Inherited Learning in an Artificial Ecology: How Controls and Update Allocation Shape Benefits

Xuening Wu; Lei Li; Shan Yu

cs.NEOct 1, 2026

Inherited Learning in an Artificial Ecology: How Controls and Update Allocation Shape Benefits

Authors: Xuening Wu, Lei Li, Shan Yu

Organizations: Pfizer, Shanghai, China · Independent Researcher

Abstract

Learning can improve an individual's behavior, yet a population risks losing that experience whenever individuals die and are replaced. Inheriting learned preferences offers a way to preserve useful behavior across generations, raising a question for artificial populations: when does inheritance improve collective performance, and how can its benefits be measured fairly? The challenge is that inheritance changes not only offspring behavior but also survival, reproduction, and opportunities for further hereditary updates. Random controls with equal update magnitudes may therefore yield misleading comparisons if they alter different states or obey different stability constraints. We investigate this problem in a resource-limited artificial ecology, combining structured random controls with interventions on newborn preferences and the allocation of hereditary updates. Preserving the state structure of random updates substantially narrows the apparent inheritance advantage, while a conditional establishment-speed benefit remains. Preference erasure and faster-learning compensation support a contribution from reduced offspring relearning. Update allocation also changes the comparison: event quotas and common time cutoffs can reverse rankings, although they also change realized update amounts. With update count and cumulative magnitudes matched, staged release improves occupancy but does not achieve the prespecified establishment criterion. These findings provide a framework for distinguishing the value of inherited preferences from the effects of control design and update allocation, clarifying how inherited learning should be evaluated in artificial populations.

Figures & tables

Panel of Figure 1 — Figure 1: Study overview. Lifetime learning can enter offspring initialization through proportional writeback (top; $\mu=0$ in the central experiments). Controls preserve state-wise update structure and impose shared stability bounds. Newborn interventions test preference expression and faster-learning rescue. Allocation experiments compare event and time cutoffs, then early and staged release with matched counts and cumulative magnitudes. These interventions estimate distinct effects. Stopping writeback preserves lifetime learning and inheritance of existing $g$ .

Stage / seed block	Conditions	Runs
Control confirmation / 51000–51019	Four update methods without quota, plus no writeback	100
Quota comparison / 52000–52019	Four methods at five quotas; shared no writeback	420
Representation / 61000–61019	Two binnings, two quotas, two directions; references	200
Expression / 62000–62019	Two directions, two expressions, three newborn learning rates	240
Ecological sensitivity / 63000–63019	Six settings, two directions and no writeback	360
Native connection / 81000–81019	Two energy shares, two quota rules, three strengths, two directions; references	520

Table 1: Formal experiment inventory. Counts are condition runs, not independent seeds. Shared no-writeback references are counted once per specified setting.

Panel of Figure 2 — Figure 2: Fixed-norm comparison at $B=512$ . Bars show mean capped time across 20 seeds; labels give the number establishing out of 20 runs. Failed runs remain at the 20,000-sweep cap, so these are not means conditional on success. The stronger random control sharply reduces the apparent attainment gap. All four groups use 512 updates with identical per-update norm.

Panel of Figure 3 — Figure 3: Expression and learning-rate intervention beginning with the birth that consumes the 512th fixed-norm update. The labels specify newborn expression and $\eta_{c}$ . Each bar includes all 20 runs; attainment counts and auxiliary zero-learning results are in Table 2 . The same-direction branches share their pre-intervention histories.

$\eta_{c}$	Expression	Reached D	Reached R	$\bar{T}_{D}^{*}$	$\bar{T}_{R}^{*}$	AUC D/R
0	Keep	20/20	6/20	1390	15540	0.959/0.379
0	Erase	0/20	0/20	20000	20000	0.009/0.009
0.2	Keep	20/20	18/20	2480	6450	0.934/0.827
0.2	Erase	6/20	5/20	18280	17900	0.702/0.649
0.8	Keep	20/20	20/20	1210	2090	0.966/0.934
0.8	Erase	20/20	20/20	1610	2240	0.955/0.929

Table 2: All expression-intervention conditions. D denotes directed inheritance and R denotes state-preserving randomization. Reached entries give successful runs out of 20; AUC D/R lists the two normalized occupancy areas. Times are capped at 20,000 sweeps.

Panel of Figure 4 — Figure 4: Native writeback: paired differences in capped establishment time. Positive values favor directed inheritance. Points are means across 20 seed pairs; intervals are descriptive 95% paired bootstrap intervals, without multiplicity correction. The zero difference for $f=0.65$ , $\lambda=0.25$ , $B=1024$ reflects complete nonattainment in both groups, not equivalence.

$f$	$B$	$\lambda$	Reached D/R	$\bar{T}^{*}$ D/R	AUC D/R	Late D/R
0.5	$\infty$	0.25	20/20	2490/4040	0.927/0.856	0.999/0.999
0.5	$\infty$	0.5	20/20	1490/2840	0.957/0.908	0.999/0.999
0.5	$\infty$	1.0	20/20	930/2330	0.975/0.927	0.999/0.999
0.5	1024	0.25	7/20	17790/4900	0.844/0.830	0.948/0.988
0.5	1024	0.5	20/20	2040/2910	0.939/0.906	0.990/0.998
0.5	1024	1.0	20/20	1000/2240	0.973/0.930	0.998/0.999

Table 3: All native variation conditions (20 seeds per direction). Each paired entry lists the directed value followed by the random value. In the Reached column, these are counts out of 20 in each group; for example, 20/20 means that both groups have 20 successful runs.

B=\infty

denotes continuous writeback. All listed groups have zero extinctions. Late is the final-five-sample occupancy mean.

Rule	Attained D/R	$\bar{T}^{*}$ D/R	AUC D/R	Mean writes D/R
Continuous	20/20	1000/1870	.982/.947	46888/47796
1,024 events	0/14	20000/10590	.800/.898	1024/1024
150 sweeps	0/0	20000/20000	.814/.688	1073/444
750 sweeps	20/18	1000/7520	.979/.907	3910/1094

Table 4: Common-cutoff diagnostic at

f=0.65

\lambda=1

; 20 runs per direction. Entries list directed/random values; attainment entries are two counts, each out of 20. Failed runs retain the 20,000-sweep time cap.

Schedule	Direction	AUC	Late occupancy	Mean exhaustion sweep
Earliest	Directed	.6786	.7010	142.3
Earliest	Random	.6274	.7140	803.7
Staged	Directed	.7611	.7919	777.9
Staged	Random	.6312	.7339	1416.2

Table 5: Fixed-step allocation (

q=0.02

B=1024

). Each group has 20 seeds, zero attainment and zero extinction. All groups use exactly the same event count and cumulative magnitudes.

$B$	Reached D	Reached R	$\bar{T}_{D}^{*}$	$\bar{T}_{R}^{*}$	Extinct D/R
128	0/20	0/20	20000	20000	20/20
256	0/20	0/20	20000	20000	3/13
512	20/20	18/20	2290	7160	0/0
1024	20/20	20/20	1440	3080	0/0
2048	20/20	20/20	1300	3010	0/0

Table 6: Fixed-norm quota comparison. D: directed; R: state-preserving random. Each group has 20 seeds. Times are sweeps; unreached runs contribute 20,000. Extinct D/R lists the extinction count in each group, not a fraction.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Setting	Reached D/R	$\bar{T}^{*}$ D/R	Extinct D/R	AUC D/R
baseline	20/20	1460/3190	0/0	0.960/0.895
low death	20/20	1000/1730	0/0	0.978/0.959
high death	0/0	20000/20000	20/20	0.002/0.002
low child energy	20/20	1530/3160	0/0	0.953/0.903
high child energy	0/18	20000/5290	0/0	0.814/0.908
no birth bonus	20/20	2160/3560	0/0	0.931/0.881

Appendix

Table 7: Ecological sensitivity. Paired entries list directed and random values; each group has 20 seeds. Reached and Extinct entries are two counts, each out of 20, not fractions. The high-mortality capped-time tie reflects nonattainment in both groups, not equivalence.

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