On climate science, the New York Times blows it

Bret Stephens is a right-wing journalist and climate-science denier who spent most of his career writing for the Wall Street Journal. He was hired as an opinion writer by the New York Times in early 2017, and wrote his first column on April 28.

I first learned about Mr. Stephens’s new job at the New York Times from a blog posting by Joe Romm, a physicist who writes extensively about climate science and energy economics. Romm pointed out an inconsistency between the current advertising campaign of the Times – “Truth. It’s more important now than ever” – and Stephens’s history of writing about climate change and other issues. The Times received more than 1500 comments and 550 letters to the editor about Stephens’s first column within 48 hours of its appearance on April 29. Romm, Susan Matthews, David Roberts, and others wrote thorough rebuttals of Stephens’s argument, such as it was. I won’t reiterate these rebuttals, but wish to make a few additional points about denial of climate science in Stephens’s New York times column.

Mr. Stephens claims to accept the fact that the average temperature on Earth has increased in the last 150 years due in part to human activity. This gives his column a patina of plausibility compared to the claims of others who deny climate science. But this apparent plausibility is really only a pretense. He ignores all of the other evidence of recent, rapid climate change – melting glaciers, shrinking ice caps on Greenland, decreased ice in the Arctic Ocean, melting permafrost, rising sea levels, more extreme weather events. He fails to acknowledge that our addition of greenhouse gases to the atmosphere is the primary cause of recent climate change.

Stephens’s biggest problem is with the mathematical models that are used to project future climate conditions under various scenarios. He incorrectly implies that climatologists claim certainty about these projections, and constructs an analogy between this purported certainty of climatologists and the supposed certainty of the Hillary Clinton presidential campaign that she would win the election last November. According to Stephens, the Clinton campaign was wrong, so the climatologists might also be wrong. This analogy is phony at several levels. The politicians weren’t as certain as Stephens implies. The climatologists include uncertainty in all of their model projections. And the climate models are based on detailed knowledge of atmospheric chemistry and physics, unlike the statistical models of polling data that politicians and the news media use, which depend on extrapolating from surveys of a small number of voters to the voting population as a whole. In addition, there are various ways of testing global climate models by comparing observed data to predictions of the models. The figure below shows one example illustrating that these models can account for measured average temperature of Earth’s surface between 1860 and 2000 only if models include both emission of greenhouse gases by burning fossil fuels and natural factors such as variation in solar radiation and volcanic activity.

Average annual temperature of Earth’s surface from 1860 to 2000 (red lines) compared to projections of three sets of global climate models: models with only natural forcings such as changes in solar radiation and sunspot activity (a), models with only anthropogenic forcings such as release of greenhouse gases into the atmosphere (b). and models with both natural and anthropogenic forcings (c). The gray bands show the range of projections for four models in case. The temperature anomaly shown on the vertical axes of these graphs is the deviation from the average temperature between 1880 and 1920 in degrees Celsius (multiply these values by 1.8 for degrees Fahrenheit). Projections shown in these graphs are hindcasts, tests of how well models fit existing data, rather than forecasts, or predictions of future data.

For Stephens, the uncertainty surrounding predictions of climate models appears to justify a wait-and-see approach to dealing with climate change. This ignores three fundamental principles of climate change that I discuss in my book “Tools for Critical Thinking in Biology”: inertia, positive feedback, and tipping points. About 20% of the carbon dioxide that we add to the atmosphere by burning fossil fuels today will remain in the atmosphere for 1000 years (inertia). Increased temperatures in the arctic cause less ice in the Arctic Ocean, making the surface darker, meaning more heat is absorbed, warming the arctic region further, melting more ice, and so forth (positive feedback). Finally, some effects of anthropogenic climate change may cause transitions to dramatically different conditions (tipping points) that will be irreversible fur hundreds of human generations. For example, sea level was 23 feet higher during the Eemian interglacial period that ended, 125,000 years ago, but temperature was only a fraction of 1oF higher than today. As global temperatures continue to increase in response to continued addition of greenhouse gases to the atmosphere, with arctic temperatures rising much faster than those at lower latitudes, we may reach a tipping point in which the Greenland ice cap melts, causing sea levels similar to those in the Eemian that will remain elevated for many generations. Inertia, positive feedback, and tipping points in the global climate mean that Stephens’s wait-and-see approach is indefensible.

Stephens seems to be fixated on trying to undermine the overwhelming consensus among climate scientists in the basic facts of climate change and the resulting projections of what we face if we continue business as usual in our use of fossil fuels. Contrary to his claim, this consensus doesn’t mean that the science is settled. Far from it: I’m not a climatologist, but climatology is one of the most active and exciting areas of research today, with new findings reported almost weekly (most of which should make us even more worried about the future).

The heroes of Stephens’s story are ordinary citizens, who may be “indifferent to … the prospect of planetary calamity”, but “have a right to be skeptical of an overweening scientism.” Stephens implies that climate scientists are often villains, but I see climate scientists who forge ahead with their research in the face of abuse from politicians beholden to fossil fuel interests as heroic. Ordinary citizens can also be heroic if they nurture their curiosity about science, develop real skepticism instead of the faux skepticism of science deniers, and above all demand honesty in themselves and others.

Posted in Climate change, Evaluating evidence, Journalism, Modeling, Science and politics | Leave a comment

“This is a sad day for the children of the U.S.”

Howard Mielke is a toxicologist at the Medical School of Tulane University in New Orleans. He described March 21, 2017 as “a sad day for the children of the U.S.” in response to news that the Environmental Protection Agency (EPA) plans to eliminate two programs that protect children from exposure to lead in paint. One program supports public education on risks of lead-based paint and trains contractors to do remodeling projects without releasing lead into the atmosphere from old paint; the second provides grants to states and Indian tribes to deal with these risks in their jurisdictions. These programs currently cost $16 million and have 73 full-time employees.

Tools for Critical Thinking in Biology is about various kinds of evidence that scientists use to answer questions and test hypotheses. Evidence can take many forms, from systematic observations to results of experiments to comparisons and correlations. Some questions that scientists ask have implications for public policy, including questions about the effects of lead exposure on health. In Chapter 5, I use two main questions to illustrate the possibilities and pitfalls of inferring causation from comparisons and correlations: Do cell phones cause brain cancer? Does lead exposure in childhood make individuals more likely to commit crimes later in life? In the first case, a correlation between cell phone use and brain cancer is not convincing evidence that cell phone use causes brain cancer (see my book for an explanation). In the second case, scientists have found a host of correlations between lead exposure and rates of violent crime about 20 years later: in different countries of the world, different states and cities of the U.S., and different neighborhoods of New Orleans. Together with detailed studies of the impact of lead exposure on brain development, these correlations imply that early exposure to lead has adverse, longterm consequences for the health of children. In particular, children exposed to lead in childhood have lower IQs, a greater risk of attention deficit / hyperactivity disorder and other behavioral problems, and a greater likelihood of being arrested for violent crimes later in life.

Children in the U.S. have been exposed to lead from two main sources: paint and gasoline. Use of lead in gasoline was phased out in the 1970s. Lead-based paint was outlawed for residential use in 1978, although its use had declined substantially after a peak in the 1920s. Nevertheless, many older homes in poor neighborhoods of cities have flaking and chipping paint containing lead. This is why the EPA has supported the removal of paint from older homes in a careful process that doesn’t produce lead-filled dust that can be inhaled by children, as well as adults and pets.

President Trump released a budget on March 15, 2017 that proposed cuts across the government with the exception of the departments of Defense, Homeland Security, and Veterans Affairs. The EPA was targeted for the largest percentage cut of 31.4%, for a total decrease of $2.6 billion. In this context, elimination of two programs to protect children from exposure to lead-based paint seems like small potatoes: $16 million is less than 1% of the total cut proposed for the EPA budget. Trump’s plans will harm the environment in many ways, but this small part of his plans seems particularly petty and mean-spirited. The evidence is strong that lead exposure is harmful to kids and society; this has been recognized for a long time and led to elimination of lead from paint and gasoline 40 years ago; the cost to continue remediation efforts is minuscule. Perhaps Congress will recognize these facts and reject this and other parts of Trump’s agenda that adversely affect the environment and human health.

Posted in Causation, Ethics, Medicine, Science and politics | Leave a comment

Monarch butterflies, milkweed, and migration: The law of unintended consequences

I described the magic of migration by monarch butterflies in Chapter 1 of Tools for Critical Thinking in Biology. These tiny animals fly from breeding areas in the northern US and Canada to overwintering sites in high-elevation forests in central Mexico each fall. After a period of semi-dormancy until spring, the adult monarchs mate, return to the southern US to lay eggs on milkweed plants, and then die. Larvae hatch from these eggs to feed on milkweed foliage, then pupate on milkweed (or nearby lawn furniture) until adult butterflies emerge. Some of these adults fly further north to reproduce, and these successive journeys north continue for 3 or 4 generations until monarchs have reached southern Canada again. In fall, the process repeats itself, with Canadian monarchs flying 2,500 miles to Mexican overwintering sites that they have never seen.

Tagged monarch butterfly

Monarch butterfly wearing an ID (photo by Jim Gagnon)

This story of migration by monarch butterflies is magical because it took 40 years and the help of thousands of volunteers for two Canadian scientists, Fred and Norah Urquhart, to discover the wintering area in the mountains of central Mexico. The Urquharts developed a method of tagging butterflies; volunteers throughout North America reported their captures of tagged butterflies to the Urquharts and did tagging of their own to gradually extend the known range of movement of the animals. The story is also magical because scientists have used observations and experiments to learn what triggers migration in the fall, how monarchs from as far north as Canada find their way to Mexico, and why migration may benefit monarchs. I describe some of this research in my book, but the research continues and important new discoveries have extended the story since the book was published in April 2015. One of these stories links migration and milkweeds, with potential unintended consequences for conservation of monarchs, so I need to give a little background about milkweeds and conservation before telling this story.

Why is milkweed important for monarch butterflies?

Adult monarchs eat nectar from a large variety of flowers, helping to pollinate the flowers in the process. Females lay eggs only on milkweed, however, and larvae eat only milkweed as they grow and develop. Milkweeds contain compounds called cardenolides that are toxic to many vertebrates; these compounds ingested by monarch larvae remain in the tissues of adults that develop from the larvae. Cardenolides make adult monarchs poisonous to predators such as blue jays, which can learn to avoid monarchs from trying to eat a single individual. This is another fascinating story that you can learn about here.

What is the conservation status of monarch butterflies?

Monarch butterflies face many risks, both during their breeding season in the United Sates and southern Canada and in their overwintering sites in central Mexico (and along the Pacific coast of California where monarchs breeding west of the Rocky Mountains spend the winter). Breeding habitat is lost to growth of cities, shopping malls, roads, and agriculture. The milkweed that monarchs depend on grows in and adjacent to agricultural fields; farmers now plant seeds of corn and other crops that are genetically engineered to be resistant to a herbicide called Roundup. This enables farmers to use Roundup to control weeds without killing their crops. These weeds include milkweed, so this process is detrimental to monarchs.

Some overwintering sites along the Pacific coast of California are in towns and cities, making them vulnerable to further development and loss of habitat, although local governments have set aside parks to protect monarchs that winter there. Most monarchs overwinter in the highlands of central Mexico, which have a history of disturbance by logging and cattle grazing. Monarchs in Mexico occupy a handful of sites with a total area of 1 to 18 hectares (2.5 to 45 acres; an acre is about the size of an American football field without the end zones). The Mexican overwintering population fluctuates from year-to-year depending on how successful breeding was the previous summer, how much mortality occurred during migration, and weather conditions in the overwintering sites, but the general trend has been downward since 1995. The lowest estimate of the Mexican overwintering population was 25 million in 2014, although the population rebounded to 150 million in 2016. These may seem like very large numbers, but the Mexican overwintering population has decreased by more than 25 million monarchs eight times since 1995. If this had happened between 2014 and 2015, monarch butterflies east of the Rocky Mountains would be extinct.

Monarch Butterfly Overwintering Populations.

Estimates of number of monarch butterflies overwintering in Mexico, 1995-2016. From Center for Biological Diversity.

What can citizens do to help protect this charismatic insect? One strategy is to plant milkweed in our yards to compensate for the loss of milkweed in agricultural areas. There are about 100 species of milkweeds native to North America, most of which are used by monarch butterflies. However, the most common milkweed available to gardeners in plant nurseries is an exotic species called tropical milkweed. Unlike North American milkweeds, tropical milkweed remains green and continues to flower in fall and winter in places with mild climates, like the Gulf coast states. Because of this newly available food supply, some monarchs migrating from farther north remain through the winter in areas along the Gulf coast rather than continuing to Mexico. These monarchs breed through the winter and have established non-migratory populations that remain along the Gulf coast all year.

Common milkweed, native to North America, and tropical milkweed, often sold in plant nurseries and planted by gardeners in North America, to the possible detriment of monarch butterflies.

Does this sound like a problem? Probably not, until I give you one more piece of information. As I described above, monarchs have an effective chemical defense against many vertebrate predators. They are also attacked by several parasites, the most common of which is a protozoan called Ophryocystis elektroscirrha (OE). There are populations of monarchs that are year-round residents in Hawaii and Florida, and OE is much more prevalent in these populations than in migrating populations, perhaps because migration culls infected butterflies, who can’t fly as well as healthy ones, or because migration enables butterflies to escape areas where they can become infected. In a recent study, Dara Satterfield and colleagues found that the new, non-migratory populations along the Gulf coast have higher infection rates than migratory monarchs. Satterfield’s group suggests that these sedentary monarchs along the Gulf coast could act as a reservoir for OE, causing infection of migrants as they pass through this area on their way to or from the wintering sites in Mexico. In trying to help monarchs by planting exotic tropical milkweed in our gardens, we may instead be putting them at greater risk. If you’re interested in contributing to the conservation of monarch butterflies, why not share this story with your local nurseryman, and ask him to sell native milkweed instead of the exotic tropical species that contributes to the unintended consequence described here?

Monarch migration

Migration of monarch butterflies in eastern North America. Green diamonds show the main locations of overwintering monarchs in the highlands of central Mexico. Red squares show alternative sites where small numbers of migrating monarchs spend the winter. Blue dots show locations of new sedentary (non-migratory) populations along the Gulf Coast. From “Loss of migratory behaviour increases infection risk for a butterfly host”, by D. A. Satterfield et al., 2015.

Posted in Causation, Citizen Science, Conservation, Ecology, Migration, Observations | Leave a comment

Medical use of marijuana revisited

I described two experimental studies of the use of marijuana to reduce pain in Tools for Critical Thinking in Biology and discussed two technical reviews of the medical value of marijuana in a subsequent blog posting. The gist of these reviews was that there was limited but adequate evidence that marijuana could help patients suffering from chronic pain, but little evidence for other beneficial health effects. Additional research reinforces the evidence supporting use of marijuana for pain control, especially as an alternative to opioid drugs, which are widely abused in the US. This research has an important flaw, however, that was ignored in recent news stories.

In 2014, Michael Bachhuber and colleagues at the Philadelphia Veterans Affairs Medical Center compared death rates caused by overdoses of opioid painkillers such as oxycontin in US states with and without laws allowing medical use of marijuana. They used data through 2010 when 13 states had passed such legislation. Bachhuber’s group found that annual death rate due to opioid overdoses was 25% less in these states than in the remaining 37 states that didn’t allow medical use of marijuana.

In a follow-up study published in July 2016, Ashley Bradford and her father David, graduate student and professor respectively at the University of Georgia, compared Medicare data on prescription drug use in states with and without medical marijuana legislation. On average, individual doctors wrote almost 2000 fewer prescriptions for opioids and other typical painkillers in states in which medical marijuana was legal.

Bachhuber’s group and the Bradfords infer from their comparisons of states with and without legalization of medical marijuana that individuals might benefit by having marijuana available to control pain. For example, in a news story in Science magazine, Greg Miller quotes David Bradford describing his results as “suggestive evidence that medical marijuana might help divert people away from the path where they would start using [an opioid drug], and of course if they don’t start, they’re not on that path to misuse and potentially death”.

These analyses illustrate a classic breakdown of logic called the ecological fallacy: reaching conclusions about individuals from aggregated data for groups to which the individuals belong. The groups are states where individuals live; in Bachhuber’s study the data are death rates in each state due to opioid overdoses, and in the Bradfords’ study the data are numbers of prescriptions for opioid painkillers written by doctors in each state. Average death rates and opioid prescription rates are lower in US states with legal use of medical marijuana than in the remaining states. Paradoxically, individuals who use medical marijuana might also use more opioids or have a greater likelihood of dying than individuals who don’t use medical marijuana, despite the opposite effect in comparing average rates of opioid prescription and death between states with and without laws for medical use of marijuana.

Bachhuber’s group was fairly cautious in interpreting their results, although news reports such as “Could pot help solve the U.S. opioid epidemic?” in the November 4, 2016, issue of Science ignored the caveats discussed by Bachhuber and colleagues. For example, Bachhuber’s group mentioned the alternative hypotheses that “increased access to medical cannabis may reduce opioid analgesic use by patients with chronic pain” or act as a “’gateway’ or ‘stepping stone’ leading to further . . . opioid analgesic overdoses”. However, the researchers weren’t able to discriminate between these hypotheses because they only used statewide averages, not data for individual patients.

How could it be possible for medical marijuana to be a stepping stone for individuals to overdose on opioids and at the same time for states without legal access to medical marijuana to have more deaths from opioid overdoses? One reason is that other differences between states with and without laws allowing medical use of marijuana might account for greater death rates from opioid overdoses in the latter states. These other potential differences are called confounding variables. Bachhuber’s team considered unemployment rate as one possible confounding variable, on grounds that higher unemployment might cause more drug abuse, but they found no differences in unemployment rates between states with and without medical marijuana. Unemployment rate is only one of many possible confounding variables, however; states without legal access to medical marijuana might have older residents, with more pain, or younger residents, with more propensity to abuse drugs, or lower educational levels, or more military veterans suffering from PTSD, than states with legal access to medical marijuana. Indeed, one of the most dramatic differences between states that do and don’t allow medical use of marijuana is that all of Hillary Clinton’s 232 electoral votes in the 2016 presidential election came from states with laws allowing medical marijuana while only 23 of Donald Trump’s electoral votes came from such states. This certainly doesn’t mean that having medical marijuana available caused people to vote for Clinton and not having it available caused them to vote for Trump, but it illustrates the pitfalls of drawing conclusions about causation from purely correlational data. I illustrate this point in more detail in Chapter 5 of Tools for Critical Thinking in Biology.

Map of US states with and without legalization of medical marijuana.

US states with operational legalization of medical marijuana as of December 28, 2016. This excludes Arkansas, Florida, and North Dakota that legalized medical marijuana in November 2016 but haven’t yet established a process for patients to obtain marijuana. It also excludes Texas that legalized medical marijuana in 2015 with a doctor’s prescription, ignoring the fact that federal law forbids doctors from prescribing marijuana. Instead, doctors may issue a letter to the patient recommending marijuana for certain medical conditions, as occurs in the states where legalization is operational.

To test the alternative hypotheses proposed by Bachhuber’s group that medical marijuana may be a safer alternative to opioid drugs for treating pain or that medical marijuana may be a stepping stone to opioid abuse, we really need data on individual people who do and don’t have access to medical marijuana. Even better would be experimental data, although it’s hard to imagine an ethical study that could test these hypotheses. However, experiments are possible to test the efficacy of marijuana compared to opioids for pain control. For example, Colorado recently legalized marijuana for recreational use as well as medical use, and the state is using $9 million of the taxes collected from sales of marijuana to support experimental studies, much as California did in the early days of marijuana research (see Chapter 4 of Tools for Critical Thinking in Biology). Emily Lindley is in charge of one of the Colorado studies; her group will use 50 volunteer patients with back or neck pain who will be assigned randomly to receive either vaporized marijuana, an opioid drug, or a placebo on three visits to the hospital, after which they will report any pain relief they experience.

So, does legalization of marijuana for pain control reduce the likelihood of patients overdosing on opioids? We don’t know the answer at this time, so we shouldn’t use this possibility as an argument in support of legalization of marijuana. Uncertainties like this can be frustrating to those interested in promoting or opposing particular policies, but such uncertainties are embraced by scientists as challenges to be overcome. Be on the lookout for further research that may help answer this question!

Posted in Causation, Correlation & Causation, Evaluating evidence, Experimentation, Medicine | Leave a comment

Storytelling in science: What can we learn about critical thinking from stories about mountain lions and sea otters?

Tools for Critical Thinking in Biology is a book of stories about doing science. Most of these stories are incomplete because science is a work in progress, therefore one of my great pleasures is learning about new research that extends the stories in the book. Two new books tell exciting stories that complement stories in my book, and I encourage you to read these new books to learn more about how science works. The new books are Heart of a Lion: A Lone Cat’s Walk across America, by William Stolzenburg, and Serendipity: An Ecologist’s Quest to Understand Nature, by James A. Estes. Heart of a Lion describes a remarkable journey by a young male mountain lion from South Dakota to Connecticut and illustrates what we can learn from purely observational evidence, and Serendipity is Jim Estes memoir of his lifetime studying sea otters and killer whales in the Aleutian Islands.

Scientists use many different tools to learn how the world works. These tools include ways of studying nature such as comparative studies and experiments. Some studies use fancy equipment such as DNA sequencers; others use complex statistical methods. Regardless of the approach used and the technology employed, all science depends on reliable observations as the basic source of information. I illustrate this idea in my book with two brief stories about the evaluation of observational evidence in studies of ivory-billed woodpeckers and wolverines. In 2004, a birder in Arkansas reported the first sighting of an ivory-billed woodpecker since 1944, but extensive follow-up work didn’t confirm this observation, so ivory-billed woodpeckers are still considered extinct. In 2008, a graduate student set up remotely activated cameras to study pine martens in northern California. One of her cameras recorded a wolverine, the first definitive evidence of this rare and elusive carnivore in California since 1922. The graduate student and her team collected hair and fecal samples which yielded DNA confirming that the subject of their photo was a wolverine, probably a migrant from 650 kilometers away in Idaho.

Mountain lion

Mountain lion in Yellowstone National Park (photo by K. Fink).

Mountain lions once occupied most of the western hemisphere, but were extirpated east of the Rocky Mountains following European settlement. Except for a small, isolated population in Florida, the easternmost population in North America is now found in the Black Hills of South Dakota. Mountain lions are solitary and territorial, and young disperse from their natal areas at 12 to 18 months of age. By dispersing, young males avoid being killed by adult males that defend territories encompassing the ranges of several females.

Biologists documented dispersal of mountain lions from the Black Hills in the 1990s by attaching radio transmitters to young animals. Some dispersers went west, looking for openings in the matrix of mountain lion territories in the Rockies where they could establish territories of their own. Other dispersers went east, where opportunities to establish territories were virtually limitless but opportunities to mate were scarce or nonexistent, though the dispersers didn’t know this. Will Stolzenburg tells the story of one such disperser in Heart of a Lion. The hero of this story is a juvenile male that left its birthplace in the Black Hills in summer 2009. After a journey of more than 2000 miles through Minnesota, Wisconsin, Michigan, probably Canada, and New York, the lion was killed by a car in southwestern Connecticut in June 2011. Unlike other dispersers that traveled shorter distances, this lion did not carry a radio transmitter that enabled researchers to follow him day-by-day. His story as told by Stolzenburg is about the use of bits and pieces of observational evidence to reconstruct his route. This evidence includes sightings of tracks, photographs from remotely activated cameras, video recordings, hair samples, and scat. Researchers extracted DNA from the hair and scat that the lion left along his route, confirming that a single male had left these samples in Minnesota, Wisconsin, and New York and that this same male was the one killed by a car in Connecticut. This is similar to the wolverine story I told in my book, but much more detailed since the mountain lion’s journey was traced from beginning to end.

The scientific consensus is that mountain lions no longer live in eastern North America, but many locals believe that mountain lions were never completely extirpated from this region. As explained by Stolzenburg, this belief is based on numerous reported sightings over many years in many locations. Some of these observations were supported by photographs that turned out to be domestic cats, golden retrievers, and various other animals. In other cases, people really did see mountain lions, but ones that had escaped from captivity. In 2011, the US Fish and Wildlife Service reviewed the evidence for persistence of mountain lions in eastern North America and concluded that none of it was credible. Besides giving us an important history of our evolving relationship with wildlife, Stolzenburg shows how observational evidence can be evaluated for reliability and can contribute to our understanding of nature.

Sea otter

Sea otter at Morro Bay (photo by Mike Baird).

Serendipity: An Ecologist’s Quest to Understand Nature by Jim Estes is the second book I encourage you to read. I discuss the complexity of causation in Chapter 8 of my book using the ecology of sea otters in the Aleutian Islands as a case study. Jim Estes started research on sea otters in in the Aleutians in 1970 when he was a graduate student and has studied them ever since. Estes discovered that sea otters are a keystone species that has dramatic impacts on nearshore environments in the Pacific Ocean. Sea otters eat sea urchins, which graze on large marine algae called kelp. Where sea otters are absent, the ocean floor near shore is carpeted by sea urchins; where sea otters are present, sea urchin populations are much smaller and forests of kelp develop. These kelp forests provide habitat for fish, which provide food for eagles and other predators.

After working in the Aleutians for 20 years, Estes and his coworkers observed a sharp drop in the population of sea otters during the 1990s, which they eventually attributed to predation on otters by killer whales. With a declining sea otter population, sea urchins began to increase and kelp was reduced, changing many nearshore environments from kelp forests to sea urchin barrens. This is an example of a trophic cascade, in which a top predator influences the abundance of species below it in the food chain, including the vegetation at the base of the food chain.

Serendipity: An Ecologist’s Quest to Understand Nature is a wonderful memoir of Estes’ long career in science, including not only the details of what he did and learned but also an explanation of the thinking that led him from one project to another during his career and discussion of the broader implications of his work. Many of us can identify chance events that changed the direction of our lives; Estes entitled his book Serendipity because it shows how he was able to capitalize on these events in his own life to make fundamental contributions to our understanding of ecology. Read his book if you want to learn more about sea otters and killer whales and, more generally, about how science works.

Ecologists have identified several examples of trophic cascades driven by top predators in recent years. I discuss wolves in Yellowstone National Park as well as killer whales in the Aleutians in Chapter 8 of my book, while Will Stolzenburg devoted an entire book called Where the Wild Things Were: Life, Death, and Ecological Wreckage in a Land of Vanishing Predators to this topic. Stolzenburg emphasizes implications for conservation of new knowledge about trophic cascades.

While writing this posting, I learned about a new study that nicely illustrates an implication of a trophic cascade that may be surprising to you. Several ecologists used a mathematical model to predict the effects of recolonization of eastern North America by mountain lions. According to the model, control of eastern deer populations by mountain lions would reduce collisions of vehicles with deer, resulting in 155 fewer human deaths, 21,400 fewer human injuries, and savings of $2.1 billion over a period of 30 years. Between 1890 and 2008, mountain lions attacked humans 153 times and killed humans 21 times in the entire US and Canada, so occasional attacks and deaths would occur in the east if mountain lions were reintroduced, but these would almost certainly be far less than the number of injuries and deaths avoided due to the reduction in deer-vehicle collisions.

Posted in Ecology, Evaluating evidence, General material, Long-term study, Observations | Tagged , , , , , | 1 Comment

Careful readers are a writer’s best friends

Writing for publication entails many drafts and many reviews of these drafts by friends, colleagues, copyeditors, and critics. The credibility of science depends on peer review, as explained by Frederick Grinnell in The Everyday Practice of Science and by me in Chapter 9 of Tools for Critical Thinking in Biology, where I give personal examples, historical examples, and contemporary examples that have been prominent in the news media.

Two readers of the published version of my book made several suggestions for corrections. I wish to thank them here and explain what they found in their careful reading. Don’t get bogged down in the first explanation dealing with a problem that appears earliest in the book, but return to it after reading some of the later explanations that are more straightforward.

1) In Chapter 5, I use two main examples to show how researchers use, and sometimes abuse, comparative and correlational data to answer questions about causation. For instance, people have wondered whether microwave radiation emitted by cell phones can cause brain cancer. One source of evidence to address this question comes from comparison of past cell phone use by people with and without brain cancer; this is called a retrospective case-control study. Cases are people with brain cancer, controls are people without brain cancer, and the study is retrospective because the data come from estimates by cases and controls of how much they used cell phones in the past. Case-control studies often use odds ratios to report results: what are the odds of brain cancer for a cell phone user compared to those for a nonuser? More specifically, what is the ratio of these odds? If this ratio is greater than 1, a cell phone user is more likely to get brain cancer than a nonuser, although we also have to consider the possibility that a ratio greater than 1 could simply be due to chance.

Odds ratios are a little tricky to understand, so I use a completely different example to show how they are calculated. When the Titanic sank in 1912, 650 adult males died and 132 survived, while only 102 adult females died and 300 survived. Therefore the odds of dying for males were 650/132 = 4.92 while the odds of dying for females were 102/300 = 0.34. These translate to an odds ratio of 4.92/0.34 = 14.5. I then wrote “adult male passengers were almost 15 times as likely to die when the Titanic sank as adult female passengers.” As one post-publication reviewer noted, this is incorrect; the odds ratio really means that the odds of dying were 15 times greater for males than females. We can also express the difference in mortality of male and female passengers on the Titanic as a relative risk. The likelihood of death for males was 650/(650+132) = 0.83; the likelihood of death for females was 102/(102+300) = 0.25. Therefore males were 3.32 times as likely to die as females (relative risk = 0.83/0.25). This is a pretty dramatic difference, but not as dramatic as I implied in the book.

Using odds to express probabilities of events has a long history that is intertwined with the history of gambling. According to FanGraphs on March 8, 2016, the Chicago Cubs have an 18.6% chance of winning the 2016 World Series. This means that the odds against the Cubs winning are 81.4%/18.6% = 4.38 to 1. If you bet $1 on the Cubs today, your friend should be willing to pay you $4.38 if they win in exchange for collecting $1 from you if they lose. Although odds and odds ratios are somewhat indirect measures of relative probabilities, they have some advantages for statistical analysis of medical questions like the relationship of cell phone use to brain cancer.

2) I describe how interactions between genes and environments influence human traits in Chapter 7, using studies of twins to develop this theme. I introduce this topic with a story about two genetically identical twins that were adopted at an early age and raised by separate families. These twins were reunited at age 39 and discovered that they shared a remarkable set of traits, starting with the fact that both of their adoptive families named them Jim. In addition, as I wrote, “both Jims smoked the same brands of cigarettes and beer – amazing!” As one post-publication reviewer noted, smoking beer is pretty amazing.

3) In Chapter 8, I used Hurricane Katrina to introduce the idea that events often result from complex webs of causation. About 1800 deaths and $81 billion in property damage in New Orleans were attributed to Katrina, which hit the Gulf Coast on August 29, 2005, but several other factors also contributed to this devastation. My diagram of this web of causation implies that George W. Bush’s praise of his director of the Federal Emergency Management Agency (“Brownie, you’re doing a heckuva job”) was one of these contributing factors. Instead, I should have described this praise as a symptom of an underlying cause, appointments of unqualified people to lead agencies such as FEMA.

4) Jim Estes of the University of California, Santa Cruz and the US Geological Survey has studied sea otters and other marine mammals in the Aleutian Islands for more than 40 years. Chapter 8 describes some of their research, including their discovery that predation by killer whales caused the population of sea otters to crash in the 1990s. This is a fascinating, multidimensional story involving questions such as these: The researchers first saw an attack by a killer whale on a sea otter in 1991 – why did killer whales switch from larger mammalian prey to sea otters at this time? The researchers saw six total attacks in the early 1990s, yet estimated that the sea otter population declined from 53,000 in 1991 to 12,000 in 1997 – could predation by killer whales account for such a large decline without more attacks being seen by humans? Sea otters are much smaller than other mammalian prey of killer whales – how many sea otters would supply the daily energy needs of a killer whale? I address this last question in Box 5.2. Killer whales require about 247,500 kilocalories of energy per day, and five sea otters would supply this amount of energy. One kilocalorie equals 1 Calorie in human nutrition (not 1000 Calories, as I state in the book). We use 2,000 to 3,000 Calories per day, only about 1% of the energy a killer whale uses. Of course, we’re much closer in size to a sea otter than a killer whale.

5. Chapter 8 features several predators – sea otters that eat sea urchins, killer whales that eat sea otters, and wolves that eat elk. It describes the big effects that these predators can have on their prey and on the habitats where both live. I emphasize different kinds of evidence that researchers have gathered to understand these relationships between predators and prey in ecological communities, but I also ask readers to consider how humans influence these communities. These aren’t purely scientific issues, but entail decisions about management – commercial fishing in the Aleutians, hunting in the Rockies, removal of wolves that kill livestock near Yellowstone National Park. These decisions involve not only science but ethics. In closing Chapter 8, I quote A Sand County Almanac by the conservationist Aldo Leopold: “I was young then, and full of trigger itch; I thought that because fewer wolves meant more deer, that no wolves would mean hunter’s paradise. But after seeing the green fire die, I sensed that neither the wolf nor the mountain agreed with such a view.” As one of my post-publication reviewers reminded me, the “green fire” refers to the wolf’s eyes.

6. I use a rubric called FiLCHeRS to summarize six key tools for critical thinking: evaluation of claims by assessing their Falsifiability, Logic, Comprehensiveness, Honesty, Replicability, and Sufficiency. James Lett proposed this rubric in 1990 and illustrated its use in evaluating paranormal beliefs such as astrology and extrasensory perception. I apply FiLCHeRS to claims by those who dispute the scientific evidence for human impacts on climate change. In discussing sufficiency, I quote Lett: “extraordinary claims demand extraordinary evidence.” This idea actually has a long history, starting with the philosopher David Hume in 1748, continuing with a restatement by Laplace in 1812, another restatement by Carl Sagan in 1980, and finally Lett’s version in 1990 that changed Sagan’s verb from “require” to “demand”.

7. Finally, I use the classic case of industrial melanism to explain how evolution works in Appendix 2. Peppered moths fly at night and rest on tree trunks during the day. All peppered moths collected in England before 1948 were light-colored, providing effective camouflage against predation by birds when resting on patches of whitish lichens growing on tree trunks. People began to collect dark-colored moths in the mid-1800s, and virtually all moths collected in industrial areas were dark by 1898. By this time, soot from factories had killed the lichens and coated the tree trunks, so dark moths were better camouflaged, as illustrated in Figure A2.1. In short, pollution had two effects that changed the environment for peppered moths – it killed lichens on tree trunks, exposing the naturally darker color of the trunks, and the particulate components of the pollution (soot) made the trunks even darker. With pollution controls starting in England in the 1950s, soot on trees was gradually washed away by rain, lichens returned to the trees, and light-colored moths were again favored by natural selection. H. B. D. Kettlewell did several experiments in polluted and unpolluted woods to test the hypothesis that predation by birds was the agent of selection on moth populations, with light moths being better camouflaged in unpolluted woods and dark moths being better camouflaged in polluted woods.

Light and dark peppered moths resting on a lichen-covered tree trunk (left panel) and on a soot-covered trunk (right panel). Look carefully to see the light moth on the lichen-covered trunk in the left panel. From Ecological Genetics, by E. B. Ford (1964, Methuen & Co.)

Light and dark peppered moths resting on a lichen-covered tree trunk (left panel) and on a soot-covered trunk (right panel). Look carefully to see the light moth on the lichen-covered trunk in the left panel. From Ecological Genetics, by E. B. Ford (1964, Methuen & Co.)

Posted in Causation, Correlation & Causation, Ecology, Ethics, Evaluating evidence, Evolution, General material, Probability & Statistics, Twins | Leave a comment

More politicians talking science

I wrote about politicians talking science for a blog hosted by Oxford University Press in June 2015. In that posting, I focused on statements by Jeb Bush and Ted Cruz illustrating their misunderstanding of the scientific consensus about climate change. This new posting was inspired by Rand Paul’s answer to a question about climate change in the November 11th debate among Republican presidential candidates and illustrates a valuable aid to critical thinking called argument mapping.

In an interview a year ago, Paul expressed some support for regulating carbon dioxide emissions, but in the recent debate he stated that his first action as president would be to repeal President Obama’s regulations to control emissions that contribute to climate change. Paul argued for an “all of the above” energy policy, including not only sustainable sources like solar power but also traditional fuels like coal that release greenhouse gases contributing to climate change. In making this argument, Paul said: “The planet’s 4.5 billion years old. We’ve been through geologic age after geologic age. We’ve had times when the temperature’s been warmer, we’ve had times when the temperature’s been colder. We’ve had times when the carbon in the atmosphere’s been higher.” Unlike some candidates, Paul accepts the fact that humans influence climate, but, like all climatologists, he believes that “nature also has a role”.

What kind of argument is Paul making here? How does his plan to repeal emissions controls in support of an all of the above energy policy relate to his riff about the climate history of Earth? He doesn’t make an explicit connection between energy policy and climatology, but his main claim seems to be that we can continue to burn fossil fuels without adverse effects because current carbon levels in the atmosphere and current global temperatures are within the range of values that Earth has experienced in the past. Here is a diagram that illustrates his argument:

Rand Paul's argument that humans won't be harmed by continuing to burn fossil fuels.

Rand Paul’s argument that humans won’t be harmed by continuing to burn fossil fuels.

This diagram is called an argument map. The sentence in the top box is Paul’s main contention; the two sentences in the green box below are linked premises that explain his contention by acknowledging that burning fossil fuels causes climate change but suggesting that we can do so safely. The two sentences in the lowest box are the crux of his argument in support of his contention. The premise on the left in this lowest box is what Paul said about carbon in the atmosphere and is a true statement of what climatologists have discovered from various kinds of evidence. The co-premise on the right is an unstated assumption of Paul’s argument that links this climatological record to Paul’s claim about the safety of continuing to burn fossil fuels.

Although the main premise of Paul’s argument is true, the co-premise is irrelevant because humans have never existed with atmospheric carbon dioxide levels as high as they are today. This makes Paul’s contention a non sequitur and refutes Paul’s argument, as illustrated in this expanded argument map:

Refutation of Rand Paul's argument that continued use of fossil fuels won't be harmful.

Refutation of Rand Paul’s argument that continued use of fossil fuels won’t be harmful.

This story of obfuscation by a presidential candidate has several additional dimensions. Besides claiming that humans won’t be harmed by continuing to burn fossil fuels, Paul argues that regulations to control emissions will hurt our economy. Two recent analyses (here and here) by separate groups of researchers independent of the government imply quite the opposite, as illustrated below:

Refutation of Rand Paul's argument that new regulations to control emissions of fossil fuels will harm our economy.

Refutation of Rand Paul’s argument that new regulations to control emissions of fossil fuels will harm our economy.

Another set of researchers estimated that new regulations on emissions would prevent 3500 premature deaths per year, with the greatest benefit in states that rely heavily on coal such as Paul’s home state of Kentucky. How would you extend the argument map to incorporate this information?

Paul discussed only impacts of climate change on humans in his brief comments in the Republican debate. How about impacts on wild plants and animals? Humans have increased atmospheric carbon dioxide from 280 parts per million (ppm) before the Industrial Revolution to 400 ppm now, a level unprecedented in our history as a species. Global temperatures have increased correspondingly, and will continue to increase even if we gradually phase out use of fossil fuels. The rates of change in climatic conditions are also unprecedented, certainly in our history as a species and probably in the entire history of life on Earth. There have been five mass extinctions during Earth’s history, most recently about 66 million years ago when about 75% of all species became extinct, including all of the dinosaurs except their avian descendants. We are now in the midst of a sixth mass extinction, triggered by human activities such as overhunting, destruction of natural habitats, and burning of fossil fuels causing climate change. Many species of plants and animals can adapt to gradually changing climates, but adaptation to the rapidly changing conditions happening now is less likely.

I discuss argument mapping more fully in Tools for Critical Thinking in Biology, and illustrate another faulty argument of climate contrarians at a website with many other examples of argument maps. The Australian philosopher Tim van Gelder described the rationale for argument mapping and developed the software used for my argument maps, which can be found at the ReasoningLab website, together with links to tutorials and other resources for learning about argument mapping.

Posted in Argument mapping, Climate change, Science and politics | Leave a comment

Research on medicinal uses of marijuana: Is the cart before the horse?

I describe two studies of medicinal uses of marijuana in Chapter 4 of Tools for Critical Thinking in Biology to illustrate why experiments are considered the gold standard for research. In June 2015, two months after the book appeared, the Journal of the American Medical Association (JAMA) published two reviews and an editorial about research on medicinal uses of marijuana. In their editorial, D’Souza and Ranganathan concluded that: “Since medical marijuana is not a life-saving intervention, it may be prudent to wait before widely adopting its use until high-quality evidence is available to guide the development of a rational approval process. Perhaps it is time to place the horse back in front of the cart.” Before explaining why D’Souza and Ranganathan think the cart is before the horse in marijuana research, I want to tell you what the reviews in JAMA have to say about the two studies I discussed in detail in my book.

Marijuana plant.

Marijuana plant growing in Sherburne National Wildlife Refuge, Minnesota
(US Fish and Wildlife Service).

In one of the studies I discussed, a group of researchers in San Francisco studied the effects of smoking marijuana on a type of pain called peripheral neuropathy experienced by HIV/AIDS patients; in the other, a group of researchers in San Diego studied effects of marijuana on experimentally induced pain in healthy volunteers. Both studies were randomized controlled trials: subjects were randomly assigned to treatments and one of the treatments was a placebo, or control, in which THC, one of the main active ingredients of marijuana, had been removed from cigarettes used by the volunteers. In addition, the experiments were double-blind trials: the subjects were ostensibly unaware of the treatment they received in each phase of the experiments, as were the researchers until the experiments were completed and the researchers started analyzing the data.


Chemical structure of THC, one active ingredient of marijuana, by Yikrazuul.

Neither set of reviewers for JAMA mentioned the San Diego study, presumably because these researchers worked with healthy volunteers rather than testing marijuana for treating a specific disease. I included the San Diego study in my book because it illustrated some important considerations in designing experiments. For example, the researchers asked whether there was a relationship between the dose of THC received by subjects and alleviation of pain. They found that an intermediate dose of THC was more effective than either a lower or higher dose; patients actually felt the most pain with the highest dose. These results are clearly relevant to using marijuana for treating pain caused by a disease such as HIV/AIDS, even though the JAMA reviewers didn’t see fit to mention this study in their papers.

One of the JAMA reviews was couched as a response to a patient who had been treated for chronic back pain for 18 years with only modest success. The patient began using marijuana shortly after it was legalized for medical use in his state. The second review was a quantitative analysis of evidence for the effectiveness of marijuana for treating several medical conditions. Both reviews focused on experimental studies and they reached similar conclusions about strengths and weaknesses of evidence for effectiveness of marijuana for treating various conditions.

Penny Whiting and her colleagues considered 79 randomized controlled experiments in their quantitative analysis. In 28 of these experiments, including the San Francisco study that I described in my book, marijuana was used in an attempt to alleviate chronic pain. Most of these experiments used an oral spray containing purified forms of two active ingredients extracted from marijuana, but the San Francisco volunteers smoked marijuana cigarettes. Subjects in the treated groups felt less pain than subjects in the control groups in most of these experiments, with the greatest reduction in pain for the San Francisco experiment. I used the San Francisco study in my book because it was a good example of how to design a randomized controlled experiment. With Whiting’s review, I can go further and say that the results of this experiment are consistent with those of other recent experiments addressing similar questions; if anything, the results of the California study are even more persuasive than those of similar experiments.

In addition to finding credible evidence that marijuana can benefit patients with chronic pain, the JAMA reviewers found moderate support from experimental studies that marijuana can reduce spasticity in patients with multiple sclerosis but only weak evidence that it can reduce nausea and vomiting associated with chemotherapy. The reviewers found essentially no evidence that it helps patients with depression, anxiety disorders, sleep disorders, psychoses, Tourette syndrome, Parkinson’s disease, inflammatory bowel syndrome, or glaucoma. Whiting’s group also found evidence for many adverse side effects, at least in the short term.

Why did the editorial accompanying these reviews in Journal of the American Medical Association conclude we should put the horse back in front of the cart in marijuana research? About half of the US states allow residents to use marijuana for medical purposes, but each state lists a specific set of allowable conditions and these lists are very diverse. In most cases, support for including a medical condition on a state list is not based on randomized, controlled experiments – the gold standard for research – but on weak evidence at best: “anecdotal reports, individual testimonials, legislative initiatives, and public opinion.” Marijuana contains at least 400 secondary compounds, including 70 related to THC, the best known active ingredient. There is great variation in the chemical composition of different samples of marijuana, leading to unpredictable effects on the body. Interactions of marijuana with other drugs that may be taken concurrently are uncertain. There are numerous short-term side effects and potential long-term risks, especially for children and young adults whose brains are still developing, since brain development depends on a natural compound in the brain that is similar to THC and binds to the same receptor molecule on the membranes of brain cells. For these and other reasons, D’Souza and Ranganathan argue in JAMA that we need to gather more and better evidence to justify or discredit use of marijuana for specific medical conditions.

Posted in Experimentation, Medicine | 1 Comment

Brownie, you’re doing a heckuva job

I discuss several examples of the complexity of causation in Tools for Critical Thinking in Biology, ranging from interactive effects of genes and environments on humans and other organisms to webs of relationships connecting predators and prey such as killer whales, sea otters, and sea urchins in the Aleutian Islands. Hurricane Katrina has been in the news because it hit New Orleans 10 years ago. In Chapter 8 of my book, I used the damage from Hurricane Katrina to introduce the idea that events happen due to complex webs of causation: mistakes by the Corps of Engineers that built the levees that were supposed to protect New Orleans, inadequate funding to build effective levees, development of wetlands in the Mississippi Delta, ineffectual responses by government agencies such as the Federal Emergency Management Agency (FEMA) due to patronage appointments of leaders for these agencies. I also discussed the potential role of climate change in increasing the average severity of hurricanes in the coming decades.

Hurricane katrina and New orleans

Web of causation for damage in New Orleans attributed to Hurricane Katrina.

President George W. Bush had appointed Michael D. Brown as head of FEMA two years before Katrina, despite Brown’s complete lack of prior experience in emergency management. Bush told Brown he was doing “a heckuva job” a few days after Katrina hit New Orleans; Brown resigned on September 12 when it had become abundantly clear that FEMA’s response was inadequate and ineffective.

I didn’t think much about Michael Brown when I wrote the book, but this tenth anniversary of Katrina inspired Emily Atkin of ThinkProgress to interview Brown about his activities since Katrina. Despite his ignominious departure from FEMA, Brown continued to do consulting work on emergency management, without much success, then became a talk radio host, where he promotes his views that humans have little if any effect on climate change. For example, he doesn’t believe that rising sea levels are much of a problem. According to Atkin, Brown thinks that “this is partially proven . . . by the fact that people are still buying and developing big properties on the more vulnerable areas of the East Coast”.

It probably shouldn’t be surprising that Michael Brown denies the evidence that humans influence global climate, although I would have hoped that his trial by fire during Katrina might have inspired a more thoughtful approach to this critical issue of our time.

Posted in Causation, Science and politics | 1 Comment

Vaccination and the Eradication of Human Diseases

Smallpox was a scourge of humanity for centuries, but in 1977 became the first human disease eliminated by a worldwide vaccination campaign. In Chapter 6 of Tools for Critical Thinking in Biology, I explain how the reproductive rates of disease organisms influence the potential success of vaccination campaigns. Smallpox virus has a much lower reproductive rate than measles virus, making it easier to protect an entire population against the spread of smallpox than measles. This is important because no campaign, no matter how intense, can vaccinate everyone – even if it would be logistically possible to do so, some people can’t be vaccinated because they are too young, too old, or have compromised immune systems.

After the success with smallpox, public health agencies began a campaign to eradicate polio. This has reduced cases of paralysis caused by the polio virus from about 350,000 in 1988 to fewer than 2000 per year since 2001, and only 359 in 2014. These few cases occurred in Nigeria, Afghanistan, and Pakistan; polio has persisted in these countries in part because extremist groups such as Boko Haram in Nigeria have blocked vaccination efforts, sometimes by killing vaccinators.

Public health groups working in Africa have stepped up their efforts and adjusted some of their tactics to gain more support for vaccination from local populations. On August 11, 2015, the Global Polio Eradication Initiative reported that for the first time ever, Africa had gone a full year without a case of polio. The last reported case was in August 2014 in Somalia; if there are no more cases in the next two years, the World Health Organization will declare Africa free of polio, putting us even closer to eliminating a second human disease from the world.

I discuss smallpox and polio briefly in Chapter 6 of Tools for Critical Thinking in Biology, but the main purpose of this chapter is to explain how biologists use models to help answer important practical questions. I describe a simple model that we use to estimate the fraction of a population that must be vaccinated to prevent a disease from spreading and apply this model to measles and whooping cough, two diseases with much higher reproductive rates than smallpox and polio. It will be extremely difficult if not impossible to eradicate these diseases. In fact, there are still large numbers of cases in less developed countries as well as outbreaks in more developed countries with good health care systems. In addition to describing this model in the book, I discuss its ethical implications. Do parents have a social obligation to have their children vaccinated, in order to protect not only their own children but the community as a whole, including those who can’t be vaccinated because of age or compromised immune systems? This bears on a movement to reject routine vaccination that has many adherents in some parts of the US and other countries. For whooping cough, those who reject vaccination make a logical error in thinking about causation. Anti-vaccinators want to attribute recent outbreaks of whooping cough to use of a less effective (but safer) vaccine rather than a decline in the rate of vaccination associated with their campaign against vaccination. In making this claim, anti-vaccinators fail to appreciate that events can have multiple, interacting causes. Decreased rate of vaccination probably acted synergistically with use of a less effective vaccine to cause recent outbreaks of whooping cough. See “Complexities of causation” for further explanation and Tools for Critical Thinking in Biology for other complexities of causation.

Posted in Modeling, Vaccination | Leave a comment