as carrying two copies of the genome.  It carries one.

1. 28a.

   “The bottom line is that mutation to chloroquine resistance is going to be rare even if only two mutations are required and they occur sequentially.  If four mutations are required for substantive chloroquine resistance then it's not at all surprising that so few resistant strains have been observed.  There's no need to invoke simultaneous mutations and no need to assume that one of the mutations is deleterious.”  Near the end of the post. ↩

2. 28b.

   “What this means is that if you start with an infection by a cell that has none of the required mutations then you will only get the right pair of mutations once in one million infected people.”  A million patients at 10¹² parasites each is 10¹⁸ parasites.  Moran used a mutation rate of 2.5 × 10⁻⁹, ten times the rate measured since. ↩

Lents, Nathan H. et al.  “The end of evolution?”  Science 363(6427):590.  Feb 8, 2019.  A review of Behe's Darwin Devolves.  Read from the text posted on the journal's book blog, by way of the Wayback Machine.

1. 29a.

   “Behe doubles down on his claim that the evolution of chloroquine resistance in malaria by random mutations is exceedingly unlikely because at least two mutations are required, neither of which is beneficial without the other.  His calculations have already been refuted (5), and it has long been known that neutral and even deleterious mutations can provide stepping stones to future adaptations.” ↩

Luskin, Casey.  “On Chloroquine Resistance, Nathan Lents Severely Misrepresents Behe's Arguments.”  Evolution News.  Feb 19, 2019.  Retrieved Sep 27, 2026.

1. 30a.

   “Behe never says that chloroquine resistance is too complex to evolve.  As was explained previously, he observes that it does evolve and he cites public health data showing that it arises in approximately 1 in 10²⁰ cells.” ↩

Miller, Kenneth R.  Edging towards Irrelevance, part 5: Been There, Done That.  2014.  Retrieved Sep 27, 2026.

1. 31a.

   Section Been There, Done That:  “In reality, none of the criticisms took issue with that number at all.” ↩

Nair, Shalini et al.  “A selective sweep driven by pyrimethamine treatment in Southeast Asian malaria parasites.”  Molecular Biology and Evolution 20(9):1526–1536.  2003.  Read in abstract only, from the Europe PMC record.

1. 32a.

   Section Abstract:  “Pyrimethamine resistance is generally assumed to have evolved multiple times because the genetic basis is simple and resistance can be selected easily in the laboratory.  Yet our data clearly indicate a single origin of resistant dhfr alleles sampled over a large region of SE Asia.” ↩

Roper, Cally et al.  “Intercontinental spread of pyrimethamine-resistant malaria.”  Science 305(5687):1124.  Aug 20, 2004.  Read in abstract only, from the Europe PMC record.

1. 33a.

   Section Abstract:  “Here we present molecular evidence demonstrating that malaria parasites bearing high-level pyrimethamine resistance originally arrived in Africa from southeast Asia.” ↩

Pearce, Richard J. et al.  “Multiple origins and regional dispersal of resistant dhps in African Plasmodium falciparum malaria.”  PLoS Medicine 6(4):e1000055.  2009.  Open access, CC BY.  Read from the Europe PMC full text.  The senior author is Cally Roper.  Mirror:  PMC

1. 34a.

   Section Introduction:  “In east Africa, mutations at codons A437G and K540E of dhps, together with the triple mutations of dhfr were shown to be a significant predictor of SP treatment failure in Kenya, Malawi, and Uganda”. ↩ ↩

2. 34b.

   Section Abstract:  “We used microsatellite polymorphism flanking the dhps gene to determine which resistance alleles shared common ancestry and found five major lineages each of which had a unique geographical distribution.”  “Resistant dhps has emerged independently in multiple sites in Africa during the past 10–20 years.” ↩

Looareesuwan, Sornchai et al.  “Clinical studies of atovaquone, alone or in combination with other antimalarial drugs, for treatment of acute uncomplicated malaria in Thailand.”  American Journal of Tropical Medicine and Hygiene 54(1):62–66.  1996.  Read in abstract only, from the Europe PMC record.  This is the clinical study behind Behe's statement that resistance to atovaquone appears in every third patient, which he cites through a 1999 review by White.

1. 35a.

   Section Abstract:  “However, irrespective of the duration of therapy, overall cure rates were approximately 67%.  In vitro sensitivity studies on parasites taken from patients prior to treatment and at the time of recrudescence showed a marked decrease in susceptibility to atovaquone in the recrudescent parasites.” ↩

Korsinczky, Michael et al.  “Mutations in Plasmodium falciparum cytochrome b that are associated with atovaquone resistance are located at a putative drug-binding site.”  Antimicrobial Agents and Chemotherapy 44(8):2100–2108.  2000.  Read from the PubMed Central page, which has no page numbers.  Mirror:  PMC

1. 36a.

   Section Abstract:  “A single amino acid mutation was detected in parasites isolated from a recrudescent patient following atovaquone treatment.”  Section Results:  “The TM93-C1088 isolate (Y268S) showed a 9,354-fold-higher IC50 than the K1 parent line.”  The source prints IC50 with a subscript. ↩ ↩

Fisher, Nicholas et al.  “Cytochrome b mutation Y268S conferring atovaquone resistance phenotype in malaria parasite results in reduced parasite bc1 catalytic turnover and protein expression.”  Journal of Biological Chemistry 287(13):9731–9741.  2012.  Open access.  Read from the Europe PMC full text.  Mirror:  PMC

1. 37a.

   Section Abstract:  “The Y268S mutation is shown to confer a 270-fold shift of the inhibitory constant (Ki) for atovaquone with a concomitant reduction in the Vmax of the bc1 complex of ∼40% and a 3-fold increase in the observed Km for decylubiquinol.”  The source prints Ki, Vmax, bc1 and Km with subscripts. ↩

Price, Ric N. et al.  “Mefloquine resistance in Plasmodium falciparum and increased pfmdr1 gene copy number.”  Lancet 364(9432):438–447.  2004.  Read from the author manuscript at PubMed Central, which has no page numbers.  Mirror:  PMC

1. 38a.

   Section Summary:  “In 1984 mefloquine was introduced as treatment for uncomplicated falciparum malaria, but substantial resistance developed within 6 years.”  “Amplification in pfmdr1 is the main cause of resistance to mefloquine in falciparum malaria.” ↩

Ariey, Frédéric et al.  “A molecular marker of artemisinin-resistant Plasmodium falciparum malaria.”  Nature 505:50–55.  Jan 2, 2014.  Read from the author manuscript at PubMed Central, which has no page numbers.  The senior author is Didier Ménard.  ART is artemisinin.  Mirror:  PMC

1. 39a.

   Section A candidate molecular marker of ART resistance:  “The ART-resistant F32-ART5 parasite line was selected by culturing the ART-sensitive F32-Tanzania clone under a dose-escalating, 125-cycle regimen of artemisinin for 5 years”.  “Subsequent PCR analysis of the PF3D7_1343700 locus detected the M476I mutation after 30 drug-pressure cycles”.  Section Emergence and spread of K13-propeller mutants in Cambodia:  “This analysis reveals overall 17 mutant alleles, including three high-frequency (> 5%) alleles (C580Y, R539T and Y493H).”  PF3D7_1343700 is the gene for kelch13. ↩ ↩

Takala-Harrison, Shannon et al.  “Independent emergence of artemisinin resistance mutations among Plasmodium falciparum in Southeast Asia.”  Journal of Infectious Diseases 211(5):670–679.  2015.  Read from the PubMed Central page.  The senior author is Christopher Plowe.  Mirror:  PMC

1. 40a.

   Section Abstract:  “Haplotype analysis revealed both population-specific emergence of mutations and independent emergence of the same mutation in different geographic areas.” ↩

Uwimana, Aline et al.  “Emergence and clonal expansion of in vitro artemisinin-resistant Plasmodium falciparum kelch13 R561H mutant parasites in Rwanda.”  Nature Medicine 26:1602–1608.  2020.  Open access, CC BY.  Read from the Europe PMC full text.  Mirror:  PMC

1. 41a.

   Section Abstract:  “While cure rates were >95% in both treatment arms, the Pfkelch13 R561H mutation was identified in 19 of 257 (7.4%) patients at Masaka.  Phylogenetic analysis revealed the expansion of an indigenous R561H lineage.  Gene editing confirmed that this mutation can drive artemisinin resistance in vitro.” ↩

Balikagala, Betty et al.  “Evidence of Artemisinin-Resistant Malaria in Africa.”  New England Journal of Medicine 385(13):1163–1171.  Sep 23, 2021.  Read in abstract only, from the Europe PMC record.  The senior author is Toshihiro Mita.

1. 42a.

   Section Abstract:  “The independent emergence and local spread of clinically artemisinin-resistant P. falciparum has been identified in Africa.”  The study was done in northern Uganda.  The mutations were A675V and C469Y, which differ from the Rwandan one. ↩

Birnbaum, Jakob et al.  “A Kelch13-defined endocytosis pathway mediates artemisinin resistance in malaria parasites.”  Science 367(6473):51–59.  Jan 3, 2020.  Read in abstract only, from the Europe PMC record.  The senior author is Tobias Spielmann.

1. 43a.

   Section Abstract:  “Parasites with inactivated Kelch13 or a resistance-conferring Kelch13 mutation displayed reduced hemoglobin endocytosis.  ARTs are activated by degradation products of hemoglobin.  Hence, reduced activity of Kelch13 and its interactors diminishes hemoglobin endocytosis and thereby ART activation, resulting in parasite resistance.” ↩

Feleke, Sindew M. et al.  “Plasmodium falciparum is evolving to escape malaria rapid diagnostic tests in Ethiopia.”  Nature Microbiology 6:1289–1299.  2021.  Open access, CC BY.  Read from the Europe PMC full text.  The senior author is Jonathan Parr.  RDT is rapid diagnostic test.  Mirror:  PMC

1. 44a.

   Section Abstract:  “we estimate that HRP2-based rapid diagnostic tests would miss 9.7% (95%CI 8.5-11.1) of P. falciparum malaria cases owing to pfhrp2 deletion.”  “We propose a model in which pfhrp3 deletions have arisen independently multiple times, followed by strong positive selection for pfhrp2 deletion owing to RDT-based test-and-treatment.” ↩

Roberts, David J. et al.  “Rapid switching to multiple antigenic and adhesive phenotypes in malaria.”  Nature 357:689–692.  Jun 25, 1992.  Read from the author manuscript at PubMed Central, which has no page numbers.  Mirror:  PMC

1. 45a.

   Section Abstract:  “Our data show that antigens at the parasitized cell surface undergo clonal variation in vitro in the absence of immune pressure at the rate of 2% per generation with concomitant modulations of the adhesive phenotype.” ↩

Stubbs, Janine et al.  “Molecular mechanism for switching of P. falciparum invasion pathways into human erythrocytes.”  Science 309(5739):1384–1387.  Aug 26, 2005.  Read in abstract only, from the Europe PMC record.

1. 46a.

   Section Abstract:  “We show that switching from sialic acid-dependent to -independent invasion is reversible and depends on parasite ligand use.  Expression of P. falciparum reticulocyte-binding like homolog 4 (PfRh4) correlates with sialic acid-independent invasion, and PfRh4 is essential for switching invasion pathways.” ↩

Nair, Shalini et al.  “Adaptive copy number evolution in malaria parasites.”  PLoS Genetics 4(10):e1000243.  2008.  Open access, CC BY.  Read from the Europe PMC full text.  CNP is copy number polymorphism.  Mirror:  PMC

1. 47a.

   Section Abstract:  “Two percent of chromosomes had amplified copy number in Laos, while 72% carried multiple (2–11) copies in Thailand, and differentiation exceeded that observed at 73 synonymous SNPs.”  “We found five amplicon types containing one to greater than six genes and spanning 1 to >11 kb, consistent with parallel evolution and strong selection for this gene amplification.”  “These results demonstrate that CNP at gch1 is adaptive and the associations with dhfr-164L strongly suggest a compensatory function.”  Section Results:  “The simplest explanation is that the 2.2 kb, 8.7 kb, and >11 kb amplicon share the same origin, and that the 1.7 kb and 7.3 kb amplicons have evolved independently.” ↩

Volkman, Sarah K. et al.  “A genome-wide map of diversity in Plasmodium falciparum.”  Nature Genetics 39(1):113–119.  Jan 2007.  Read in abstract only, from the Europe PMC record.  The abstract does not name the chromosome.  Lozovsky and colleagues, who cite this paper, place the region on chromosome 13.

1. 48a.

   Section Abstract:  “We identified multiple regions with signatures of selective sweeps in drug-resistant parasites, including a previously unidentified 160-kb region with extremely low polymorphism in pyrimethamine-resistant parasites.” ↩

Amino-acid changes in the most changed form of each gene:  PfCRT 10,⁶ DHFR 4,⁸ DHPS 2,³⁴ cytochrome b 1,³⁶ kelch13 1.³⁹  Total 18.  Each amino-acid change needs at least one nucleotide change, so 18 is a floor.  The alternative forms in other lineages, which include 17 kelch13 forms and several PfCRT forms, were not counted one by one.  The figure of 100 is a round upper limit for them and is an estimate.  Low end:  18 ÷ 7.5 × 10²¹ = 2.4 × 10⁻²¹.  High end:  100 ÷ 1.5 × 10²¹ = 6.7 × 10⁻²⁰.  The denominators are from the ledger.³  For HIV, the published article gives no more than 5,000 constructive changes among 6 × 10²² particles, and 5,000 ÷ 6 × 10²² = 8 × 10⁻²⁰. ↩

Greenspoon, Lior et al.  “The global biomass of wild mammals.”  Proceedings of the National Academy of Sciences 120(10):e2204892120.  2023.  Open access.  Read from the Europe PMC full text, which has no page numbers.  The paper does not print a total count of individuals in its main text.  Mirror:  PMC

1. 50a.

   Section Abstract:  “We present a detailed assessment, arriving at a total wet biomass of ≈20 million tonnes (Mt) for all terrestrial wild mammals (95% CI 13-38 Mt), i.e., ≈3 kg per person on earth.”  Section Results:  “Bats (Chiroptera), for example, comprise one-fifth of species and two-thirds in terms of individual mammals, but only contribute less than one-tenth of the total biomass of wild land mammals”. ↩ ↩

Kong, Augustine et al.  “Rate of de novo mutations and the importance of father's age to disease risk.”  Nature 488(7412):471–475.  Aug 23, 2012.  Read from the author manuscript, which has no journal page numbers.  The senior author is Kari Stefansson.  Mirror:  PMC

1. 51a.

   Section Abstract:  “Here we show that in our samples, with an average father’s age of 29.7, the average de novo mutation rate is 1.20×10⁻⁸ per nucleotide per generation.”  Section Results:  “a total of 4,933 de novo mutations, or an average of 63.2 per trio, were called.”  A trio is two parents and a child, so 63.2 is the count per child. ↩ ↩