Reproductive allocation

Optimality models as tools

In previous research, we have empirically measured the growth, survival, preference, or movement responses of individuals and used these empirical estimates to define rates in our models. Now we are working toward understanding what drives these individual responses. As a result, we have been developing and using optimality models (dynamic programming models, in particular) as tools to help understand how or why particular behaviors or patterns in nature may exist. Our Energy Allocation and Parental Care research have relied heavily on these models. In addition, we are linking models of optimal behavior with individual-based simulation models. This is a promising approach to answering questions in ecology and resource management. With this approach, we can explore population-level consequences of individual decisions and life-history traits.

Dr. Elizabeth Marschall

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Energy allocation

Garvey, J. E. and E. A. Marschall. 2003. Understanding latitudinal trends in fish body size through models of optimal seasonal energy allocation [abstract]. Canadian Journal of Fisheries and Aquatic Sciences 60: 938-948. For fish at high latitudes, short growing seasons should constrain size-at-age, although the converse often occurs. We used a dynamic state variable model to find energy allocation strategies to length, fat, and ovaries that maximize expected egg production of largemouth bass (Micropterus salmoides). We determined how latitudes and rations affect optimal allocation and then simulated growth using optimal strategies. A theoretical reciprocal transplant explored how latitude-specific optimal strategies affected growth at other latitudes. At low ration, allocation and growth were similar among latitudes, with length selected in small individuals and reproductive tissue and fat in large counterparts. At high rations, low-latitude fish invested most energy to length and reproduction; high-latitude fish allocated to length during summer and fat during fall and developed ovaries earlier in the year. Transplants revealed that smaller size-at-age occurs in the north than in the south, consistent with field patterns for largemouth bass. Although northern strategies allowed fish to be successful in the south, southern strategies were unsuccessful in the north. Latitude-specific energetic adaptations may compromise success of fish transplanted beyond their native distribution.

Bunnell, D. B. and E. A. Marschall. 2003. Optimal energy allocation to ovaries after spawning. Evolutionary Ecology Research 5: 439­457. For iteroparous organisms in which fecundity is positively related to body size, a trade-off exists between allocation of energy to gonads, thus ensuring some reproductive output, and allocation to somatic growth, thus increasing potential fecundity in the future. This tradeoff can influence several life-history patterns, including when, for organisms that grow after maturity, allocation to gonads begins following the previous reproductive event. White crappie Pomoxis annularis, a spring-spawning freshwater fish, began allocating energy to ovaries in autumn at the expense of continued somatic growth and higher potential fecundity. Within five populations, the amount of early allocation varied between years. We combined dynamic programming with an individual-based model to determine how summer and spring feeding conditions interact to influence when allocation to reproduction should begin. Model results indicated that autumn allocation to ovaries was in response to future spring feeding conditions rather than recent summer feeding conditions. At least a 10% probability of poor spring feeding conditions resulted in ovary investment patterns that matched field observations. The model was unable to explain the inter-annual variation in autumn energy observed in the field. Early allocation of energy to ovaries is probably an evolutionary adaptation to the possibility of poor spring feeding conditions.

Seasonal patterns in energy allocation across latitudes and life histories [project page]. (Joe Beuchel, M.S. student, D.D. Aday, and E.A. Marschall). Using a combination of empirical measurements and optimality models, we are examining how latitudinal and seasonal differences in environmental conditions affect energy allocation in fish with different reproductive strategies. Crappie (Pomoxis spp.) spawn once in the spring each year while bluegill (Lepomis macrochirus) spawn multiple times over the course of a long spawning season in the summer. Previous work has suggested that seasonal patterns of energy allocation in crappie are driven by the need to build gonads well in advance of the spawning season. Our currently limited empirical data on patterns in gonadal size in bluegills suggest a much more rapid development of gonadal tissue, allowing them to spawn repeatedly through the summer.

Parental care decisions

Mauck, R. A., E. A. Marschall, and P. G. Parker. 1999. Interaction of adult survival and uncertainty of paternity in parental care decisions [abstract]. The American Naturalist 154:99-109. We generally assume that males deciding whether to provide parental care to offspring should consider probable relatedness of offspring, but we often ignore the importance of knowing the reliability of these estimates of probable relatedness. Using a dynamic programming model, we show that too little annual variation (which should lead to great certainty in estimates) of extra-pair fertilization (EPF) rates or too much annual variation combined with low precision of estimates of EPF rate (i.e., low certainty) should both lead to little effect of EPF rate on male parental care decisions. At intermediate levels of certainty, these decisions should be driven by relative present/future trade-offs. Most striking, adult survival rate has the greatest influence on male decisions such that, for any given cost of reproduction and value of male care, tolerance of EPFs decreases as adult survival increases.

Steinhart, G.B., E.E. Dunlop, M.S. Ridgway, and E.A. Marschall. (ongoing). Should I stay or should I go: optimal parental care decisions of a nest-guarding fish. Smallmouth bass in Lake Erie have recently experienced a combination of selection pressures that are quite different from those they have historically experienced. The combination of anglers removing guarding males from the nest and high densities of round gobies, an exotic egg predator that moves in when the nests are left unguarded, has potentially devastating impacts on smallmouth bass nest success. In addition, the severe storms in a lake the size of Lake Erie wipe out a large proportion of the nests in any given year. We set out to explore how these conditions affected optimal nest-guarding/abandonment decisions for male bass. Including on from smallmouth bass from a more typical northern lake, Lake Opeongo, we used a dynamic programming model to compare optimal behavior under historic Lake Erie conditions (no anglers, no round gobies), current Lake Erie conditions, and Lake Opeongo conditions (no anglers, no round gobies, and less severs storms). We found that optimal males were less likely to abandon their nests when adult annual survival and offspring daily survival were low than when survival was high. High parental care costs (i.e., reduced parental growth and survival) led males to abandon larger broods than when costs were low. The addition of round gobies, which both decreased offspring survival and increased parental care costs, caused males to abandon more frequently than when the gobies were absent. Adult annual survival was the most significant factor in determining optimal parental care decisions for smallmouth bass. We concluded that age-dependent parameters (e.g., adult survival or cost of providing care) that differentially affected current and future fitness were more important in determining parental behavior than age-independent variables (e.g., offspring survival or probability of nest success.

Maternal Effects

We have begun to expect the existence of maternal effects (offspring traits that are correlated with environmentally induced phenotypic traits of mothers) in our studies of fish recruitment. We now include the phenomenon of maternal effects in studies of yellow perch and walleye in Lake Erie. Both of these studies are aimed at understanding 1) differences in parental (both maternal and paternal) attributes among spawning stocks and 2) relative contributions of each spawning stock to the lakewide population of each species.