Not a straight line
Textbook "march of progress" pictures are misleading. Hominin species overlapped (at 1.8 Ma at least three lived in Africa and western Asia), several lineages died out, and traits such as big brains, small teeth and upright posture arrived at different times in different groups. Dates have uncertainties of tens of thousands to hundreds of thousands of years; the family tree is still argued (is Sahelanthropus a hominin? is H. habilis one species?). Chimpanzees are cousins, not ancestors.
Skulls and brain size
Each skull was modelled in Blender from published measurements: the amber endocast is an ellipsoid whose volume equals the species' typical cranial capacity (V = π/6 · length · width · height, scaled to the table value). The bone shell is that ellipsoid plus a few mm of bone thickness; faces, brow ridges, jaws and teeth are schematic reconstructions, not scans.
EQ = E / (0.12 M0.67) (E = brain mass g, M = body mass g; Jerison)
EQ compares a brain with that of an average mammal of the same body mass. Fossil EQs depend heavily on body-mass guesses (±30 %), and other scaling exponents (e.g. 0.76) shift all values. Brain tissue costs ~11.5 W/kg versus ~1 W/kg for resting muscle, giving the human brain ~20 % of basal metabolism with BMR = 3.39 M0.75 W (Kleiber). The "expensive tissue" idea (a smaller gut paying for a larger brain) is one hypothesis among several, including cooking and diet quality.
Walking: inverted pendulum
In walking, the body vaults over a stiff stance leg of effective length Le = ρL (ρ = hip height as a fraction of straight-leg length). Dynamic similarity uses the Froude number:
Fr = v²/(g Le); walk to run near Fr = 0.5; step length s ≈ 1.15 Le Fr0.3
Wstep = ½ v² sin²(2α), α = asin(s / 2Le) (step-to-step transition, Kuo 2002)
P = Pbase + Wstep f / η + k g (11.25 sin(φ/2)); COT = P / v
η = 0.35 is muscle efficiency, f = v/s steps per second, Pbase = 2.23 W/kg (resting plus posture), φ = knee flexion with cos(φ/2) = ρ. The last term is a quasi-static cost of the quadriceps holding the body when the knee is bent (the ground force passes d = (L/2) sin(φ/2) from the knee, moment arm ~0.044 L), with k = 0.039 m/s calibrated so a 25 % crouch roughly doubles the net cost. This is a toy model: it reproduces the human cost (~3.4 J/kg/m gross at 1.3 m/s) and the roughly doubled cost of chimpanzee-like walking, but it does not capture the exact preferred-speed minimum, the elastic tendons or the real chimp gait. Knuckle-walking is modelled as bent hindlimbs carrying 62 % of the weight plus lightly flexed arms. Body proportions are published estimates; Lucy's are least certain.
Genetic drift and selection
A population of N diploid individuals has 2N alleles. Each generation the new allele count is a binomial sample (Wright-Fisher model) after selection with fitness AA : Aa : aa = 1+2s : 1+s : 1:
p′ = p (1 + s + sp) / (1 + 2sp); k′ ~ Binomial(2N, p′); Var(Δp) = pq / 2N
Hardy-Weinberg: AA = p², Aa = 2pq, aa = q²; E[Ht] = H0 (1 - 1/2N)t (neutral)
Kimura (1962): u(p) = (1 - e-4Nsp) / (1 - e-4Ns); s = 0 gives u = p
Assumptions: constant size, random mating, additive selection, no mutation or migration, N = effective size. Real human populations had small effective sizes (~10,000 for most of the past million years), so drift was strong. The Monte Carlo experiment tests the simulator against Kimura's diffusion result; the heterozygosity-decay readout (s = 0) is a second independent check.
Molecular clock
d = 2μyr (T + tcoal); μyr = μ/g; tcoal = 2 Ne g
Two lineages each gain μ mutations per site per generation, so sequences differ by 2μ per generation. The human-chimp difference is ~1.2 %. Pedigree studies give μ ≈ 1.2×10-8 per site per generation, which with g = 29 yr implies a very old split (~12 Ma after subtracting coalescence in the ancestral population); the rate calibrated on fossils implies faster evolution in the past or a shorter generation time. This unresolved "slow versus fast clock" tension is why the fossil record matters. Presets are illustrative, not fitted.
Independent checks (shown live)
(1) Simulated fixation probabilities vs Kimura's formula across eight selection strengths; (2) neutral heterozygosity decay vs H0(1-1/2N)t; (3) RK4 swing-leg pendulum period vs the analytic series; (4) forward-simulated substitutions recover the input divergence; (5) the human EQ and brain-energy share (~7.4 and ~21 %) agree with literature values.