Oikos 125: 1027–1034, 2016 doi: 10.1111/oik.02859 © 2015 The Authors. This is an Open Access article Subject Editor: Karin Johst. Editor-in-Chief: Dries Bonte. Accepted 27 November 2015 Autocorrelated environmental variation and the establishment of invasive species Kim Cuddington and Alan Hastings K. Cuddington (http://orcid.org/0000-0003-1191-6973)([email protected]), Dept of Biology, Univ. of Waterloo, Waterloo, ON N2L 3G1, Canada. – A. Hastings, Dept of Environmental Science and Policy, Univ. of California – Davis, Davis, CA 95616, USA. Environmental parameters such as temperature and rainfall have a positively autocorrelated variance structure which makes it likely that runs of good or bad conditions will occur. It has previously been demonstrated that such autocorre- lated environmental variance can increase the probability of extinction in small populations, in much the same way that increased variance without autocorrelation can increase extinction risk. As a result, it has also been suggested that positive autocorrelation will decrease the probability that a species will establish in a novel location. We suggest that describing the probability of invasion success as the probability of indefinite persistence may be an inappropriate definition of risk. Economic or ecological damage may be associated with a population that initially reaches high densities before going extinct in the new location. In addition, such populations may spread to new locations before extirpation. We use a model- ing approach to examine the effect of positively autocorrelated conditions on the probability that small populations will reach large size before extinction. We find that where variance is high and the geometric mean of the population growth rate is low, autocorrelation increases the risk that a population will pass a an upper threshold density, even when extinction probability is unaffected. Therefore species classified as having low probability of invasion risk on the basis of population growth rates measured in low variance environments may actually have quite a substantial probability of establishing a large population for a period of time. The mechanism behind the effect is the disproportionate influence of short runs of good conditions initially following introduction. Abiotic conditions in a new environment fundamentally the sudden increase in availability of a limiting resource. influence the establishment probability and spread rates of Johnstone (1986) proposes a similar “invasion window” non-native species. More common approaches to determin- theory: opportunities for invasion change in time in response ing the effect of abiotic conditions on potentially invasive to removal of obstacles. Data both support (Davis and Pelsor species depend on matching average climate conditions in 2001, Foster and Dickson 2004) and refute these claims the native range to those in the new location (Drake and (Gilbert and Lechowicz 2005, Walker et al. 2005). For exam- Bossenbroek 2004, Roura-Pascual et al. 2006). Typically, ple, according to Davis and coauthors, periodic increased factors such as minimum average winter temperatures or availability of water should lead to increased invasion suc- minimum average precipitation are targeted as important cess in dry climates. In support of this theory, Hobbs and predictors (Evans and Gregoire 2007). However, the Mooney (1991) found that the probability of Bromus mollis temporal variability of abiotic conditions is also likely to establishment in California serpentine grasslands increased have a large impact on invaders. We use the term temporal in the presence of local gopher disturbance and in years environmental variation to refer to the year to year or day following heavy rains, but it decreased dramatically after two to day variability in environmental conditions that occurs consecutive years of drought. In contrast, Brown and Archer separately from the effects of predictable cyclic variation (1999) found that recruitment of the invasive honey mes- such as seasonal or El Niño events, and which is also dis- quite, Propsis glandulosa, did not depend on variable rainfall tinct from trended phenomena such as global change. Using events in a semi-arid Texas savannah. a modeling approach, we show that characteristics of tempo- The probability that a species will persist in a new ral environmental variation which alter population growth location is intimately related to extinction probabilities. rates, such as the variance and degree of autocorrelation, can Where environmental fluctuations are assumed to be inde- alter the invasion process. pendent, increases in environmental variation increase It has been previously suggested that temporal variation extinction risk (Lewontin and Cohen 1969, Lande 1993). in environmental factors can affect the establishment of Haccou and Iwasa (1996) were the first to realize this non-native species (Gabler and Siemann 2012). Davis et al. significance of the finding for the modeling of invasive (2000) propose that plant invasion success depends on species. They used an inhomogeneous Markov process to 1027 study the combined effects of environmental and demo- Moreover, individuals in dense populations may be more graphic stochasticity on establishment probability, and likely to disperse and to reach locations with different abiotic found lower establishment for greater variance. Drake and and biotic risk factors. Highly dense, widely spread popula- Lodge (2004) tested this claim using Daphnia magna, where tions can also be expected to have greater impact than those variance was introduced by providing varying amounts of species that successfully establish a small persistent popula- food on each day to 281 replicate populations. In agreement tion in a given location (Parker at al. 1999). Consequently, with theory, the authors found reduced establishment while one may be tempted to argue that invasion probability probability with increased variance. is merely the flip side of extinction probability, an alternate The empirical studies make it clear that environmental measure of invasion risk, the probability that a population variation may affect the success of invasive species and the will surpass a given threshold density before crossing an modeling efforts suggest that increased variation reduces extinction threshold, may be of importance when calculat- the probability of permanently colonizing a new area. These ing the risk that a novel species will have a large impact. model predictions regarding environmental variation may We note that when variation in environmental conditions not hold, however, if the underlying description of environ- is autocorrelated, the population dynamics in finite time can mental variation is inaccurate. It may seem that environ- be very different than the asymptotic behavior. The extreme mental variation is easily quantified with a single measure, case, where autocorrelation is approaching its maximum variance, and thus is simply incorporated into predictive value, provides intuition. Consider the most extreme exam- models of invasive dynamics. With this conceptual model, ple of almost complete correlation first. Only one environ- the variance in a given environmental signal that cannot mental condition will be experienced by the population in a be attributed to trends or cycles is assumed to arise from given finite period of time and that condition may be either statistically independent deviations from some expected beneficial or detrimental to population growth. We can then value. Many types of environmental variation, however, are use this intuition to examine the impact of different levels positively autocorrelated (Steele 1985, Halley 1996, Király of autocorrelation on population growth over finite periods. et al. 2006), and autocorrelation has been demonstrated to If we relax the extreme assumption and instead assume just alter the predictions regarding variation and extinction risk moderate autocorrelation, it becomes clear that again over (Cuddington and Yodzis 1999, Petchey et al. 1997). short finite periods it is likely that the environment will be in Autocorrelation in environmental variation indicates only one state. Low autocorrelation makes the finite period that departures from the mean expectation are correlated during which conditions are similar very short. Therefore, in time. If environmental fluctuations were independent, a we expect that autocorrelation in environmental conditions cold winter would be equally likely to be followed by a cold will increase the length of windows of time where there is an winter or a mild winter; however, climate data suggest that increase (and a decrease) in the likelihood that a population the best predictors of conditions of this year are the condi- will reach a large size before going extinct. tions last year. A cold winter this year is more likely to be In the following, we use a simple density-independent followed by a cold winter next year. Such positive autocor- population model to investigate invasion success defined relation leads one to suspect that a set of conditions favorable as surpassing a given population threshold before extinc- to establishment and spread are likely to persist for several tion and compare it to persistence probability. We find that time periods, and of course, vice versa. This question is positively autocorrelated environmental variation that yields especially of interest in devising management strategies for similarly correlated population growth