Dr. M. Shamshad

Sugarcane Breeder && Data Science

Recent posts

Spatial Analysis with AR1 × AR1 Model: Theory & Complete R Analysis

19 minute read

Updated:

Field experiments are routinely affected by spatial heterogeneity — systematic variation in soil fertility, moisture, drainage, pH, and microclimate that creates patches of high and low performance across the trial. When this variation is ignored, it inflates the residual variance, reduces heritability estimates, biases treatment comparisons, and misranks genotypes. The AR1 × AR1 model (first-order autoregressive process in both row and column directions) is the gold standard for capturing and removing this spatial structure from field trial data.

Partially Replicated (p-rep) Design: Theory & Complete R Analysis

16 minute read

Updated:

The Partially Replicated (p-rep) design — formally developed by Cullis, Smith & Coombes (2006) — is the modern standard for Stage 1 multi-environment plant breeding trials. It overcomes the key limitation of the augmented design (zero replication of test entries) by replicating a controlled fraction (typically 20–30 %) of test entries twice, while the remainder appear only once. This provides direct within-trial error estimation for all genotypes and enables powerful spatial modelling of field heterogeneity.

Augmented Design: Theory & Complete R Analysis

14 minute read

Updated:

The Augmented Design — proposed by Federer (1956) — is a field experimental design specifically developed for early-generation plant breeding trials, where a large number of new (unreplicated) test entries are evaluated alongside a small set of replicated check (standard) varieties. It allows breeders to screen hundreds of genotypes within a single trial without the cost of fully replicating every entry, while still enabling valid statistical inference through the checks.

Alpha (α) Lattice Design: Theory, Layout & Complete R Analysis

12 minute read

Updated:

The Alpha (α) Lattice Design — introduced by Patterson & Williams (1976) — is an incomplete block design built for large-scale experiments where the number of treatments exceeds the practical block size. It is the standard design for plant breeding trials evaluating hundreds of genotypes, offering superior error control over RCBD while remaining flexible in treatment and block size combinations.

Latin Square Design (LSD): Theory & Complete R Analysis

15 minute read

Updated:

The Latin Square Design (LSD) extends blocking to two simultaneous directions of environmental variation. By controlling both a row gradient and a column gradient, it achieves greater error reduction than RCBD while using the same number of experimental units. It is the design of choice when two orthogonal sources of heterogeneity are known in advance — such as row (fertility) and column (irrigation) gradients in a field, or row (day) and column (technician) effects in a laboratory.