A habitat that receives more immigrants than it exports, and whose population would fall without them, is the textbook signature of a sink. But two very different situations produce that same signature, and confusing them leads to opposite conservation mistakes. One is a habitat so attractive that animals pour into it even though it is killing them. The other is a perfectly good habitat that only looks like a sink because it is overcrowded. This post separates the ecological trap from the pseudo-sink.
Start with the reassuring case. A pseudo-sink (Watkinson and Sutherland 1995 Journal of Animal Ecology 64(1):126-130) is a habitat whose local growth is density-dependent and genuinely good, but which receives so much immigration that it is pushed above its own carrying capacity. Crowded past capacity, its local growth rate drops below one, and a snapshot calls it a sink. Contrast it with a true sink, where the growth rate is below one at every density, immigration or no.
lam_true <- function(N) rep(0.85, length(N)) # below one at every density
lam_pseudo <- function(N) pmax(1.6 - 0.006*N, 0.01) # good, but density-dependent
rbind(at_crowded_180 = c(true = lam_true(180), pseudo = lam_pseudo(180)),
at_sparse_10 = c(true = lam_true(10), pseudo = lam_pseudo(10))) true pseudo
at_crowded_180 0.85 0.52
at_sparse_10 0.85 1.54At an immigration-inflated density of 180, both look like sinks: the true sink at 0.85 and the pseudo-sink even lower at 0.52. Drop the density to 10 and they part company: the true sink is still 0.85, below one, while the pseudo-sink is 1.54, comfortably above. The test that settles it is to cut the immigration and watch.
iso <- function(lam, N0, yr = 40) { N <- N0; for (t in 1:yr) N <- N * lam(N); N }
c(true_sink_isolated = iso(lam_true, 180), pseudo_sink_isolated = iso(lam_pseudo, 180)) true_sink_isolated pseudo_sink_isolated
0.2704142 100.0000000 Isolated from a starting 180, the true sink collapses to 0.3, extinct, while the pseudo-sink relaxes down to its own carrying capacity of 100 and persists indefinitely. Write off a true sink and you lose little; write off a pseudo-sink and you have abandoned good habitat because a headcount was crowded.
Ng <- seq(0, 200, 1)
d <- rbind(data.frame(N = Ng, lam = lam_true(Ng), kind = "true sink"),
data.frame(N = Ng, lam = lam_pseudo(Ng), kind = "pseudo-sink"))
ggplot(d, aes(N, lam, colour = kind)) +
geom_hline(yintercept = 1, colour = col_ref, linetype = "dashed") +
geom_line(linewidth = 1) +
scale_colour_manual(values = c("true sink" = col_true, "pseudo-sink" = col_pseudo)) +
labs(x = "Density", y = "Local growth rate", colour = NULL,
title = "A pseudo-sink is above one until immigration crowds it")
The other deception runs the opposite way. An ecological trap is a genuine sink that animals actively prefer (Schlaepfer et al. 2002 Trends in Ecology and Evolution 17(10):474-480; Battin 2004 Conservation Biology 18(6):1482-1491). Habitat choice evolved to track cues that once predicted quality, and when human change breaks the link between cue and quality, the cue can point the wrong way: a freshly mown field that signals lush grassland, asphalt that polarises light like water, a forest edge that looks safe but concentrates predators. Settlers choose the trap over better habitat and pay for it.
A trap is worse than an ordinary sink, because an ordinary sink is at least avoided when better options exist, whereas a trap pulls animals out of sources. Plotting habitats by their quality and their attractiveness makes the danger zone explicit: quality and preference should rise together, and a trap is the habitat that sits where they come apart, high preference, low quality.
set.seed(409)
q <- runif(12, 0.4, 1.6); pref <- pmin(pmax(q + rnorm(12, 0, 0.12), 0.2), 1.7)
hab <- data.frame(quality = q, preference = pref, type = "matched")
hab <- rbind(hab, data.frame(quality = 0.6, preference = 1.55, type = "trap"))
ggplot(hab, aes(quality, preference, colour = type)) +
geom_abline(slope = 1, intercept = 0, colour = col_ref, linetype = "dotted") +
geom_vline(xintercept = 1, colour = col_ref, linetype = "dashed") +
geom_point(size = 3) +
annotate("text", x = 0.62, y = 1.62, label = "trap", colour = col_true, size = 3.6) +
scale_colour_manual(values = c("matched" = col_pseudo, "trap" = col_true), guide = "none") +
labs(x = "Habitat quality (local growth rate)", y = "Attractiveness to settlers",
title = "A trap is preferred but poor")
The management response depends entirely on which of the three you have. A true sink is low-quality habitat that animals rightly avoid when they can; often it can be left alone. A pseudo-sink is good habitat that a headcount slandered; protect it. A trap is low-quality habitat that animals wrongly love, and it is the dangerous one, because it drains the sources and can pull the whole population down; the response is to fix the cue, remove the attractive lure or restore the quality behind it. Telling them apart cannot be done from counts or from occupancy, only from the local demography and the settlement behaviour, which is where the checking post goes next.
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