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R & QGIS tutorials
for ecologists.

Field data, cleanly analysed: reproducible R & QGIS workflows for ecologists who'd rather spend their time on the ecology than on fighting their tools.

Latest tutorials ↓

// Latest

PET-PEESE and publication bias under heterogeneity

PET-PEESE removes publication bias that grows with the standard error, not a significance filter on studies that differ by site. Measured in base R simulations.

Sep 18, 2026

The mid-domain effect as a null for richness

A range-shuffling mid-domain null fits a central environmental hump with r-squared near 0.9. An envelope and a species midpoint test in R tell geometry apart.

Sep 18, 2026

Flight-season shifts and false occupancy trends

A flight season moving towards the edge of a fixed recording window gives a false occupancy decline that a year term on detection misses. Simulated in R.

Sep 18, 2026

Harvest surveys and the late respondent

Wave extrapolation in a hunter harvest survey removes some respondent bias, but the returned forms cannot show how much. Checking it in R against a follow-up.

Sep 18, 2026

Pollen rate of change and uneven sample spacing

Pollen rate of change on unevenly spaced cores peaks at short gaps. Simulated in R: pooled time bins find a large turnover, one level per bin mostly does not.

Sep 18, 2026

Sediment quality guidelines from co-occurrence

At a correlation of 0.8, an inert chemical passes the ERL/ERM reliability check in contaminated databases and the real toxicant fails it in clean ones. R.

Sep 18, 2026

Lost collar signals and informative censoring

When dead animals silence their collars, Kaplan-Meier survival runs high. Testing in R how far a battery-life likelihood and a cut-off rule can be trusted.

Sep 18, 2026

Interaction rewiring and its sampling floor

Two samples of one pollination web differ, and Poisot’s partition calls that rewiring. The sampling floor in closed form, and a permutation test on bouts.

Sep 17, 2026

Extrapolating a species-area curve beyond the plots

A power law fitted to small nested plots wins on AIC yet misjudges richness at larger areas, by a factor set by aggregation and pool saturation. Tested in R.

Sep 17, 2026

Revisits triggered by sightings in occupancy data

Revisits after a recorded sighting leave occupancy unbiased; revisits led by local knowledge inflate it. Tested in R, with a visit-count repair that can fail.

Sep 17, 2026

Likert items: when group means lie

A polarised stakeholder group can score lower on a 1 to 5 item with the same mean attitude. Simulating in R how t tests and polr fail, and a scale model holds.

With random fires, a mean fire interval from a short fire-scar record runs short, censoring both open gaps overshoots, and fire counts err less. Tested in R.

Sep 16, 2026

Model discrepancy in simulator calibration

simulation models

Gaussian processes

calibration

model misspecification

ecology tutorial

Calibrating a linear intake simulator against a saturating truth in R: a GP discrepancy stays honest only while its amplitude is set from outside the data.

Sep 16, 2026

Heatwave counts: persistence, rule order, warming

How many heatwaves a year depends on persistence and on the order of the duration and gap rules. Simulating the Hobday marine heatwave definition in R.

Sep 16, 2026

Related founders and marker kinship in a studbook

conservation genetics

Studbooks that treat related founders as unrelated overstate diversity; it costs breeding decisions only when sib groups differ in size. Markers tested in R.

A bout-ending criterion fitted to binned log frequencies moves with bin width and sample size. Simulating behaviour bouts in R; the likelihood fit holds steady.

Sep 15, 2026

Genetic rescue: how many migrants, for how long

Genetic rescue in R: a migrant pulse only delays extinction of an inbred isolate, one a generation holds it off while it lasts, and migrant ancestry runs high.

Sep 15, 2026

Rapoport’s rule and the Stevens method

Stevens’ band-mean method finds Rapoport’s rule in worlds with none, and pole clipping biases the species midpoint method too. Edge treatments tested in R.

Light-level geolocators turn daylength into latitude. Simulating in R how canopy shading, the equinox and Hill-Ekstrom calibration bend a songbird track.

Sep 14, 2026

Mean kinship breeding in a captive population

conservation genetics

Mean kinship breeding keeps more founder diversity than equal family sizes only when founders start unequal; unknown sires as founders undo much of it. In R.

Sep 14, 2026

Trawl selectivity when hauls differ

Pooling covered-codend hauls into one logistic selectivity curve gives an L50 interval that misses. Why quasi-binomial fails in R, and why the haul is the unit.

Sep 13, 2026

Instrument drift, run order and check standards

Samples run through an analyser in treatment order turn instrument drift into an effect. Measuring in R what check standards fix and what run order does.

Pooled PCR of mosquitoes within trap-nights biases the pool MLE low and its interval undercovers. Simulating in R what randomising the pools can and cannot fix.

Sep 12, 2026

Map accuracy and false fragmentation

At one overall accuracy a land-cover map can give eight times the true patch count or nearly the right one. Which errors do that, and what filters cost, in R.

Enclosure trials tell density- from frequency-dependent transmission apart only over a wide range of group sizes. A cloglog GLM, its interval and repairs in R.

Sep 10, 2026

Biotic index scores and sorting effort

Average-score biotic indices drift with the number of animals sorted when sensitive families are rarer, so clean sites get flagged. Measured in R, with repairs.

Sep 10, 2026

Borrowed age-length keys and strong year classes

An age-length key borrowed from another year halves a strong year class. In R: the exact forward bias, the inverse EM key, and where a growth curve fixes it.

Sep 9, 2026

Reset time and the double-counted hot day

A min-max thermometer reset in the afternoon counts hot afternoons twice. Simulating time-of-observation bias in R: its size, its cause and its correction.

Sep 9, 2026

Growth from tag-recapture increments

Fabens fits to tag-recapture increments do not estimate the length-at-age curve. Measuring in R how asymptote spread and length error bias Linf and K.

Sep 9, 2026

Checking a phylogenetic regression’s branch lengths

Wrong branch lengths make PGLS find slopes that are not there. How often the Garland check notices, on coalescent and Yule trees of 20 to 80 species, in R.

Sep 8, 2026

Patches cut by the edge of the map

Mean patch size from a map window is biased low, and dropping border patches is worse. Measuring the Miles-Lantuejoul edge correction for habitat patches in R.

Sep 8, 2026

Faecal egg count reduction tests at low counts

At McMaster egg counts a drug that works 99 per cent usually reads as 100 and its interval collapses. Coverage and resistance calls are measured in R.

Sep 8, 2026

Removal estimates when catchability falls

When fish get harder to catch on each electrofishing pass, the Zippin removal estimate runs low and its interval fails. Measuring the bias and a repair in R.

Sep 7, 2026

Sap flow and the zero-flow baseline

Thermal dissipation sap flow needs a zero-flow baseline. Simulating in R how night transpiration and probe noise bias tree water use under each baseline rule.

Sep 7, 2026

Detecting sex-biased dispersal from genotypes

Testing sex-biased dispersal in R with Fst and assignment indices: calibrated permutation tests and why power is signal over noise, not immigrant counts.

Sep 7, 2026

Leaf area from gap fraction: the segment length

Inverting canopy gap fraction to leaf area index in R: why long segments underestimate a clumped canopy, and why short ones saturate. Choosing segment length.

Sep 6, 2026

population genetics

effective population size

simulation

ecology tutorial

Temporal Ne from cohorts a few years apart can be negative. An R simulation shows the Waples 1989 plan II term sets the bias, and when adding it back works.

Sep 4, 2026

Fertility control versus culling in R

Culling and permanent sterilisation at the same treatment rate share one long-run population. Measuring in R the years and animals handled that separate them.

Sep 4, 2026

Light response curves: the curvature you drop

Fitting photosynthesis light response curves in R: the rectangular hyperbola’s bias is arithmetic, but ten noisy points rarely show it or pin down curvature.

Tolerance bounds versus percentiles for impairment thresholds from reference sites in R: the false alarm guarantee, its cost in power, and skewed indices.

Sep 2, 2026

Open N-mixture models and the detection trap

Open N-mixture models in R: a hand-coded forward algorithm fits survival and recruitment to repeat counts, and tests which detection errors the visits catch.

Sep 2, 2026

Distributed lag models versus the climate window

A smooth climate effect over 52 weekly lags, a searched window and an mgcv distributed lag model in R: interval coverage for the total and where the peak sits.

Sep 1, 2026

Net primary production from repeated harvests

Harvest ANPP depends on the estimator. Simulating in R how noisy clip means inflate summed increments and peak standing crop, and how tissue turnover hides.

Sep 1, 2026

Individual growth curves with nlme

Averaging per-fish nls fits overstates how much fish differ in asymptotic length when ages stop short. Individual von Bertalanffy growth curves in R with nlme.

Sep 1, 2026

Patch-leaving rules and prey clumping

Fixed number, fixed time or giving-up time: which patch-leaving rule pays depends on how prey are spread among patches. Measured in R for a blind forager.

Aug 31, 2026

Observer effects and the first-year dip

Adding an observer effect to a route count trend turns a novice first-year deficit into a spurious increase. Measuring the bias and the one-term fix in R.

Aug 31, 2026

Rock-paper-scissors needs local interaction

community ecology

evolutionary game theory

A well-mixed rock-paper-scissors community soon loses a type; small neighbourhoods on a 40 by 40 lattice keep all three. Censored extinction times in R.

Aug 31, 2026

Critical patch size and the dispersal kernel

Critical patch size in R: eigenvalues show a peaked dispersal kernel needs less habitat than a Gaussian, and demographic noise lifts the practical threshold.

Aug 30, 2026

NOEC rewards noisy toxicity tests

The NOEC rises with residual scatter and falls with replication, while a fitted EC10 stays centred on the truth. Both measured on simulated toxicity tests in R.

Aug 30, 2026

Ratio indices or ANCOVA for body size

Dividing organ mass by body mass invents group effects when fish differ in size. Measuring in R when ratio indices fail, and when ANCOVA fits the wrong curve.

Aug 30, 2026

Within- and between-individual effects in R

A random intercept slope blends within- and between-female effects. Centring in R with nlme separates them, and why a few records bias the between slope.

Aug 29, 2026

Deleting outliers before the test

Dropping points with large standardised residuals or Cook’s distance, then refitting, is a test with its own error rate. Measured in R on null regressions.

Aug 29, 2026

Evolutionary rescue and starting population size

evolutionary ecology

quantitative genetics

extinction

simulation

ecology tutorial

Evolutionary rescue in R: a branching process and an individual-based model show even odds need a Gomulkiewicz-Holt minimum of 5 to 15 individuals, not one.

Aug 29, 2026

Red noise and extinction risk in a Ricker model

population dynamics

extinction

stochastic simulation

time series

ecology tutorial

At equal variance, red environmental noise raises extinction risk for an undercompensating Ricker population and lowers it for an overcompensating one, in R.

Aug 28, 2026

Zeros and ones in beta regression

The usual squeeze for exact zeros and ones makes a beta regression slope depend on sample size. Measuring it in R, with censored and inflated beta models.

Aug 28, 2026

Pitfall catches and the depletion zone

A pitfall keeps what it catches, so nearby beetles thin out. Simulating in R how that depletion zone bends the effort offset and how diffusion sets its size.

Aug 28, 2026

Line transects along tracks and avoidance

Line transects on tracks animals avoid: a half-normal fit can lose over half the density, and the fit test mostly misses the costliest gradients. In R.

Aug 27, 2026

Acoustic indices and species richness

Acoustic entropy and the ACI on simulated spectrograms in R: the sign of their link to species richness follows the noise floor, call energy and note length.

Checking equal variances before choosing the pooled t test is a test with its own error rate. Measured in R: passing the pretest makes the pooled t less safe.

Aug 24, 2026

Dirichlet-multinomial models for read counts

Why a multinomial interval for a metabarcoding diet share is too narrow, and how the Dirichlet-multinomial in R turns deep libraries into a few hundred reads.

Aug 24, 2026

Self-exciting events and the Hawkes process

A clustered event series fits a Hawkes process and a changing background rate alike. Simulating, fitting and checking both in R shows when time separates them.

Aug 24, 2026

Species synchrony and community stability

The Loreau-de Mazancourt synchrony index splits community variability exactly. Simulating in R how synchrony and mean-variance scaling set the diversity slope.

Aug 23, 2026

Spatial synchrony and the Moran effect

Shared weather gives populations its correlation only under narrow conditions, and dispersal synchrony depends on whether regulation cycles. Moran effect in R.

Aug 23, 2026

Seasonal matrix models and the census date

Lambda from a seasonal matrix model does not depend on the census date, but the annual matrix and its elasticities do. Periodic sensitivity analysis in R.

Aug 23, 2026

Census interval bias in tree mortality rates

Unseen differences in risk make annual tree mortality fall as the census interval lengthens. Measuring the bias in R with gamma frailty and a cohort of trees.

Aug 22, 2026

Identification errors in capture-recapture

A missed photo match inflates a capture-recapture estimate and a false match deflates it. Measuring in R why a cancelling pair still costs interval coverage.

Aug 22, 2026

Change-in-ratio population estimates in R

Population size from a sex ratio measured before and after a known harvest. Why the estimate divides by the ratio change, and when it stops meaning anything.

Aug 22, 2026

Particle MCMC for state space models

A particle filter’s likelihood estimate is noisy but unbiased, so Metropolis-Hastings built on it samples the exact posterior. A Gompertz count model, in R.

Two criteria for local adaptation in a reciprocal transplant, the main effect each mistakes for adaptation, and why populations, not plants, are the replicate.

Window length sets a ceiling on which short behaviours accelerometer data can detect. Measuring ODBA, VeDBA and LDA classification in R for animal behaviour.

Aug 18, 2026

Spatial+ and the attenuated slope

Adding a spatial smooth to a GAM moves a confounded slope only part of the way back. Spatial+ in R with mgcv, and the plot-level variation it needs to work.

Aug 17, 2026

Separable space-time covariance, tested

A separable space-time covariance turns one Cholesky into a Kronecker product, but fixes one spatial range for every time lag. Measuring the cost in R.

Aug 17, 2026

Conditional simulation versus kriging

A kriged map is the best guess cell by cell but too smooth for the area above a threshold, the peak or the patch count. Conditional simulation in base R.

Aug 17, 2026

Random effects with too few levels

With five streams the variance component is most often exactly zero. Measuring in R why dropping that singular random term barely harms a group-level test.

Aug 16, 2026

Join counts for presence-absence maps

spatial statistics

Slope and aspect: what a DEM does not measure

Slope depends on the neighbourhood rule and the cell size, both through surface roughness, and aspect is an angle that must be split into two components.

Aug 12, 2026

What a shapefile loses: names, times and types

spatial

data management

ecology tutorial

A shapefile round trip returns the geometry exactly and then rewrites the attribute table: names abbreviated, the clock dropped, logicals made integer.

Aug 12, 2026

Georeferencing RMS is not accuracy

The QGIS Georeferencer reports the residual at its own control points, not the accuracy of the result. Measured with GDAL on a sheet whose truth is known.

Aug 12, 2026

When redrawing zones flips the sign

Redrawing survey zones at a fixed unit count can reverse the sign of an ecological relationship. Measured in R, with the variance check that predicts it.

Aug 12, 2026

Selection models for publication bias

meta-analysis

publication bias

ecology tutorial

Fit the publication filter into the likelihood with base R, and measure how many ecological studies a weight-function selection model needs before it pays.

Aug 11, 2026

Running QGIS from the command line

Scripting QGIS with qgis_process, and measuring where its algorithms match sf and terra exactly and where a different default moves an ecological number.

Aug 11, 2026

Coordinate error and habitat assignment

GIS

spatial

ecology tutorial

Coordinate error flips a record’s habitat class at a rate set by the perimeter of the habitat map, not by the GPS. Measured in R with sf, on synthetic layers.

Aug 11, 2026

Rasterising a vector layer

terra

GIS

ecology tutorial

Turning habitat polygons into a grid is a measurement with a rule: the cell centre rule drops narrow features, touches inflates them. Measured in R with terra.

Aug 11, 2026

Checking a vector layer before you measure

GIS

spatial

ecology tutorial

A self-intersecting polygon has an area of exactly zero and sf says nothing. Eight geometry checks in R, each one measured on a synthetic habitat patch layer.

Weighted averaging infers past pH from fossil assemblages, and it compresses the answer twice. Here is the deshrinking step and the analogue check it needs.

Comparing soil carbon to a fixed sampling depth invents a difference whenever bulk density differs between treatments. The equivalent soil mass fix, in R.

Aug 6, 2026

Latent variables in an SEM, from scratch in R

structural equation models

measurement error

ecology tutorial

Soil fertility is not measured, three imperfect indicators are. A one-factor model recovers the slope that every composite of them gets wrong, in base R.

Aug 6, 2026

Values below the detection limit in R

Substituting half the detection limit for a non-detect is not neutral, and a laboratory that improves over time turns a flat series into a decline. Worked in R.

Aug 6, 2026

hypothesis testing

nonparametric statistics

ecology tutorial

The Wilcoxon rank sum test does not compare medians. It compares whole distributions, and with unequal spread it rejects when the medians agree. Simulated in R.

Build a slice sampler in base R on an ecological count posterior, and measure the claim that it needs no tuning against a random-walk sampler that does.

Aug 3, 2026

Bridge sampling for marginal likelihoods

Estimating a marginal likelihood in base R: the harmonic mean measured against an exact answer, the bridge identity derived, and three ecological posteriors.

Aug 3, 2026

Reversible jump MCMC from scratch

Code a reversible jump sampler by hand in R to count abundance zones on a saltmarsh transect, and check its model probabilities against exact enumeration.

Aug 3, 2026

Checking a remote sensing covariate

A simulated year of half-hourly eddy covariance data measures the friction velocity filter: what it recovers, what it discards and what it costs a budget.

Aug 2, 2026

Robust regression for ecological outliers

regression

MASS

ecology tutorial

An outlier is a claim about the model, not about the point. Measuring leverage, breakdown points and the real price of robust regression on grassland data.

Aug 1, 2026

Tail dependence and joint extremes

A correlation from the middle of a distribution says nothing about the corners. Simulating copulas in R to measure joint extreme risk in a reserve network.

Papers print a median and quartiles, not a standard deviation. Measuring what recovered SDs cost an ecological meta-analysis: weights, coverage, bias.

Aug 1, 2026

Digit preference and heaping in field data

Recorders drift towards round numbers and the mean drifts with them. Measuring digit heaping in R: the Whipple index, the bias it hides, and a mixture repair.

Pushing two decades of records onto one taxonomic backbone destroys information. Measuring the cost: hidden trends, lost richness and a silent trait join.

Jul 31, 2026

Taxonomic revision and species trends

monitoring

data cleaning

ecology tutorial

A long monitoring series records names, not species. Simulate a split and a lump in R, measure the false richness trend, and price the two available repairs.

Jul 31, 2026

Interference between experimental plots

causal inference

experimental design

ecology tutorial

When treatment leaks between plots the estimated contrast shrinks while the standard error does not. A simulation measures the bias, the buffer cost and a fix.

Jul 30, 2026

mixture models

ecology tutorial

Separate fish age classes in a length-frequency sample with a finite mixture of normals: the EM algorithm written by hand in base R, and where it breaks down.

Jul 29, 2026

Checking a Bayesian computation

Four measured checks on an MCMC run in R: an exact benchmark, simulation-based calibration, divergences with the energy diagnostic, and Monte Carlo error.

Jul 29, 2026

Reparameterisation and Neal’s funnel

Why hierarchical ecological models warn in Stan: measure the centred parameterisation failing on Neal’s funnel, fix it, and find where centred wins again.

Jul 29, 2026

The Laplace approximation in R

Fit a Gaussian at the posterior mode in base R: marginal likelihoods, where the approximation is excellent, and the three ways it fails in ecological models.

Jul 28, 2026

Hamiltonian Monte Carlo from scratch

MCMC

Bayesian statistics

ecology tutorial

Build Hamiltonian Monte Carlo in base R: leapfrog integration, energy error, and a measured comparison with random-walk Metropolis on a collinear posterior.

Jul 28, 2026

Checking a stochastic simulation

stochastic simulation

model checking

ecology tutorial

Four measured checks on a stochastic ecological simulation in R: replicate count, sampler validation, survivorship bias in the output, and seed handling.

Jul 28, 2026

Mean time to extinction, exactly

stochastic simulation

population models

extinction

ecology tutorial

An exact double sum gives the mean time to extinction of a birth-death population in base R, checked against Gillespie simulation and diffusion theory.

Jul 28, 2026

Tau leaping and the cost of a bigger step

stochastic simulation

population models

ecology tutorial

Tau leaping in base R: measuring what a larger simulation step costs in the mean, the variance and the whole distribution of an ecological birth-death model.

Jul 28, 2026

The Gillespie algorithm from scratch

stochastic simulation

population models

ecology tutorial

Build the exact Gillespie stochastic simulation algorithm in base R, validate it against a Poisson stationary distribution, and measure what exactness costs.

Jul 28, 2026

Checking a repeatability analysis

Four measured checks on a behavioural repeatability estimate in R: design efficiency, the gap between repeats, observer confounding, and the zero boundary.

Four checks on a conservation decision analysis in R: weight and table sensitivity, the value of information, the alternative set, and the attitude to risk.

Jul 20, 2026

Adaptive management and learning

Two hypotheses about harvest mortality in a hunted population, Bayesian model weights updated each year, and the horizon at which active management pays off.

Jul 20, 2026

The expected value of information

Compute the expected value of perfect, partial and sample information by hand in R for a conservation decision, and measure when uncertainty is worth nothing.

Jul 20, 2026

Structured decision making in R

Build a conservation consequence table in R, screen out dominated options, and measure how much of the final ranking is ecology and how much is bookkeeping.

Jul 20, 2026

Checking a reintroduction analysis

Four checks on a stage structured population viability projection in R: the horizon, the variance budget, correlated vital rates and density dependence.

Jul 20, 2026

Restoration trajectories and recovery

Measure how far a restored site has recovered in R: metric choice, chronosequence bias, a drifting reference and the trouble with extrapolating an asymptote.

Jul 20, 2026

SLOSS and reserve configuration

Single large or several small? Simulate reserve configurations in R and measure the two properties that decide it: beta diversity and environmental correlation.

Jul 19, 2026

Reintroduction release strategies

Release size, schedule and stage composition compared in R against a stochastic Lefkovitch model, with post-release mortality and a measured stopping rule.

Jul 19, 2026

Checking a climate window analysis

Four checks for a climate window analysis in R: shared trends, the choice between weather variables, held-out years, and what the search grid alone is worth.

Jul 19, 2026

Climate window analysis in R

Slide every candidate weather window past a yearly ecological response in R, measure how often the naive best window is significant, and correct it properly.

Jul 19, 2026

Drought indices for ecologists

Build SPI, SPEI and a climatic water balance by hand in R, and measure how much the accumulation window, baseline and evapotranspiration decide a drought year.

Jul 19, 2026

Degree days and thermal time in R

Build degree day models in R, compare the average, triangle and sine methods, estimate a base temperature from data, and measure what each choice costs.

Jul 19, 2026

Checking an epidemic estimate

Four checks for an epidemic reproduction number in R: reporting delay, under-reporting, weekly aggregation and an assumption sweep priced against the interval.

Jul 19, 2026

Seasonality and recurrent epidemics

An SIR model with host turnover in R: measure the intrinsic epidemic period, the seasonal forcing that turns annual cycles biennial, and stochastic fadeout.

Jul 18, 2026

Estimating R0 from incidence data

Estimate the reproduction number from an epidemic curve in R: Poisson growth rates by hand, the generation interval map, and a renewal equation Rt estimate.

Jul 18, 2026

The SEIR model and the latent period

Add an exposed class to the SIR model in R, integrate it with a hand written RK4 solver, and measure how a latent period biases the reproduction number.

Jul 18, 2026

Checking an isotopic niche analysis

Four checks for an isotopic niche analysis in R: sample size and power, the C:N lipid correction, a pipeline sweep, and tissue turnover in trophic ecology.

Jul 18, 2026

Isotopic niche overlap between groups

Code ellipse overlap for isotopic niches in R and measure how the headline percentage moves with the denominator, the containment probability and sample size.

Jul 18, 2026

Trophic position from stable isotopes

Estimate trophic position from nitrogen isotopes in R, and measure how much of a consumer’s place in the food web rests on the assumed enrichment factor.

Choosing a decision threshold in R: the cost ratio hidden in every ecological cut-off, decision curves and net benefit, and the price of miscalibration.

Jul 16, 2026

Data leakage in ecological model validation

Four routes by which information crosses from a held-out fold into an ecological model fit, each measured in R: preprocessing, screening, grouped sites, tuning.

Jul 16, 2026

Calibrating predicted probabilities in R

Reliability diagrams, the Brier decomposition, Platt scaling and isotonic regression in base R for occupancy models whose probabilities cannot be trusted.

Jul 15, 2026

Class imbalance in species presence models

machine learning

model evaluation

species distributions

ecology tutorial

ggplot2

What class imbalance does to a species presence model in R: why the positive count and not the ratio limits the fit, and what downsampling really changes.

Simulating an acoustic recogniser in base R to show why automated detection counts are an affine index of true call rate, with a false-trigger floor underneath.

Jul 15, 2026

Checking a genetic clustering analysis

Four checks for a genetic clustering analysis in R: unbalanced sampling, linked loci, variation between runs, and whether the structure survives a subsample.

Jul 14, 2026

Assignment tests and self-assignment

population genetics

ecology tutorial

ggplot2

Build genotype assignment likelihoods in base R, measure the leave-one-out bias in self-assignment, and run an exclusion test for an unsampled source.

Jul 14, 2026

Choosing K in genetic clustering

Implement the log-likelihood curve, cross-validation and the Evanno delta K in R, then watch all three choose clusters in a cline of demes that has none.

Jul 14, 2026

Circuit theory and effective resistance

Solve a landscape as an electrical circuit in base R, map current density, and measure the thing least-cost paths cannot see: whether a redundant route exists.

Jul 12, 2026

Least-cost paths and resistance surfaces

Compute cost distance and least-cost paths in base R with iterative sweeps, then measure how much the answer depends on the resistance values you chose.

Jul 12, 2026

Patch metrics and fragmentation in R

Label habitat patches with base R, measure fragmentation at a fixed habitat amount, and watch the percolation threshold and the grain change the answer.

Jul 12, 2026

Checking a coalescent analysis

Four checks for coalescent inference in R: what one locus can say, what recombination buys, whether demography mimics selection, and where to spend effort.

Jul 11, 2026

Tajima’s D and the frequency spectrum

population genetics

ecology tutorial

ggplot2

Build Tajima’s D from the site frequency spectrum in R and measure what it detects: growth, structure and bottlenecks all move it, and so does selection.

Jul 11, 2026

Nucleotide diversity and Watterson theta

population genetics

ecology tutorial

ggplot2

Put mutations on coalescent trees in R, compare the two classical estimators of theta, and measure why many short loci beat one long sequence of the same size.

Jul 11, 2026

The coalescent and gene trees

population genetics

ecology tutorial

ggplot2

Simulate the coalescent in R, check the tree height and total branch length against theory, and see why a single gene tree says almost nothing about history.

Jul 11, 2026

Checking an effective size estimate

Four checks for an Ne estimate in R: which time window it covers, what sampling relatives does to it, how wide the interval is, and what linkage costs.

Jul 11, 2026

Bottlenecks and genetic diversity

population genetics

ecology tutorial

ggplot2

Push a simulated population through a bottleneck in R and watch which measures of diversity notice: allelic richness, heterozygosity and the M ratio disagree.

Jul 11, 2026

Estimating Ne from genetic data

population genetics

ecology tutorial

ggplot2

Implement the temporal and linkage disequilibrium estimators of effective size in R, and measure how much data each needs before its answer means anything.

Jul 10, 2026

Effective population size in R

population genetics

ecology tutorial

ggplot2

Simulate what Ne means in R: the sex ratio, the variance in offspring number and the harmonic mean across bad years, each measured against its formula.

Jul 10, 2026

Checking a population genetics analysis

Four checks for an Fst analysis in R: loci against individuals, separating substructure from marker error, filtering rare variants, and outlier tests.

Jul 10, 2026

Drift, migration and isolation by distance

population genetics

ecology tutorial

ggplot2

Simulate drift and gene flow in R, check the Fst equilibrium against 1/(1 + 4Nm), and see how little a measured Fst says about the number of migrants.

Jul 10, 2026

F-statistics and population structure

population genetics

ecology tutorial

ggplot2

Compute Fis, Fst and Fit in R from three heterozygosities, see why Gst is capped by diversity within populations, and estimate Fst without the sampling bias.

Jul 10, 2026

The multivariate breeder’s equation

evolutionary ecology

quantitative genetics

natural selection

ecology tutorial

Predict multi-trait evolution in R with the Lande equation delta z = G beta: correlated responses, genetic constraints, and the line of least resistance.

Jul 6, 2026

The breeder’s equation in R

A raw forecast score means nothing without a baseline. In R, the same ecological forecast is skilful against one reference and useless against another.

Jun 25, 2026

The CRPS and the Brier score

forecasting

model evaluation

ecology tutorial

Two proper scores for ecological forecasts: the Brier score for presence, the CRPS for abundance, built from scratch in R with the identities linking them.

Why the first flowering date advances as monitoring effort grows while the mean date stays put: the extreme-value bias behind phenological shifts, in R.

The Levins model of patch occupancy from scratch in R: the colonisation-extinction balance, the equilibrium fraction, and the extinction threshold it implies.

Jun 21, 2026

Checking a coexistence analysis

Three diagnostics for an annual plant coexistence result in R: mutual invasibility, whether your design identifies self-limitation, and stability to model form.

Jun 21, 2026

Assumptions behind coexistence

A coexistence verdict extrapolates far past the competition data. See in R how model form and demographic rates decide the outcome where no data constrain it.

Jun 20, 2026

Niche and fitness differences

Turn fitted annual plant competition coefficients into niche and fitness differences in R, and see why the stronger competitor need not exclude its rival.

Jun 20, 2026

Fitting annual plant competition models

Fit Beverton-Holt competition coefficients to annual plant fecundity data in R, and see why the experimental design decides which coefficients you can estimate.

Jun 20, 2026

Checking a stable isotope mixing model

Three checks for a stable isotope mixing model in R: is the consumer inside the mixing polygon, is the posterior data-driven, and does source aggregation hold.

Jun 20, 2026

Discrimination and concentration in mixing models

In stable isotope mixing models the assumed discrimination factor and elemental concentrations drive the diet estimate more than the consumer data do.

Jun 20, 2026

Bayesian stable isotope mixing models

Why additive beta on the Gini-Simpson index is bounded by alpha, how Jost’s alpha fixes it, and the exact identity that turns Hill beta into the Sorensen index.

Jun 16, 2026

Checking a camera trap density estimate

camera traps

abundance

ecology tutorial

Three checks for a random encounter model density estimate in R: the independence filter, interval coverage in a patchy landscape, and where the error lives.

Jun 16, 2026

Staying time and the REST model in R

The REST model estimates animal density from how long animals stay in view, with no external speed. Little’s law and Cauchy’s chord identity, tested in R.

Three checks for approximate Bayesian computation in ecology: rank calibration of the sampler, posterior width of the answer, acceptance distance for the model.

Jun 14, 2026

ABC-MCMC and sequential ABC samplers

stats

ggplot2

ecology tutorial

Rejection ABC draws from the prior and throws almost all of it away. ABC-MCMC and sequential Monte Carlo recycle the good draws; a Ricker model prices the gain.

Jun 14, 2026

Choosing summary statistics for ABC

approximate Bayesian computation

simulation

ecology tutorial

In ABC the summaries are the data. Sufficiency, the price of a useless summary, distance scaling and semi-automatic ABC, in R on normal and Ricker models.

Connectance, generality, vulnerability and the specialisation indices H2’ and d’ for a plant-pollinator web, in base R, with the sampling caveats spelled out.

Jun 9, 2026

Checking a survival model

survival analysis

model checking

ecology tutorial

Diagnostics for survival models: the proportional hazards test, martingale residuals for functional form, and Cox-Snell residuals. None proves the model right.

Jun 9, 2026

Frailty and recurrent event models

survival analysis

ecology tutorial

Survival times that share a cluster or repeat within an individual are not independent: the naive model understates uncertainty, and units limit the correction.

Jun 9, 2026

Parametric survival and the AFT model

survival analysis

ecology tutorial

A parametric survival model reads a covariate two ways, as a clock acceleration or a hazard ratio, and predicts absolute survival that Cox cannot give directly.

Diagnosing a time series model in base R: residual whiteness with Ljung-Box, prewhitening before cross-correlation, and why passing every check proves nothing.

Jun 6, 2026

Spectral analysis of population cycles

time series

spectral analysis

ecology tutorial

Periodograms for population cycles in R: why the raw version is noisy, how aliasing turns a fast cycle into a slow one, and why a peak needs a red-noise null.

Jun 6, 2026

Fitting ARIMA models to ecological time series

time series

forecasting

ecology tutorial

Identify an ARMA model from the ACF and PACF, fit it with arima() in base R, and avoid the twin traps of over-differencing and plug-in prediction intervals.

ecology tutorial

regression

model checking

Deviance residuals mislead for beta, ordinal and Tweedie models. Use randomised quantile residuals, a proportional-odds test and held-out calibration instead.

Jun 5, 2026

Tweedie regression for biomass and cover with zeros

ecology tutorial

regression

GLM

Biomass and catch per unit effort mix exact zeros with a skewed positive part. Fit Tweedie regression with mgcv, and see why logging with a constant is biased.

Jun 4, 2026

distributional regression

ecology tutorial

ggplot2

Model the spread, not just the mean. A base-R location-scale fit, why naive prediction intervals miscalibrate, and how it connects to quantile regression.

Jun 1, 2026

Heteroscedasticity and limiting factors

Building the centred, additive and isometric log-ratio transformations by hand, with Aitchison distance, perturbation and powering, using base R only.

Why single imputation misleads: mean imputation attenuates the slope, regression imputation inflates correlations, and one dataset hides the real uncertainty.

When both variables carry error, ordinary regression is biased either way. Deming regression uses the error-variance ratio to recover the true slope in R.

May 27, 2026

Measurement error and regression dilution

ecology tutorial

regression

structural equation models

regression

ecology tutorial

Split an ecological correlation into direct and indirect routes with lm in base R: standardised path coefficients, the tracing rules, and why a slope misleads.

May 24, 2026

Checking for publication bias

meta-analysis

ecology tutorial

publication bias

Detect small-study effects in an ecological meta-analysis with base R: funnel plots, Egger’s regression test, and trim-and-fill, with the limits of each.

May 24, 2026

Meta-regression with moderators

meta-analysis

ecology tutorial

meta-regression

Explain heterogeneity with a study-level moderator in base R: weighted meta-regression, residual tau-squared, an R-squared analogue, and error control.

May 24, 2026

Heterogeneity in meta-analysis

meta-analysis

ecology tutorial

heterogeneity

Measure disagreement among ecological studies in base R: Cochran’s Q, I-squared with an interval, tau-squared, and a prediction interval for a new study.

A community occupancy model can return sensible parameters yet fit badly. A posterior predictive check in base R catches unmodelled detection heterogeneity.

May 23, 2026

Community covariates and species traits

Give each species its own slope on a site gradient, and use a trait to explain the variation. A hierarchical model in base R, set against the two-stage fit.

May 23, 2026

Species richness by data augmentation

Estimate how many species a survey missed. A community occupancy model with data augmentation counts the undetected tail in base R, and beats a Chao estimator.

May 23, 2026

Multi-species occupancy models

Build a Gibbs sampler in base R for the mean and variance of a trait, and see why the mean’s posterior is a t distribution rather than a narrow normal.

May 18, 2026

Metropolis-Hastings from scratch

Code a random-walk Metropolis sampler by hand in R to estimate a survival probability, and see why the posterior beats a Wald interval that dips below zero.

May 18, 2026

Validating a step selection model

Used-habitat calibration plots from scratch: simulate used locations from a fitted step selection model and check if it reproduces the chosen habitat.

May 18, 2026

Availability sampling for step selection

movement ecology

habitat selection

ecology tutorial

How many available steps per used step, and from which distribution: extra steps buy precision in R, and the tentative kernel is a choice worth checking.

May 18, 2026

Integrated step selection analysis in R

movement ecology

habitat selection

ecology tutorial

Integrated step selection analysis from scratch: add movement covariates to a conditional model to debias habitat selection and recover the movement kernel.

May 18, 2026

Step selection functions for animal movement

movement ecology

habitat selection

ecology tutorial

Fit step selection functions in R from scratch: matched steps, a conditional logistic likelihood by hand, and why pooling strata attenuates selection.

May 17, 2026

Checking a state-space movement model

Check a fitted state-space movement model with one-step-ahead residuals in base R: QQ plots and autocorrelation reveal what a misspecified model quietly hides.

May 17, 2026

A particle filter for animal movement

Build a bootstrap particle filter from scratch in base R for animal tracks with heavy-tailed Argos errors that drag a Gaussian Kalman filter off course.

May 17, 2026

Regularising irregular animal tracks

Turn gappy, irregular animal tracks into a regular series with a continuous-time integrated random walk and Kalman smoother in base R, with honest gap error.

May 17, 2026

State-space models for animal movement

Fit a linear-Gaussian correlated random walk to noisy telemetry in base R: a hand-coded Kalman filter and smoother that split movement from observation error.

May 17, 2026

Checking a movement HMM

ecology tutorial

movement ecology

hidden Markov models

Two checks a fitted movement HMM needs: forecast pseudo-residuals to test the model, and forward-backward posterior probabilities for what Viterbi hides.

May 17, 2026

Covariates in a movement HMM

ecology tutorial

movement ecology

hidden Markov models

Let HMM transition probabilities depend on time of day through a multinomial logit, recover a diurnal activity budget, and see what a homogeneous model hides.

May 17, 2026

How many states in a movement HMM?

ecology tutorial

movement ecology

hidden Markov models

Choose how many states a movement HMM needs without overfitting: AIC and BIC across candidate models, why an extra state splits a real one, and label switching.

Fitting the theta-logistic population growth model in R by maximum likelihood, and why the shape parameter theta is barely identifiable from one time series.

May 15, 2026

Estimating population trends in R

Why one linear rate can hide a population crash and recovery, using a GAM in R to show trend shape, and why count data need a count model rather than log-OLS.

May 15, 2026

Gompertz state-space model in R

Separating process noise from observation error in a population time series with a Gompertz state-space model in R, fitted by a hand-coded Kalman filter.

May 15, 2026

Detecting density dependence in R

Fitting a Gompertz model to a population time series in R, why the ordinary regression test for density dependence over-rejects, and the bootstrap fix.

May 14, 2026

Cormack-Jolly-Seber survival models in R

survival analysis

capture-recapture

ecology tutorial

Estimate apparent survival and recapture from open capture histories in R: build the m-array and fit a Cormack-Jolly-Seber model by maximum likelihood.

May 14, 2026

Nest survival with logistic exposure in R

survival analysis

nest survival

ecology tutorial

Estimate daily nest survival in R with the logistic-exposure model, compare it against the Mayfield estimate, and let daily survival vary with nest age.

May 14, 2026

Cox proportional hazards and the PH assumption

survival analysis

model diagnostics

ecology tutorial

Fit a Cox proportional hazards model in R, read the hazard ratios, test the proportional-hazards assumption with Schoenfeld residuals, and stratify to fix it.

May 14, 2026

SDM

cross-validation

spatial autocorrelation

mgcv

ecology tutorial

Why random cross-validation overstates SDM accuracy when occurrences cluster in space, and how spatial block cross-validation gives an honest estimate, in R.

May 11, 2026

Evaluating species distribution models in R

Test an SDM in R against held-out data: the ROC curve and AUC, a confusion matrix with sensitivity, specificity and TSS, and how to pick a good threshold.

May 10, 2026

Pseudo-absence and background points for SDMs

How many background points an SDM needs, why predicted values are relative rather than probabilities, and how case weights stabilise the scale, worked in R.

May 10, 2026

Species distribution modelling with GLM in R

Fit a species distribution model in R with a binomial GLM: draw presence and background points, model humped responses, and map predicted habitat suitability.

Occurrence records from GBIF and iNaturalist need cleaning. In R: drop impossible and duplicate coordinates, flag low precision, and map the result with sf.

May 9, 2026

Species-area relationships in R

Fit species-area relationships in R: the power law and the logarithmic model, why the power exponent z matters, and how nls differs from log-log regression.

May 9, 2026

Additive diversity partitioning in R

Split gamma diversity into alpha and beta additively in R with vegan adipart, test it with a null model, and see why Hill numbers matter for diversity indices.

May 9, 2026

Nestedness, NODF, and null models in R

Measure community nestedness with the NODF metric in R using vegan, then test it with fixed-margin null models and see why the null choice decides the verdict.

May 9, 2026

Distance decay of community similarity in R

Run a power analysis by simulation in R: build a power curve over sample size, check the Type-I rate, and see why post-hoc power and low-power studies mislead.

May 6, 2026

GLM residual diagnostics with simulation in R

Why Pearson and deviance residuals mislead for GLMs, and how to build simulation-based quantile residuals in R to spot overdispersion and zero-inflation.

May 6, 2026

Model selection with AIC in R for ecology

model selection

RDA vs CCA for community ecology: by gradient length

ordination

constrained ordination

community ecology

vegan

ecology tutorial

Redundancy analysis versus canonical correspondence analysis on community data: what the DCA gradient-length rule can settle, and where Hellinger fits.

May 4, 2026

From QGIS to R: a spatial join with GeoPackage

Load occurrence points in QGIS, tag each with the habitat patch it falls in by a spatial join, export to GeoPackage, and continue the analysis in R with sf.

May 4, 2026

Spatial autocorrelation and Moran’s I in R

Nearby sites resemble each other, breaking the independence regression assumes. Moran’s I measures it, a correlogram shows its scale, a residual test finds it.

May 3, 2026

capscale vs dbrda: same axes, different test

vegan has two functions for distance-based constrained ordination. On Bray-Curtis they return the same axes but a different pseudo-F: the negative eigenvalues.

May 3, 2026

Modelling nonlinear species responses with GAMs

A count GLM forces a single direction of response. When a species peaks at an intermediate optimum, a generalised additive model lets the data choose the shape.

May 3, 2026

Raster data in R with terra: DEMs and extraction

spatial

raster data

ecology tutorial

What a raster really is, how to read its structure, map algebra and slope from an elevation model, what coarsening the grain does, and pulling values at points.

May 3, 2026

Poisson and negative binomial GLMs in R

regression

count data

ecology tutorial

Why logging abundance counts is a poor reflex, how to fit a Poisson GLM, how to tell it is too tight, and how a negative binomial and an effort offset fix it.

Turn a dissimilarity matrix into groups with hclust: a dendrogram, a linkage choice, a cut into clusters, and what that cut can and cannot prove about them.

May 2, 2026

Rarefaction and accumulation curves in R

community ecology

diversity

ecology tutorial

More individuals and more plots both raise the species count, whatever the true richness. Rarefaction and accumulation curves separate diversity from effort.

May 2, 2026

Indicator species analysis with IndVal in R

community ecology

indicator species

ecology tutorial

PERMANOVA says groups differ; indicator species analysis says which species drive it. A walk through multipatt, the IndVal index, specificity and fidelity.

May 2, 2026

Beta diversity in R: turnover vs nestedness (betapart)

community ecology

beta diversity

ecology tutorial

A single dissimilarity number hides two processes: species replacement and species loss. Separate them in R with the betapart package and the Baselga framework.

May 2, 2026

Constrained ordination with distance-based RDA in R

vegan

ordination

constrained ordination

community ecology

ecology tutorial

NMDS shows all compositional variation and overlays environment afterward; distance-based RDA builds the ordination from predictors and tests what they explain.

May 1, 2026

Mapping species richness in R with sf

Turn species occurrence records into a gridded richness map in R with the sf package, then export a GeoPackage you can open and style further in QGIS.

May 1, 2026

Statistics on an ordination: envfit and PERMANOVA in R

An NMDS shows the pattern. Use envfit to fit environmental variables onto it, adonis2 to test whether groups differ, and betadisper to keep the test honest.

May 1, 2026

Ordination with NMDS in R

Turn a site-by-species table into a map of community composition with vegdist and metaMDS, then read the stress and decide how many dimensions you need.

May 1, 2026

Computing diversity indices in R with vegan

biodiversity

ecology tutorial

Compute species richness, Shannon and Simpson diversity from a site-by-species community matrix in R with vegan, with reusable code and a small worked example.

May 1, 2026