R &amp; QGIS tutorials for ecologists.

Fit the same model at every site in R with split, lapply and purrr, and catch the silent faults: sapply changing shape, empty loops and failed sites dropped.

Residuals of a model with smooth predictors have a lower null mean than raw data. Why moran.test and moran.mc lose size and power there, and lm.morantest in R.

Sep 26, 2026

Spatial cross-validation when the target is a map

Block or random cross-validation for a kriged map? Simulated in R: block folds overstate a random sample’s map error, random folds understate a clustered one.

Sep 26, 2026

Geographical detector: the interaction rule

interactions

variance partitioning

The geographical detector calls independent, additive drivers a nonlinear enhancement in over half of datasets. Why, what q is, and where shift tests fail.

QGIS NULL and R NA agree on comparisons and filters, but not on bare [ indexing, aggregates or pasted text, and a CSV export merges NULL with empty text.

Sep 26, 2026

Area in QGIS and R: which call matches which

QGIS $area, area() and sf st_area() give different areas for one habitat patch. Each has an exact partner in the other tool, and headless QGIS hides a trap.

Attrition in a field experiment: when pots die first

When a treatment changes which pots survive to harvest, the survivor contrast is not the effect. Lee bounds, Imbens-Manski intervals and the survival gap in R.

Randomising treatments to plots in R

Randomise treatments to plots in R with sample(): two sample() traps, what pairing plots on a gradient buys, and how analysing the pairs as two groups loses it.

Adaptive second-phase tows and the low mean

Sending second-phase trawl tows where phase-1 variance looks high biases the pooled stratified mean low. In R: why, by how much, and what allocation repairs it.

Estimating an inclusion probability you already know

Refitting an inclusion probability the design already fixed gives a more precise weighted mean. Measuring the gain in R, and the variance that must change too.

Sampling until the standard error is small

Counting quadrats until the running standard error is a quarter of the mean misses that precision. In R: the cost of a variable sample, and Green’s stop line.

Design weights in a stratified regression

A design weight is compulsory for a stratified mean but optional for a regression slope. Measuring in R what it costs, what it fixes, and the test that decides.

Weighted draws without replacement: sample() in R

R’s sample(prob =) without replacement does not select sites at n w / sum(w). What that does to a Horvitz-Thompson mean, and two survey samplers that do.

A year list logs a species once per recorder, so the occupancy bias changes sign with sites per recorder. In R: why the site-level removal cut fails, and a fix.

Sep 24, 2026

SDM

invasion

species distributions

A presence-absence SDM fitted to a species still spreading puts its optimum at the founding site’s climate and maps a third of the potential range. In R.

Trap-specific responses in spatial capture-recapture

When animals learn one baited trap, spatial capture-recapture in R reads the pile-up of recaptures as a short sigma. A global Mb cannot fix it; Mbk can.

Misread colour rings and apparent survival

Misread colour rings revive dead birds as resightings: in R, CJS survival bias grows with study length and a two-sighting filter fails when sightability varies.

Transients and the single-capture rule in CJS

Deleting birds caught only once before a CJS fit makes survival a readout of detection and study length. The two-age model and TEST 3.SR instead, in R.

Home-range overlap is not contact

Two collared animals can share one home range and meet rarely or often. Contact from paired GPS tracks in R, and why a time-shuffle test overstates it.

A familiarity covariate built from an animal’s own past fixes can absorb a layer or home range left out of a step selection model. Measured in R, with placebos.

Missing GPS fixes in step selection

GPS fixes fail under cover. Dropping irregular steps biases step selection, bridging the gaps trades one bias for another, and weights cost precision. In R.

Spatial capture-recapture on a meandering stream

A planar SCR model on a meandering stream inflates abundance and shrinks sigma. Measuring in R which error a habitat mask fixes and which needs stream distance.

GPS fix loss and the collars you drop

Canopy blocks GPS fixes, so the used points in a resource selection function are selected by the habitat under test. Why dropping bad collars is worse, in R.

Downstream gene flow and the phantom dam

Headwater sites hold less genetic diversity than the mainstem with no barrier anywhere on the river. Simulating the false dam signal, and its repair, in R.

Chilling, forcing and projected leaf-out

A forcing-only degree day model of spring leaf-out misstates the advance under warming, and gets its sign wrong where winter chill runs out. Measured in R.

Gill-net selectivity and the fish it cannot see

Gill-net mesh series leave a blind zone that the SELECT correction cannot fill. Measuring the corrected share of large fish in R, and what one more mesh buys.

Thermal death time and the ramping rate

A ramp CTmax moves with the heating rate along the thermal death time line. Designing static knockdown assays in R, and why the survivors must stay in the fit.

Activation energy and the rising limb

With only high temperature deactivation, an Arrhenius slope fitted below the optimum still underestimates activation energy, by an amount set by Eh. In R.

Genotype-environment scans under shared ancestry

A per-locus scan of allele frequency on a spatial gradient flags half a neutral genome under isolation by distance. The repair uses the other loci, not the map.

Fitting a senescence model to individual records

Fitting reproductive senescence in R with nlme: selective disappearance and its repair, and why year effects leave the ageing slope and peak age unidentified.

Runs of homozygosity and realised inbreeding

inbreeding

conservation genetics

Simulate a linked genome in R and score runs of homozygosity, SNP homozygosity and pedigree F against the realised inbreeding they are meant to measure.

Earlier maturation: evolution or faster growth?

A falling age at maturity can mean evolution or faster growth. Simulating a fish survey in R to compare A50 with the PMRN midpoint and what the PMRN costs.

Purging siblings before estimating Ne

effective population size

Removing putative siblings from a random sample inflates a linkage disequilibrium estimate of effective size several fold. A simulation of the purge in R.

Nonlinear selection on BLUPs and on raw means

When assay counts track lifespan, BLUPs fake disruptive selection and raw means fake stabilising selection. Quadratic selection gradients simulated in R.

Siblings in an assignment baseline

Full-sib families in an assignment baseline make the exclusion test reject genuine residents. In R: how often, why, and a null that simulates the family design.

Pseudocounts turn read depth into a result

A fixed 0.5 pseudocount makes a sparse taxon’s log-ratio a function of library size, so unequal sequencing depth is reported as a group effect. Worked in R.

Seed dispersal: the nearest adult is not the parent

Taking the nearest adult as the parent caps seed dispersal at the tree spacing. In R: that bias in closed form, and where the inverse seed-trap model fails.

Misread rings and the dispersal tail

Misread ring numbers join bird recoveries to the wrong ringing site and fake a fat dispersal tail. In R, a mixture with a ring-register null repairs it.

Sep 19, 2026

Global sensitivity analysis with Sobol indices

Sobol indices by hand in R for a stage matrix and a harvest model: when they only repeat elasticity times input spread, and where interaction sets them apart.

Sep 19, 2026

Drone flushing pushes a survey count both ways

Simulating a lawnmower drone survey in R: flushing recounts animals that fly into the not yet imaged strip, and loses the ones driven off the block edge.

Sep 19, 2026

Reconstructing a population from ages at harvest

Ages at harvest alone leave the harvest rate on an exact ridge, so abundance is a guess. Cohort analysis, the flat profile and what known effort buys, in R.

PET removes publication bias proportional to the standard error, PET-PEESE not reliably; neither removes a significance filter on studies that differ by site.

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.

Flight-season shifts and false occupancy trends

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

Harvest surveys and the late respondent

Wave extrapolation in a hunter harvest survey can cut respondent bias or overshoot it, and the forms cannot show which. Checking it in R against a follow-up.

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.

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.

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.

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

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 log frequencies with empty bins dropped moves with bin width and sample size. Simulating bouts in R; likelihood holds steady.

Sep 15, 2026

Observation error in a count-based PVA

Counting error inflates the variance of log growth, and a count-based PVA overstates extinction risk. Three repairs in R, and when the naive risk is no worse.

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

Size-class boundaries in a matrix population model

Equal-width size classes can turn a declining population into a stable or growing one. In R: how quantile boundaries protect lambda in a matrix model.

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.

CUSUM for die-offs when reporting effort persists

A CUSUM and a historical-limits alarm on weekly carcass reports at matched false alarm rates: lasting reporting surges reverse which finds a fortnight die-off.

Interpolated cores and false slowing down

early warning signals

Interpolating an unevenly sampled core to a regular grid can fake or hide critical slowing down. In R: when it happens, why, and a null that corrects the test.

Negative binomial k from small host samples

From 15 to 40 hosts the aggregation k often has no finite estimate. Measuring in R how the rule for those samples creates false k-burden relationships.

Smoothing a series before testing a forecast

Smoothing a population index over the whole record flatters a one-step hindcast in R. Refitted at each forecast origin, the same smoother loses to raw AR(1).

Omitted random slopes and false positives

A random intercept model that leaves out a real random slope finds a mean effect that is not there. Measuring in R why the slope variance test cannot warn you.

Binning a time series invents a reverse cause

Summing two time series into coarser bins makes a one-way driver look driven by its follower. A Granger test in R, with the repair: point samples, not sums.

Detecting a die-off from carcass reports

A historical-limits alarm on weekly carcass reports: the variance model sets the real false alarm rate, and decides detection when noise varies by season. In R.

Lasso, stepwise and the dropped confounder

Choosing adjustment covariates by lasso or stepwise AIC drops a confounder the treatment then absorbs. Simulating in R why double selection repairs it.

Centring a quadratic before lasso or ridge

Standardising does not move the origin of a squared covariate. Simulating in R how lasso and ridge lose a thermal optimum on Celsius that centring keeps.

Infection rates from pooled vector samples

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.

Tuned shrinkage and the penalty your data needed

regularisation

calibration

Cross-validated ridge is right on average and wrong per dataset. Simulating in R why a species model’s tuned penalty ranks opposite to the one its data needed.

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.

Sep 11, 2026

Classifier scores over a camera-trap sequence

Averaging calibrated per-image scores over a camera-trap burst: a closed form for the calibration slope, what empty frames do to it, and recalibration in R.

Sep 11, 2026

species richness

Stacking thresholded species distribution models over-predicts richness and stretches its contrast. Summing probabilities does not; with an interval, in R.

Sep 11, 2026

measurement error

Plots read from a coarse climate grid carry Berkson error and the fitted niche widens. Why a pooled correction fails on rugged cells, and a per-cell fix in R.

Novel climate combinations and the MESS map

When temperature and rainfall are correlated, a warmer and wetter future passes a one-covariate MESS check yet leaves the data. Measuring the damage in mgcv.

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.

betadisper with unequal group sizes

With five plots against fifty, betadisper often finds a dispersion gap that is not there. Testing bias.adjust in R on three distances, and what it leaves.

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.

Forward selection in RDA: ordistep or ordiR2step

vegan

ordination

constrained ordination

model selection

With one real driver among ten candidates, vegan’s ordiR2step often returns an empty RDA. The adjusted R2 ceiling behind it, and its trade-offs, measured in R.

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.

Repeated-measures PERMANOVA in R: what to permute

Repeated-measures or paired PERMANOVA in R: shuffle whole sites to test a site-level treatment, within sites to test time. Free shuffling errs both ways.

Permutation nulls that keep the map

A site shuffle over-rejects when two maps are smooth. Moran spectral randomisation in R nearly holds its size on a fitted kernel, not on kNN or dbMEM graphs.

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.

Standardising variables before clustering sites

Z-scores, range or MAD before k-means? Simulated site typologies in R show the shape of the variables carrying no groups decides which scaler works best.

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.

Pielou’s evenness under unequal sampling effort

Pielou’s J can rank two communities by sampling effort, not evenness, when effort differs. Simulate it in R, rarefy to a common n, and see what coverage adds.

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.

Phylogeny in a multi-species meta-analysis

Ignoring the tree shrinks the pooled interval of a multi-species meta-analysis, and the right model still undercovers. Measured in R with ape, plus a t repair.

Correlations from gradients of different length

Studies that share one slope but sample gradients of different length give heterogeneous correlations. Simulating the meta-analysis in R, and two repairs.

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.

Cluster bootstrap at six sites, and what beats it

At six catchments the cluster bootstrap and sandwich errors over-reject a site-level treatment. Measuring in R why the six site means are the analysis.

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.

Permutation tests with a covariate in the model

With a covariate in the model, shuffling labels or the response gives opposite wrong answers for a raw slope. Measuring in R why a t statistic repairs both.

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.

Missing values in a predictor: why, not how many

With 40 per cent of a predictor blank, the reason for the gap decides whether deletion or multiple imputation is right. A simulation in R for field ecologists.

Confidence intervals in quantile regression

The default quantreg interval is a 90 per cent rank interval that assumes equal spread. Measuring in R how it undercovers when the scatter fans out with x.

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.

Chi-squared approximation may be incorrect

What the chisq.test warning means for a small two by two table in R: exact sizes and power show Yates’ correction, not the warning, is what costs you power.

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.

Choosing a factor smooth for a half-sampled group

When one group is sampled on half the gradient, the sz factor smooth runs an unpenalised line into the gap. Measuring in R which hierarchical GAMs hold up.

Carcass searches and fatality estimates

Fatality totals from carcass searches depend on whether missed carcasses stay findable. Shoenfeld and Huso bracket the truth when persistence is right, in R.

Overdispersion, year noise and a wiggly GAM trend

A Poisson GAM reads extra-Poisson spread as a wiggly trend. In R: why nb() fixes spread between sites, but only a year random effect removes year noise.

Vuong test for zero inflation, and what to use instead

A Poisson is a zero-inflated Poisson with no inflation, so the Vuong test misfires. In R: its lost power, its false Poisson verdicts and the score test to use.

Heterozygosity-fitness correlations and power

Simulate heterozygosity-fitness correlations in R: how often a dozen microsatellites detect real inbreeding depression, and what the g2 test can and cannot say.

AIC on REML fits: when units choose the model

lme4 ranks REML fits with different fixed effects without a word. Measuring in R how writing elevation in metres or kilometres then decides the chosen model.

Extra-pair paternity from parentage mismatches

A fixed mismatch rule turns genotyping error into extra-pair paternity as loci are added. Measuring in R the brother problem and two repairs that fit the rate.

The lme4 max|grad| warning and predictor scale

Raw calendar year in a glmer sets off the max|grad| warning. Measuring in R when the estimates are fine, when the standard error is not, and which check to run.

Sequential sampling for pest decisions

A Wald sequential plan decides whether to spray after every plant, but its boundaries contain the negative binomial k. Checking the plan by simulation in R.

Per chick or per nest: informative cluster size

When brood size tracks territory quality differently in fed and control nests, per-chick and per-nest effects can take opposite signs. Six estimators in R.

Extinction dates from sighting records

Dating extinctions from sighting records in R: the Solow test’s false alarm rate in closed form, and how often the linear estimation bound misses a decline.

Chamber fluxes: linear or exponential fits

Closed chamber fluxes in R: the linear slope’s bias is a formula, while four syringe samples leave an exponential fit scattered and model choice adds error.

Counting a female’s mates as the sires found among her offspring builds a Bateman gradient with no benefit of mating. Simulating the artefact in R and its size.

Sep 3, 2026

Declaring eradication after empty traps

A run of empty trap sessions sized from the removal capture rate is calibrated only when every animal is equally catchable. Testing eradication rules in R.

Sep 3, 2026

Fishing, age truncation and spawning variability

Fishing old fish raises the CV of spawning output by a closed-form filter. In R: a 50-year survey index often misses it; the naive variance test is oversized.

Sep 2, 2026

Reference sites and tolerance bounds

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

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

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

time series

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 exactly zero in over 40 per cent of datasets. R shows why dropping the stream 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 through roughness and on cell size through roughness and landform, and aspect is an angle to split into two components.

What a shapefile loses: names, times and types

data management

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

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.

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.

Selection models for publication bias

publication bias

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.

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.

Coordinate error and habitat assignment

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

Rasterising a vector layer

terra

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.

Checking a vector layer before you measure

structural equation models

A self-intersecting polygon can have an area of exactly zero and sf says nothing. Eight geometry checks in R, each 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

measurement error

Soil fertility is not measured, three imperfect indicators are. A one-factor model recovers the slope a composite of them hits only by coincidence, 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

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

MASS

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

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

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

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.

Hamiltonian Monte Carlo from scratch

MCMC

Bayesian statistics

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

Checking a stochastic simulation

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

Mean time to extinction, exactly

population models

extinction

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.

Tau leaping and the cost of a bigger step

population models

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.

The Gillespie algorithm from scratch

population models

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

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.

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.

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.

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.

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.

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.

SLOSS and reserve configuration

Single large or several small? Simulate reserve configurations in R and measure the two properties at its centre: beta diversity and environmental correlation.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

Tajima’s D and the frequency spectrum

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.

Nucleotide diversity and Watterson theta

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.

The coalescent and gene trees

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.

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.

Bottlenecks and genetic diversity

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

Estimating Ne from genetic data

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

Effective population size in R

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.

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.

Drift, migration and isolation by distance

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.

F-statistics and population structure

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.

The multivariate breeder’s equation

evolutionary ecology

quantitative genetics

natural selection

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

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: an extreme-value bias that can fake 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.

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.

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.

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.

Discrimination and concentration in mixing models

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

Bayesian stable isotope mixing models

Why additive Gini-Simpson beta is capped by one minus 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

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

approximate Bayesian computation

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

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

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 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

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

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

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.

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

distributional 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

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

structural equation models

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

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-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

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, compared with Chao2.

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.

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.

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.

Availability sampling for step selection

habitat selection

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.

Integrated step selection analysis in R

habitat selection

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

Step selection functions for animal movement

habitat selection

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

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.

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.

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.

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.

Checking a movement HMM

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.

Covariates in a movement HMM

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.

How many states in a movement HMM?

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.

Cormack-Jolly-Seber survival models in R

capture-recapture

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.

Nest survival with logistic exposure in R

nest survival

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.

Cox proportional hazards and the PH assumption

model diagnostics

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.

SDM

cross-validation

spatial autocorrelation

mgcv

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, low-precision and duplicate coordinates, and map the result with sf.

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.

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.

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.

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

vegan

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.

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.

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.

Raster data in R with terra: DEMs and extraction

raster data

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.

Poisson and negative binomial GLMs in R

count data

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.

Rarefaction and accumulation curves in R

diversity

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

Indicator species analysis with IndVal in R

indicator species

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

Beta diversity in R: turnover vs nestedness (betapart)

beta diversity

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

Constrained ordination with distance-based RDA in R

vegan

ordination

constrained ordination

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

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.

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.

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.

Computing diversity indices in R with vegan

biodiversity

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.