Quiz 6

Empirical evidence for MPA effects More than 5000 MPAs have been declared, covering 1.2% of the world’s oceans Gather evidence of effects on size, growth, catches, etc. What does this evidence show? Within MPAs that are enforced, average size and abundance increases, often dramatically Evidence for spillover effect is hard to tease out from environmental factors

Halpern and Warner (2002) “112 independent measurements of 80 reserves to show that the higher average values of density, biomass, average organism size, and diversity inside reserves (relative to controls) reach mean levels within a short (1-3 y) period of time and that the values are subsequently consistent across reserves of all ages (up to 40 y)”. Halpern BS & Warner RR (2002) Marine reserves have rapid and lasting effects. Ecology Letters 5: Ben HalpernRobert Warner

Scientific method Using local unprotected areas as “controls” is problematic – Protected areas may be different and more productive before protection – Effort not going into protected areas goes into the unprotected ones Alternative: control areas with no MPAs and compare total abundance in large areas including MPAs to large areas without MPAs Or BACI (before-after control-impact) design, with before and after plus controls and MPA data

Limited BACI results 7 studies, 9 MPAs Before MPAs, future unprotected areas similar to future MPA areas After MPAs, increased density and biomass in unprotected areas Small sample size Halpern BS et al. (2004) Confounding effects of the export of production and the displacement of fishing effort from marine reserves. Ecological Applications 14: Ben HalpernRobert WarnerSteve Gaines

File-drawer effect Studies are more interesting and publishable when there are significant positive effects Most studies by reserve managers or proponents Studies showing no effects are less scientifically interesting, and possibly politically embarrassing, and may be “shelved” in a “file drawer” instead of being published So meta-analysis of many published studies can experience a “publication bias” towards positive effects Møller AP & Jennions MD (2001) Testing and adjusting for publication bias. Trends in Ecology and Evolution 16:

File-drawer effect Probable area of non-significance True relation between estimated effect and sample size Values from published studies Probable area of significance Modified from Møller AP & Jennions MD (2001) Testing and adjusting for publication bias. Trends in Ecology and Evolution 16: Log (sample size) Estimated effect size Probable area of non-significance Probable area of significance

Spillover (Roberts et al. 2001) Roberts CM et al. (2001) Effects of marine reserves on adjacent fisheries. Science 294: Don’t do this! Y-axis should start at 0 Callum Roberts

Problems with Roberts’ study Effort was excluded from protected areas and went to unprotected areas In the first year, most fishers had to increase effort to catch the same amount of fish Yet biomass in the unprotected areas still increased in the first year Average age at maturity for key species is 3-4 yr How could spillover occur so quickly? What about joint environmental change?

Conclusions MPAs offer benefits beyond fishery catches – Biodiversity protection – Insurance against management error – Tourism Spillover of effort needs to be taken into account – Unlikely to generate increased overall catches unless heavily overfished at present Assessing benefits is difficult – Controls, environmental changes – File drawer effect

Modeling catastrophes

Background readings Gerber LR & Hilborn R (2001) Catastrophic events and recovery from low densities in populations of otariids: implication for risk of extinction. Mammal Review 11: Ward EJ et al. (2007) A state-space mixture approach for estimating catastrophic events in time series data. CJFAS 64:

Causes of extinction Gradual declines – Habitat loss – Environmental change – Competition – Predation – Harvest Catastrophic events

Types of catastrophes El Niño Epidemics Invasion by competitor or predator Fires Hurricanes Oil spills Freezes Droughts

“Catastrophic mortality dominates estimates of population viability” (Menges 1990) Catastrophes “may be more important in determining persistence time than any other factor usually considered.” (Mangel and Tier 1994) Menges ES (1990) Population viability analysis for an endangered plant. Conservation Biology 4:52-62 Mangel M & Tier C (1994) Four facts every conservation biologist should know about persistence. Ecology 75: Eric Menges Marc Mangel

What are catastrophes? Mortality events beyond the range of normal variation Probability density Survival rate

Initial motivation Status of Hooker’s sea lion in New Zealand Endemic, about 13,000 individuals Abundance trends indicate steady or slow growth Five locations hence endangered IUCN (“red list”) criteria – 1 location (critically endangered) – ≤ 5 locations (endangered) – 6-10 locations (vulnerable) Subject to killed per year in commercial trawl fishery

Questions that started study What level of bycatch should be allowed What is the risk of extinction – Should this species really be listed? – How important is bycatch in extinction risk

The action is in catastrophes That is why IUCN has the five-location criterion That is the only way that a population that has not shown a declining trend is going to go extinct Catastrophic mortality events have been seen in marine mammals – El Nino – Disease outbreaks

Topics in talk Modeling catastrophes Estimating catastrophe frequency and intensity Calculating extinction risk

Modeling catastrophes Logistic growth model with process error Probability of a catastrophe Average process error in a year of catastrophic mortality Variability in catastrophes

The distribution of process errors Probability density Process error (w t ) 20 Catastrophes.xlsx, sheet Process error

Simulated time series Abundance Year 20 Catastrophes.xlsx, sheet Catastrophe sim

20 Catastrophes.xlsx sheet Catastrophe sim

Estimating catastrophe frequency Annual data Non-annual data

St. Paul Island northern fur seals Abundance Year 20 Catastrophes.xlsx, sheet Real data

St. George Island fur seals Abundance Year 20 Catastrophes.xlsx, sheet Real data

St. Miguel Island northern fur seals Abundance Year 20 Catastrophes.xlsx, sheet Real data

California sea lion Abundance Year 20 Catastrophes.xlsx, sheet Real data

Estimation options When you have annual counts you can calculate the process error directly and make a frequency distribution Only problem is distinguishing between pup mortalities and adult mortalities

Distribution of residuals Process error Year Process error Year California sea lion St. Miguel St. GeorgeSt. Paul Process error Year 20 Catastrophes.xlsx, sheet Residuals

Non-annual data (Ward et al. 2007) Much more difficult Requires a full model with observation and process error Hierarchical model (shares parameters across stocks) Bayesian model (to incorporate other information) Applied to four fur seal populations Ward EJ et al. (2007) A state-space mixture approach for estimating catastrophic events in time series data. CJFAS 64:

Abundance counts Year San Miguel St. GeorgeSt. Paul Bogoslof

San Miguel Island Bering Sea San Miguel Island Bering Sea Ward EJ et al. (2007) A state-space mixture approach for estimating catastrophic events in time series data. CJFAS 64: Density Prob. of catastrophe Normal CVCatastrophic CV Magnitude of catastrophe

Ward, pers. comm. 25 yr projections Density Percent of initial state

Impact of multiple populations Run forward simulations Assume each population has same starting size Assume catastrophes are independent events for each population Assume catastrophe is 50% mortality of all ages including pups Probability p of catastrophe is 0.02 Total population is 5000 Look at population after 100 years

Modeling catastrophes Logistic growth model with process error Probability of a catastrophe Average process error in a year of catastrophic mortality Variability in catastrophes

One location Population 5000, p = 0.02, 0% rate of increase Frequency of occurrence Population size after 100 years Zero catastrophes One catastrophe Two or more catastrophes

Mean > 5000 for zero catastrophes? I forgot to include the bias correction factor… Wrong Right

Two locations Population 5000, p = 0.02, 0% rate of increase Frequency of occurrence Population size after 100 years

Five locations Population 5000, p = 0.02, 0% rate of increase Frequency of occurrence Population size after 100 years

Summary Catastrophes are important elements in extinction and endangered species classification It is possible to estimate catastrophe frequency in a formal statistical model Classification as vulnerable, threatened or endangered depends on number of populations